The 365-Day Sothic Companion to the Key of 23

The 1460/1460.5 pair, the 10220 Creation bridge, the divided seven, the SKL Mirror field, and the AD 29465 Pillar

Date: September 6 2026
Working edition: v0.3 — consolidated Sothic–Mosaic selection, Long-variant audit, and bounded source amendments
Authorial proposals: Dean, present discussion, points 1–9
Status: Consolidated discussion and amendment ledger; Report V is the recommended new-chat synthesis. Three separate full-replacement working amendments are prepared and verified; neither Finalization nor central registration is claimed.
Verification: Current consolidation audit: 116 exact scalar equalities checked in Fraction and SymPy; 141 phase/set/sensitivity/rejection assertions. Earlier 127/127 and v0.2 audit figures are preserved as historical records, not added to this count. Executable: ../03_Verification/verify_sothic_consolidation.py. This is bounded verification, not a full repository pressure test. Canonical source state: Existing repository files and all four control files remain unchanged.
Prepared source homes: File_12 §5A for calendar definitions and the Sothic/Key-23 comparison; File_22 §§5A/9B for the cumulative–regular Creation and Pillar application; Supplement A §13/Appendix H for the finite-field and anchor-selection proof. Other reciprocal changes remain affected-only.
Companions: The earlier arithmetic and Mirror audits and v0.1/v0.2 ledgers are preserved in ../05_Frozen_Parents/. The current executable is ../03_Verification/verify_sothic_consolidation.py, with the current scalar manifest and phase/closure report in the same directory. The earlier script name check_sothic_mirror_closure.py is historical and is not required for this package.

0. Principal result

The proposed half-step Sothic ratio is mathematically coherent:

It belongs to the broader one-year-completion grammar on a half-23 grid:

The original three ratios and the proposed companion are instances at:

However, the proposed Sothic companion does not preserve the original three Keys' exact common schematic year:

The distinction is fundamental:

The exact 365-day continuation that does preserve K is a different ratio:

Both are retained in this ledger, with separate meanings: H is Sothic/Julian-adjacent and half-23-aligned; G preserves the original common schematic day-volume. Neither is silently added to the canonical operator register. [F00; SG]

The strongest chronological result is:

This makes the two Cainan-bearing Creation fields uniformly seven ordinary Sothic blocks apart. The proposed half-step changes a seven-cycle carrier by 3.5 years and a ten-cycle carrier by 5:

These are exactly the half-week and Creation-head-to-Year-6 separations used in the proposed construction. This is a compact explanation of several coordinate results, not proof of ancient conscious design.

1. Source and state register

1.1 Existing versus newly proposed relationships

The 365, 1460, 1380, and Sothic-to-Exodus comparisons are not all new. File_51a already places the Rounded/−215 Enoch ascension at 2906 BC, followed by 1460 to Exodus and 1380 to Moses. File_33 already contains a ten-1461 Sothic Exodus application.

The present candidate is the explicit 1460.5/1461.5 half-23 companion, together with its seven-cycle Creation bisection, ten-cycle head/Year-6 relation, declared SKL Mirror enumeration, and Pillar comparison. The searched controls do not contain the literal ratio; this is not a claim of exhaustive conceptual novelty throughout every historical repository edition.

2. Corrections and interpretations of the informal input

These corrections preserve the evident intended structure. They are not unannounced emendations to the canonical sources.

3. The drift grammar and the three reference standards

3.1 One extra calendar year

Let d be a short calendar's year-length in days, Y a selected longer reference year, and q the reference-year count at which the short calendar accumulates one additional year:

Then:

This is the mathematical principle shared with idealized Sothic reckoning. It does not establish historical transmission from one named calendar to every other.

With the allowed half-23 measure u=11.5:

The first three reproduce the same K when multiplied by 336/360/364. The fourth does not reproduce it when multiplied by 365.

3.2 Existing schematic and calibrated values

The unchanged definitions are:

K is the exact schematic equivalent; S_K is the repository's calibrated reference. Neither is silently replaced by the Julian mean 365.25. [F00; SG]

The primitive Priestly comparison is:

Thus the user's “about 4200 versus 4200.3 days” is correct as an approximate day-volume comparison.

3.3 Enochian partners

The exact year implied by the side comparison is:

Against the unchanged S_K:

whereas:

The two ratios can therefore serve complementary purposes: closer physical calibration versus participation in the 23×13 architecture. That distinction already exists in the controls and File_53. It does not license switching ratios invisibly.

Source precision note: File_53's printed 107016=293×365.2423 is rounded-display language. Strict multiplication gives 107015.9939, a difference of 0.0061 day. This ledger uses ≈ for the rounded decimal and exact 107016/293 where needed. No File_53 rewrite is made here.

3.4 Ordinary and half-step Sothic

The ideal ordinary equality is:

Censorinus supplies an ancient witness to the underlying Egyptian drift account. The equality is a statement about ideal mean year-lengths; no observed Sirius-rising chronology is computed here. [CENS]

The proposed half-step ratio satisfies:

Consequently:

The mismatch is only three hours in this mean-year calculation. This is not an assertion that a particular half Julian year contains exactly 182.625 calendar days.

Against the common repository reference instead:

Thus H is extremely close to the Julian/Sothic standard, but not an equally close tropical-year realignment. Its structural coherence does not depend on pretending those standards coincide.

3.5 A bounded check at the Exodus epoch

The Observatoire de Paris source gives the following P. Bretagnon (2000) mean tropical-year expression, in Julian millennia T from J2000:

At the approximate 1446 BC epoch, T≈−3.445, it gives:

This lies very close to the unchanged S_K. The new half-step block's mismatch is then approximately 10.98724 days. The physical conclusion remains the same. [AST]

This is a bounded mean-year calibration, not a calculation of a particular equinox-to-equinox year, heliacal visibility, ancient civil-calendar epoch, or a varying tropical-year integral across the entire deep-time chronology. File_00's wording associates S_K with the time of Christ; the numerical epoch check here instead demonstrates a close approximation at the proposed Exodus epoch. That wording discrepancy is recorded for source review, not silently rewritten.

A strict “nearest half-23 realignment to this common tropical reference” criterion would give:

The nearest 11.5-multiple is 1506.5=131×11.5, giving the separate sensitivity candidate 3015/3013, for which:

This is a diagnostic counter-test, not a new active repository ratio and not a substitute introduced to improve the date matches. It makes explicit that the choice 127, rather than 131, preserves Sothic/Julian adjacency rather than optimal common-tropical calibration.

3.6 Exact continuation of the common K

Preserving the original exact common schematic value instead forces:

Here 1679=23×73=146×11.5. Thus G also belongs to the general half-23 one-year-completion form, but occupies a different point in it.

Three distinct questions must remain distinct: nearest Julian/Sothic companion; closest common-tropical realignment; exact preservation of K.

4. SKL, Moses, Joshua, Exodus, and Tabernacle

The 1446 BC Exodus is the repository's primary chronographic anchor, not an independently established Egyptian Sothic-reset date. Acts 7:22 supplies the Egyptian-wisdom context; it does not attest Moses' use of the proposed ratio. The Egypt–Sumer–Rome comparison is retained as a thematic/providential interpretation of the source-defined systems. [F05; BIB; CENS]

4.1 Ordinary Sothic carrier

The parallel Joshua comparison is:

Its expanded terminal is 1475n BC, a generated companion, not a replacement birth date.

The preceding Tishri states give:

1447t retains the plague-period comparison; 1477t/1476n is the assumed intended Joshua pair. No new literal historical birth-day precision is asserted.

Exodus 40:17 places the Tabernacle on the first day of the first month in the second year. Accordingly, 1445n is a year/phase-label correspondence. The equation does not assert that the Tabernacle was erected exactly one elapsed year after the Exodus departure on Nisan 15. The Tishri companion is not a second erection date. [BIB]

4.2 Moses' 1380 and 120

Applying the Priestly ratio:

The expanded endpoints are therefore:

The 120 is the expansion gain, echoing Moses' lifetime; the calculation is not 120×25/23=120.

4.3 Moses' 80.5 and the half-step Sothic whole

The existing half-scale instance is:

The two explicitly crossed phase branches are:

The second is a Tishri comparison branch, not a claim that the historical Exodus took place in Tishri. Same-phase 1526n→1446n remains 80. [F12; F17]

Now:

and the half-23 structure is transparent:

The two complete Sothic-Key branches become:

The Priestly and half-step Sothic transformations are alternative measurements, not compounded here:

5. The seven-cycle cumulative–regular Creation bridge

5.1 Corrected component-wise field

The source-controlled Cainan-bearing wrappers are:

The entries are respectively the Creation head, Year-6/Adam comparison, and Creation close. Each must retain its own node-class. [R1; F09; F18; F69]

Every corresponding difference is:

Its derivation from Report III is:

This connects the proposed family directly to the earlier comparative engine rather than using two unexplained fitted dates.

5.2 Seven ordinary cycles complete to the next week

The Creation envelope 4251–4244 is thus translated to the following seven-year envelope 4244–4237 in the repository's Creation/Fall interpretation.

Execution control: This table applies the same seven-cycle carrier to each corresponding source node. It preserves the width of the source envelope. It is not one global dilation of every date about a single fixed anchor; such a dilation would also rescale the envelope's internal seven-year width.

5.3 The AD 135 7+3=10 closure

Therefore:

carries:

AD 135 is retained as the chosen repository era-boundary and historical catastrophe comparison. Cassius Dio supplies the devastation context, not a claim that the Jewish people or every form of Israel's history ended then. [F69; DIO]

6. Seven half-step cycles and the divided week

6.1 Head to midpoint

Under the repository's explicitly opened schematic phase model:

The target nodes are exactly:

Thus seven half-step cycles lead from the cumulative head to the midpoint of the regular Creation week; expansion leads to the midpoint of the following week.

6.2 Midpoint to close

The cumulative Creation midpoint is:

From it:

This verifies the user's complementary midpoint-to-close description.

6.3 Ten cycles and the five-year head displacement

Together with the ordinary result:

the five-year source displacement is explained by:

A generated companion follows if both complete ten-cycle spans are expanded with their respective ratios:

AD 145 is an arithmetic output only. No historical-event identification or prediction is attached to it.

7. The complete twelve-node SKL paired-Mirror test

7.1 Declare the Mirror before calculating

The active Mirror is File_09's phase-resolved paired form:

It is not Rounded Protocol 1, raw coordinate addition without state declaration, or the separate standalone same-numeric-year Mirror. [F09; REG]

Write the upper +30 pair as (U+1)t/U n BC and the lower pair as (D+1)t/D n BC, with:

The lower pair's Mirror is AD D t/(D+1)n. Both corresponding components have span:

7.2 Exhaustive three-by-three span matrix

The two four-cycle conversions are:

The two examples in the original message therefore have their cycle labels reversed:

7.3 Explicit coverage routes

For ordinary Sothic, two anchored routes cover all six source pairs:

The first holds the upper pair fixed and moves the AD endpoint forward four years. The second holds the AD endpoint fixed and moves the BC source four years earlier. Both transform 5840 to 5844.

For the half-step family:

The first two are fixed-end routes. The third explicitly distributes the four-year gain bilaterally as 2+2; it is not a hidden fixed-anchor operation. All transform 5842 to 5846.

Across these declared routes, all three upper pairs and all three lower pairs occur: six phase pairs, or twelve distinct source phase nodes. The Mirror targets are their defined counterparts, not another twelve independent source witnesses.

Strengthened result (v0.2, superseding the former affine qualification): In addition to the selected-route coverage, one fixed translation by 5842=4×1460.5 maps all twelve source phase-nodes onto exactly their paired-Mirror target set. Following that translation by inverse Mirror gives the affine involution R(x)=−5842−x, which permutes all twelve original nodes in six transpositions. This does not assert self-correspondence of each individually named node, global closure under each of the other three four-cycle translations, or identical 1476/1446 interior landings on every route. See §§7.5–7.9 for the complete proof and the conditional uniqueness statement.

The selected central one-cycle links do remain exact:

7.4 Compressed explanation

Let the upper and lower Gear offsets be g,h∈{−2,0,2}. Then:

The central cross-Mirror span is:

The ordinary and half-step input/output cells occupy this constrained matrix. This explains why a four-year expansion is compatible with the existing two-year Gear spacing. Matrix repetitions should not be counted as independent probabilities.

7.5 The common center and the complete coordinate set

This section records Dean's clarification and replaces the v0.1 stopping point at selected-route coverage. It uses File_09 Appendix A.3, not Rounded A-space or the standalone same-number Mirror. Define x as elapsed schematic years from January 1, AD 1:

The phase model is schematic. It does not assert literal equal Gregorian/Julian month lengths or observed ancient month starts. The paired Mirror is M(x)=−x on this point set, with its outputs displayed in chronological t/n order. Pointwise reflection reverses that order; it is not the separate same-numeric-year standalone Mirror. [F09; REG]

The outer coordinates are:

Thus:

The center is the boundary December 31, 2922 BC / January 1, 2921 BC. Its distance to January 1, AD 1 is exactly 2921 years. Its reflected center is January 1, AD 2922, not January 1, AD 2921.

All twelve nodes are exactly:

The factors represent the two 30-separated rails, three local Gears, and two half-year phase endpoints. The full width is 30+4+0.5=34.5; each node is a distinct quarter-coordinate.

The already registered Short-ladder center-pair 2922t/2921n BC brackets this January instant. The pair's individual endpoints remain distinct from the exact center between them. [SA; REG]

7.6 One affine involution and one uniform four-cycle translation

The offset set around c is closed under sign reversal. Therefore:

satisfies:

This is an actual affine permutation of the twelve coordinates, not only participation in different routes. Its pointwise transpositions are:

Writing T_L(x)=x+L, the chronological four-cycle map is:

Since 5842=4×1460.5, exactly four equal half-step input cycles carry every original node to one of the twelve paired-Mirror target nodes, with no output outside that set:

Each row has two equal component spans. For example, 2939+2904−1=2938+2905−1=5842. Pair-display ordering must not be mistaken for a pointwise phase-preserving reflection: T preserves phase, whereas M and R reverse it.

The affine self-maps of this fixed finite set that are bijections are exactly the identity and R. Proof: a bijective affine map ax+b preserves the set's nonzero diameter, hence |a|=1. For a=1, the fixed extrema force b=0. For a=−1, exchanging the extrema forces b=−5842; the interior sign symmetry establishes sufficiency. The accompanying script also enumerates all possible images of the extrema and obtains exactly these two maps.

The Sothic ratio itself remains a different operator: a dilation with factor greater than one cannot preserve the nonzero diameter of this same finite set. The global permutation is translation plus inverse Mirror, not the claim that 2923/2921 alone permutes all dates.

7.7 The exact roles of all four cycle lengths

Four equal cycles per route are intended. No arbitrary mixing of the four periods within a route is introduced.

The counts assume the same translation is attempted from every source node, with no wrapping or state-dependent reassignment. The former selected-route constructions remain valid. The table specifies why those constructions are not four independent global permutations of one fixed finite set.

For example, 2939t BC + 5846 years = AD 2908t remains within the target set, but 2935t BC + 5846 years = AD 2912t is outside it. Therefore an unrestricted assertion that all four periods land only on the twelve targets from every possible source node is false.

The overlapping maps reduce to:

The offsets are respectively +2,0,−2,−4 in forward-running phase coordinates. Their intersections with \mathcal X explain the 8/12/8/4 counts through the three-Gear spacing. No modular wraparound is licensed.

7.8 What is unique

Within the already fixed 30-rail, local ±2, and half-year paired-phase template, a uniform 5842-year all-node closure pins the center uniquely:

At L=5842, c=−2921. Since E is already fixed by the SKL template, this produces exactly Dean's twelve date/phase coordinates. Any nonzero uniform displacement of this fixed template destroys the 5842 all-node closure against the unchanged BC/AD datum.

This is uniqueness of placement of the prescribed template, not derivation of that template from cycle periods alone. A symmetric field with a different rail separation can have the same center and the same 5842 closure. Merely requiring all four durations to occur somewhere is also weaker: shifting the full prescribed field one BC label earlier gives center January 1, 2922 BC and intersection counts 4/8/12/8; all four durations still occur, but 5842 no longer closes all twelve. This counter-test does not dispute the result with the original center and 5842 closure explicitly held fixed.

Thus the valid strengthened claim is: the fixed SKL template has a unique placement under the central half-step four-cycle closure. Global uniqueness across every possible node pattern or weaker selected-route test is not established.

7.9 Opposed ±720 continuation is exact

The source controls explicitly permit the nested local wheel on each admitted macro member. Opening that comparison here adds the coordinate offsets k∈{−720,0,720} without identifying those offsets with the local two-year unit. [F21/F34; REG §D.38]

In forward-running coordinates:

Hence the earlier macro copy crosses to the Mirror of the later copy, and vice versa. The central copy crosses to its own paired-Mirror set. The union of the three explicitly opened copies has 36 phase-nodes and obeys the same all-node closure:

These 36 are comparison-overlay coordinates, not new raw textual rows or independent witnesses.

For paired cross-axis spans using BC Nisan labels U,D, the simpler invariant is:

Both phase components retain that exact span. Thus every valid 5840/5842/5844/5846 relation in the original field has an opposed macro counterpart with the same span; this is a theorem of the declared translations, not a coincidence checked separately at each node.

For the central row:

has 3657+2186−1=3656+2187−1=5842, and the target is the paired Mirror of 2187t/2186n BC.

The same-sign shift of both BC-label endpoints would instead change the span by 2k; it is the opposed, crisscrossed assignment that preserves the four-cycle carrier. Fixed 1476/1446 internal landmarks are not consequences of this endpoint identity and remain route-specific.

7A. Final discussion refinement: anchored selection and the Long family

The following supersedes the final assistant reply where its qualifications were incomplete. Full source context and proof remain in Report V.

7A.1 Why this center: the Sothic–Mosaic selection mechanism

Internal symmetry alone would allow many shapes. Dean's subsequent refinement supplies the missing placement rationale: the principal flanks stand one ordinary Sothic cycle before Joshua's birth and the plague/Exodus packet.

The corresponding January centers are:

Thus the source midpoint is:

The previously controlled source anchors and target packet co-register. The 1380→1500 Priestly route supplies another operator-based compatibility check, not independent source testimony.

7A.1.1 The twenty-year calendar interchange

At the fixed Exodus target:

Therefore:

The inherited 30|20|30 SKL corridor contains exactly the displacement required to interchange these two fourfold calendar-body counts without moving Exodus. 720+720=1440 is the 360-based realization; 1460 is the 365-based realization. They are structurally comparable counts, not equal elapsed durations or an unannounced calendar conversion. [F21/F34; SA]

7A.1.2 A smaller reconstruction of the corridor

Let e=1446, Q=4×365=1460, and F=4×360=1440. With the inherited 30-year rail:

Its spacings are 30, Q−F=20, and 30. The Moses/Joshua comparisons become:

Their 50-year rectangle is consequently compatible with:

This clarifies evidence accounting. The corridor, both 1380 differences, the 20, and the 50 are not independent after the listed inputs are fixed. The explanatory advance is that a small input packet reconstructs all of them. A probability claim would have to charge for the choices of calendar bodies, anchors, rail, and endpoint classes.

7A.2 Joshua to the paired Mirror of Exodus

The paired target is AD 1446t/1447n. Writing that set in reverse order does not change its members, but component-wise pairing must be stated.

Hence:

Dean's average intuition is correct when interpreted as the average of the two doubled completed totals; the ordinary one-period average is 1461.25.

The exact outer-span midpoint is x=−15, January 1, 15 BC. The corresponding-phase midpoints are 16t BC and 15n BC, straddling that January center. The interval 1t BC→AD 1n does straddle the epoch datum, but it is not automatically the midpoint or an internal-cycle landing of these Joshua/Exodus paths. The prior assistant's loose suggestion that the epoch straddle had been established is superseded by this phase calculation.

7A.3 The Long SKL family and the Moses–Joshua fifty

The Long branch has its own legitimate roles:

AD 33n retains its preferred Passion comparison, AD 35 its separate comparison role, and AD 65 the schematic Christ-generation terminus—not the literal duration of Jesus' earthly life. [F13; F43; F54; F68]

The reversed 50-year relation is exact:

Moving the BC source forward 50 and its mirrored target forward 50 preserves the span. In source-year magnitudes, the source labels decrease while the target AD labels increase. This is the appropriate reversed orientation of the Moses–Joshua birth separation.

The complete fixed-field test, assuming the obvious typo 2859t/2558n intended 2859t/2858n, is:

The matrix contains 3×1460, 3×1460.5, and 3×1461.5, but not 3×1461=4383. The earlier suggestion that adjacent/single-date variants could supply the missing member was not accompanied by a fixed alternative endpoint declaration. It is not promoted to a result. A future extended test may specify such a field before calculation; the fixed matrix remains unchanged.

The Long twelve-node field is centered at January 1, 2871 BC. Its own self-Mirror translation is 5742, not 5842. Its genuine Sothic paths are not evidence that both variants separately satisfy the same four-cycle whole-field theorem.

8. The AD 29465 Pillar and Apparent Adam

8.1 Inherited square and the ordinary Sothic product

From actual regular MT Year 6, Cainan OFF:

The Priestly conversion gives:

The arithmetic in point 9 is correct through this step. The factor is Priestly 25/23, not the ordinary Sothic ratio itself.

8.2 Half-step product and the 34.5 displacement

Hence:

Fixing the Pillar at AD 29465n makes the phases explicit:

Actual Apparent Adam is 4146n BC, whose Pillar span is 33610. The proposed output differs by:

Thus the 34.5 construction is exact, while its identification with the 30 Apparent-Age shift is incomplete by 4.5. The existing Supplement A uses 34.5/4.5 under its own operators, but shared numbers do not automatically license the missing operation in this Pillar construction. [F22; SA]

8.3 Exact common-K companion reaches Rounded Apparent Adam

A distinct consequence of the forced G=1680/1679 continuation is:

Therefore, with the Pillar fixed:

4136 BC is already the Rounded Apparent-Adam state controlled by File_51a. It is not the actual 4146 BC Apparent-Adam state. The two resulting calendar counts have identical schematic day-volume:

This comparison follows from the same seed and common K; it is not an independent second physical synchronization or a reason to redefine either Adam state. [F51a; F00; SG]

9. What this family contributes to the unification strategy

The new analysis has both a positive result and a useful constraint.

The positive result is that much of the family compresses to:

with:

The 7, 10, and 23 applications then produce the observed half-week, Creation head/Year-6, and Pillar offsets. The Mirror adds the already admitted local Gear field:

The constraint is that a shared grammar is broader than a shared calibration. The original three exact Keys share K. The proposed H shares the half-23 completion grammar and the Sothic/Julian neighborhood, not the same K. The forced G shares K but not optimal tropical calibration.

Under the author's providential premise, different scribal/calendrical traditions could preserve different compatible features of this grammar. The mathematical investigation does not require every participant to know the complete cross-tradition field. Direct historical dependence, statistical rarity, and a claim that ancient scribes explicitly used 2923/2921 remain unproved.

The principal source-placement burden is now narrow: explain why the received Cainan-adjusted Creation separation is 7×1460, why the selected terminal occurs at 10×1460, and whether additional previously bounded families follow without adding discretionary operators. The week bisections are then consequences of one half-year displacement rather than separate discoveries requiring separate mechanisms.

10. Executed bounded amendment preparation

The author authorized consolidation and necessary repository updates with discretion over implementation. The following three additive replacements are prepared in ../02_Repository_Amendments/, with frozen parents, reconstructible patches, and separate verification. No live source, existing control document, archive, or publication manifest is overwritten.

The detailed Mirror/SKL proof now belongs with Supplement A rather than becoming an oversized appendix to File_22. This is the only substantive routing change from v0.2.

Taxonomy is resolved for these working amendments: H=2923/2921 is a locally opened Sothic-adjacent Key-of-23 companion; G=1680/1679 is a locally opened exact common-K 365-day extension. The default original three-Key inventory is not silently enlarged.

The candidate additions remain verification-complete working text pending explicit author Finalization. Proposed central entries and exact new guards are supplied separately in ../04_Registration_Proposals/; existing Register and Capsule editions remain unchanged. Reports I–IV remain unchanged; Report V and Strategy v0.2 provide the current research checkpoint.

10.1 Open issues retained

The Pillar half-step remains 4.5 years from actual Apparent Adam. The fixed Long–Moses matrix does not contain 4383. The Joshua/Mirrored-Exodus outer interval has its midpoint at January 1, 15 BC, not the epoch datum. The full remote SKL Creation/Flood continuation is still untested. No heliacal-reset epoch or historical proof of scribal use of H/G is claimed.

The pre-existing File_00 solar-epoch wording and File_53 rounded-decimal equality are recorded for separate source review, not silently rewritten. Optional adjacent-date/Mirror variants are not added to repair the fixed-field misses.

11. Portable external references

Retrieved September 6 2026. The repository supplies the chronographic anchors; outside sources provide only the historical/calendar context named above.

• Censorinus, De die natali, chapter 18, Egyptian/canicular-year discussion: https://topostext.org/work/741
• Observatoire de Paris, Patrick Rocher, Soleil Terre Lune — Phénomènes, historical tropical-year section, P. Bretagnon (2000) formula: https://media4.obspm.fr/public/ressources_lu/pages_stlp/impression.html
• Exodus 40:17, official ESV text: https://www.esv.org/Exodus%2B40%3A17%3BExodus%2B40%3A34/
• Cassius Dio 69.12–14, translated account of the Bar Kokhba war: https://www.livius.org/sources/content/cassius-dio/cassius-dio-on-bar-kochba/
• File_33 read-only Sothic precedent: https://490d.com/source/490d-unified-chronology/File_33.Ordinal_Lock.md
• Canonical raw-source index: https://490d.com/source/490d-unified-chronology/

The epoch calculation uses an approximate epoch argument; its printed digits identify the calculation, not a claim of observational accuracy to those digits. No modern paper's proposed new calendar or historical reconstruction has been adopted.

Appendix A. Exact-token novelty check and parent identity

An exhaustive literal-token scan of the complete three mounted vocabulary controls was executed before recording the proposed ratios as absent from their literal vocabulary. Absence of a literal ratio is not proof of conceptual novelty. 2921 already occurs as the SKL Short midpoint; its new use as a denominator must not replace that state.

The scan includes plain, comma-grouped, and spaced-ratio forms. The literal Sothic already occurs in the Capsule; the existing source-defined residual nomenclature must not be overwritten by the new operator symbol.

Read-only mounted-source fingerprints

Appendix C. v0.2 bounded revision record

September 6 2026: Dean identified the January 1, 2921 BC common center and challenged the former affine qualification. The new whole-field proof supersedes that qualification while retaining the prior selected-route calculations, calendar-calibration distinctions, and all Creation/Pillar material. No canonical file or control document is changed.

Preserved v0.1 parent: 365_Sothic_Key23_Discussion_and_Amendment_Ledger_v0_1_20260906.md

SHA-256: 9f69f73da84e9a5dd13f8ab87a2344902a841c347d15bf689576559d9edc4a75

New executable verification: check_sothic_mirror_closure.py. Its scope is the new mathematical module, not recertification of the whole inherited ledger.

Appendix D. v0.3 consolidation record

September 6 2026: incorporated Dean's Mosaic–Joshua location argument, the 30|20|30 fourfold-calendar corridor, and the Long-SKL comparisons; added exhaustive six-by-two phase audit; corrected assistant overstatements about independent witnesses, 4383, and the epoch straddle; prepared Report V, Strategy v0.2, three bounded source amendments, and registration proposals. All prior source and research parents remain preserved. New canonical Final status is not claimed.