File: File_52c (tentative identifier) Title: Rounded Whole-Span Inversions — Narrative Correspondences, the 529 Family, the 6 BC Concentration, and the 12026 BC Actual Chronology Key; LXX Comparative Spines and the Accepted SP Fall Solution Status: Draft; original report pressure test retained; author-requested backbone extension verified; ten positive hits to 6 BC in 66 constructions across five targets; Actual chronology continuation at 12026 BC partially explored; author regards its major anchor role as strongly supported; not marked Final; September 28 LXX secondary comparison and accepted SP solution integrated as Appendix D Primary domain: Rounded; Actual; Regular; Cumulative; Mirror; Statistical; Methodological Traditions: MT; bounded restored second-Cainan companion; bounded LXX / SP offset and SKL comparisons; Septuagint textual comparison; biblical and Enochic narrative comparisons; LXX native-Cainan regular/cumulative inverse spines; accepted SP regular/cumulative Fall construction Canonical source: Markdown Primary anchors: 6 BC; 1 BC; AD 6; AD 25 (civil comparison); 966 BC (reference only); 1406 BC; 1401 BC; 1400 BC; 1446 BC; 1846 BC; 1876 BC; 2458 BC; 3056 BC; 3654 BC; 4106 BC; 4114 BC; 8066 BC; 12026 BC; 14004 BC; 14006 BC; 14726 BC Related files: File_00; File_01; File_05; File_11; File_16; File_18; File_21; File_22; File_34; File_46; File_51a; File_51b; File_52a; File_52b; File_54; File_61; existing File_52c second-order-closure reference; File_12; File_20; File_29; Rounded MT-SP-LXX Report IV Major operators: placeholder-preserving decimal reversal; declared segmentwise reversal and summation; source-ending anchor selection; signed anchor offset for the uncounted Temple reference; same-side subtraction; Rounded coordinate width; explicitly selected civil cross-axis count; 25/23; 70/69; 300/299; SP Creation-to-Fall forward-five-year selection; legacy 1496/1495 comparison in Appendix D only Major modal states: Rounded regular whole-span birth/event inversion; separately referenced Temple construction at 966 BC; bounded cumulative trunk comparison; admitted segmented backbone extension at 12026 and 14726 BC; self-inverse source; bounded restored second-Cainan companion; provisional inverse terminal-date reconstruction; Rounded Mirror coordinate-completion; exploratory target-frequency scan; original-Flood-held 8066 BC construction; Actual Creation 1:4 bridge at 12026 BC; selected Jared / Noah Gear 1 / Flood Gear 2 comparison; partially explored 598-multiple anchor structure; LXX secondary inverse-spine comparison; LXX 13636 BC expansion key; accepted SP Fall nodes 4406 / 13396 BC; SP inverse heads 11606 / 14306 and 11416 / 14116 BC; possible LXX–SP reciprocal relation in Appendix D Revision basis: 490d Repository Style Guide v2.5; Project Procedures v3.5; supplied Restart Capsule v11.54; supplied State_Vocabulary_Register v1.55, especially §D.12–§D.13; File_00 and File_54 style precedents; September 25 2026 author clarifications in Files 51a, 51b, 52a, and 52b; author decisions in the present discussion; September 28 author-authorized integration of the LXX/SP comparative supplement and its latest 1700-year addition

File_52c — Rounded Whole-Span Inverse Detailed Study

0. File-function

This report records the detailed study of Rounded birth and event dates under whole-span decimal inversion. Its subject includes the narrative correspondences involving Joseph, Joshua, the 1876 BC Nexus, and Creation; the selected 529 = 23² relations; the 1846 BC hub associated with the 1876 BC Nexus; and the bounded survey of inverse dates against five comparison targets. The numerical–narrative study is wider than the count of multiples of 115.

The original whole-span result is nine positive-span hits to 6 BC among 64 anchored inversions of 32 source dates. The author now admits the major segmented Creation backbone: its completed Nativity-stage endpoint is 14726 BC, with $14726-6=14720=640\times23$. This supplies the tenth incident. Including both backbone anchor stages, 12026 BC and 14726 BC, gives an expanded set of 66 constructions. Its five positive counts are ten to 6 BC, two to 1406 BC, one to 1446 BC, two to 1 BC, and three to AD 6. Appendix A retains all original outcomes and adds both supplementary constructions, including their misses.

The importance of 14726 BC extends beyond that tenth incident. Its 14720 span to 6 BC converts to 16000, and its relations to inverse Shem, the unchanged cumulative Flood, and expanded cumulative Creation yield 11270 = 23 × 490, 9890 = 23 × 430, 9200 = 23 × 400, and 49680 = 23 × 6 × 360. Section 3.6 records the exact endpoints and explains why the author calls 12026 / 14726 BC the shared backbone of the regular and cumulative Rounded inverse constructions.

The author further proposes 14726 BC as a Creation pillar that helps interpret the original nine intersections with 6 BC. Holding this earlier endpoint during 25/23 expansion sends Terah's inverse 3226 BC to the +60-state firstborn threshold at 2226 BC, and the affliction hub 1846 BC to the schematic Samaria node at 726 BC, 720 years before 6 BC. Section 3.7 records these examples and all nine complementary spans under the same held-anchor rule.

Section 3.8 develops three further companion relations: the Entry inverse / Mirror span 22540 → 24500, compared with the earlier 9660 → 9800 conversion; the Nativity-held Creation–Shem partition 16000 = 10000 + 6000; and the Temple inverse's convergence at Rounded AD 526 with expansion from the reflected 12026 BC backbone. The operators, held endpoints, and textual comparisons are identified separately.

Section 3.9 extends that convergence: the second 25/23 expansion from AD 12026 reaches 476 BC, matching the Creation-held expansion of inverse Moses at 1616 BC. Expanding the 920 interval forward from AD 526 reaches Moses' reflected birth at AD 1526. The result is a Rounded 1000 + 1000 arrangement centered on AD 526, with the 80-year expansion gain matching Moses' birth-to-Exodus interval.

Section 3.10 develops Abraham's generated 976 BC endpoint: Entry → Exodus → Conquest → 976 BC forms 430 + 40 + 430, while the 1100-year movement from inverse Abraham at 2076 BC is bisected by Moses' birth at 1526 BC, giving 550 + 550. The 390-year continuation to 586 BC completes the existing 1290 Entry-to-Jerusalem span.

Section 3.11 develops the Flood-countdown inverse at 8516 BC. Its 6210 span from Creation expands to 6300 or 6750 under 70/69 or 25/23, producing 8426 or 7976 BC and intervals of 6900 = 15 × 460 or 6450 = 15 × 430 to Moses' birth. Its ten-member inventory records the author's organizing thesis and now links each member to a stated contextual interpretation.

Section 3.12 supplies a cursory exploration of Mahalalel, Shelah, and Eber as one joint Cainan pattern, giving the final three members an initial contextual interpretation. The omitted-Cainan connection is its main point; the author's selected observations do not constitute a thorough examination of the trio's much more complex relations. The inverse 6900 + 690 arrangement becomes 7500 + 750, or 23 × 330 → 25 × 330, while restored Cainan's 2551–2091 BC life provides the 130 + 330 comparison. The generated 601 BC midpoint, at 1950 + 1950, links Cainan's birth to reflected expanded Shelah. Civil AD 30 comparisons and the Rounded Mirror spans retain separate counting rules; the restored companion adds no statistical source.

Sections 3.13–3.15 add the author's proposed counterpart key at 12026 BC for Actual MT regular and cumulative chronology. The three starting levels introduce 8066 BC and its 6660 / 6666 relations; inverse cumulative Creation supplies 23 × 1260 and the 43000-year Exodus expansion. The Actual 14004–4114 BC Creation bridge divides at 12026 BC into a 1:4 pair, while Jared, Noah, and the Flood stand at 14, 15, and 16 multiples of 598. Their expansions, complete resulting-interval table, and selected Creation / SKL / AD 25 connections are preserved as a partially explored treatment. The author regards the evidence for the major anchor role as strong; the unfinished work concerns the fuller explanation of its details. These additions do not enlarge the statistical ledger.

Appendix D incorporates the complete LXX comparative report and the accepted SP solution. The LXX supplies secondary regular heads 10436/13136 BC and cumulative heads 10936/13636 BC. The final SP construction selects rounded Fall nodes 4406/13396 BC, giving regular heads 11606/14306 BC and cumulative heads 11416/14116 BC through the 2736 BC intermediate. It includes the latest 8820/6120/1700 LXX–SP comparison. The SP solution is accepted on the author's instruction; the possible reciprocal relationship remains an interpretation. The original MT statistical ledger is unchanged.

The unadjusted independent-trial benchmark for ten or more hits among 66 trials at $p=1/23$ is approximately 0.0545%, or one in 1834. Section 9.6 also records ten among 65 if only the final backbone stage is added. These are conditional model calculations; the original whole-span scan and the author-requested segmented extension remain identifiable.

The 1846 BC observation belongs to the structural study in §5.6: Abram and Moses invert to dates centered on it at 230 + 230, while Terah's inverse stands 1380 earlier. The author identifies this hub as second in importance to 1876 BC in the relevant Egypt / affliction field and proposes it as a main artery for further expansion. It remains outside the statistical target list.

The report preserves the author's reason for continuing the inquiry: several different kinds of numerical relation appear appropriate to their particular persons, events, and narrative settings. The 6 BC divisibility scan supplies one tractable diagnostic within that wider inquiry. It does not assign a joint probability to the whole system.

Audit note — tentative file identity: the supplied Register §D.12 and existing File_52a / File_52b references already assign File_52c to inverse-of-the-inverse, second-order closure, and square / gate-field interpretation. The present report retains the author's requested tentative identifier as a separate draft. It does not replace that existing work or claim to complete its proof burden. Final numbering or integration remains an editorial decision.

0.1 Working state register

All numerical results below retain their stated source layer and operator. A shared date label alone does not establish identity between layers.

0.2 File map

0.3 Claim-status control

The date transformations, factorizations, and counts are arithmetic facts under the stated conventions. The selection of particular correspondences as meaningful is a structural inference or typological reading. The binomial calculation is a statistical result of a simplified model; its application to the study remains exploratory.

The use of a modern era display and decimal reversal does not by itself establish ancient authorial intention. A theological interpretation extending beyond demonstrable human intention remains a proposed providential synchronization. Neither that interpretation nor the proposed third-axis analogy is established by a factorization alone.

The author's September 27 assessment specifically distinguishes confidence in the 12026 BC anchor from completeness of its interpretation. He regards the evidence for its major key role as strong and that role as not in doubt within his model. Sections 3.13–3.15 preserve this judgment while marking the exploration of the wider pattern as partial.

0.4 Machine Guards

Machine Guard [FILE_52C WHOLE-SPAN ANCHORS]: Select the anchor from the original source date's ending digit before inversion. Use 6 / 1406 BC for dates ending in 6 and 1 / 1401 BC for dates ending in 1. Preserve the source date. The survey has two routes per source, not four. Its 1446 BC column is a comparison target, not a third inversion route.

Machine Guard [FILE_52C OPERATOR SEPARATION]: Whole-span inversion, segmented inversion, Mirror reflection, civil elapsed counting, and subsequent Key-of-23 expansion are separate operations. Record the active operation and held anchor at each transition. Do not count a later expanded landing as a direct inverse hit.

Machine Guard [FILE_52C ROUNDED / CIVIL WIDTH]: Use signed q arithmetic for a Rounded coordinate width. Opposite-side symmetric labels give $W_R=B+A-2$. The ordinary civil elapsed count between those printed labels is $C=B+A-1=W_R+1$. Retain the extra year only when the construction expressly chooses the civil count.

Machine Guard [FILE_52C FROZEN COUNT]: Preserve the original 32 dates in §2.1 and their 64 whole-span routes. The expanded tally adds only the two declared segmented backbone endpoints, 12026 BC and 14726 BC, once each, giving 66 constructions. Alternative regular / cumulative derivations of these endpoints corroborate them without extra counts. Exclude zero-span overlaps from positive hits. Keep other cumulative examples, reconstructed deaths, additional variants, Mirror doubles, later expansions, and the separately referenced 966 BC Temple routes outside both tallies.

Machine Guard [FILE_52C STRUCTURAL HUB]: Treat 1846 BC as a structural hub and proposed expansion anchor, not an additional statistical target. The fixed targets remain 6 BC, 1406 BC, 1446 BC, 1 BC, and AD 6. Retain the already admitted 1846 BC affliction source and its two routes in the 32-date manifest. The shared 115-year grid and the Abram–Moses / Terah relations belong to the narrative and structural discussion.

Machine Guard [FILE_52C CREATION-HELD EXPANSION]: In §3.7, hold 14726 BC fixed and expand the positive span toward the later BC endpoint: $X^*=14726-(25/23)(14726-X)$. Preserve each source's original inversion anchor before this separate expansion. The 2226 BC comparison uses the +60 Terah firstborn state; the 726 BC comparison uses the schematic Samaria state. The shared residue class does not supply additional independent hits. The Creation-pillar analogy does not redefine the named SKL / Temple-Time Projective Boundary Pillars.

Machine Guard [FILE_52C ACTUAL 12026 KEY]: Keep the Actual 14004 / 4114 BC completion endpoints separate from the Year-6 and Rounded Creation pairs. In §3.15, hold 12026 BC and compute the forward BC result as $12026-r(12026-X)$. Preserve Noah 3056 BC as selected Gear 1 and Flood 2458 BC as Gear 2; do not treat their 598 years as a replacement lifespan or extend gears into the earlier genealogy. Retain the Creation asterisk, the 2276 BC Noah identity, and the civil count for AD 25. The strong authorial anchor assessment and the partially explored interpretive scope coexist; no new statistical admission follows.

Machine Guard [FILE_52C STATISTICAL STATUS]: The approximate 1-in-571 baseline and 1-in-1834 expanded tails assume 64 and 66 independent trials respectively, each with probability 1/23. The segmented extension changes the admitted operation set and is correlated with the existing chronology. These figures are not corrected significance levels, probabilities that the system is accidental, or probabilities against authorial or providential design.

Machine Guard [FILE_52C COMPARATIVE SUPPLEMENT]: Appendix D retains MT primacy, the LXX native-Cainan source state, and the author's accepted SP Fall construction. Its new comparison heads and generated dates do not enter the original 32-source / 64-route manifest, the 66-construction extension, or the five-target counts. Preserve the separate regular, cumulative, Rounded, Actual, and civil-count states and the scoped legacy Egyptian operator.

1. Arithmetic conventions

1.1 Rounded dates and source identity

The base survey uses explicitly Rounded dates. It does not treat every clean or mod-5 value in the repository as part of the Rounded Scaffold. In particular, Joseph's 1916–1806 BC pair belongs to the present Rounded comparison. It must not overwrite the Actual Joseph chronology controlled elsewhere.

The source chronology follows File_51a §3.1 without adding Shem's +2. The survey does not open +60 Terah, the −215 Sojourn variant, restored Cainan, apparent-age overlays, or the wider Three-Gear field. Their existence elsewhere is not permission to multiply this manifest. The restored-Cainan companion expressly opened for §3.12 is outside that survey.

The cutoff is applied to the statistical source manifest: no date later than the Exodus at 1446 BC enters that list. A generated inverse endpoint may lie later than the cutoff. Thus Adam's inverse at 1406 BC remains a valid generated endpoint. The Temple at 966 BC is separately referenced in §2.5 because of its explicit 480-year Exodus synchronism; its two inverse routes remain outside the statistical manifest.

1.2 Placeholder-preserving decimal reversal

For a positive integer $n=10^k m$, where $m$ is not divisible by ten, define:

$I(n)=10^k\operatorname{rev}(m).$

The trailing-zero placeholders remain at the same magnitude. Define $I(0)=0$ for completeness.

The following examples all use this primary register.

This operation is digit reversal, not the reciprocal $1/n$. In this register, $I(I(n))=n$. A self-inverse span returns its source date when rebuilt from the same anchor.

Digit reversal preserves the digit sum, so the difference between a span and its inverse is divisible by 9. That elementary decimal property does not imply preservation of divisibility by 23.

The older segment-level Rounded inverse axiom remains a separate dependency. For example, a segment of 365 reverses to 563 and is normalized to 565 when that chain procedure is explicitly opened. The matched-anchor whole spans in this survey are multiples of ten and need no such normalization.

1.3 The two anchor families

For an admitted source date $D$ BC, select one anchor from each family according to its final digit.

For either selected anchor $A$ BC, calculate:

$s=D-A,\qquad s'=I(s),\qquad D'=A+s'.$

The result $D'$ BC is the rebuilt inverse date. The printed BC year number is not itself reversed.

Shelah illustrates the importance of retaining the source date and selecting the matching anchor. From 2421 BC, the Nativity-family span is $2421-1=2420$, which is self-inverse and returns 2421 BC. The Conquest-family span is $2421-1401=1020$, which reverses to 2010 and rebuilds 3411 BC.

Using 6 BC for that 1-ending source would introduce an unmatched-anchor span and a later normalization step. That is not the agreed primary operation. The selection rule introduces no 1441 BC anchor and does not re-anchor the rows of existing begetting or lifespan chains.

1.4 Rounded coordinates, Mirror labels, and civil counts

The September 25 author clarification controls the pure Rounded coordinate convention:

$q(B\text{ BC})=-(B-1),\qquad q(\text{AD }A)=A-1.$

A nonzero coordinate is displayed with numeral $|q|+1$ and the era supplied by its sign. Reflection changes $q$ to $-q$. Thus 1406 BC and AD 1406 display the coordinate pair −1405 and +1405.

For this study, the origin comparison is labeled 1 BC at $q=0$. Zero is the algebraic Mirror origin; it is not a civil year zero. The symmetric convention is not a single ordinary astronomical-year coordinate map.

The following coordinates identify the five statistical targets, the subsidiary Conquest construction anchor, and the separate structural hub at 1846 BC. The Role column distinguishes their functions.

For opposite-side labels $B$ BC and AD $A$, keep the two counts distinct:

$W_R=B+A-2,\qquad C=B+A-1=W_R+1.$

In particular, the Rounded width from an inverse date $D'$ BC to AD 6 is $D'+4$. The corresponding ordinary civil count is $D'+5$. The AD 6 scan uses the former, as expressly requested by the author through the coordinate +5.

Earlier sources sometimes display a positive Mirror coordinate $q$ as civil AD $q$. The current symmetric Rounded display is AD $(q+1)$. An explicitly civil equation retains its stated labels and count. No global one-year shift is applied to Actual or phase-resolved chronology.

2. The frozen source manifest

2.1 The 32 admitted dates

The first 23 entries are the Rounded birth dates of File_51a §3.1. Aaron, Moses, and Joshua complete the 26 birth entries. Six event entries complete the manifest. All dates in this table are BC, and each row generates one Nativity-family route and one Conquest-family route.

Arphaxad and the Flood occupy one admitted numerical date, 2456 BC. Their shared label is counted once, not as two source trials. In this table the Flood label belongs to the selected Rounded model; it does not override the repository's other Flood states.

Aaron's 1531 BC value is the elected Rounded companion. It is not a revision of the Actual Aaron/Moses chronology. Joshua's 1476 BC birth is a model date associated with the selected 1406 BC Conquest framework; his lifespan of 110 is a textual datum, whereas an absolute BC birth date is not stated in the biblical text.

2.2 Inclusion and exclusion decisions

The final manifest records the author's decisions, including decisions made during the exploratory discussion.

The author's restriction on additional round-number constructions does not remove all spans ending in zero: preserving those placeholders is essential to the inverse operation. No new rounded variants are manufactured to improve the result. Once a source is retained in the final manifest, both of its prescribed routes remain in the tables, including misses.

The four supplementary nodes considered earlier were reduced by excluding Sarah, Ishmael, and Reuben while retaining Enoch's ascension. The settled whole-span denominator is therefore 32 × 2 = 64. Earlier working counts are superseded by this manifest. The subsequent backbone extension adds two constructions of the already discussed Creation structure, not a 33rd source date (§8.7).

2.3 Enoch's provisional terminal node

The direct date 3121 BC follows from $3486-365=3121$. Enoch's 365 years and being taken by God are textual data (Genesis 5:23–24). The uncertainty in this study concerns the operation to be applied to that terminal event.

Direct inversion of 3121 BC produces 2131 BC from the 1 BC anchor and 4111 BC from the 1401 BC anchor. A reconstruction from an inverted birth and an inverted or retained lifespan is a different operation. The present scan uses only the direct-date version, by the author's explicit provisional inclusion. Both routes miss all five targets.

2.4 Routes, source dates, and unique endpoints

There are 32 distinct source dates, comprising 23 dates ending in 6 and nine ending in 1. Two routes per source give 64 comparisons with any one target.

The 64 routes yield 63 distinct numerical endpoints. Jacob at 2006 BC is self-inverse in both families and therefore occurs twice as a route endpoint. The count remains route-based, consistently with the question asked. Those two Jacob routes miss all five tested targets.

These facts also show why 64 routes should not automatically be treated as 64 independent statistical trials.

The paired backbone extension yields 66 constructions and 65 distinct endpoints. Its two new endpoints are absent from the original ledger. The Jacob duplicate remains a miss at every named target, and no repeated regular / cumulative derivation is counted again.

2.5 The Temple at 966 BC: explicit Exodus anchor, reference only

The author adds the beginning of Solomon's Temple construction at 966 BC to the report's references. The reason is the explicit chronological statement in 1 Kings 6:1: construction begins in Solomon's fourth regnal year, identified in the MT as the 480th year after the Exodus. Under the repository's adopted 480-year relation and primary Exodus anchor, the placement is:

$1446-480=966\text{ BC}.$

The textual datum is the Exodus-to-Temple synchronism; the absolute BC placement follows the adopted chronology (File_05 §1.1). This supplies a defined basis for referencing this post-Conquest event in the inverse study. The criterion is specifically its explicit span from the Exodus, rather than a general extension of the survey into later regnal events.

The author had been uncertain whether to include this event in the sample. Accordingly, it is discussed here but remains excluded from the statistics. Neither Temple route enters the original 64-route scan or the expanded 66-construction tally; the backbone amendment does not change this decision.

Both reference routes use the normal anchors for a 6-ending date. The Conquest route requires retaining the Temple's position later than its anchor. Use the magnitude for digit reversal and preserve the sign of the original BC-label offset:

$s=D-A,\qquad D'=A+\operatorname{sgn}(s)I(|s|).$

This signed placement is stated locally for the uncounted Temple reference. All source offsets in the frozen statistical scan remain positive, so its existing calculation and reproduction code require no change.

Thus the Temple date remains 966 BC under its Conquest-family inverse and becomes 696 BC under its Nativity-family inverse. The self-inverse 440 also places the Temple and the already discussed affliction node on opposite sides of the Conquest anchor:

$1846-1406=1406-966=440.$

This is a structural companion to the 1846 BC discussion. The explicit 480-year biblical anchor explains why the Temple is referenced; the author's uncertainty about statistical admission explains why neither Temple route enters the counted sample.

Section 3.8.3 develops the subsequent Temple comparison: the 696 BC inverse expands from the 14726 BC pillar to Rounded AD 526, also reached by expanding the reflected Exodus interval with AD 12026 held. That structural use preserves the Temple's exclusion from the statistical sample.

3. Creation trunks and the 6 BC intersection

3.1 Whole-span trunk inversions

The following table distinguishes the regular and cumulative source layers. Only the regular Creation row belongs to the frozen source manifest; the cumulative rows are contextual comparisons.

The underlying cumulative-to-regular difference is $14006-4106=9900$. File_52a controls the architectural role of that transfer constant. The present report uses it as inherited context and does not reproduce the full second-order closure argument.

3.2 The 8600 span to 6 BC

The Conquest-anchored inverse of regular Creation supplies the example emphasized by the author:

$8606-6=8600=4300+4300.$

The equal division has arithmetic midpoint 4306 BC. No new event at that midpoint is introduced into the manifest.

The 4300 units are decimal-scale comparisons with the 430 Sojourn register; the text itself supplies the 430-year datum (Exodus 12:40–41). The scale comparison is a structural reading. It is not a claim that the biblical text directly gives an 8600-year span.

This illustrates why 6 BC was already an intersection of interest before the present probability calculation. The 8600 span is itself a miss in the 115 test. Its role in the broader inverse study is retained despite that miss.

3.3 The segmented 12026 BC convergence

Whole-span inversion is not additive in general. The following independently stated segmentations therefore remain distinct from the whole-span regular trunk $2700\rightarrow7200$.

Each row holds the Conquest anchor at 1406 BC and inverts the listed components separately.

The cumulative components use $14006-4836=9170$ and $4836-1406=3430$. The regular components use $4106-2456=1650$ and $2456-1406=1050$. File_52a §§5–6 and §10, and File_52b §2, control these source constructions.

Their common 12026 BC endpoint provides a same-side 529 relation to the Exodus in §6.2. It is not an extra whole-span route in the 64-route survey. The author's subsequent admission of the major backbone includes this Conquest-stage endpoint once as the companion to the completed Nativity-stage endpoint below.

3.4 The completed backbone: 14726 BC and the tenth incident

The additional third partition is the 1406 BC → 6 BC interval. Read chronologically from Creation, the regular three-part outline is Creation → Flood → Conquest → 6 BC, with spans 1650 + 1050 + 1400. The cumulative primary outline has spans 9170 + 3430 + 1400. Their reversed sums are respectively 5610 + 5010 + 4100 and 7190 + 3430 + 4100, both equal to 14720. When rebuilding from the held 6 BC anchor, this last chronological partition is processed first.

Source trace: File_52a §7, “Christ anchor and the optional 2700 shift,” explicitly records 1406 BC → 6 BC = 1400, its inverse 4100, the resulting 2700 displacement, and 14726 BC. The author also gave the complete three-part equation in the preceding backbone amendment to this report. Thus the 1406-to-6 BC partition was already stated; the present clarification identifies its position in the chronological outline.

The regular backbone extends naturally from 6 BC through the Conquest and Flood to Creation:

$6\text{ BC}\rightarrow1406\text{ BC}\rightarrow2456\text{ BC}\rightarrow4106\text{ BC}.$

Its successive spans, read toward earlier dates, are 1400 + 1050 + 1650. Invert all three separately and rebuild from 6 BC:

$I(1400)+I(1050)+I(1650)=4100+5010+5610=14720.$

$6+14720=14726\text{ BC},\qquad14726-6=14720=640\times23=128\times115.$

The three rebuilt steps are explicit in the following table. The first endpoint shares the label of regular Creation, but its role here is the rebuilt inverse of the Conquest leg.

Thus 14726 BC is the natural third step of this admitted regular backbone. File_52a §7 already records the endpoint, its 14720 span to 6 BC, and the exact conversion $14720\times25/23=16000$. The construction predates its present admission to the statistical tally.

The same endpoint survives the following stated alternatives. All displayed dates in the path column are BC.

The regular chronology remains the main focus. Noah's two-leg alternative reverses the order of 1050 and 1650, leaving their inverted sum unchanged. The finer 1050 + 600 + 1050 backbone also agrees because $I(1650)=5610=600+5010$. These are specific structural agreements, not a general additivity rule for digit reversal or extra independent target hits.

The completed endpoint stands 2700 earlier than the Conquest-stage endpoint because $I(1400)-1400=4100-1400=2700$. Consequently $12026+2700=14726$. At the earlier stage of this calculation, $12026-1446=10580=5290+5290=20\times529$. The author reads this Exodus relation, the regular Noah alternatives, and the cumulative primary repetition as reinforcement of one major backbone. Only one 14726 BC incident is added to the 6 BC hit count.

Scope of the repetition: File_52a §11 also gives secondary cumulative paths through Shem or Noah that reach 13016 BC from 1406 BC. Completing their 6 BC leg would give 15716 BC. Those are distinct branches; the claim above concerns the primary cumulative Flood path and the specified regular Noah alternatives. They are referenced to delimit the repeat, not admitted as additional constructions in this regular-backbone extension.

3.5 Earlier Shem, Flood, and Creation evidence for the 6 BC anchor

The importance assigned to 6 BC did not begin with the count of nine whole-span hits. The earlier files connect it with Shem, the Flood, and the Creation backbone, alongside the 8600 = 4300 + 4300 relation in §3.2.

In the Rounded cumulative state, Shem's birth is 5436 BC and the end of his 600-year life is the 4836 BC Flood boundary (File_51a §24). This is a cumulative construction; it does not relocate the death of Shem in regular chronology. The Flood remains fixed under its Conquest-held inverse because its 3430 span is self-inverse. The discussion's term non-inversable means unchanged by inversion in this instance.

The 5436 → 3456 BC result uses a single whole-span inverse from 6 BC. The 14006 → 64406 BC chain instead combines inverse and expansion; it is not literal double decimal reversal. Under the defined operation, $I(I(12600))=12600$, restoring 14006 BC when rebuilt from the same 1406 BC anchor.

These references explain why the author treats Shem, the Flood, and Creation as the backbone of the wider 6 BC pattern. They are not separate additions to the present statistical denominator. The new counted construction is the regular segmented backbone of §3.4, with its Conquest-stage companion; the cumulative primary path corroborates the same endpoints.

3.6 Why 12026 and 14726 BC form the shared backbone

The author assigns great importance to this pair because the primary regular and cumulative segmentations converge on the same rebuilt Creation endpoint at each anchor: 12026 BC with 1406 BC held, and 14726 BC after including the 1406-to-6 BC partition and holding 6 BC. The regular chronology remains the principal study; the cumulative primary route supplies the matching construction. The specified Noah alternatives reinforce the regular result (§§3.3–3.4).

The Nativity span of the completed backbone gives the exact Priestly conversion already recorded in File_52a §7:

$14726-6=14720=23\times640,$

$14720\times\frac{25}{23}=16000=40\times400.$

Holding 6 BC during this conversion places the expanded upper endpoint at 16006 BC. The converted quantity is the 16000-year interval. The original inverse endpoint remains 14726 BC.

The following comparisons show how that same backbone endpoint connects the inverse Shem and Flood states with expanded cumulative Creation. All endpoint labels in the table are BC; each companion retains its stated construction anchor.

Label clarification: 11270 is the span to inverse cumulative Shem at 3456 BC. The Flood at 4836 BC supplies the separate 9890 span. Both calculations are exact. The 4836 BC Flood is the Conquest-held self-inverse companion; its anchor is retained when comparing it with the 6 BC-held backbone endpoint. Likewise, 5526 BC is the Nativity-family whole-span inverse of regular Shem, not a reconstruction from an inverse begetting chain.

The 9890 relation recovers the same total as the ordinary Actual cumulative-to-regular MT Creation bridge. File_22 §5.1 records its endpoint form, $14004-4114=9890$, and §7.1 its Year-6 / Adam-state form, $14006-4116=9890$. The agreement is a comparison between declared states. The original Rounded Creation gap remains $14006-4106=9900$; the inverse comparison $14726-4836=9890$ reproduces the Actual bridge's value without changing either chronology.

The 64406 BC endpoint is the expanded cumulative-Creation result discussed in §7 and referred to as the residual endpoint in the conversation. Its 49680 span reconnects that result to the common regular / cumulative inverse backbone through 23 × 6 × 360. The author reads the combined 490, 430, 400, and sixfold 360 relations, together with the 16000 Nativity conversion, as evidence of the structural importance of 14726 BC. At the Conquest stage, 12026 BC supplies the corresponding 10580 = 5290 + 5290 relation to the Exodus. These named relations explain the backbone designation more fully than the divisibility count alone.

Source-history check of the available earlier inverse files:

The earlier files do contain 11270 in another relation, 12746 BC to 1476 BC (File_52a §8.1; File_52b §6.2). That occurrence is distinct from the present Shem comparison. The source-history conclusion is limited to the available copies checked here.

These are structural comparisons involving the already admitted backbone. They do not add new entries to the five-target scan: the expanded tally remains ten hits to 6 BC among 66 constructions. The endpoints' common residue class accounts for their mutual divisibility by 23; their particular quotients and source associations are the numerical–narrative relations being recorded.

3.7 The Creation pillar: a common anchor for the original nine hits

The author proposes that 14726 BC is a key date for interpreting the other nine incidents to 6 BC. It represents Creation within this construction because the original string 6 BC → 1406 BC → 2456 BC → 4106 BC terminates at Creation. After segmentwise inversion, the corresponding terminal endpoint is 14726 BC (§3.4). Its use as a pillar is therefore attached to an already defined node-role and shared regular / cumulative backbone.

The comparison uses a different held endpoint from the Nativity-held 16000 conversion in §3.6. Hold Creation at 14726 BC and expand the interval to a later inverse endpoint X by 25/23. In positive BC year labels:

$X^*=14726-\frac{25}{23}(14726-X).$

The increased interval moves the later endpoint forward in time, reducing its BC label. All dates in the following examples remain on the BC side, so ordinary same-side subtraction applies.

3.7.1 Terah's inverse and the firstborn threshold

The original Nativity-held inverse is:

$2236-6=2230\xrightarrow{I}3220,\qquad6+3220=3226\text{ BC}.$

Now hold the Creation pillar:

$14726-3226=11500=500\times23,$

$11500\times\frac{25}{23}=12500,\qquad12500-11500=1000,$

$14726-12500=2226\text{ BC}.$

The generated label agrees with Terah's firstborn threshold in the +60 state: $2236+60=2296$ and $2296-70=2226$. File_18 §4A.5 explicitly records this threshold and routes its firstborn interpretation to File_69 §5B.5 and File_70 §2.3. The route compares two declared states: Terah's source birth is 2236 BC, while the resulting 2226 BC is a firstborn node in the +60 Terah state. It does not change the source birth to 2296 BC before inversion or propagate +60 through the rest of this survey.

3.7.2 The affliction hub and the Samaria node

The admitted 1846 BC source is unchanged by its Conquest-family inverse because $1846-1406=440$ and $I(440)=440$. Holding the Creation pillar now gives:

$14726-1846=12880=560\times23,$

$12880\times\frac{25}{23}=14000,\qquad14000-12880=1120,$

$14726-14000=726\text{ BC},\qquad726-6=720=2\times360.$

Thus the same expansion rule connects the Egypt / affliction hub to the repository's schematic Samaria siege / collapse node, followed by 720 years to 6 BC. The author's SKL comparison concerns the importance of this 720 interval; File_21's 360:1 scalar and 720 Shem-variable framework provide the relevant span context. No SKL rail is moved by this calculation.

Dependency note — Samaria state: File_16 §7.1, under File_00's Samaria Node control, identifies 726 BC as the idealized siege / collapse label within the 726–721 BC envelope. The present example retains that schematic status and does not promote 726 BC to an independently established civil siege date.

3.7.3 The complete nine-member complementary relation

The common grid explains why all nine original hits can be compared with the same pillar:

$14726-6=14720=128\times115,$

$X-6=115k\quad\Longrightarrow\quad14726-X=115(128-k).$

Each original inverse endpoint lies between 6 BC and 14726 BC, so both complementary spans are positive. Their 25/23 expansions are exact multiples of 125. The following table applies the single Creation-held rule to all nine entries of §8.3; it does not select only the two interpreted examples.

Every row's two unexpanded spans sum to 14720. These are complementary descriptions of the existing nine incidents, so their shared divisibility is algebraically inherited. The event associations at 2226 BC and 726 BC supply the specific interpretive observations developed here; the other generated endpoints remain arithmetic outputs without newly assigned event identities.

The two possible held anchors also have a fixed relation. If $N(X)=6+(25/23)(X-6)$ denotes expansion with 6 BC held, and $P(X)=14726-(25/23)(14726-X)$ denotes expansion with the Creation pillar held, then:

$N(X)-P(X)=\frac{2}{23}(14726-6)=1280.$

Thus changing the held endpoint shifts every expanded BC label by the same 1280 years. The original Abram–Moses symmetry is preserved as well: their generated endpoints 976 BC and 476 BC lie 250 years on either side of the generated affliction node at 726 BC. This is the image of the 230 + 230 arrangement around 1846 BC in §5.6 under one common affine expansion.

Structural inference: 14726 BC functions as a candidate Creation pillar paired with the 6 BC Nativity anchor. Its construction, all nine complementary intervals, and the two contextual landings support examining that role. Subsequent sections develop the other members: Shem's partition in §3.8, Moses through the Temple convergence in §3.9, Abraham through the Entry–Exodus–Conquest symmetry in §3.10, the countdown through paired ratios in §3.11, and the Mahalalel–Shelah–Eber trio through Cainan in §3.12. All nine now have stated contextual interpretations, whose explanatory force remains a question for the wider study. The existing statistical tally remains ten hits to 6 BC among 66 constructions; this common-anchor interpretation adds no count entries.

3.8 Further pillar relations: Entry Mirror, Shem, and the Temple

The author adds three examples connecting the 14726 BC backbone with nodes already defined in the study. Each example retains its own operation and held endpoint. They supplement the structural interpretation without changing the statistical manifest.

3.8.1 The Entry Mirror: 24500 = 14700 + 9800

The inverse of the 1876 BC Entry is 7816 BC. Its Rounded coordinate −7815 reflects to +7815, displayed as AD 7816 under §1.4. The author here uses AD 7815 in the earlier civil-style display. Both statements of the intended durations are exact when their counting conventions are identified:

AD 7815 and AD 7816 are not interchangeable labels under one counting rule. The present report continues with the symmetric Rounded display, preserving the author's intended durations.

The earlier hub relation is $4830+4830=9660$, followed by the Prophetic conversion $9660\times70/69=9800$ (§5.7). The larger span supplies:

$22540=23\times980,\qquad22540\times\frac{25}{23}=24500=490\times50.$

Comparing the two converted durations gives:

$24500-9800=14700,$

$24500=14700+9800=(30\times490)+(20\times490).$

Both the 9800 inner duration and the full 24500 therefore have exact 490-based descriptions. This connects the same Entry inverse / Mirror endpoint with the affliction hub and the Creation pillar.

Operator note: the larger duration uses 25/23, whereas the earlier 9800 result uses 70/69. The 14700 remainder is consequently a partition of separately converted durations. If both original segments were expanded uniformly by 25/23, the original partition $22540=12880+9660$ would instead become $24500=14000+10500$. The 700 difference between 10500 and 9800 accounts exactly for $14700=14000+700$. This preserves the author's relation without attributing it to a single uniform expansion.

3.8.2 Creation and inverse Shem: 10000 + 6000 with 6 BC held

The original same-side partition is:

$14726\text{ BC}\xrightarrow{9200}5526\text{ BC}\xrightarrow{5520}6\text{ BC},$

$9200+5520=14720.$

Here 5526 BC is the Nativity-family whole-span inverse of Shem's Rounded regular birth at 2556 BC (§§3.6 and 8.3). Apply 25/23 to the whole arrangement with 6 BC held:

$9200\times\frac{25}{23}=10000,\qquad5520\times\frac{25}{23}=6000,$

$14720\times\frac{25}{23}=16000=10000+6000.$

The rebuilt positions are therefore:

$16006\text{ BC}\xrightarrow{10000}6006\text{ BC}\xrightarrow{6000}6\text{ BC}.$

Equivalently, $6+(25/23)(14726-6)=16006$ and $6+(25/23)(5526-6)=6006$. This is one common affine expansion with 6 BC fixed. It differs from the Creation-held operation in §3.7, which keeps 14726 BC fixed and sends 5526 BC to 4726 BC.

The author reads 6000 = 10 × 600 as a decimal-scale echo of Shem's 600-year life, and 10000 as an Enochic confinement comparison. The textual basis for the latter is specific: 1 Enoch 18:13–16 and 21:3–6 describe the imprisonment of seven transgressing heavenly stars and give a 10000-year duration. These passages belong to the Book of the Watchers and support the broad Watcher-confinement association. Their immediate subjects and duration remain distinct from the seventy-generation sentence for Shemihazah / Semjaza and his associates in 1 Enoch 10:11–12.

File_11 §9.1 already uses 9200 → 10000 in its SP cumulative-to-regular Watcher Bridge. That earlier relation has different source dates and chronological states. The present example reproduces the span mechanism within the Rounded inverse Creation–Shem arrangement; it does not equate the SP endpoints with the present MT-derived inverse endpoints. The partition is arithmetic fact; its Shem / Enochic reading is a stated numerical–narrative comparison.

3.8.3 The Temple inverse and two routes to Rounded AD 526

The separately referenced Temple construction date is 966 BC, anchored to the Exodus by the adopted 480-year relation. Its Nativity-family inverse is 696 BC (§2.5): $966-6=960$, $I(960)=690$, and $6+690=696$.

Hold the Creation pillar at 14726 BC and expand toward the Temple inverse:

$14726-696=14030=23\times610,$

$14030\times\frac{25}{23}=15250.$

The rebuilt endpoint crosses the era boundary, so the report's Rounded coordinate rule must be applied explicitly:

$q(14726\text{ BC})=-14725,$

$-14725+15250=525=q(\text{AD }526).$

Thus the result is AD 526 in the symmetric Rounded display. The ordinary civil count from 14726 BC to the same printed AD 526 label would be 15251; a literal civil 15250-year interval would end at AD 525. The present result uses Rounded width throughout this route.

Now reflect both endpoints of the existing Conquest-backbone / Exodus comparison:

$12026\text{ BC}\leftrightarrow\text{AD }12026,\qquad1446\text{ BC}\leftrightarrow\text{AD }1446.$

The two positive Rounded coordinates are 12025 and 1445. Their same-side difference remains:

$12026-1446=10580=5290+5290=20\times529.$

Hold the reflected backbone at AD 12026 and expand backward from it toward the reflected Exodus:

$10580\times\frac{25}{23}=11500,$

$12026-11500=526.$

The expanded endpoint is again AD 526. Its displacement from the reflected Exodus is the expansion gain:

$1446-526=920=11500-10580.$

The two stated routes therefore meet at one coordinate, q = +525. A full-width check confirms their placement:

$14726+12026-2=26750=15250+11500.$

The two expansion gains also fill the original interval between the Temple inverse and reflected Exodus:

$15250-14030=1220,\qquad11500-10580=920,$

$1220+920=2140=696+1446-2.$

This makes the relation more specific than two unrelated target differences: expanding the two outer intervals closes the 2140-wide gap at the same Rounded coordinate.

The author associates the resulting $11500=5\times2300$ with sanctuary cleansing. Daniel 8:14 supplies the 2300 evenings-and-mornings / sanctuary-restoration theme, rendered as cleansing in the KJV. The fivefold numerical correspondence and the Temple source identity motivate this typological reading. The 11500-year derived span is not the passage's literal stated duration, and Rounded AD 526 remains a generated coordinate rather than an asserted historical Temple-cleansing event.

3.8.4 Scope of the companion examples

These three examples retain distinct constructions: comparison of durations expanded by different ratios; a uniform Nativity-held expansion; and two 25/23 expansions from different fixed backbone anchors that converge at one Rounded coordinate. The Creation-pillar role connects them, while the labels and operators determine each calculation.

The Temple source and both of its inverse routes remain outside the statistics, as requested in §2.5. None of the converted spans, the Enochic comparison, or the common AD 526 endpoint adds a statistical entry. The tally remains ten positive hits to 6 BC among 66 constructions. The new material develops the interpretation of already referenced nodes and records the exact mathematical conditions of the proposed relations.

3.9 Moses–Temple closure: the second expansion and 1000 + 1000

The author extends the Temple convergence by applying 25/23 a second time to the interval held at the reflected backbone. This returns the 476 BC endpoint already generated from inverse Moses and adds a corresponding forward relation to Moses' reflected birth.

Era-label clarification: the opening reference in the author's amendment is read as AD 12026 to AD 1446, first expanding to AD 526. This is the reflected interval established in §3.8.3. The second expansion then crosses to 476 BC. Literal AD 12026 to 1446 BC would have Rounded width 13470, not 10580, so the BC labels on 1446 and the first 526 in that opening sentence are treated as slips. All relations below use the existing symmetric Rounded convention.

3.9.1 Repeat the expansion with AD 12026 held

The original reflected interval contains the second factor of 23:

$12026-1446=10580=5290+5290=20\times23^2.$

Its successive exact expansions are:

$10580\xrightarrow{\times25/23}11500\xrightarrow{\times25/23}12500,$

$20\times23^2\rightarrow20\times23\times25\rightarrow20\times25^2.$

With AD 12026 fixed, q = +12025:

The first gain is 920 and the second is 1000. The second gain moves the endpoint from AD 526 to 476 BC by a Rounded width of 1000:

$476+526-2=1000.$

This is the second exact expansion already permitted by the 20 × 529 structure in §6.2, now given its explicit endpoint.

3.9.2 The same 476 BC from inverse Moses

Moses' Rounded birth at 1526 BC inverts from the 1406 BC Conquest anchor to 1616 BC:

$1526-1406=120,\qquad I(120)=210,\qquad1406+210=1616.$

The Creation-held result from §3.7 is:

$14726-1616=13110=570\times23,$

$13110\times\frac{25}{23}=14250,\qquad14726-14250=476\text{ BC}.$

Thus the second expansion held at AD 12026 and the first expansion of inverse Moses held at 14726 BC meet at the same Rounded coordinate, q = −475.

The source connection identified by the author is exact. Inverse Moses and inverse Temple stand 920 years apart:

$1616-696=920=40\times23.$

A common 25/23 expansion with Creation held sends that pair to 476 BC and AD 526. Their separation becomes:

$920\times\frac{25}{23}=1000,$

$q(\text{AD }526)-q(476\text{ BC})=525-(-475)=1000.$

Moses' inverse was constructed from the Conquest anchor, while the Temple inverse was constructed from 6 BC. Those original routes remain distinct. The common Creation-held expansion operates on their already established endpoints.

3.9.3 The forward counterpart reaches Moses' reflected birth

The interval from the shared AD 526 endpoint to the reflected Exodus at AD 1446 is also 920:

$1446-526=920.$

Now hold AD 526 and expand this interval forward by 25/23:

$920\times\frac{25}{23}=1000,\qquad526+1000=1526.$

The result is AD 1526, the Rounded Mirror of Moses' adopted birth at 1526 BC. The conversion adds 80:

$1000-920=80=1526-1446.$

That gain is exactly the birth-to-Exodus interval in the adopted Moses chronology. In the reflected display, the birth label lies later than the Exodus label; the operation preserves this stated Mirror orientation.

The resulting arrangement is:

$476\text{ BC}\xrightarrow{1000}\text{AD }526\xrightarrow{1000}\text{AD }1526.$

In Rounded coordinates it is the equally spaced triple −475, +525, +1525. AD 526 is its exact midpoint, and the total Rounded width is:

$476+1526-2=2000.$

The ordinary civil cross-axis counts between these printed labels would be one year larger. The 1000 + 1000 statement belongs to the report's declared Rounded coordinate system.

3.9.4 Structural meaning and dependence

The combined construction connects four specified source roles: Moses' birth, the Temple, the reflected Exodus, and the shared regular / cumulative Creation backbone. It uses the same 25/23 ratio throughout the present section. The held endpoint is AD 12026 for the repeated backbone expansion, 14726 BC for the inverse Moses / Temple pair, and AD 526 for the forward counterpart to Moses' reflected birth.

The relation is algebraically coherent. Given the AD 526 convergence of §3.8.3 and the shared original 920 gap, the common Creation-held expansion must place inverse Moses 1000 before the expanded Temple. The second expansion of 11500 adds that same 1000, and the forward expansion of the other 920 interval places Moses' reflected birth 1000 after the center. These consequences explain how the parts fit together; they are not independent probability trials.

The author reads this person- and Temple-specific closure as strengthening the proposed role of 14726 BC as an interpretive pillar. The arithmetic is exact under the declared model. Its evidential weight remains a structural assessment of the connected construction; no new coincidence probability or statistical admission is asserted. The Temple remains reference-only, and the ten-of-66 tally is unchanged.

3.10 Abraham: the 430 / 470 symmetry and Moses at the midpoint

The author develops the Abraham member already present in the complete nine-member table (§3.7.3). Abraham's Rounded birth is 2166 BC. Its Conquest-family whole-span inverse is:

$2166-1406=760\xrightarrow{I}670,\qquad1406+670=2076\text{ BC}.$

This is one of the original nine hits to 6 BC:

$2076-6=2070=18\times115.$

3.10.1 Creation-held expansion to 976 BC

Hold 14726 BC and expand the interval to inverse Abraham:

$14726-2076=12650=550\times23,$

$12650\times\frac{25}{23}=13750=550\times25.$

The gain is 1100 years. The later endpoint moves forward in time from 2076 BC to 976 BC:

$13750-12650=1100,$

$14726-13750=2076-1100=976\text{ BC}.$

The author's forward-time notation “2076 BC + 1100” describes this movement; subtraction is used for the positive BC year labels. The result 976 BC was already computed in the full pillar table. Its contextual relations are now made explicit.

3.10.2 The Entry–Exodus–Conquest symmetry

The generated 976 BC endpoint completes two routes from the 1876 BC Entry:

The complementary order is equivalently expressed as one four-node sequence:

$1876\text{ BC}\xrightarrow{430}1446\text{ BC}\xrightarrow{40}1406\text{ BC}\xrightarrow{430}976\text{ BC}.$

Thus the Exodus and Conquest occupy symmetric positions between Entry and the generated Abraham endpoint. Both the outer pair and the inner pair have midpoint 1426 BC:

$\frac{1876+976}{2}=\frac{1446+1406}{2}=1426.$

This is an arithmetic center, with no new event assigned to 1426 BC. The 430 / 470 reversal follows the existing 40-year Exodus-to-Conquest separation.

The author's further 390-year relation is exact:

$976-586=390.$

It partitions the existing Entry-to-Jerusalem interval controlled by File_16:

$1876-586=1290=900+390=430+40+430+390.$

The 586 BC node retains its repository Jerusalem-destruction state. The generated 976 BC endpoint has a structural role within this partition; it is not identified with the separately retained 966 BC Temple construction date.

3.10.3 Moses' birth bisects the 1100-year movement

The expansion's 1100-year gain has the stated midpoint:

$2076-1526=550,\qquad1526-976=550,$

$2076\text{ BC}\xrightarrow{550}1526\text{ BC}\xrightarrow{550}976\text{ BC}.$

Thus Moses' adopted birth at 1526 BC lies exactly between inverse Abraham at 2076 BC and Abraham's Creation-held expanded endpoint at 976 BC.

The arithmetic can also be read directly from the expansion factor: the input span is 550 × 23, the output is 550 × 25, and their difference is 2 × 550. The midpoint identity selects Moses' existing birth node within that movement. No further transformation of Moses' birth is used here; this midpoint differs from the inverse-Moses and reflected-birth constructions of §3.9.

3.10.4 Narrative interpretation and scope

The author reads the symmetry as coherent with Abraham's role in the foretelling of his descendants' foreign sojourn, affliction, departure, and return to the land (Genesis 15:13–16). The Entry, Exodus, and Conquest are therefore contextually relevant comparison nodes for an Abraham-derived endpoint. The 430-year Entry-to-Exodus register retains its own source and adopted chronology (Exodus 12:40–41; Files 05 and 16); it is not substituted for the 400 years stated in Genesis 15:13.

The two observations are specific: the generated endpoint closes the 430 + 40 + 430 sequence, while the gain from inverse Abraham to that endpoint is centered on Moses' birth at 550 + 550. Their arithmetic is exact. Their interpretation as a connected Abraham–Moses / Egypt–land pattern is a structural and narrative reading within the model.

The 430 / 470 routes, the four-node sequence, and the 1426 BC center are related descriptions of one configuration. The 390 extension reconnects that configuration to the existing 1290 Nexus span. They do not supply separate independent statistical counts. The original Abraham hit, source manifest, and ten-of-66 tally remain unchanged.

3.11 The Flood countdown: 6900, 6450, and the ten-member interpretation

The author connects the inverse Abraham–Moses pair with the 120-year countdown to the Flood and develops two expansions from the same Creation pillar. This gives the countdown member of the original nine-hit table an explicit role in the proposed interpretation of the ten-member family.

3.11.1 Seven named generations and the inverse 460 interval

Abraham and Moses bound the seven named generations Abraham, Isaac, Jacob, Levi, Kohath, Amram, and Moses. File_61 explicitly lists this seven-member sequence. The count is inclusive of both endpoints and contains six parent–child links.

Their Conquest-family inverses are already established:

$2166\text{ BC}\rightarrow2076\text{ BC},\qquad1526\text{ BC}\rightarrow1616\text{ BC}.$

The inverse endpoints stand 460 years apart:

$2076-1616=460=20\times23.$

The Rounded 120-year countdown source is 2576 BC, 120 before the Rounded Flood at 2456 BC. Its Conquest-family inverse is:

$2576-1406=1170,\qquad I(1170)=7110,\qquad1406+7110=8516\text{ BC}.$

The countdown inverse is 6900 before inverse Moses:

$8516-1616=6900=15\times460.$

The corresponding interval to inverse Abraham is $8516-2076=6440=14\times460$. Thus the three endpoints have the explicit partition:

$8516\text{ BC}\xrightarrow{14\times460}2076\text{ BC}\xrightarrow{460}1616\text{ BC}.$

These are endpoint intervals. The 460 is not divided into six equal biological generation lengths.

3.11.2 Two expansions with 14726 BC held

The shared input span is:

$14726-8516=6210=90\times69=270\times23.$

Both named Key-of-23 ratios therefore operate exactly:

The Prophetic route gives:

$6210\times\frac{70}{69}=6300,\qquad14726-6300=8426,$

$8426-1526=6900.$

Its 90-year displacement matches the difference between inverse Moses and Moses' adopted birth:

$8516-8426=1616-1526=90.$

Consequently the pair 8516 / 1616 BC becomes 8426 / 1526 BC by the same forward-time displacement of 90 at each end, preserving the 6900 interval. Only the countdown endpoint is generated by the displayed Creation-held 70/69 expansion; the Moses endpoint is compared with its already adopted birth date.

The Priestly route gives:

$6210\times\frac{25}{23}=6750,\qquad14726-6750=7976,$

$7976-1526=6450.$

Audit correction: the author's 7926 BC is read as 7976 BC. The multiplication gives 6750 and therefore fixes the endpoint at 7976 BC; this agrees with the pre-existing full pillar table in §3.7.3 and with the author's stated 6450 span. Literal 7926 BC would instead stand 6400 before 1526 BC.

3.11.3 The 460 / 430 comparison and the call-to-Exodus span

The two resulting countdown-to-Moses intervals have matching fifteenfold descriptions:

$6900=15\times460,\qquad6450=15\times430.$

Their difference is:

$8426-7976=450=15\times(460-430).$

The author's call-to-Exodus comparison also checks:

$2091-1446=645,\qquad6450=10\times645=15\times430.$

The 645 comparison uses the adopted 2091 BC call and 1446 BC Exodus anchors. It does not identify the whole call-to-Exodus interval with the 430-year Entry-to-Exodus register. Those two source spans remain distinguishable even though their scaled forms coincide here.

The relations connect the countdown, the inverse endpoints of the Abraham–Moses genealogy, Moses' birth, and the earlier Abraham call / Exodus interval. The shared 6210 input and held Creation pillar control both expansions; changing only the declared ratio gives the 6900 and 6450 outcomes.

3.11.4 The ten-member interpretive program

The author proposes that the entire ten-member family of 6 BC intersections can be understood through the 14726 BC key. This is recorded as the organizing thesis of the continuing study. With the joint Mahalalel–Shelah–Eber treatment in §3.12, the following inventory now gives each member a stated contextual interpretation.

All nine original source members now have proposed contextual interpretations in these pillar sections; the Creation backbone supplies the tenth member's documented anchor role and Nativity-span interpretation. Mahalalel, Shelah, and Eber receive a cursory joint exploration centered on their connection to the omitted Cainan. This completes the inventory's coverage, while the trio's wider complexity remains unexamined. Historical intention, theological meaning, and joint statistical significance remain separate questions.

The tenth member is the common pillar itself. Its meaningful comparison here is its nonzero span to 6 BC; expanding its zero displacement from itself would add no information. Accordingly, the proposed interpretation concerns the Creation–Nativity framework and explicitly stated held-anchor operations, rather than ten identical nonzero operations with Creation held.

All new spans are arithmetic facts under the specified constructions. Their narrative coherence is the author's structural reading. The 14 + 1 partition, matched 90-year shifts, and 15 × 460 / 15 × 430 comparison are algebraically related parts of this example. Neither they nor the inventory alter the original source manifest or the ten-of-66 statistical tally.

3.12 Mahalalel, Shelah, and Eber: a cursory exploration of the joint Cainan pattern

The remaining three source members receive one connected, preliminary interpretation. Their Nativity-family inverses place Shelah between intervals of 690 and 6900. Expansion from the common 14726 BC pillar produces 601, 1351, and 8851 BC, while preserving that 1:10 relation. The author reads the resulting intervals through the restored second Cainan's 130 + 330 lifespan and his declared 2551–2091 BC companion state.

Scope — cursory exploration: the author closely examined the relationships that caught his attention. The trio is substantially more complex than this account, and a thorough examination would be too demanding for the present treatment. Its principal observation is the connection to Cainan, omitted in the MT genealogy and understood as expunged under the author's restoration hypothesis. Section 3.12.7 records further examples to illustrate that wider complexity.

This locally opens restored Cainan for structural comparison. It does not insert him into the frozen MT source manifest, re-date its upstream generations, or add an inverse route to the statistical tally.

3.12.1 Source inversions and the common expansion

The source dates remain Mahalalel 3711 BC, Shelah 2421 BC, and Eber 2391 BC. Mahalalel and Shelah are initially $3711-2421=1290$ apart. Each uses the 1 BC anchor for the whole-span inversion:

Shelah's source is self-inverse. In chronological order, the inverse endpoints give:

$9321\text{ BC}\xrightarrow{6900}2421\text{ BC}\xrightarrow{690}1731\text{ BC}.$

Shelah is the internal junction of the two spans, dividing them in a 10:1 ratio when read in that order. The author's description of Shelah as “centered” is understood in this structural sense; Shelah is not their arithmetic midpoint.

Holding 14726 BC gives the three exact conversions:

Among the three admitted ratios 25/23, 70/69, and 300/299, only 25/23 yields integral expanded year-spans for these inputs. The other two yield, respectively, $16450/3$, $37450/3$, $39550/3$ and $70500/13$, $160500/13$, $169500/13$. Thus “only” refers to exact whole-year conversion by this stated ratio set, not to uniqueness among all conceivable multipliers.

The resulting order is:

$8851\text{ BC}\xrightarrow{7500}1351\text{ BC}\xrightarrow{750}601\text{ BC}.$

Both gaps undergo the same dilation: $6900\to7500$ and $690\to750$. The preserved 1:10 partition follows from applying one affine expansion to all three points.

3.12.2 The 330 / 460 structure and Cainan's restored state

The original inverse trio has the total width:

$6900+690=7590=23\times330=33\times230=\frac{33}{2}\times460.$

After expansion:

$7500+750=8250=25\times330.$

The gain across the outer endpoints is $8250-7590=660=2\times330$. These are related descriptions of one conversion, $23\times330\to25\times330$.

The textual comparison concerns the second, post-Flood Cainan. The MT-derived Genesis 11:12 connects Arphaxad directly with Shelah. The consulted Septuagint translation of Genesis 11 places Cainan between them and gives him 130 years before Shelah's birth and 330 afterward. This supports the numerical partition $130+330=460$. The same age pair also occurs for Shelah in that rendering, so the numbers alone do not uniquely identify Cainan.

The author's description of Cainan as “expunged” expresses the restoration hypothesis used in this study; the textual difference by itself does not establish the historical direction or intention of the change. Shelah occupies the immediate-son position under Arphaxad in the MT line and follows Cainan in the restored companion.

Files 18 and 16 supply the selected regular restored-Cainan state:

$2551\text{ BC}\xrightarrow{130}2421\text{ BC}\xrightarrow{330}2091\text{ BC}.$

Here 2421 BC is Shelah's birth, and 2091 BC is Cainan's death, sharing the adopted Abraham-call label. The full lifespan is 460. The regular insertion operator remains the 130-year begetting interval; measuring Cainan's lifespan as 460 does not replace that operator with the cumulative +460 rule. The other Cainan date variants are not opened.

This supplies the proposed contextual link: the self-inverse Shelah is the junction of both Cainan's 130 + 330 life partition and the trio's 6900 + 690 arrangement, whose total carries 330 under the 23-to-25 conversion.

3.12.3 Cainan's companion inverse and the 12000 Mirror width

Cainan's excluded source date can be examined separately with the same 1 BC selector:

$2551-1=2550,\qquad I(2550)=5520,\qquad1+5520=5521\text{ BC}.$

With 1 BC held, the 5520 span expands to 6000:

$5520\times\frac{25}{23}=6000,\qquad1+6000=6001\text{ BC}.$

Rounded reflection gives AD 6001, and the full symmetric width is:

$W_R(6001\text{ BC},\text{AD }6001)=6001+6001-2=12000.$

The civil elapsed count between those same printed labels would be 12001. The 12000 here is expressly the Rounded Mirror width.

The corresponding Conquest-family anchor relations are:

Their difference is $1150-690=460=20\times23$, preserving the lifespan. These are supporting companion calculations; Cainan remains outside the original 32-date survey and the 66-construction tally.

3.12.4 Christological comparisons and the explicit counting split

For the author's selected AD 30 death-of-Christ comparison, the civil elapsed count gives:

$C(8851\text{ BC},\text{AD }30)=8851+30-1=8880,$

$C(1351\text{ BC},\text{AD }30)=1380=3\times460,$

$C(601\text{ BC},\text{AD }30)=630.$

The author reads 8880 as a new-creation number. That meaning and the selected AD 30 event label belong to the theological / chronological interpretation; the present calculation establishes the stated duration under civil counting.

The 31 BC comparison requires an explicit local Mirror convention. In the ordinary astronomical map $a(B\text{ BC})=1-B$ and $a(\text{AD }A)=A$, AD 30 has coordinate +30 and reflects to −30, displayed as 31 BC. Accordingly:

$8851-31=8820=49\times180.$

Under this report's symmetric Rounded map, however, 31 BC reflects to AD 31, while AD 30 reflects to 30 BC. The author's “31 BC Mirror of AD 30” is retained only as the stated civil-display reflection; it does not redefine the Rounded Mirror elsewhere.

The mixed-count examples are therefore recorded side by side:

Thus $11270=23\times490$ is exact for 8851 BC to Rounded AD 2421. The civil 8880 / 1380 / 630 comparisons retain AD 30 as supplied. They would have those same numerical widths under the Rounded convention if the positive endpoint were instead labeled AD 31, but that is a different displayed construction and is not silently substituted.

3.12.5 The 1950 + 1950 midpoint and the 430 family

Mahalalel's expanded endpoint has the same-side relations:

$601-1=600,$

$2551-601=1950=15\times130,$

$2421-601=1820=14\times130.$

The latter two differ by Cainan's 130-year interval to Shelah. The first 1950 interval continues across the Rounded Mirror to the reflection of expanded inverse Shelah:

$2551\text{ BC}\xrightarrow{1950}601\text{ BC}\xrightarrow{1950}\text{AD }1351.$

In q coordinates these points are −2550, −600, and +1350. Therefore 601 BC is their exact Rounded midpoint. The outer width is 3900; reflecting the complete arrangement gives the corresponding 1351 BC → AD 601 → AD 2551 sequence, also 1950 + 1950. This is the same 3900 structure as the Shelah-to-reflected-Cainan comparison in the table, read in its reflected orientation.

Expanded Shelah also stands 1200 after Cainan's birth on the BC side:

$2551-1351=1200.$

Toward the reflected death / call and Exodus labels, the Rounded widths are:

$W_R(1351\text{ BC},\text{AD }2091)=1351+2091-2=3440=8\times430,$

$W_R(1351\text{ BC},\text{AD }1446)=1351+1446-2=2795=\frac{13}{2}\times430=13\times215.$

Their difference is $3440-2795=645=2091-1446$, preserving the adopted call-to-Exodus span already used in §3.11.3. The author thus connects the 130 / 330 Cainan partition with the 430 / 215 Exodus family through the expanded trio.

Rounded reflection preserves all q widths, so each complete Rounded arrangement can be read on the opposite side with its endpoint order reversed. This symmetry does not automatically transfer the separately chosen civil AD 30 calculations into the Rounded register.

3.12.6 The Conquest-held 70-year continuation

The additional expansion from 601 BC changes the held anchor from Creation to Conquest:

$1406-601=805=23\times35,$

$805\times\frac{25}{23}=875,\qquad875-805=70.$

With 1406 BC fixed, the rebuilt endpoint is:

$1406-875=531\text{ BC}.$

Thus the stated local continuation is 601 → 531 BC, a forward-time displacement of 70 years. It is a second expansion of a newly selected 805-year interval, not a repeat of the original 12995-year Creation interval.

The author proposes a Babylonian seventy-year echo, for which Jeremiah 29:10 supplies the textual duration. The generated 601–531 BC pair functions here as a symbolic numerical comparison, without asserting it as the historical dating of that captivity.

3.12.7 Cursory scope and place in the ten-member interpretation

Mahalalel, Shelah, and Eber receive an initial joint interpretation through Shelah and the restored-Cainan companion. Their common expansion, the 23 × 330 → 25 × 330 total, the Cainan 130 / 330 references, and the 1950 + 1950 arrangement belong to that proposed connection. The main point is the trio's relation to Cainan, omitted from the MT genealogy and described as expunged under the author's restoration hypothesis.

The following additional branches illustrate why the account remains cursory. Each expansion holds the stated later BC anchor and extends the earlier endpoint backward in time:

With Cainan's original 2551 BC birth retained, the first branch leaves:

$2551-2151=400.$

The second branch changes the Rounded interval to reflected expanded Shelah from 3900 to 4000:

$W_R(2551\text{ BC},\text{AD }1351)=2551+1351-2=3900,$

$W_R(2651\text{ BC},\text{AD }1351)=2651+1351-2=4000.$

The last two branches begin with the previously established 1 BC whole-span inverse $2551\text{ BC}\to5521\text{ BC}$. Its 5520-year interval permits both 70/69 and 25/23, yielding 5601 or 6001 BC with 1 BC held. This does not change the earlier observation that only 25/23 gives integral outputs for the three original Creation-held spans.

These examples illustrate the branching complexity beyond the relationships initially noticed. The author examined selected observations closely; a thorough examination of the trio would be too demanding for the present treatment and has not been undertaken. The Christological, Babylonian, and other subsidiary associations retain their stated interpretive status.

Together with the earlier examples, each of the ten members in §3.11.4 now has an initial contextual interpretation. Completion refers to coverage of that inventory; the trio remains a cursory exploration centered on its omitted-Cainan connection. The shared affine ratios, Mirror duplicates, and equivalent partitions are dependent relations within the pattern. Cainan's companion calculations add no new counted source or independent success, and the existing ten-of-66 tally remains unchanged.

3.13 The 12026 BC counterpart key: strong anchor assessment, partial exploration

3.13.1 Authorial assessment and the two anchor roles

The author regards 12026 BC as a major anchor node acting as a key comparable to 14726 BC. In his assessment, its importance is not in doubt within the developing model: the evidence is strong even though the detailed interpretation remains incomplete. The present addition is therefore marked partially explored. That qualification concerns the extent of the examination and the interpretation of its many relations; it does not dilute the author's confidence in the central anchor role.

The proposed pairing is specific. The 14726 BC pillar organizes the Rounded inverse dates associated with 6 BC (§§3.7–3.12). Its 12026 BC counterpart organizes Actual, non-Rounded MT regular dates associated with 1446 BC, with cumulative chronology supplying both the matching inversion route and the Actual Creation bridge. The principal numerical themes proposed for this second field are 1260, 13, and 666, together with Creation, the Watchers, judgment, and restoration.

The existing Exodus relation is:

$12026-1446=10580=460\times23=20\times529.$

For an Actual source date $X$ between these endpoints,

$12026-X=10580-(X-1446).$

Thus a multiple of 23 to 1446 BC also gives a multiple of 23 to 12026 BC. This common divisibility explains why the anchor can organize such dates; the specific expansion results and narrative associations supply the further interpretation. The present discussion examines the Creation and Jared–Noah–Flood examples. It does not claim that every remaining date in the supplied chart has already received an individual examination.

The source layers remain distinct. The original direct Rounded whole-span scan has zero positive hits to 1446 BC; the separately admitted segmented 12026 BC backbone contributes the one positive hit in the expanded ledger. The Actual-date study below is a structural continuation, not a change to that frozen survey.

3.13.2 Three starting levels and the newly introduced 8066 BC node

The two Rounded source chains, read backward from 6 BC, are:

• Regular: 6 → 1406 → 2456 → 4106 BC, with spans 1400 + 1050 + 1650.
• Cumulative: 6 → 1406 → 4836 → 14006 BC, with spans 1400 + 3430 + 9170.

Their placeholder-preserving inverse spans are 4100, 5010, 5610, 3430, and 7190 respectively. Sections 3.3–3.4 already establish the two- and three-segment constructions. Holding the original Flood endpoint and reversing only its remaining Creation segment supplies the third starting level.

For the regular Flood, inversion of its Conquest span gives $1406+I(1050)=6416$ BC. The last row nevertheless holds the original 2456 BC Flood, as the stated operation requires:

$2456+I(4106-2456)=2456+5610=8066\text{ BC}.$

For the cumulative Flood, $4836-1406=3430$ is self-inverse. Its Conquest-held inverse therefore remains 4836 BC, and:

$4836+I(14006-4836)=4836+I(9170)=4836+7190=12026\text{ BC}.$

This explains the repeated cumulative 12026 BC endpoint. The underlying 3430 span is unchanged by reversal; the printed date 4836 is not being declared literally incapable of digit reversal.

The newly introduced 8066 BC node has the following relations. All dates in this table are BC.

Isaac was sixty at Jacob's birth (Genesis 25:26), and his lifespan was 180 = 3 × 60 years (Genesis 35:28). The discussion's initial “60 × 6” lifespan expression is corrected to 60 × 3; 360 would represent two such lifespans. Likewise, the 6666 interval terminates at 1400 BC, while the interval to 1406 BC is 6660.

3.13.3 The 1260 / 666 theme and the 43000-year Exodus expansion

The author's proposed Revelation setting begins with the beast's forty-two months and the number 666 in Revelation 13:5, 18. Revelation 11:2–3 places forty-two months beside 1260 days; the schematic thirty-day-month relation is $42\times30=1260$. These passages supply the textual numerical context for the author's comparison, without making the newly calculated BC dates explicit dates in Revelation. The factor 13 also enters the arithmetic directly through $598=2\times299=2\times13\times23$ and the 650 / 1300 expansions below.

Source texts: Revelation 13 and Revelation 11.

Holding 6 BC, the cumulative Rounded Creation inverse is:

$14006-6=14000,\qquad I(14000)=41000,\qquad6+41000=41006\text{ BC}.$

Its relation to the 12026 BC key is:

$41006-12026=28980=23\times1260,$

$28980\times\frac{25}{23}=31500=25\times1260.$

The gain is $31500-28980=2520=7\times360=2\times1260$. The author reads this seven-year schematic-calendar total alongside Creation's seven-day / seven-year pattern. The unexpanded Rounded cumulative Creation has the companion interval $14006-12026=1980=66\times30$.

The inverse Creation also reaches the Exodus by an exact 23-multiple:

$41006-1446=39560=23\times1720,$

$39560\times\frac{25}{23}=43000=100\times430.$

Here the Exodus at 1446 BC is held while the earlier endpoint moves backward:

$1446+43000=44446\text{ BC},$

$44446-6=44440=5\times8888.$

The author associates 43000 with the adopted 430-year Egyptian-sojourn register, and contrasts the resulting 8888 multiple with the preceding 666 field. These are identified numerical–theological readings of the exact spans. The earlier study's distinction between the adopted 430-year chronology and Genesis' 400-year formulation remains in force.

The relation to the existing Exodus backbone is also transparent: $39560-28980=10580$, while the two converted durations differ by $43000-31500=11500$. This recalls the previously established 10580 → 11500 conversion; the difference of the converted durations is not an additional independently counted construction.

3.14 The Actual Creation bridge divided by 12026 BC

3.14.1 The chart's origin and selected source states

The supplied image, “Covenantal thread of multiples of 23-years to 1446 BC (Exodus),” expresses its chronology from the 4114 BC Creation endpoint. Its printed year 1 is the origin, so an ordinal year $N$ represents $N-1$ elapsed years:

$\text{date BC}=4114-(N-1).$

The following selected chart nodes control the present examination. The chart's other covenantal nodes remain available for later study.

The author explicitly selects Noah 3056 BC as Gear 1. The 2458 BC Flood is the Gear-2 / Shem-axis Flood under File_18's controlling table. Their 598-year separation is therefore a comparison between these selected states, not a replacement of Noah's stated 600 years at the Flood. Jared's chart coordinate is retained without extending gear transport into the earlier genealogy.

The Actual Creation completion endpoints used here are cumulative 14004 BC and regular 4114 BC. File_22 §5.1 controls that pair. They are distinct from the Actual Year-6 pair 14006 / 4116 BC and from the Rounded Creation pair 14006 / 4106 BC.

3.14.2 One key divides the bridge in the ratio 1:4

The 12026 BC anchor divides the Actual cumulative-to-regular Creation bridge as follows:

The original total is $1978+7912=9890$. Its expanded counterpart is $2150+8600=10750$; the expanded parts are not subdivisions of an unexpanded 9890-year total.

Both before and after conversion, the division is exactly 1:4:

$7912=4\times1978,\qquad8600=4\times2150,$

$12026=\frac{4\times14004+4114}{5}.$

The Rounded pair retains the same dividing date:

$14006-12026=1980,\qquad12026-4106=7920=4\times1980.$

Moving from the Rounded endpoints to these Actual completion endpoints shortens the earlier part by 2 and the later part by 8. Their common 1:4 division survives, while the Actual parts 1978 and 7912 are divisible by 23. The Rounded total remains 9900; the Actual total remains 9890.

Holding 12026 BC and expanding its interval toward regular Creation gives:

$12026-8600=3426\text{ BC}.$

This generated Creation endpoint is marked 3426 BC* throughout the following tables because its original span, $7912=344\times23$, is not divisible by 299. It belongs to the 25/23 comparison but not to the 299-multiple family of Jared, Noah, and the Flood.

3.15 Jared, Noah, and the Flood: the 598-year sequence, partially explored

3.15.1 The central 14 / 15 / 16 structure

The author's main point is the exact integration of the previously derived 12026 BC key with the selected Jared–Noah–Flood sequence:

$3654-3056=3056-2458=598=26\times23=2\times299.$

The combined span is $598+598=1196$, while 1058 is the separate Creation-to-Noah interval $4114-3056=460+598$. These two totals must not be interchanged.

The anchor places these three selected dates at consecutive 14, 15, and 16 multiples of 598. Under the same ratio applied to each anchor span, the entire progression becomes consecutive multiples of 600 or 650:

At the two-step scale, $1196\times300/299=1200=600+600$, and $1196\times25/23=1300=650+650$. The author connects the latter with the cursed-land / judgment theme of 1300 in his wider study.

Jared's anchor span also has the factorization:

$8372=14\times598=7\times1196=28\times299=23\times364.$

Its 25/23 expansion therefore gives $25\times364=9100$, a gain of $2\times364=728$. Its 300/299 expansion gives 8400, a gain of 28. The 460 in the chart is Creation → Jared; the 364 arises from the anchor-span factorization. Neither is being substituted for Jared's lifespan.

The narrative setting is supplied by the Watchers' descent in Jared's days on Mount Hermon (1 Enoch 6:6), Enoch's presentation of their petition (13:4–7), and the 364-day year (72:32). The comparison of 364-year blocks with that calendar is a proposed day–year echo, with the units distinguished. Source: 1 Enoch, R. H. Charles translation.

3.15.2 Complete expansion table with 12026 BC held

For every row below, the forward BC endpoint is computed as:

$X^*=12026-r(12026-X),$

where $X$ is the original BC date and $r$ is the declared ratio. Moving forward in BC time reduces the printed year number.

Creation's original 7912 span is not a multiple of 299. The other seven rows arise from the three 299-multiple source spans. There are eight construction rows but seven distinct resulting dates because 2926 BC occurs twice.

Among these three source spans, Noah's $8970=30\times299$ alone is divisible by 69 as well as by 23 and 299. Its three integral conversions are:

$8970\times\frac{300}{299}=9000=25\times360,$

$8970\times\frac{70}{69}=9100=25\times364,$

$8970\times\frac{25}{23}=9750.$

The cumulative forward shifts are 30, 130, and 780 years. The successive movements between the original and the three generated Noah dates are instead:

$3056\rightarrow3026\rightarrow2926\rightarrow2276\text{ BC}: \quad30+100+650=780.$

The author relates 30 to the leap-month unit, 130 to the restored regular Cainan variant, and 780 to the selected LXX–MT difference. File_18's controlled Flood dates give LXX 3238 − MT 2458 = 780, SP 3108 − MT 2458 = 650, and LXX 3238 − SP 3108 = 130. These differences retain their declared source states. The 100 also recalls Shem's hundred-year begetting register near the Flood, with Genesis 11:10's two-year qualification retained.

Reconstructing SP and LXX chronology from these building blocks is outside this addition's scope. The suggestion is retained as context for the selected 30 + 100 + 650 pattern.

3.15.3 Two equal-step sequences and the shared 2926 BC endpoint

Holding the same anchor produces two complete equal-step sequences:

• Under 300/299: Jared 3626 → Noah 3026 → Flood 2426 BC, with 600 + 600.
• Under 25/23: Jared 2926 → Noah 2276 → Flood 1626 BC, with 650 + 650.

The separation between a source's two branch results increases from Jared's 700 to Noah's 750 to the Flood's 800 years.

Noah's third ratio joins the two source interpretations at one endpoint:

$8970\times\frac{70}{69}=9100=8372\times\frac{25}{23},$

$12026-9100=2926\text{ BC}.$

Thus 2926 BC is both Jared's 25/23 result and Noah's 70/69 result. The equal step sizes follow from applying a common linear span ratio to the original equal 598-year intervals; they are coordinated expressions of this structure.

3.15.4 The resulting blocks: orientation before fuller interpretation

The following table contains every interval between the seven distinct Result BC dates. The duplicate 2926 BC construction has zero separation from itself and repeats the same relations to the other dates.

The asterisk preserves the Creation exception defined above.

The chronological adjacent gaps are $200+400+100+500+150+650=2000$. This inventory was produced to establish the blocks available for interpretation. The author subsequently clarified that it is preparatory; the main result remains the integration of 12026 BC with the 598-multiple sequence.

The author's Noah–Shem life-pattern context is the familiar 500 + 100 + 350 + 150 outline. Its application remains subject to the explicit two-year gear distinctions. Within the present seven-date table, 500, 100, and 150 occur as direct intervals; 350 does not. The table therefore does not yet reproduce that entire life-pattern as one continuous sequence.

The author's selected annotations are:

The same 500-year interval, 2926–2426 BC, participates in both 500 + 500 = 1000 and 500 + 150 = 650.

Two different measurements underlie the author's two-year / two-day comparison. Jared's 728 = 364 + 364 is his forward displacement from 3654 to 2926 BC. The 2000 years instead run from Jared's 300/299 result at 3626 BC to the Flood's 25/23 result at 1626 BC. The latter is not a direct conversion of 728 by one of the three ratios. The interpretation associates two calendrical years of years, two thousand-year days, and the two-year steps in the Japheth–Shem–Ham gear scheme. The thousand-year-day comparison has its textual analogue in 2 Peter 3:8; the 500 + 500 first-day reading remains expressly tentative.

3.15.5 Creation, Abraham, the SKL comparison, and AD 25

The expanded Creation and Flood endpoints inherit the familiar 1656-year source interval because both are produced by the same 25/23 expansion:

$3426-1626=(4114-2458)\times\frac{25}{23}=1656\times\frac{25}{23}=1800.$

Within that 1800-year span, the selected SKL 2886 BC anchor and Abraham's 2166 BC birth give a symmetric partition:

$3426\rightarrow2886\rightarrow2166\rightarrow1626\text{ BC},$

$540+720+540=1800.$

The overlapping intervals are $3426-2166=1260$ and $2886-1626=1260$. File_21 / File_34 identify 2886 BC as the SKL Long +30 rail. The author's local application of its ±720 macro bracket gives 3606 / 2886 / 2166 BC, placing Abraham's birth at the later member. This comparison retains the distinction between the SKL's 720-year scale and ordinary two-year gears.

The two AD 25 continuations use the civil no-year-zero count $C=B+A-1$, expressly distinct from the Rounded width $B+A-2$:

The 2276 BC node is Noah's 25/23 result, correcting the discussion's incidental Flood label. The Flood results remain 2426 and 1626 BC. The cross-axis equations are $2276+25-1=2300$, $1446+25-1=1470$, and $2426+25-1=2450$.

Within the adopted 6 BC Nativity chronology, $6+25-1=30$, so AD 25 supplies the proposed age-thirty Christological comparison. This is a relation within that adopted chronology, not a newly established historical ministry date.

3.15.6 What is retained, and what remains to be examined

The author considers this a cursory exploration of a more complex pattern. The exact 14 / 15 / 16 multiples of 598, the coherent 600 / 650 expansions, the Noah–Jared convergence, the Actual Creation bridge, and the earlier cumulative relations support his strong assessment of 12026 BC as a major key. A comprehensive explanation of all the generated blocks and all the chart's other 23-multiple dates has not yet been worked out.

The Moses comparison was intentionally left to the end of the proposed investigation. The retained contextual suggestions are his small ark on the Nile (Exodus 2:3), his 120-year lifespan (Deuteronomy 34:7), its placeholder-preserving inverse $I(120)=210$, and the author's broader reading of Revelation through Mosaic, Babylonian, 1260, and 666 themes. No additional Moses-date construction is supplied by this amendment.

The date calculations above are verified; their fuller narrative interpretation remains partially explored. The author's confidence in the anchor itself is preserved as an explicit structural judgment. No new source rows, target cells, independence claims, or probability estimates are added to the existing statistical study.

4. Joseph and Joshua: the 110-year correspondences

4.1 Textual lifespans and Rounded placements

Joseph and Joshua both live 110 years in the biblical account (Genesis 50:26; Joshua 24:29). File_51a §7.6 supplies their Rounded placements.

The birth-to-birth and death-to-death separations both equal $440=4\times110$. The absolute death placements belong to the Rounded comparison layer. The 110-year lifespans retain their textual status.

4.2 Joseph's inverse lifespan placement at the Exodus

Joseph's whole-span Conquest-anchor inverse is:

$1916-1406=510\xrightarrow{I}150,\qquad1406+150=1556\text{ BC}.$

The inverse birth then stands exactly one Joseph lifespan before the Exodus:

$1556-1446=110.$

In the provisional terminal-reconstruction reading, $I(110)=110$, so applying the 110-year lifespan forward from inverse birth 1556 BC reaches 1446 BC. The original Rounded life pair 1916–1806 BC and the reconstructed pair 1556–1446 BC both span 110.

This is a contextual inverse correspondence outside the 115 test. The 110 span is a miss for divisibility by 115. Its narrative interest is not reduced to that test's pass/fail classification.

4.3 Joshua's inverse birth and the 50/51–54/55 sequence

Joshua's whole-span Nativity-anchor inverse is:

$1476-6=1470\xrightarrow{I}7410,\qquad6+7410=7416\text{ BC}.$

From this inverse birth, the four comparisons identified in the discussion are all exact multiples of the common lifespan 110. All endpoints in this table are BC.

The sequence reflects the two original 110-year lives and their 440-year separation. Once one starting alignment is fixed, the differences between these four values are constrained by that source structure. The four comparisons display a coherent relation; they are not four independent statistical successes.

4.4 The provisional 5750 bridge

Applying the self-inverse lifespan 110 to Joshua's inverse birth gives a provisional terminal placement:

$7416-110=7306\text{ BC}.$

Its separation from Joseph's inverse birth is:

$7306-1556=5750=23\times250=50\times115.$

This is a bridge between the lifespan comparison and the Key-of-23 register. It remains outside the frozen birth/event scan because 7306 BC is a reconstructed terminal endpoint, and 1556 BC is not one of the scan's five comparison targets.

4.5 Narrative setting

Typological note: the Joseph–Joshua comparison is anchored in more than two equal lifespan totals. Joseph's final instructions anticipate Israel's departure; Moses carries his bones from Egypt; and their burial is recorded near Joshua's death at the close of Joshua (Genesis 50:24–26; Exodus 13:19; Joshua 24:29–32). These passages connect Joseph's death, the Exodus, and settlement in the land.

The inverse placement of Joseph's 110-year terminal span at the Exodus and the Joshua lifespan sequence are therefore read against an existing narrative connection. The arithmetic is exact under the model. The inference that the inversion captures an intended or providential structure remains separate.

5. The 1876 BC Nexus

5.1 The two inverse routes

The source event is Jacob's entry into Egypt at 1876 BC. His age of 130 at the encounter with Pharaoh is a textual datum (Genesis 47:9); the Rounded birth 2006 BC gives $2006-1876=130$.

The two whole-span routes preserve the same source event and use the normal 6-ending anchors.

5.2 The 700 and the 300 + 400 division

The 2146 BC inverse stands 700 years before the Exodus:

$2146-1446=700=14\times50.$

The 1846 BC affliction node divides this interval into $2146-1846=300$ and $1846-1446=400$. The latter is the selected 400-year affliction construction, whose textual duration is supplied by Genesis 15:13. The absolute 1846 BC placement is a chronological construction controlled by the Egypt/affliction field, not an independently stated biblical BC date.

The same 1846 BC node stands $1846-6=1840=80\times23$ from the Nativity anchor. Its Priestly expansion is:

$1840\times25/23=2000,\qquad6+2000=2006\text{ BC}.$

Holding 6 BC and extending backward therefore reaches Jacob's Rounded birth. This later expansion is retained as a structural relation. It is distinct from the direct inverse event at 2146 BC.

5.3 The 6370 and Jacob's 130 years

The Nativity-anchored inverse gives the parallel 49-register relation:

$7816-1446=6370=130\times49.$

The quotient 130 corresponds to Jacob's stated age at entry. The comparison therefore joins the selected Entry event, its inverse, the Exodus anchor, and the 49-year register.

Structural inference: the two inverse routes associate the same Entry event with $14\times50$ and $130\times49$ to the Exodus. The author's interest concerns that event-specific fit as well as the integer relations themselves. No probability for this combined narrative pattern was calculated.

5.4 Abraham's call at 2091 BC

The 2091 BC call / departure date is retained because it is a major event, despite having been overlooked in the first informal enumeration. Its original span to the appropriate 1-ending Conquest anchor is:

$2091-1401=690=30\times23=6\times115.$

This is an original-date relation. The two inverse dates are 9021 BC from 1 BC and 2361 BC from 1401 BC. Neither gives a hit to 6 BC. The event stays in the manifest because its admission is based on the agreed scope, not on producing a favorable result.

5.5 The Nexus and the AD 6 comparison

The same inverse Entry date 7816 BC appears among the AD 6 hits:

$W_R=7816+6-2=7820=340\times23=68\times115.$

The 6370 span to the Exodus and the 7820 Rounded width to AD 6 are different comparisons from the same generated endpoint. Their arithmetic is preserved without treating the endpoint as a new source date.

5.6 The 1846 BC hub: Abram–Moses symmetry and Terah's 1380

Authorial structural reading: 1846 BC is an important hub, second to 1876 BC in the relevant Egypt / affliction field. Its existing 400-year relation to the Exodus and its relation to the Entry Nexus already give it a defined place in the chronology (§5.2; File_16). The author's purpose in mentioning its common 115-year grid with 6 BC is to identify a possible main artery from which further relations can expand. It is not a request to add another target to the statistical study.

Three already established inverse routes show the local structure. All dates and held anchors in this table are BC.

Abram and Moses place the affliction hub exactly at their inverse midpoint:

$2076-1846=230,\qquad1846-1616=230,$

$\frac{2076+1616}{2}=1846,\qquad2076-1616=460=2\times230.$

Terah's inverse lies on the same local 230-year structure:

$3226-1846=1380=6\times230=60\times23.$

Thus Terah lies six 230-year units before the hub; Abram lies one before it; and Moses lies one after it. The named sources matter to the structural reading: Terah and Abram belong to the ancestral call setting, while Moses belongs to the Exodus setting. The exact inverse placements and centered spans are arithmetic facts within the elected Rounded model; the interpretation as a main artery is the author's proposed reading of their connection.

The proposed expansion role has a direct bounded illustration. Hold 1846 BC fixed and apply 25/23 to each signed displacement from that center. The common units become:

$230\times25/23=250,\qquad1380\times25/23=1500=6\times250.$

The Abram–Moses pair therefore retains the same midpoint while 230 + 230 expands to 250 + 250. Terah retains the six-unit relation. These rebuilt labels illustrate the declared expansion and are not assigned new event identities. They do not enter the source manifest or target count. The general claim that a wider artery will develop from this hub remains a direction for further study.

The earlier shared-grid observation is retained in this structural setting:

$1846-6=1840=16\times115,$

$D'-1846=(D'-6)-16\times115.$

Consequently the nine inverse routes on the 115-year grid through 6 BC also belong to the grid through 1846 BC; one of those endpoints coincides with the hub itself. This congruence supplies a connection between the two centers. The midpoint and Terah relations specify why the already important 1846 BC date is worth examining as a hub in its own right.

The admitted backbone endpoint extends that shared membership: $14726-1846=12880=112\times115$. There are therefore ten members of this grid in the expanded tally, still including the one exact 1846 BC overlap. This continues the structural hub observation without adding 1846 BC to the statistical targets.

Section 3.7 develops the author's subsequent Creation-pillar reading of this 12880 span. With 14726 BC held, the 1846 BC hub moves to 726 BC and the Abram–Moses pair moves to 976 / 476 BC, retaining the expanded 250 + 250 symmetry. That operation holds Creation fixed; the earlier illustration in this section holds 1846 BC fixed.

5.7 The paired Entry hub: 9660 to 9800 through the Rounded Mirror

The author adds a further connection between the paired Egypt nodes, 1876 BC and 1846 BC. Their original separation is 30 years. The Nativity-family inverse of the Entry at 1876 BC is already established in §5.1:

$1876-6=1870\xrightarrow{I}7810,\qquad6+7810=7816\text{ BC}.$

Apply the Rounded Mirror to that inverse endpoint. Its coordinate −7815 reflects to +7815, displayed as AD 7816. The affliction hub at 1846 BC has coordinate −1845. The width between them is therefore:

$W_R=7815-(-1845)=9660,$

or, using the symmetric Rounded labels directly:

$1846+7816-2=9660=140\times69.$

The stated conversion is the Prophetic ratio 70/69:

$9660\times70/69=9800=4900+4900.$

The equal halves display the conversion explicitly:

$9660=4830+4830,\qquad4830=70\times69,$

$4830\times70/69=4900=70^2.$

Thus the span from the 1846 BC hub to the Mirror of the Entry inverse converts into two equal 4900-year units. The sequence retains its distinct operations and endpoints.

The 9660 value uses the Rounded coordinate convention throughout the cross-axis comparison. The ordinary civil count between the same printed labels would be 9661. The 70/69 conversion here is also distinct from the 25/23 expansion illustrated around the 1846 BC center in §5.6.

Structural inference: the Entry source supplies the inverse / Mirror endpoint, and its paired affliction hub supplies the other end of the duration that converts to 4900 + 4900. This gives a further explicit relation linking 1876 BC and 1846 BC within the proposed hub structure. It belongs to the structural study; the converted duration is not assigned a new historical event or entered in the target-frequency scan.

Section 3.8.1 compares this 9800 result with the 24500 expansion of the longer span from the 14726 BC Creation pillar to the same Entry inverse / Mirror endpoint. It records the resulting 14700 + 9800 partition and distinguishes its two expansion ratios.

6. The 529 family and repeated expansion

6.1 The common arithmetic

The significance of 529 = 23 × 23 in this discussion is that it permits two exact successive applications of the Priestly ratio:

$k\times23^2\xrightarrow{25/23}k\times23\times25\xrightarrow{25/23}k\times25^2.$

The four selected durations below are discussed with their own endpoints and operators in the following subsections. Their shared expansion form is an arithmetic consequence of the factor 529.

The two exact expansion steps are not independent confirmations of the factorization. They explain what the factorization makes possible within the stated operator system.

6.2 The 20 × 529 same-side relation

The segmented regular / cumulative convergence at 12026 BC (§3.3) yields:

$12026-1446=10580=20\times529=23\times460.$

The exact expansion chain is $10580\rightarrow11500\rightarrow12500$ under two applications of 25/23. The same-side span uses ordinary subtraction and needs no cross-axis correction.

This relation is inherited from the source architecture, where the 10580 value is already recorded as 23 × 460. Expressing it as 20 × 529 makes its second exact Priestly expansion explicit. It is not an additional hit in the 64-route whole-span scan.

The first expansion also participates in the Temple convergence of §3.8.3. After reflecting both backbone and Exodus endpoints, hold AD 12026: expanding 10580 to 11500 moves AD 1446 back by 920 to Rounded AD 526, the same coordinate obtained from the Creation-held Temple inverse.

The second expansion to 12500 reaches 476 BC in the same Rounded display (§3.9). That is also the Creation-held expansion endpoint of inverse Moses, 1616 BC. The successive gains are 920 and 1000, connecting the two exact expansions of 20 × 529 with the Moses–Temple pair.

6.3 The 19 × 529 civil comparison

The regular whole-span inverse Creation at 8606 BC is compared with the AD 1446 counterpart in the selected cross-axis construction.

The two possible widths must be shown together.

The factor 529 belongs to the expressly selected civil count:

$8606+1446-1=10051\xrightarrow{25/23}10925\xrightarrow{25/23}11875.$

It does not belong to the neighboring Rounded width 10050. The arithmetic verifies the selected civil construction; it does not erase the difference between the two conventions.

6.4 The 104 × 529 civil comparison and the 299 connection

The cumulative Nativity-anchor inverse is 41006 BC. The selected opposite-side companion is AD 14011, the symmetric Rounded display of coordinate +14010.

The source of the 55016 duration is therefore:

$41006+14011-1=55016.$

The first Priestly expansion has an additional exact factorization, which permits the stated Enochian conversion.

The starting date of the 55016 comparison is 41006 BC. The earlier mistaken substitution of 14006 BC is not retained.

6.5 Reapplying a converted duration on the Rounded grid

The author separately specified a launch from 14006 BC using the converted duration 59800. That launch has its own held starting point; it is not the original span that generated 55016.

On the Rounded grid:

$-14005+59800=+45795\quad\longrightarrow\quad\text{AD }45796.$

The resulting Rounded width is 59800. The literal civil elapsed count between the printed labels 14006 BC and AD 45796 is 59801.

This example records the full sequence: an expressly selected civil duration is converted, a new launch anchor is declared, and the converted duration is then applied using Rounded coordinates. The mixed construction remains explicit and provisional as a structural interpretation.

6.6 Seth, 7935, and its Rounded Mirror

Seth's Rounded birth at 3976 BC gives the Nativity-anchor inverse:

$3976-6=3970\xrightarrow{I}7930,\qquad6+7930=7936\text{ BC}.$

Its span to 1 BC is:

$7936-1=7935=15\times529=345\times23=69\times115.$

The corresponding Rounded coordinate is −7935. Reflection gives +7935, displayed as AD 7936. The full Rounded Mirror width is therefore:

$7935+7935=15870=30\times529.$

The literal civil count between the printed labels 7936 BC and AD 7936 would instead be 15871. The 15870 value is expressly a Rounded coordinate width.

The one-sided 7935 duration expands to 8625 and then 9375. Seth's 1 BC hit, its Mirror double, and its two exact expansion steps describe one underlying 529 relation. They are not additional independent hits in the scan.

6.7 The proposed third-axis reading

Exploratory note: the discussion considered whether inverse structure might act analogously to a further axis alongside the ordinary and Mirror displays. The examples show that distinct transformations can generate compatible numerical relations. A geometric interpretation requires a defined mapping and an account of what is preserved; the factorization of selected durations does not alone supply that account.

The present report records the analogy as a proposal. It does not promote the inverse operation to the same established coordinate status as the Mirror or replace the second-order treatment already assigned to the existing File_52c.

7. The cumulative 62100 chain and the return to 6 BC

7.1 The direct inverse holds 1406 BC

The cumulative Creation-to-Conquest span is:

$14006-1406=12600\xrightarrow{I}62100=2700\times23.$

The anchor remains 1406 BC, so the direct rebuilt date is $1406+62100=63506$ BC. Its span to 6 BC is $63506-6=63500$, which is not divisible by 115.

The direct 62100 inverse therefore belongs to the Conquest-held construction. It is not itself a direct inverse hit to 6 BC.

7.2 The stated expansion sequence

The subsequent sequence uses the Prophetic ratio 70/69 and then the Priestly ratio 25/23. All expansions in this table are whole-year conversions.

Correction retained: the ratio taking 62100 to 63000 is 70/69. The reverse ratio 69/70 does not yield that result.

Terminology retained precisely: 64406 BC is an inverse-plus-expansion endpoint. Calling it a double inverse would conflate operators, since two applications of the defined reversal restore the original 12600 span and its 14006 BC endpoint.

7.3 Why the later span is divisible by 23

The increase of 900 combines with the 1400-year separation between the two anchors:

$900+1400=2300=100\times23.$

Thus the new Nativity span is $62100+2300=64400$. Once that expansion and anchor change are chosen, the divisibility follows from this identity.

The term residual in the discussion referred here to a remaining or recomputed interval. No fractional physical residue, residual day-year lift, or other File_00 Residue Protocol operation is being invoked.

This chain helps explain the author's interest in 6 BC as an intersection across more than one construction. It remains outside both the direct 64-route tally and the expanded 66-construction tally. The counted backbone addition uses segmented inversion, without this later expansion.

8. The original target scan and the backbone extension

8.1 Test definition

For each inverse endpoint $D'$ BC and each target with Rounded coordinate $q_T$, calculate:

$W=\left|q_T-(1-D')\right|.$

A positive hit requires $W>0$ and $23\mid W$. Every width in this scan is a multiple of five. Consequently:

$23\mid W\quad\Longleftrightarrow\quad115\mid W.$

Zero is mathematically divisible by 23, but a zero-span overlap is not a positive hit. No 6 BC-to-itself match enters either the original nine hits or the expanded ten. The target dates 6 BC and 1 BC are not source rows in the manifest.

A self-inverse source is a different case. It may produce a positive span to a target and is admitted under the stated rule. Shelah and the 1846 BC affliction node illustrate that distinction in the 6 BC results.

8.2 Original whole-span counts for all five targets

The same 64 routes are used in every row. The BC comparisons use absolute separations; the AD 6 comparison uses the Rounded coordinate +5.

The first comparison of 6 BC, 1406 BC, and 1446 BC comprises 192 route–target comparisons: 11 positive hits, two zero-span overlaps, and 179 misses. Adding 1 BC and AD 6 gives 320 comparisons: 16 positive hits, two overlaps, and 302 misses. These are bookkeeping totals, not counts of independent statistical trials.

8.3 The original nine whole-span hits to 6 BC

All source dates, held anchors, and inverse dates in this table are BC. Each listed span is the inverse date minus 6.

Five hits arise from the Nativity family and four from the Conquest family. The nine positive spans do not include a zero-distance anchor identity, a cumulative source, a reconstructed death, or an expanded duration.

The two self-inverse entries are Shelah's Nativity-family route and the affliction node's Conquest-family route. Their inclusion preserves the agreed rule; neither is a target-to-itself match.

8.4 The 1406 BC and 1446 BC comparisons

The 1406 BC target has two positive hits, both from Nativity-family inversions.

Adam's Nativity-family inverse lands exactly at 1406 BC. That zero-span overlap is recorded separately.

The 1446 BC target has no positive 23-multiple hits in the original whole-span scan. The Exodus source remains 1446 BC under its Conquest-family inverse, producing the one zero-span overlap in that column. The separately admitted 12026 BC backbone endpoint adds one positive hit in the expanded tally (§8.7).

The low 23-multiple count does not summarize all numerical activity at these anchors. Joseph's 110 to the Exodus, the Entry inverse's 700, and its other route's 6370 remain explicit examples outside that divisibility class.

8.5 The 1 BC comparison

The 1 BC target gives two positive hits.

The count is close to the approximate expectation of 2.78. Seth's internal 15 × 529 structure supplies the separate observation developed in §6.6; it does not increase the count beyond two.

8.6 The AD 6 comparison and Isaac's lifespan

For the AD 6 target, $q_T=+5$ and the Rounded width is $D'+4$. Three routes qualify.

The three-hit count is near the baseline expectation. The author nevertheless identified all three sources as central to the larger study: Enoch, Isaac, and the 1876 BC Nexus.

Isaac supplies a specific lifespan correspondence:

$2070\times25/23=2250,\qquad2250-2070=180.$

The increment is exactly Isaac's stated lifespan (Genesis 35:28). His Conquest-family inverse is self-inverse because $2066-1406=660$ and $I(660)=660$. The 2070 relation is therefore already present in the original Rounded placement and is preserved through this inverse route.

This is an interval-expansion correspondence. It does not resolve the separate procedure for reconstructing inverse deaths.

8.7 Expanded tally: the tenth incident and its companion stage

The author expressly admits the completed major backbone as the tenth incident at 6 BC. Its construction is the regular segmented path in §3.4, already present in File_52a §7. The original 32-source manifest remains intact. The extension records both anchor stages of that one backbone, so the denominator becomes 64 + 2 = 66 constructions.

This paired admission includes the 12026 BC miss to 6 BC as well as the successful 14726 BC endpoint. It also preserves the Exodus hit at the Conquest stage. Neither endpoint occurs in the original 64-route ledger.

The expanded counts below use all 66 constructions against every target. Appendix A.6 supplies both additions' complete five-target outcomes, including every miss.

The 6 BC count is now six Nativity-stage hits and four Conquest-stage hits. The first three target columns comprise 198 comparisons: 13 positive hits, two overlaps, and 183 misses. All five columns comprise 330 comparisons: 18 positive hits, two overlaps, and 310 misses. These totals describe comparisons, not independent trials.

The regular Noah alternatives and cumulative primary Flood path support the same two backbone endpoints and add no further entries. The 5290 + 5290 relation strengthens the author's structural reading but is one Exodus hit, not two. The Temple at 966 BC, expanded 64406 BC endpoint, and other referenced branches remain outside the tally.

9. Probability benchmark and its scope

9.1 Why the working density is 1/23

Among successive multiples of five, one in every 23 is divisible by 115. Equivalently, division by five turns the question into divisibility by 23. This supplies the simple working density:

$p=\frac{1}{23}.$

The last-digit split does not supply an additional factor of two. For a 6-ending inverse date measured to 6 BC, the span is divisible by ten and a successful quotient in units of 115 is even. For a 1-ending inverse date, the span ends in 5 and the successful quotient is odd. Each class has one qualifying position per 23 successive ten-year positions.

This is a density statement on complete residue cycles. It is not a demonstration that the historically related source dates, or the inverse outputs of this finite selected sample, are uniformly distributed among those residues.

9.2 Original benchmark: the nine-hit excess

Under the simple model, the expectation for one target is:

$E[X]=\frac{64}{23}\approx2.7826.$