moses centred construction.json

{
  "title": "Moses-centred rounded construction: complete source path and proposed constraint analysis",
  "status": "FROZEN preparatory derivation only; no numbered action; no canonical modification",
  "created_utc": "2026-09-28T05:33:56.480651+00:00",
  "questions_declared_before_calculation": [
    {
      "id": "MC_Q1",
      "question": "Do all rounded MT nodes from Adam through Moses follow from the frozen begetting rows and declared Joseph/Entry/Moses tail, without inputting2580,2450 or1960?"
    },
    {
      "id": "MC_Q2",
      "question": "Which source path supplies the Adam/Seth/Enoch prefixes, and which part of the cycle alignment remains a downstream placement condition?"
    },
    {
      "id": "MC_Q3",
      "question": "Does the entire Actual strict129|801 partition become rounded130|800 through identifiable row residuals while preserving930?"
    },
    {
      "id": "MC_Q4",
      "question": "Which equalities in the130|800 comparison and Shem-death430 display follow from the same source constraints?"
    },
    {
      "id": "MC_Q5",
      "question": "How does the previously frozen common post-Flood begetting amplitude transfer the complete two-part path to SP and native LXX?"
    },
    {
      "id": "MC_Q6",
      "question": "Does native LXX regenerate the stated3960 span from its complete source chain, retaining Cainan exactly once?"
    },
    {
      "id": "MC_Q7",
      "question": "What part of SP4411 is literal transmitted block data, and what remains the inherited conditional53-versus52 reconstruction?"
    },
    {
      "id": "MC_Q8",
      "question": "How do the explicitly admitted Terah and Cainan choices change the whole MT family at fixed Moses, without retuning anchors?"
    },
    {
      "id": "MC_Q9",
      "question": "Which source equations are independent in a compact prefix/path description, and which cycle/biography displays are dependent consequences?"
    },
    {
      "id": "MC_Q10",
      "question": "Which claims are arithmetic, fitted source-structural description or typology, and what uniqueness or historical claims remain untested?"
    }
  ],
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    {
      "source": "39-File_51a.Rounded_Scaffold_Mod5_Architecture.md",
      "section": "§2.1",
      "line_start": 192,
      "line_end": 212,
      "text": "## 2. The Rounded Begetting Ages\nClaim-status note: §§2.1–2.2 present arithmetic facts and residue observations. §§2.3–2.7 move into structural inference and typological reading, especially where Joseph is interpreted as the Day-7 boundary.\n\n### 2.1 Identification of Non-Multiples of 5\nModal-state note: This section operates on begetting ages only. The sign convention is Scaffold → Actual MT; it does not govern the later Shift column in §3.1.\n\nOf the 21 begetting ages from Adam to Isaac (MT), only six are not divisible by 5:\n\nSign convention: Throughout this file, adjustments are expressed as Scaffold → Actual MT (i.e., Rounded + Adjustment = Actual MT). This convention is chosen because the thesis posits the Rounded Scaffold as the underlying layer.\n\n| Patriarch | Scaffold (Rounded) | Adjustment (Scaffold → Actual MT) | Actual MT |\n| --- | --- | --- | --- |\n| Jared | 160 | +2 | 162 |\n| Methuselah | 185 | +2 | 187 |\n| Lamech | 180 | +2 | 182 |\n| Eber | 35 | −1 | 34 |\n| Reu | 30 | +2 | 32 |\n| Nahor | 30 | −1 | 29 |\n\nThe remaining 15 begetting ages are already multiples of 5: Adam (130), Seth (105), Enosh (90), Kenan (70), Mahalalel (65), Enoch (65), Noah (500), Shem (100), Arphaxad (35), Shelah (30), Peleg (30), Serug (30), Terah (70), Abraham (100), Isaac (60).\n"
    },
    {
      "source": "39-File_51a.Rounded_Scaffold_Mod5_Architecture.md",
      "section": "§§2.3.1–2.3.2",
      "line_start": 255,
      "line_end": 283,
      "text": "#### 2.3.1 The Arithmetic Lock\n\nJoseph’s age at the Entry into Egypt is explicitly calculated from three textual constants:\n\nService start: Joseph is 30 when he stands before Pharaoh (Genesis 41:46).\nYears of plenty: 7 full years pass (Genesis 41:53).\nYears of famine: 2 years of famine have passed when Jacob enters Egypt with “five more years left” (Genesis 45:6).\n$$Joseph_{\\text{Entry}} = 30 + 7 + 2 = 39\\ \\text{years old.}$$\n\nJacob’s age at the Entry is explicitly stated as a hard constant:\n\nJacob’s declaration: Jacob tells Pharaoh he is 130 years old (Genesis 47:9).\n\nTherefore, Jacob’s exact age at Joseph’s birth is a rigid textual deduction:\n\n$$Jacob_{\\text{BegatJoseph}} = 130 – 39 = 91\\ \\text{years old.}$$\n\n#### 2.3.2 The Base-13 Structural Alignment\n\nThe derived age of 91 integrates into a Base-13 pattern at the 1876 BC Entry:\n\nJoseph’s age at Entry: $39 = 13 \\times 3$\nJacob’s age at Joseph’s birth: $91 = 13 \\times 7$\nJacob’s age at Entry: $130 = 13 \\times 10$\nThis closed loop connects to the broader chronology through the 130-year interval (= 13 × 10 = Adam’s begetting age). The most direct link uses primary rounded dates only: Joseph’s rounded birth (1916 BC) to Moses’ birth (1526 BC) = 390 = 130 × 3 = Ezekiel 4:5 (see §7.4). The derived age of 91 thus anchors Joseph’s position within a 13/130-based grid extending from the Entry to the Exodus.\n\nConsistent extensions using rounded death dates [MOD-5 THEORETICAL]: Abraham’s death (1991 BC) to Jacob’s rounded death (1861 BC) = 130; Isaac’s birth (2066 BC) to Joseph’s rounded death (1806 BC) = 260 = 130 × 2. These reinforce the pattern but rest on secondary derivations (§3.4).\n\nMachine Guard [JOSEPH HARD-DEDUCTION]: When processing the Rounded Scaffold, the Logic Engine must not flag Joseph’s age of 91 as an interpolated or ‘soft’ value. It is a hard textual deduction and must function as a primary computational constant within this file, while remaining textually distinct from the explicit ‘X begot Y’ formulae such as Jared’s 162 or Lamech’s 182."
    },
    {
      "source": "39-File_51a.Rounded_Scaffold_Mod5_Architecture.md",
      "section": "§§3.1–3.3",
      "line_start": 384,
      "line_end": 439,
      "text": "## 3. The Rounded MT Chronology\n### 3.1 Full Table (without Shem’s +2, anchored to Jacob at 2006 BC)\nModal-state note: This table uses the strict regular comparison base, not the standard MT regular base. Shem’s +2 is excluded here by design. The Rounded BC column is the mod-5 scaffold state; the Actual BC column is the comparison state.\n\nNote on the Shift column: Shift = Rounded BC − Actual BC. A negative shift means the rounded date is more recent (lower BC number). This is the inverse of the §2.1 Scaffold → Actual MT convention; the +6 net adjustment to begetting ages pushes births earlier (higher BC), so the rounded dates are 6 years later (lower BC) for Adam through Jared.\n\nA-space column: A-space values are provided for reference. A = 1 − BC for BC dates (e.g., 4106 BC → A = −4105).\n\n| Patriarch | Beg. (actual) | Beg. (rounded) | Actual BC (no +2) | Rounded BC | A-space | Shift |\n| --- | --- | --- | --- | --- | --- | --- |\n| Adam | 130 | 130 | 4112 | 4106 | −4105 | −6 |\n| Seth | 105 | 105 | 3982 | 3976 | −3975 | −6 |\n| Enosh | 90 | 90 | 3877 | 3871 | −3870 | −6 |\n| Kenan | 70 | 70 | 3787 | 3781 | −3780 | −6 |\n| Mahalalel | 65 | 65 | 3717 | 3711 | −3710 | −6 |\n| Jared | 162 | 160 | 3652 | 3646 | −3645 | −6 |\n| Enoch | 65 | 65 | 3490 | 3486 | −3485 | −4 |\n| Methuselah | 187 | 185 | 3425 | 3421 | −3420 | −4 |\n| Lamech | 182 | 180 | 3238 | 3236 | −3235 | −2 |\n| Noah | 500 | 500 | 3056 | 3056 | −3055 | 0 |\n| Shem | 100 | 100 | 2556 | 2556 | −2555 | 0 |\n| Arphaxad | 35 | 35 | 2456 | 2456 | −2455 | 0 |\n| Shelah | 30 | 30 | 2421 | 2421 | −2420 | 0 |\n| Eber | 34 | 35 | 2391 | 2391 | −2390 | 0 |\n| Peleg | 30 | 30 | 2357 | 2356 | −2355 | −1 |\n| Reu | 32 | 30 | 2327 | 2326 | −2325 | −1 |\n| Serug | 30 | 30 | 2295 | 2296 | −2295 | +1 |\n| Nahor | 29 | 30 | 2265 | 2266 | −2265 | +1 |\n| Terah | 70 | 70 | 2236 | 2236 | −2235 | 0 |\n| Abraham | 100 | 100 | 2166 | 2166 | −2165 | 0 |\n| Isaac | 60 | 60 | 2066 | 2066 | −2065 | 0 |\n| Jacob | — | — | 2006 | 2006 | −2005 | 0 |\n| Joseph* | 91 | 90 | 1915 | 1916 | −1915 | +1 |\n\n*Joseph is the 23rd patriarch from Adam. His begetting age (Jacob’s age at Joseph’s birth) is derived from narrative chronology (Jacob is 130 at the Entry, Joseph is 39, so 130 − 39 = 91), not stated in a “begot” formula. Joseph’s death: 1805 BC (actual) / 1806 BC (rounded), aged 110. The rounded birth and death dates (1916, 1806) both end in ‘6’, maintaining the pattern.\n\nKey property: Every rounded date ends in either ‘1’ or ‘6’. This is mathematically guaranteed since all rounded begetting ages are divisible by 5 and the anchor (2006) ends in 6. In A-space, all rounded dates end in ‘0’ or ‘5’ — i.e., all A-space values are divisible by 5.\n\n### 3.2 The Shem +2 Question\nThe +2 at Shem (age 100 vs. 102 when Arphaxad is born) is excluded to provide an even comparison. Without +2, all dates from Adam to Noah shift by −2 relative to the standard MT. All dates from Arphaxad onward remain unchanged. The +2 option exists as a further flex point for all three chronologies.\n\nMachine Guard [MODAL STATE]: The Rounded Scaffold baseline (4106 BC) and the MT Regular baselines (4112/4114 BC) are simultaneous, non-competing modal states. The Logic Engine must preserve both layers. The 4106 BC scaffold state must not overwrite the MT Regular baselines, and vice versa. Both are valid computational entry points for their respective domains.\n\n### 3.3 Anchor Reconciliation Note\nThe baseline of 4112 BC in Table 3.1 is the strict scaffold-comparison minimum: Jacob at 2006 BC, Terah at 70, without Shem’s +2. The familiar repository anchor of 4114 BC is reached by restoring Shem’s +2 to the standard MT regular line. The further value 4116 BC belongs to a different node-class: it is the MT Year-6 Creation anchor, not merely a regular-baseline increment. The states are therefore:\n\n| Anchor | Node Class | Configuration |\n| --- | --- | --- |\n| 4106 BC | Rounded Scaffold base | mod-5 scaffold; Shem +2 excluded |\n| 4112 BC | Strict regular comparison base | no Shem +2 |\n| 4114 BC | Standard MT regular base | Shem +2 restored |\n| 4116 BC | MT Year-6 anchor | repository Year-6 state |\n\nThese are not contradictions but distinct modal states. The Rounded Scaffold must not overwrite the regular MT line, and the regular MT line must not be conflated with the Year-6 anchor.\n\nNote: In other repository files, the 4116 BC node is sometimes associated with the prime-lattice framework. In File 51, however, it is treated simply as the Year-6 anchor, since the argument here does not depend on the prime system."
    },
    {
      "source": "39-File_51a.Rounded_Scaffold_Mod5_Architecture.md",
      "section": "§3.4 Adam/Shem biographies",
      "line_start": 450,
      "line_end": 464,
      "text": "Note: Actual MT dates (columns 1–2) include Shem’s +2 as per the Actual MT. Rounded dates (columns 3–4) exclude Shem’s +2 as per the Rounded Scaffold convention. Accordingly, the difference between the actual and rounded columns is not reducible to a single uniform offset: it reflects both (1) the propagated Shem +2 and (2) the independent mod-5 rounding adjustments. The +2 component affects the pre-Flood side only; from Arphaxad onward, the comparison is governed only by the Rounded-vs-Actual lifespan/begetting adjustments within the shared post-Flood baseline. This is why Shem’s own rounded and actual row remains 2556 / 1956 in both columns: once Arphaxad is fixed as the post-Flood baseline comparator, the Shem +2 functions as a pre-Flood propagation rule rather than as a new shift applied to Shem’s displayed row itself.\n\n| Patriarch | Act. Birth | Act. Death | Act. Life | Rnd. Birth | Rnd. Death | Rnd. Life | Remaining (act → rnd) |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| Adam | 4114 | 3184 | 930 | 4106 | 3176 | 930 | 800 → 800 |\n| Seth | 3984 | 3072 | 912 | 3976 | 3066 | 910 | 807 → 805 |\n| Enosh | 3879 | 2974 | 905 | 3871 | 2966 | 905 | 815 → 815 |\n| Kenan | 3789 | 2879 | 910 | 3781 | 2871 | 910 | 840 → 840 |\n| Mahalalel | 3719 | 2824 | 895 | 3711 | 2816 | 895 | 830 → 830 |\n| Jared | 3654 | 2692 | 962 | 3646 | 2686 | 960 | 800 → 800 |\n| Enoch | 3492 | 3127 | 365 | 3486 | 3121 | 365 | 300 → 300 |\n| Methuselah | 3427 | 2458 | 969 | 3421 | 2456 | 965 | 782 → 780 |\n| Lamech | 3240 | 2463 | 777 | 3236 | 2461 | 775 | 595 → 595 |\n| Noah | 3058 | 2108 | 950 | 3056 | 2106 | 950 | 450 → 450 |\n| Shem | 2556 | 1956 | 600 | 2556 | 1956 | 600 | 500 → 500 |"
    },
    {
      "source": "39-File_51a.Rounded_Scaffold_Mod5_Architecture.md",
      "section": "§§7A–7A.5",
      "line_start": 844,
      "line_end": 925,
      "text": "## 7A. The Moses Node (1526 BC)\nClaim-status note: §7A combines arithmetic facts, structural inference, and typological reading. Moses’ cumulative position is arithmetic; the “second Adam” reading of Arphaxad is typological and should not carry the primary computational burden.\n\nModal-state note: Moses’ birth at 1526 BC is fixed in the rounded scaffold and also functions as a cross-tradition terminus in this section. Cumulative position language such as 2580 is a positional measure within the rounded sequence, not a separate civil-date node.\n\nMoses’ birth at cumulative position 2580 (= 1526 BC in the Terah = 70 scaffold) is the unique convergence point where multiple cycle families, manuscript traditions, and typological structures simultaneously intersect. This node was identified through the cycle frequency work of §4A and represents one of the densest alignment clusters in the Rounded Scaffold.\n\n### 7A.1 Dual Cycle-Family Convergence\nFrom Adam (cumul 0):\n\n$$2580 = 6 \\times 430 = 2 \\times 1290$$\n\nThe sojourn number (Exodus 12:40; Galatians 3:17) and the Daniel 12:11 number, both in clean multiples.\n\nFrom Seth (cumul 130):\n\n$$2580 – 130 = 2450 = 5 \\times 490$$\n\nFive complete “seventy-weeks” cycles (Daniel 9:24–27) from Seth to Moses.\n\nFrom Enoch (cumul 620):\n\n$$2580 – 620 = 1960 = 4 \\times 490$$\n\nFour complete 490-year cycles from the translated patriarch to the lawgiver.\n\n### 7A.2 The Bridge Equation\nFor Moses’ position to simultaneously satisfy 6 × 430 from Adam and 5 × 490 from Seth:\n\n$$6 \\times 430 – 5 \\times 490 = 2580 – 2450 = 130$$\n\nAdam’s begetting age (130) is the exact arithmetic bridge between the 430-family and the 490-family at Moses’ birth. This is a necessary structural consequence: the choice of 130 as Adam’s begetting age locks these two cycle systems into simultaneous alignment at a single downstream node.\n\n### 7A.3 The 930-Year Flood-to-Moses Span\nArphaxad/Flood (2456 BC, cumul 1650) to Moses (1526 BC, cumul 2580) = 930 years — Adam’s lifespan.\n\nThe first patriarch’s biographical total becomes the chronological span governing the entire postdiluvian era to the lawgiver.\n\nShem’s death as the 430-year trigger: Shem (born 2556 BC, lifespan 600) dies at 1956 BC. From Shem’s death to Moses’ birth: 1956 − 1526 = 430 — one complete sojourn cycle. Shem’s death closes the antediluvian world; exactly one sojourn-length later, Moses is born to open the Exodus.\n\n### 7A.4 Arphaxad as Typological “Second Adam” (The 130 + 800 Recapitulation)\nThe 930-year Flood→Moses span recapitulates Adam’s biographical arithmetic in the postdiluvian chronology.\n\nAdam’s structure: begets Seth at 130, then lives 800 more years = 930 total.\n\nArphaxad’s structure within the 930-year span:\n\n| Segment | Span | Cumulative Intervals |\n| --- | --- | --- |\n| Arphaxad (cumul 1650) → Reu (cumul 1780) | 130 | Arphaxad 35 + Shelah 30 + Eber 35 + Peleg 30 = 130 |\n| Reu (cumul 1780) → Moses (cumul 2580) | 800 | Reu 30 + Serug 30 + Nahor 30 + Terah 70 + Abraham 100 + Isaac 60 + Jacob→Joseph 90 + Joseph→Egypt 40 + In Egypt 350 = 800 |\n| Total: Arphaxad → Moses | 930 | 130 + 800 |\n\nThe parallel is exact:\n\n| Begets/marks at 130 | + 800 remaining | = 930 total |  |\n| --- | --- | --- | --- |\n| Adam | Seth born (3976 BC) | Adam lives 800 more years | Adam’s lifespan |\n| Arphaxad | Reu born (2326 BC) | 800 years to Moses (1526 BC) | Flood→Moses span |\n\nArphaxad is thus positioned as the postdiluvian Adam. The “second Adam” recapitulates the first, and the internal division point (Reu) marks the pivot from the old patriarchal order to the Abrahamic covenant.\n\nMachine Guard [COMPOSITE ALIGNMENT]: The 130-year cumulative span Arphaxad→Reu is not a single begetting age but the sum of four intervals (35 + 30 + 35 + 30). This operates at a macro-architectural level — four independent values summing to Adam’s begetting age — rather than as a direct 1-to-1 patriarchal parallel.\n\n### 7A.5 Tri-Tradition Convergence at Moses\nEach manuscript tradition’s rounded Creation connects to Moses’ birth (1526 BC) through a distinct cycle-family:\n\n| Tradition | Rounded Creation | Span to Moses | Factorization |\n| --- | --- | --- | --- |\n| MT | 4106 BC | 2580 | 6 × 430 |\n| LXX | 5486 BC | 3960 | 9 × 440 = 12 × 330 = 11 × 360 |\n| SP | 4411 BC | 2885 | — |\n\nThe LXX Creation → Moses span (3960) is simultaneously divisible by three major cycles (440, 330, 360). The transmitted SP rounded state remains structurally usable in a different way: its chief value in this comparison is the inter-tradition gap. In transmitted form, LXX − SP = 1075 = 5 × 215, so the SP preserves the 215-variant grammar directly. By contrast, the alternate 4406 alignment would yield 1080, i.e., 15 precessional days on the 25920-year system; the transmitted 4411 state instead yields 1075, i.e., 15 precessional days on the 25800-year system. Thus, the transmitted SP does not fall outside the system; it resolves onto the 215 / anomalistic-precession side of it.\n\nInter-tradition gaps remain:\n\n| Gap | Value | Factorization |\n| --- | --- | --- |\n| LXX − MT | 1380 | 3 × 460 (= 60 × 23) |\n| LXX − SP | 1075 | 5 × 215 |\n| SP − MT | 305 | — |"
    },
    {
      "source": "39-File_51a.Rounded_Scaffold_Mod5_Architecture.md",
      "section": "§§4.4–4.4a Terah alternatives",
      "line_start": 546,
      "line_end": 587,
      "text": "### 4.4 The Adam +60 Terah Framework (4166 BC)\n| From 4166 BC To | Years | Factorization |\n| --- | --- | --- |\n| Abraham’s birth (2166) | 2000 | 2 millennia |\n| Noah’s death (2106) | 2060 | — |\n| Conquest (1406) | 2760 | 6 × 460 |\n| Jared +60 (3706) to Conquest | 2300 | 5 × 460 |\n\nThe +60 of Terah activates the 460 module in clean multiples of 460, connecting to the Conquest, with 2300 falling at Jared — father of Enoch.\n\nThe 2760 = 6 × 460 from Adam (+60 Terah) to the Conquest frames the Genesis-to-Conquest era — from Creation to Israel’s entry into the promised land — as six cycles of the 460-year module. The first of those six cycles (460 years) terminates at Jared (+60 = 3706 BC), from whom the remaining 5 × 460 = 2300 years (Daniel 8:14) run to the Conquest (1406 BC).\n\nTypological reading: Jared (ירד, “descent”) is associated with the descent of the Watchers (1 Enoch 6; Genesis 6:1–4). The Conquest under Joshua is associated with the defeat of the giants (Numbers 13:33; Joshua 11:21–22). The 2300 years of Daniel 8:14 (“then the sanctuary shall be cleansed”) therefore forms a typological span from the Watchers’ descent to the cleansing of the land. The 460-year module structures this as 5 cycles of the sanctuary-cleansing number.\n\n### 4.4a The LXX Extension of the +60 Terah Framework\nModal-state note: This subsection shifts from MT rounded +60 to LXX rounded +60. The LXX state is a cross-tradition comparison state and does not alter the MT Rounded Scaffold base.\n\nThe LXX Creation endpoint stands 1380 years above the MT Creation endpoint. This is the actual cross-tradition Creation-endpoint gap, and within File 51, it is also fully compatible with the Rounded Scaffold. Applied to the +60 Terah scaffold state:\n\nLXX rounded Adam +60 = 4166 + 1380 = 5546 BC\n\n| From LXX 5546 BC To | Years | Factorization |\n| --- | --- | --- |\n| Conquest (1406) | 4140 | 23 × 180 |\n\nThis expresses the Key of 23 on the half-prophetic-year register:\n\n180 = ½ × 360\n\nThus, within the Rounded Scaffold model, the MT +60 path to the Conquest yields:\n\n4166 − 1406 = 2760 = 6 × 460\n\nwhile the LXX rounded +60 path yields:\n\n5546 − 1406 = 4140 = 23 × 180\n\nThe nested relation is:\n\n1380 = 3 × 460 = 60 × 23\n\nSo the LXX extension preserves the same structural vocabulary while shifting the dominant expression from the 460-module to the 23 × 180 register."
    },
    {
      "source": "39-File_51a.Rounded_Scaffold_Mod5_Architecture.md",
      "section": "§17 source states and native Cainan/SP block",
      "line_start": 1777,
      "line_end": 1827,
      "text": "## 17. Cross-Tradition Harmony\nClaim-status note: §17 argues for cross-tradition compatibility, not cross-tradition identity. MT, SP, and LXX remain separate modal states even when they share structural block-values.\n\nModal-state note: §17 compares traditions by preserving their transmitted or locally defined states. MT, LXX, and SP values are not harmonized by substitution; they are compared as distinct modal states.\n\n| Tradition / state | Value or block | Function in §17 | Adopted status |\n| --- | --- | --- | --- |\n| MT Rounded Scaffold | 4106 BC | base comparison state | adopted for `File_51a` |\n| LXX rounded state | 5486 BC | cross-tradition comparison state | adopted where LXX comparison is active |\n| Transmitted SP rounded state | 4416/4411 BC | ordered SP Creation block | adopted as transmitted SP state |\n| Alternate SP local option | 4406 BC where noted | local harmonic comparison state | not adopted as transmitted SP |\n| LXX with 2nd Cainan | as stated locally | restored-Cainan comparison | active only in LXX subsection |\n\n### 17.1 Why Rounding Preserves Cross-Tradition Compatibility\nThe Rounded Scaffold is most directly demonstrable in the MT, but it remains broadly compatible with the major manuscript traditions because the principal inter-tradition adjustments are commonly expressed in structured block-values such as 5, 10, 50, 100, 130, and in larger compounds derived from them. In that sense, the rounding operation is structurally transparent to the larger manuscript-level architecture, even where the resulting chronological states remain tradition-specific. File 51, therefore, treats the Rounded Scaffold as a common geometric substrate, while still preserving the distinct MT, SP, and LXX modal states required by the repository.\n\n### 17.2 The LXX with 2nd Cainan\nThe LXX includes a 2nd Cainan with a begetting age of 130, itself a clean multiple of 10 and 5. More importantly, one of the principal manuscript differential patterns in the post-Flood Shem-side sector is already exact in the unrounded traditions:\n\n| Comparison | Actual Difference | Factorization |\n| --- | --- | --- |\n| LXX → SP | 130 | 1 × 130 |\n| SP → MT | 650 | 5 × 130 |\n| LXX → MT | 780 | 6 × 130 |\n\nThis 130 / 650 / 780 pattern is stated here specifically for the Shem-side post-Flood placement, where the traditions fall into clean 130-based steps. It must not be generalized without qualification to every node in the Noah/Flood sector, because the transmitted Flood-side values are affected by the localized Shem/Flood anomaly and therefore do not always resolve to the same exact intermediate differences. Thus, the Rounded Scaffold does not create the Shem-side pattern; it preserves a structure already present in the manuscript traditions themselves. The same holds more broadly from the Flood to Abraham: the LXX-MT differential resolves as 650 + 130 = 780 = 6 × 130. At the rounded layer, the same figures remain in force apart from the localized Shem anomaly, which must be handled separately as a modal adjustment.\n\n### 17.3 The LXX Adam at 5486 BC (Rounded)\n| From LXX Adam (5486) To | Years | Factorization |\n| --- | --- | --- |\n| Joseph’s death (1806) | 3680 | 8 × 460 |\n| Fall of Jerusalem (586) | 4900 | 100 × 49 = 70 × 70 |\n\nThe 460 module organizes both traditions from their respective Creation dates to the same endpoint.\n\n### 17.4 The SP Rounded State as Transmitted\nWithin File 51, the SP pre-Flood layer is best treated as transmitted: a logically deduced alternative system that speaks the same mathematical language as the MT and LXX, while pursuing a different local resolution at the Flood boundary. Accordingly, SP in this file is treated primarily as a block-state witness rather than as a single isolated Creation node; its principal value here lies in how its transmitted Creation block resolves positively to later boundary-states and termini.\n\nIts governing objective appears coherent: to preserve the broad Adam–Noah alignment structure shared with the MT and LXX, while shifting the key emphasis so that the 1656-year total terminates at the death of Noah and so that the Flood-generation cluster is regularized around the Flood itself. In this respect, the SP is not a defective witness but a distinct mathematical recasting of the same underlying chronological grammar.\n\nAt the rounded layer, the transmitted SP is best read not as a single isolated node but as a Creation block:\n\nLXX rounded Creation block: 5491/5486 BC\nSP rounded Creation block: 4416/4411 BC\nMT rounded Creation block: 4111/4106 BC\nThus, the transmitted SP rounded block stands 305 years above the corresponding MT rounded block at both boundaries:\n\n| Comparison | Span | Factorization |\n| --- | --- | --- |\n| 4416 → 4111 | 305 | — |\n| 4411 → 4106 | 305 | — |"
    },
    {
      "source": "38-File_18.Chronological_Data_Tables-20260919-141048-.md",
      "section": "§1.6 native/restored Cainan",
      "line_start": 1118,
      "line_end": 1158,
      "text": "Active states:\nRegular restored 2nd Cainan and cumulative restored 2nd Cainan.\n\nThe 2nd Cainan, Luke 3:36 and LXX Genesis 11:12–13, is native to LXX and intentionally omitted from MT / SP. When restoring Cainan to MT / SP, the adjustment value depends on the chronological method used.\n\n#### 1.6.1 Why two different values\n\n| Method | What is added | Cainan's value | Basis |\n|---|---|---:|---|\n| Regular | Begetting ages | +130 years | Age when Shelah was born. |\n| Cumulative | Full lifespans | +460 years | Total years lived. |\n\nThis is a general principle applying to all patriarchs, not a value unique to Cainan.\n\n| Patriarch | Begetting age | Lifespan | Difference |\n|---|---:|---:|---:|\n| 2nd Cainan | 130 | 460 | 330 |\n| Shelah | 130 | 460 | 330 |\n| Eber | 134 | 504 | 370 |\n| etc. | — | — | — |\n\n#### 1.6.2 Application by tradition\n\n| Tradition / method | Handling |\n|---|---|\n| LXX Regular | Cainan is already in the baseline. `5279 BC` Adam minimum includes his `130` begetting years. No adjustment is needed. |\n| MT / SP Regular | To restore Cainan, insert 2nd Cainan by adding the `+130` begetting-age hinge between Arphaxad and Shelah. Shelah and the downstream Terah field remain four-position; Arphaxad / Flood through Adam shift by `+130` and become eight-position where the restored-Cainan state is explicitly opened. MT with Cainan: `3899 + 130 = 4029 BC`. SP with Cainan: `4199 + 130 = 4329 BC`. |\n| LXX Cumulative | Cainan is already in the baseline. His `460`-year lifespan is included in the chain. No adjustment is needed. |\n| MT / SP Cumulative | To restore Cainan, insert the `+460` lifespan hinge between Arphaxad and Shelah. In the cumulative table this shifts Adam through Arphaxad / Flood by `+460`; Shelah and downstream rows remain unchanged. MT cumulative with Cainan: `14006 + 460 = 14466 BC`, Moses line center. |\n| LXX theoretical removal | LXX could have Cainan removed: `5279 − 130 = 5149 BC`, Regular. This is not tracked in standard tables but remains architecturally valid. |\n\nAI-processing rules:\n\n| Rule | Handling |\n|---|---|\n| Regular chronology | Cainan = `+130` years, begetting age. |\n| Cumulative chronology | Cainan = `+460` years, full lifespan. |\n| LXX | Cainan already included; no adjustment. |\n| MT / SP | Add the appropriate value to restore Cainan. |\n| Method distinction | The `130` / `460` difference reflects method, not variant ambiguity. |\n"
    },
    {
      "source": "38-File_18.Chronological_Data_Tables-20260919-141048-.md",
      "section": "§2.2 MT post-Flood",
      "line_start": 1240,
      "line_end": 1252,
      "text": "### 2.2 Post-Flood to Patriarchs: MT Minimum-Regular\n\n| Patriarch / event | Birth BC | Death BC | Lifespan | Begetting age |\n|---|---:|---:|---:|---:|\n| Shem | 2341 | 1741 | 600 | 100 |\n| Arphaxad | 2241 | 1803 | 438 | 35 |\n| Shelah | 2206 | 1773 | 433 | 30 |\n| Eber | 2176 | 1712 | 464 | 34 |\n| Peleg | 2142 | 1903 | 239 | 30 |\n| Reu | 2112 | 1873 | 239 | 32 |\n| Serug | 2080 | 1850 | 230 | 30 |\n| Nahor | 2050 | 1902 | 148 | 29 |\n| Terah | 2021 | 1816 | 205 | 70/130 |"
    },
    {
      "source": "38-File_18.Chronological_Data_Tables-20260919-141048-.md",
      "section": "§2.4 fixed epoch",
      "line_start": 1301,
      "line_end": 1315,
      "text": "### 2.4 Fixed epoch: MT; no variants\n\n| Event / person | Date BC | Notes |\n|---|---:|---|\n| Aaron birth | 1529 | 3 years historical / 3.5 years harmonic; see `File_22`, §6B.5 by source reference. |\n| Moses birth | 1526 | — |\n| Joshua birth | 1476 | — |\n| Exodus | 1446 | Fixed anchor. |\n| Tabernacle | 1445 | — |\n| Aaron death | 1407 | Summer. |\n| Moses death | 1406 | Winter. |\n| Conquest begins | 1406 | — |\n| Six years' war | 1406–1400 | Source-retained range; stray source brace removed as formatting residue. |\n| First Sabbath | 1399 | First Sabbath year of rest. |\n| Joshua death | 1366 | 110 years old. |"
    },
    {
      "source": "38-File_18.Chronological_Data_Tables-20260919-141048-.md",
      "section": "§§3.2.1–3.2.2 SP",
      "line_start": 1596,
      "line_end": 1637,
      "text": "The post-Flood begetting table selects the G1 primary / Arphaxad-bound Shem row:\n\n| Patriarch / event | Birth BC | Death BC | Lifespan | Begetting age |\n|---|---:|---:|---:|---:|\n| Shem — Arphaxad-bound | 2991 | 2391 | 600 | 100 |\n| Arphaxad | 2891 | 2453 | 438 | 135 |\n| Shelah | 2756 | 2323 | 433 | 130 |\n| Eber | 2626 | 2222 | 404 | 134 |\n| Peleg | 2492 | 2253 | 239 | 130 |\n| Reu | 2362 | 2123 | 239 | 132 |\n| Serug | 2230 | 2000 | 230 | 130 |\n| Nahor | 2100 | 1952 | 148 | 79 |\n| Terah | 2021 | 1876 | 145, or 205 ideal | 70 |\n| Abraham | 1951 | 1776 | 175 | — |\n\nArithmetic verification, Arphaxad-bound standard intervals:\n\n| Row | Verification |\n|---|---|\n| Shem | `2991−100=2891`, Arphaxad. |\n| Arphaxad | `2891−135=2756`, Shelah. |\n| Shelah | `2756−130=2626`, Eber. |\n| Eber | `2626−134=2492`, Peleg. |\n| Peleg | `2492−130=2362`, Reu. |\n| Reu | `2362−132=2230`, Serug. |\n| Serug | `2230−130=2100`, Nahor. |\n| Nahor | `2100−79=2021`, Terah. |\n| Terah | `2021−70=1951`, Abraham. |\n\nConvergence note:\nSP Abraham, `1951 BC`, matches MT Minimum-Regular Abraham, `1951 BC`.\n\n#### 3.2.2 Terah Dual-Lock: `145` versus `205`\n\nIn the SP post-Flood timeline, Terah functions as a dual-harmonic pivot.\n\n| State | Lifespan | Target |\n|---|---:|---|\n| Textual / Normal | 145 years | Death at `1876 BC`. |\n| Architectural / Ideal | 205 years | Mirrors MT and enables the 1000-year harmonic from Arphaxad's birth to Abraham's birth, `100 + 1000 + 100`. |\n\nBoth values target Abraham's birth at `1951 BC` and Terah's death at `1876 BC`. The SP text officially contracts Terah's lifespan, `205 → 145`, to land his death on Abram's call at age `75`. Architecturally, however, the `205` state remains visible: the SP has not eliminated the Terah problem so much as shifted it from begetting-age tension to lifespan tension. Therefore the SP `+60 Terah` possibility remains state-valid where opened, while SP cumulative tables retain the official `145` span."
    },
    {
      "source": "38-File_18.Chronological_Data_Tables-20260919-141048-.md",
      "section": "§4.2 LXX",
      "line_start": 1712,
      "line_end": 1734,
      "text": "### 4.2 Post-Flood to Patriarchs: LXX Regular-Minimum\n\n| Patriarch / event | Birth BC | Death BC | Lifespan | Begetting age |\n|---|---:|---:|---:|---:|\n| Shem | 3121 | 2521 | 600 | 100 |\n| Arphaxad | 3021 | 2556 | 465 | 135 |\n| 2nd Cainan | 2886 | 2426 | 460 | 130, LXX native |\n| Shelah | 2756 | 2296 | 460 | 130 |\n| Eber | 2626 | 2122 | 504 | 134 |\n| Peleg | 2492 | 2153 | 339 | 130 |\n| Reu | 2362 | 2023 | 339 | 132 |\n| Serug | 2230 | 1900 | 330 | 130 |\n| Nahor | 2100 | 1892 | 208 | 79 |\n| Terah | 2021 | 1816 | 205 | 70/130 state-dependent |\n\nNote:\nThe Terah / Abraham relation is resolved by the author-clarified four-position field. The displayed LXX Regular-Minimum Terah row, `2021–1816 BC`, is the no-`+60 Terah`, no-`+215 Sojourn` minimum row. In that state, Terah begets Abraham at `70`, producing Abraham `1951 BC`. When `+60 Terah` is active, Terah shifts to `2081–1876 BC`; the `130` begetting-state then also produces Abraham `1951 BC`. With the `+215 Sojourn` state active, the corresponding pair is `2236–2031 BC` with begetting-state `70`, producing Abraham `2166 BC`, and `2296–2091 BC` with begetting-state `130`, also producing Abraham `2166 BC`.\n\nTherefore Abraham has two birth states, `1951 BC` and `2166 BC`, while Terah has four birth/death states.\n\nAuthor-confirmed LXX table correction (September 2026): the former §4.2 Peleg/Reu/Serug lifespan cells `239/239/230` were copy errors, not manuscript variants. The controlling LXX Regular-Minimum values are `339/339/330`; births remain `2492/2362/2230 BC`, so the corrected deaths are `2153/2023/1900 BC`. Begetting ages remain `130/132/130`. This correction is independent of the Lamech `182/753` source hierarchy.\n\nSee MT §2.2.1 for `±2` anomaly details at tradition-specific dates."
    }
  ],
  "source_premises": [
    {
      "premise": "Ordered genealogical begetting rows",
      "source": "frozen C749 rounding_inputs.native_rows, source-controlled by File18 §§2–4 and File51a §§2.1,3.1",
      "role": "input; Lamech182 active in MT/LXX; native LXX Cainan130 included exactly once"
    },
    {
      "premise": "Nearest5 operation on selected begetting measure",
      "source": "File51a §§2.1,3.1; inherited C749/C752/C760",
      "role": "operation; do not round BC labels independently or use cumulative lifespans"
    },
    {
      "premise": "Shem+2 excluded in strict rounded comparison",
      "source": "File51a §§3.1–3.3",
      "role": "state choice; Noah500+Shem100 used without a further boundary term"
    },
    {
      "premise": "Terah70, held full430 comparison placement",
      "source": "File51a §§3.1,7A.1–7A.4",
      "role": "state choice; Abraham2166, Jacob2006, Entry1876 and Moses1526 are one consistent placement"
    },
    {
      "premise": "Joseph narrative age39 and Jacob entry age130",
      "source": "File51a §2.3.1–2.3.2",
      "role": "input relation; 30+7+2=39 and130−39=91; Q39=40 andQ91=90 retain their distinct roles"
    },
    {
      "premise": "Declared terminal tail Entry→Moses350",
      "source": "File51a §7A.4 line894; File18 §2.4 Moses1526/Exodus1446",
      "role": "path interval; equals held Entry1876−Moses1526 or430−80; not a begetting or lifespan"
    },
    {
      "premise": "Adam biography130+800=930 and Shem biography100+500=600",
      "source": "File18 §§2.1.3–2.2, frozen rows; File51a §§3.4,7A.3–7A.4",
      "role": "separate biographical measurements; Adam lifespan is not used to build the regular begetting path"
    },
    {
      "premise": "Cycle units and multipliers430/490/1290;6/5/4",
      "source": "File51a §7A.1–7A.2",
      "role": "author-selected comparison targets, not generated independently by the130 age"
    },
    {
      "premise": "SP4411 lower transmitted rounded block boundary",
      "source": "File51a §§7A.5,17.4",
      "role": "literal comparison input; Q53 reconstruction remains conditional C762"
    },
    {
      "premise": "Chronological labels and scopes",
      "source": "File51a §7A modal note and File18 state controls",
      "role": "regular accumulated position2580 is neither a BC label nor the12600 cumulative-lifespan construction"
    }
  ],
  "late_path_packet": {
    "Joseph_service_age": 30,
    "plenty_years": 7,
    "famine_years_elapsed": 2,
    "Jacob_age_at_Entry": 130,
    "Entry_BC": 1876,
    "Moses_birth_BC": 1526,
    "Exodus_BC": 1446,
    "Joseph_age_at_Entry_derived": 39,
    "Jacob_age_at_Joseph_birth_derived": 91,
    "rounded_Jacob_to_Joseph": 90,
    "rounded_Joseph_to_Entry": 40,
    "Entry_to_Moses_derived": 350,
    "Entry_to_Exodus_derived": 430,
    "Moses_age_at_Exodus_derived": 80
  },
  "selected_source_rows": {
    "MT_native_OFF": [
      {
        "name": "Adam",
        "begetting": 130,
        "lifespan": 930,
        "remainder": 800,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Seth",
        "begetting": 105,
        "lifespan": 912,
        "remainder": 807,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Enosh",
        "begetting": 90,
        "lifespan": 905,
        "remainder": 815,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Kenan",
        "begetting": 70,
        "lifespan": 910,
        "remainder": 840,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Mahalalel",
        "begetting": 65,
        "lifespan": 895,
        "remainder": 830,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Jared",
        "begetting": 162,
        "lifespan": 962,
        "remainder": 800,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Enoch",
        "begetting": 65,
        "lifespan": 365,
        "remainder": 300,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Methuselah",
        "begetting": 187,
        "lifespan": 969,
        "remainder": 782,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Lamech",
        "begetting": 182,
        "lifespan": 777,
        "remainder": 595,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Noah",
        "begetting": 500,
        "lifespan": 950,
        "remainder": 450,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Shem",
        "begetting": 100,
        "lifespan": 600,
        "remainder": 500,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Arphaxad",
        "begetting": 35,
        "lifespan": 438,
        "remainder": 403,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Shelah",
        "begetting": 30,
        "lifespan": 433,
        "remainder": 403,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Eber",
        "begetting": 34,
        "lifespan": 464,
        "remainder": 430,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Peleg",
        "begetting": 30,
        "lifespan": 239,
        "remainder": 209,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Reu",
        "begetting": 32,
        "lifespan": 239,
        "remainder": 207,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Serug",
        "begetting": 30,
        "lifespan": 230,
        "remainder": 200,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Nahor",
        "begetting": 29,
        "lifespan": 148,
        "remainder": 119,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Terah",
        "begetting": 70,
        "lifespan": 205,
        "remainder": 135,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Abraham",
        "begetting": 100,
        "lifespan": 175,
        "remainder": 75,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Isaac",
        "begetting": 60,
        "lifespan": 180,
        "remainder": 120,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Jacob",
        "begetting": 91,
        "lifespan": 147,
        "remainder": 56,
        "remainder_status": "calculated L minus b",
        "begetting_role": "narrative-derived age at Joseph birth; collateral to cumulative Levi continuation"
      },
      {
        "name": "Levi",
        "begetting": null,
        "lifespan": 137,
        "remainder": null,
        "remainder_status": "unavailable",
        "begetting_role": "no source-admitted begetting input; do not invent a row remainder"
      },
      {
        "name": "Kohath",
        "begetting": null,
        "lifespan": 133,
        "remainder": null,
        "remainder_status": "unavailable",
        "begetting_role": "no source-admitted begetting input; do not invent a row remainder"
      },
      {
        "name": "Amram",
        "begetting": null,
        "lifespan": 137,
        "remainder": null,
        "remainder_status": "unavailable",
        "begetting_role": "no source-admitted begetting input; do not invent a row remainder"
      },
      {
        "name": "Moses",
        "begetting": null,
        "lifespan": 120,
        "remainder": null,
        "remainder_status": "unavailable",
        "begetting_role": "no source-admitted begetting input; do not invent a row remainder"
      }
    ],
    "LXX_native_ON": [
      {
        "name": "Adam",
        "begetting": 230,
        "lifespan": 930,
        "remainder": 700,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Seth",
        "begetting": 205,
        "lifespan": 912,
        "remainder": 707,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Enosh",
        "begetting": 190,
        "lifespan": 905,
        "remainder": 715,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Kenan",
        "begetting": 170,
        "lifespan": 910,
        "remainder": 740,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Mahalalel",
        "begetting": 165,
        "lifespan": 895,
        "remainder": 730,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Jared",
        "begetting": 162,
        "lifespan": 962,
        "remainder": 800,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Enoch",
        "begetting": 165,
        "lifespan": 365,
        "remainder": 200,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Methuselah",
        "begetting": 187,
        "lifespan": 969,
        "remainder": 782,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Lamech",
        "begetting": 182,
        "lifespan": 753,
        "remainder": 571,
        "remainder_status": "calculated L minus b",
        "source_status": "182 operative; 753 attested selected lifespan; 571 calculated; 188 nonoperative; 777 appendix only"
      },
      {
        "name": "Noah",
        "begetting": 500,
        "lifespan": 950,
        "remainder": 450,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Shem",
        "begetting": 100,
        "lifespan": 600,
        "remainder": 500,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Arphaxad",
        "begetting": 135,
        "lifespan": 465,
        "remainder": 330,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "2nd Cainan",
        "begetting": 130,
        "lifespan": 460,
        "remainder": 330,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Shelah",
        "begetting": 130,
        "lifespan": 460,
        "remainder": 330,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Eber",
        "begetting": 134,
        "lifespan": 504,
        "remainder": 370,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Peleg",
        "begetting": 130,
        "lifespan": 339,
        "remainder": 209,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Reu",
        "begetting": 132,
        "lifespan": 339,
        "remainder": 207,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Serug",
        "begetting": 130,
        "lifespan": 330,
        "remainder": 200,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Nahor",
        "begetting": 79,
        "lifespan": 208,
        "remainder": 129,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Terah",
        "begetting": 70,
        "lifespan": 205,
        "remainder": 135,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Abraham",
        "begetting": 100,
        "lifespan": 175,
        "remainder": 75,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Isaac",
        "begetting": 60,
        "lifespan": 180,
        "remainder": 120,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Jacob",
        "begetting": 91,
        "lifespan": 147,
        "remainder": 56,
        "remainder_status": "calculated L minus b",
        "begetting_role": "narrative-derived age at Joseph birth; collateral to cumulative Levi continuation"
      },
      {
        "name": "Levi",
        "begetting": null,
        "lifespan": 137,
        "remainder": null,
        "remainder_status": "unavailable",
        "begetting_role": "no source-admitted begetting input; do not invent a row remainder"
      },
      {
        "name": "Kohath",
        "begetting": null,
        "lifespan": 133,
        "remainder": null,
        "remainder_status": "unavailable",
        "begetting_role": "no source-admitted begetting input; do not invent a row remainder"
      },
      {
        "name": "Amram",
        "begetting": null,
        "lifespan": 137,
        "remainder": null,
        "remainder_status": "unavailable",
        "begetting_role": "no source-admitted begetting input; do not invent a row remainder"
      },
      {
        "name": "Moses",
        "begetting": null,
        "lifespan": 120,
        "remainder": null,
        "remainder_status": "unavailable",
        "begetting_role": "no source-admitted begetting input; do not invent a row remainder"
      }
    ],
    "SP_native_OFF": [
      {
        "name": "Adam",
        "begetting": 130,
        "lifespan": 930,
        "remainder": 800,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Seth",
        "begetting": 105,
        "lifespan": 912,
        "remainder": 807,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Enosh",
        "begetting": 90,
        "lifespan": 905,
        "remainder": 815,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Kenan",
        "begetting": 70,
        "lifespan": 910,
        "remainder": 840,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Mahalalel",
        "begetting": 65,
        "lifespan": 895,
        "remainder": 830,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Jared",
        "begetting": 62,
        "lifespan": 847,
        "remainder": 785,
        "remainder_status": "calculated L minus b",
        "lifespan_status": "inclusive cap count; algebraic remainder is not an ordinary elapsed-year remainder"
      },
      {
        "name": "Enoch",
        "begetting": 65,
        "lifespan": 365,
        "remainder": 300,
        "remainder_status": "calculated L minus b"
      },
      {
        "name": "Methuselah",
        "begetting": 67,
        "lifespan": 720,
        "remainder": 653,
        "remainder_status": "calculated L minus b",
        "lifespan_status": "inclusive cap count; algebraic remainder is not an ordinary elapsed-year remainder"
      },
      {
        "name": "Lamech",
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          {
            "name": "Joseph",
            "actual_input": 39,
            "edge": 40,
            "edge_type": "age at Entry, narrative-derived39→rounded40",
            "next": "Entry",
            "BC_derived": 1916,
            "position_from_Adam": 2495,
            "distance_to_Moses": 390,
            "rounding_residual": 1
          },
          {
            "name": "Entry",
            "actual_input": 350,
            "edge": 350,
            "edge_type": "Entry to Moses birth,1876−1526; not full Egyptian sojourn",
            "next": "Moses",
            "BC_derived": 1876,
            "position_from_Adam": 2535,
            "distance_to_Moses": 350,
            "rounding_residual": 0
          },
          {
            "name": "Moses",
            "BC_derived": 1526,
            "position_from_Adam": 2885,
            "distance_to_Moses": 0
          }
        ],
        "head_BC": 4411,
        "span_to_Moses": 2885,
        "coordinates": {
          "Moses": 1526,
          "Entry": 1876,
          "Joseph": 1916,
          "Jacob": 2006,
          "Isaac": 2066,
          "Abraham": 2166,
          "Terah": 2236,
          "Nahor": 2316,
          "Serug": 2446,
          "Reu": 2576,
          "Peleg": 2706,
          "Eber": 2841,
          "Shelah": 2971,
          "Arphaxad": 3106,
          "Shem": 3206,
          "Noah": 3706,
          "Lamech": 3761,
          "Methuselah": 3826,
          "Enoch": 3891,
          "Jared": 3951,
          "Mahalalel": 4016,
          "Kenan": 4086,
          "Enosh": 4176,
          "Seth": 4281,
          "Adam": 4411
        }
      },
      "strict_actual_comparison": {
        "rows": [
          {
            "name": "Adam",
            "actual_input": 130,
            "edge": 130,
            "edge_type": "selected begetting ledger",
            "next": "Seth",
            "BC_derived": 4413,
            "position_from_Adam": 0,
            "distance_to_Moses": 2887,
            "rounding_residual": 0
          },
          {
            "name": "Seth",
            "actual_input": 105,
            "edge": 105,
            "edge_type": "selected begetting ledger",
            "next": "Enosh",
            "BC_derived": 4283,
            "position_from_Adam": 130,
            "distance_to_Moses": 2757,
            "rounding_residual": 0
          },
          {
            "name": "Enosh",
            "actual_input": 90,
            "edge": 90,
            "edge_type": "selected begetting ledger",
            "next": "Kenan",
            "BC_derived": 4178,
            "position_from_Adam": 235,
            "distance_to_Moses": 2652,
            "rounding_residual": 0
          },
          {
            "name": "Kenan",
            "actual_input": 70,
            "edge": 70,
            "edge_type": "selected begetting ledger",
            "next": "Mahalalel",
            "BC_derived": 4088,
            "position_from_Adam": 325,
            "distance_to_Moses": 2562,
            "rounding_residual": 0
          },
          {
            "name": "Mahalalel",
            "actual_input": 65,
            "edge": 65,
            "edge_type": "selected begetting ledger",
            "next": "Jared",
            "BC_derived": 4018,
            "position_from_Adam": 395,
            "distance_to_Moses": 2492,
            "rounding_residual": 0
          },
          {
            "name": "Jared",
            "actual_input": 62,
            "edge": 62,
            "edge_type": "selected begetting ledger",
            "next": "Enoch",
            "BC_derived": 3953,
            "position_from_Adam": 460,
            "distance_to_Moses": 2427,
            "rounding_residual": 0
          },
          {
            "name": "Enoch",
            "actual_input": 65,
            "edge": 65,
            "edge_type": "selected begetting ledger",
            "next": "Methuselah",
            "BC_derived": 3891,
            "position_from_Adam": 522,
            "distance_to_Moses": 2365,
            "rounding_residual": 0
          },
          {
            "name": "Methuselah",
            "actual_input": 67,
            "edge": 67,
            "edge_type": "selected begetting ledger",
            "next": "Lamech",
            "BC_derived": 3826,
            "position_from_Adam": 587,
            "distance_to_Moses": 2300,
            "rounding_residual": 0
          },
          {
            "name": "Lamech",
            "actual_input": 53,
            "edge": 53,
            "edge_type": "selected begetting ledger",
            "next": "Noah",
            "BC_derived": 3759,
            "position_from_Adam": 654,
            "distance_to_Moses": 2233,
            "rounding_residual": 0
          },
          {
            "name": "Noah",
            "actual_input": 500,
            "edge": 500,
            "edge_type": "selected begetting ledger",
            "next": "Shem",
            "BC_derived": 3706,
            "position_from_Adam": 707,
            "distance_to_Moses": 2180,
            "rounding_residual": 0
          },
          {
            "name": "Shem",
            "actual_input": 100,
            "edge": 100,
            "edge_type": "selected begetting ledger",
            "next": "Arphaxad",
            "BC_derived": 3206,
            "position_from_Adam": 1207,
            "distance_to_Moses": 1680,
            "rounding_residual": 0
          },
          {
            "name": "Arphaxad",
            "actual_input": 135,
            "edge": 135,
            "edge_type": "selected begetting ledger",
            "next": "Shelah",
            "BC_derived": 3106,
            "position_from_Adam": 1307,
            "distance_to_Moses": 1580,
            "rounding_residual": 0
          },
          {
            "name": "Shelah",
            "actual_input": 130,
            "edge": 130,
            "edge_type": "selected begetting ledger",
            "next": "Eber",
            "BC_derived": 2971,
            "position_from_Adam": 1442,
            "distance_to_Moses": 1445,
            "rounding_residual": 0
          },
          {
            "name": "Eber",
            "actual_input": 134,
            "edge": 134,
            "edge_type": "selected begetting ledger",
            "next": "Peleg",
            "BC_derived": 2841,
            "position_from_Adam": 1572,
            "distance_to_Moses": 1315,
            "rounding_residual": 0
          },
          {
            "name": "Peleg",
            "actual_input": 130,
            "edge": 130,
            "edge_type": "selected begetting ledger",
            "next": "Reu",
            "BC_derived": 2707,
            "position_from_Adam": 1706,
            "distance_to_Moses": 1181,
            "rounding_residual": 0
          },
          {
            "name": "Reu",
            "actual_input": 132,
            "edge": 132,
            "edge_type": "selected begetting ledger",
            "next": "Serug",
            "BC_derived": 2577,
            "position_from_Adam": 1836,
            "distance_to_Moses": 1051,
            "rounding_residual": 0
          },
          {
            "name": "Serug",
            "actual_input": 130,
            "edge": 130,
            "edge_type": "selected begetting ledger",
            "next": "Nahor",
            "BC_derived": 2445,
            "position_from_Adam": 1968,
            "distance_to_Moses": 919,
            "rounding_residual": 0
          },
          {
            "name": "Nahor",
            "actual_input": 79,
            "edge": 79,
            "edge_type": "selected begetting ledger",
            "next": "Terah",
            "BC_derived": 2315,
            "position_from_Adam": 2098,
            "distance_to_Moses": 789,
            "rounding_residual": 0
          },
          {
            "name": "Terah",
            "actual_input": 70,
            "edge": 70,
            "edge_type": "selected begetting ledger",
            "next": "Abraham",
            "BC_derived": 2236,
            "position_from_Adam": 2177,
            "distance_to_Moses": 710,
            "rounding_residual": 0
          },
          {
            "name": "Abraham",
            "actual_input": 100,
            "edge": 100,
            "edge_type": "selected begetting ledger",
            "next": "Isaac",
            "BC_derived": 2166,
            "position_from_Adam": 2247,
            "distance_to_Moses": 640,
            "rounding_residual": 0
          },
          {
            "name": "Isaac",
            "actual_input": 60,
            "edge": 60,
            "edge_type": "selected begetting ledger",
            "next": "Jacob",
            "BC_derived": 2066,
            "position_from_Adam": 2347,
            "distance_to_Moses": 540,
            "rounding_residual": 0
          },
          {
            "name": "Jacob",
            "actual_input": 91,
            "edge": 91,
            "edge_type": "narrative-derived Jacob→Joseph",
            "next": "Joseph",
            "BC_derived": 2006,
            "position_from_Adam": 2407,
            "distance_to_Moses": 480,
            "rounding_residual": 0
          },
          {
            "name": "Joseph",
            "actual_input": 39,
            "edge": 39,
            "edge_type": "age at Entry, narrative-derived39→rounded40",
            "next": "Entry",
            "BC_derived": 1915,
            "position_from_Adam": 2498,
            "distance_to_Moses": 389,
            "rounding_residual": 0
          },
          {
            "name": "Entry",
            "actual_input": 350,
            "edge": 350,
            "edge_type": "Entry to Moses birth,1876−1526; not full Egyptian sojourn",
            "next": "Moses",
            "BC_derived": 1876,
            "position_from_Adam": 2537,
            "distance_to_Moses": 350,
            "rounding_residual": 0
          },
          {
            "name": "Moses",
            "BC_derived": 1526,
            "position_from_Adam": 2887,
            "distance_to_Moses": 0
          }
        ],
        "head_BC": 4413,
        "span_to_Moses": 2887,
        "coordinates": {
          "Moses": 1526,
          "Entry": 1876,
          "Joseph": 1915,
          "Jacob": 2006,
          "Isaac": 2066,
          "Abraham": 2166,
          "Terah": 2236,
          "Nahor": 2315,
          "Serug": 2445,
          "Reu": 2577,
          "Peleg": 2707,
          "Eber": 2841,
          "Shelah": 2971,
          "Arphaxad": 3106,
          "Shem": 3206,
          "Noah": 3706,
          "Lamech": 3759,
          "Methuselah": 3826,
          "Enoch": 3891,
          "Jared": 3953,
          "Mahalalel": 4018,
          "Kenan": 4088,
          "Enosh": 4178,
          "Seth": 4283,
          "Adam": 4413
        }
      },
      "claim_status": "conditional ledger-rounding reconstruction matching supplied SP block; inherited C762, not established provenance of transmitted block"
    }
  },
  "literal_MT_rounded_table_verification": [
    {
      "name": "Adam",
      "rounded_BC": 4106,
      "actual_no_plus2_BC": 4112,
      "source_line": 394,
      "raw": "| Adam | 130 | 130 | 4112 | 4106 | −4105 | −6 |"
    },
    {
      "name": "Seth",
      "rounded_BC": 3976,
      "actual_no_plus2_BC": 3982,
      "source_line": 395,
      "raw": "| Seth | 105 | 105 | 3982 | 3976 | −3975 | −6 |"
    },
    {
      "name": "Enosh",
      "rounded_BC": 3871,
      "actual_no_plus2_BC": 3877,
      "source_line": 396,
      "raw": "| Enosh | 90 | 90 | 3877 | 3871 | −3870 | −6 |"
    },
    {
      "name": "Kenan",
      "rounded_BC": 3781,
      "actual_no_plus2_BC": 3787,
      "source_line": 397,
      "raw": "| Kenan | 70 | 70 | 3787 | 3781 | −3780 | −6 |"
    },
    {
      "name": "Mahalalel",
      "rounded_BC": 3711,
      "actual_no_plus2_BC": 3717,
      "source_line": 398,
      "raw": "| Mahalalel | 65 | 65 | 3717 | 3711 | −3710 | −6 |"
    },
    {
      "name": "Jared",
      "rounded_BC": 3646,
      "actual_no_plus2_BC": 3652,
      "source_line": 399,
      "raw": "| Jared | 162 | 160 | 3652 | 3646 | −3645 | −6 |"
    },
    {
      "name": "Enoch",
      "rounded_BC": 3486,
      "actual_no_plus2_BC": 3490,
      "source_line": 400,
      "raw": "| Enoch | 65 | 65 | 3490 | 3486 | −3485 | −4 |"
    },
    {
      "name": "Methuselah",
      "rounded_BC": 3421,
      "actual_no_plus2_BC": 3425,
      "source_line": 401,
      "raw": "| Methuselah | 187 | 185 | 3425 | 3421 | −3420 | −4 |"
    },
    {
      "name": "Lamech",
      "rounded_BC": 3236,
      "actual_no_plus2_BC": 3238,
      "source_line": 402,
      "raw": "| Lamech | 182 | 180 | 3238 | 3236 | −3235 | −2 |"
    },
    {
      "name": "Noah",
      "rounded_BC": 3056,
      "actual_no_plus2_BC": 3056,
      "source_line": 403,
      "raw": "| Noah | 500 | 500 | 3056 | 3056 | −3055 | 0 |"
    },
    {
      "name": "Shem",
      "rounded_BC": 2556,
      "actual_no_plus2_BC": 2556,
      "source_line": 404,
      "raw": "| Shem | 100 | 100 | 2556 | 2556 | −2555 | 0 |"
    },
    {
      "name": "Arphaxad",
      "rounded_BC": 2456,
      "actual_no_plus2_BC": 2456,
      "source_line": 405,
      "raw": "| Arphaxad | 35 | 35 | 2456 | 2456 | −2455 | 0 |"
    },
    {
      "name": "Shelah",
      "rounded_BC": 2421,
      "actual_no_plus2_BC": 2421,
      "source_line": 406,
      "raw": "| Shelah | 30 | 30 | 2421 | 2421 | −2420 | 0 |"
    },
    {
      "name": "Eber",
      "rounded_BC": 2391,
      "actual_no_plus2_BC": 2391,
      "source_line": 407,
      "raw": "| Eber | 34 | 35 | 2391 | 2391 | −2390 | 0 |"
    },
    {
      "name": "Peleg",
      "rounded_BC": 2356,
      "actual_no_plus2_BC": 2357,
      "source_line": 408,
      "raw": "| Peleg | 30 | 30 | 2357 | 2356 | −2355 | −1 |"
    },
    {
      "name": "Reu",
      "rounded_BC": 2326,
      "actual_no_plus2_BC": 2327,
      "source_line": 409,
      "raw": "| Reu | 32 | 30 | 2327 | 2326 | −2325 | −1 |"
    },
    {
      "name": "Serug",
      "rounded_BC": 2296,
      "actual_no_plus2_BC": 2295,
      "source_line": 410,
      "raw": "| Serug | 30 | 30 | 2295 | 2296 | −2295 | +1 |"
    },
    {
      "name": "Nahor",
      "rounded_BC": 2266,
      "actual_no_plus2_BC": 2265,
      "source_line": 411,
      "raw": "| Nahor | 29 | 30 | 2265 | 2266 | −2265 | +1 |"
    },
    {
      "name": "Terah",
      "rounded_BC": 2236,
      "actual_no_plus2_BC": 2236,
      "source_line": 412,
      "raw": "| Terah | 70 | 70 | 2236 | 2236 | −2235 | 0 |"
    },
    {
      "name": "Abraham",
      "rounded_BC": 2166,
      "actual_no_plus2_BC": 2166,
      "source_line": 413,
      "raw": "| Abraham | 100 | 100 | 2166 | 2166 | −2165 | 0 |"
    },
    {
      "name": "Isaac",
      "rounded_BC": 2066,
      "actual_no_plus2_BC": 2066,
      "source_line": 414,
      "raw": "| Isaac | 60 | 60 | 2066 | 2066 | −2065 | 0 |"
    },
    {
      "name": "Jacob",
      "rounded_BC": 2006,
      "actual_no_plus2_BC": 2006,
      "source_line": 415,
      "raw": "| Jacob | — | — | 2006 | 2006 | −2005 | 0 |"
    },
    {
      "name": "Joseph",
      "rounded_BC": 1916,
      "actual_no_plus2_BC": 1915,
      "source_line": 416,
      "raw": "| Joseph* | 91 | 90 | 1915 | 1916 | −1915 | +1 |"
    }
  ],
  "MT_family_metrics": {
    "Adam_to_Moses": 2580,
    "Seth_to_Moses": 2450,
    "Enoch_to_Moses": 1960,
    "Adam_to_Seth": 130,
    "Seth_to_Enoch": 490,
    "Enoch_to_Arphaxad": 1030,
    "Adam_to_Arphaxad": 1650,
    "Arphaxad_to_Reu": 130,
    "Reu_to_Moses": 800,
    "Arphaxad_to_Moses": 930,
    "Shem_death_BC": 1956,
    "Shem_death_to_Moses": 430
  },
  "whole_postflood_partitions": {
    "MT_native_OFF": {
      "rounded": {
        "Arphaxad_to_Reu": 130,
        "Reu_to_Moses": 800,
        "total": 930
      },
      "strict_actual_comparison": {
        "Arphaxad_to_Reu": 129,
        "Reu_to_Moses": 801,
        "total": 930
      }
    },
    "LXX_native_ON": {
      "rounded": {
        "Arphaxad_to_Reu": 660,
        "Reu_to_Moses": 1050,
        "total": 1710
      },
      "strict_actual_comparison": {
        "Arphaxad_to_Reu": 659,
        "Reu_to_Moses": 1051,
        "total": 1710
      }
    },
    "SP_native_OFF": {
      "rounded": {
        "Arphaxad_to_Reu": 530,
        "Reu_to_Moses": 1050,
        "total": 1580
      },
      "strict_actual_comparison": {
        "Arphaxad_to_Reu": 529,
        "Reu_to_Moses": 1051,
        "total": 1580
      }
    }
  },
  "source_model_transfer": {
    "held_amplitude": "u=100 from C1154; t and a do not enter begetting-only path",
    "MT": "(A,B)=(130,800)",
    "SP_common_names": "(A+4u,B+5u/2)=(530,1050)",
    "LXX_native_ON": "(A+4u+130,B+5u/2)=(660,1050)",
    "scope": "Complete Arphaxad→Reu→Moses path at held lower placement; native Cainan contributes only the first block; this does not derive the SP pre-Flood block choice"
  },
  "finite_admitted_MT_variant_responses": [
    {
      "Terah_plus60": false,
      "Cainan_restored": false,
      "Moses_BC_held": 1526,
      "Adam_BC": 4106,
      "Seth_BC": 3976,
      "Enoch_BC": 3486,
      "Arphaxad_BC": 2456,
      "Reu_BC": 2326,
      "Adam_to_Moses": 2580,
      "Seth_to_Moses": 2450,
      "Enoch_to_Moses": 1960,
      "Arphaxad_to_Reu": 130,
      "Reu_to_Moses": 800,
      "status": "derived finite-state response from admitted row/insertion supports; no new anchor selection"
    },
    {
      "Terah_plus60": false,
      "Cainan_restored": true,
      "Moses_BC_held": 1526,
      "Adam_BC": 4236,
      "Seth_BC": 4106,
      "Enoch_BC": 3616,
      "Arphaxad_BC": 2586,
      "Reu_BC": 2326,
      "Adam_to_Moses": 2710,
      "Seth_to_Moses": 2580,
      "Enoch_to_Moses": 2090,
      "Arphaxad_to_Reu": 260,
      "Reu_to_Moses": 800,
      "status": "derived finite-state response from admitted row/insertion supports; no new anchor selection"
    },
    {
      "Terah_plus60": true,
      "Cainan_restored": false,
      "Moses_BC_held": 1526,
      "Adam_BC": 4166,
      "Seth_BC": 4036,
      "Enoch_BC": 3546,
      "Arphaxad_BC": 2516,
      "Reu_BC": 2386,
      "Adam_to_Moses": 2640,
      "Seth_to_Moses": 2510,
      "Enoch_to_Moses": 2020,
      "Arphaxad_to_Reu": 130,
      "Reu_to_Moses": 860,
      "status": "derived finite-state response from admitted row/insertion supports; no new anchor selection"
    },
    {
      "Terah_plus60": true,
      "Cainan_restored": true,
      "Moses_BC_held": 1526,
      "Adam_BC": 4296,
      "Seth_BC": 4166,
      "Enoch_BC": 3676,
      "Arphaxad_BC": 2646,
      "Reu_BC": 2386,
      "Adam_to_Moses": 2770,
      "Seth_to_Moses": 2640,
      "Enoch_to_Moses": 2150,
      "Arphaxad_to_Reu": 260,
      "Reu_to_Moses": 860,
      "status": "derived finite-state response from admitted row/insertion supports; no new anchor selection"
    }
  ],
  "additional_comparisons": {
    "LXX_OFF": {
      "head_BC": 5356,
      "Moses_span": 3830,
      "status": "explicit Cainan removal comparison; native remains ON"
    },
    "SP_completed52": {
      "head_BC": 4406,
      "Moses_span": 2880,
      "status": "inherited conditional alternate diagnostic only; transmitted4411 retained"
    }
  },
  "dependency_analysis": [
    "Let T=Adam→Moses, p=Adam→Seth, q=Seth→Enoch. The three selected spans are T,T−p,T−p−q. The source gives T2580,p130,q490. The bridge6×430−5×490=130 is necessary for the first two stated targets, but age130 alone does not determine T or select Moses.",
    "For the recapitulation, A=Arphaxad→Reu and B=Reu→Moses. A=Adam_b130 and B=Adam_r800 are two local comparison conditions; A+B=Adam_L930 then follows from L=b+r and is not a third independent constraint.",
    "Shem death→Moses equals b_Shem+(A+B)−L_Shem=100+930−600=430. It adds no independent placement after that post-Flood path and Shem biography are held.",
    "MT Actual strict post-Flood129|801 and rounded130|800 have the same930 total. Eber rounding contributes+1 to A. Reu−2 andNahor+1 contribute−1 to B; the separate Joseph91→90 and39→40 changes cancel.",
    "The native-LXX andSP source models share post-Flood begetting changes but have different lifespans. Moses regular-path results seeu, not thet/a lifespan amplitudes. The native Cainan insertion is a distinct130 path component.",
    "An unrestricted independent constraint rank is not computed here; root may declare its variable model and retained premises before that test. These source displays are not statistical witnesses."
  ],
  "guards": [
    "Use same-side BC subtraction throughout; no civil-cross-epoch correction, decimal inversion, Gear or Mirror operation is introduced.",
    "File51a identifies Arphaxad/Flood2456 in its strict rounded display. Do not identify this role with the distinct Actual MT Flood2458 and Arphaxad2456 in the standard+2 frame.",
    "Position2580 is measured from rounded Adam; it is not2580BC and not a cumulative lifespan date.",
    "The130 Arphaxad→Reu segment sums four begetting intervals; it is not Arphaxad's single begetting age. The800 tail contains genealogical and declared event intervals, not one lifespan.",
    "The source typological second-Adam interpretation is preserved as typology; it neither supplies numeric corrections nor establishes historical authorial intent.",
    "No uniqueness or cycle-frequency claim is verified. File51a's selected comparison family is the bounded object, not a new statistical search.",
    "SP4411 and LXX5486 are compared in the exact states source51a selects. SP alternative4406 must not replace the transmitted state, and LXX native Cainan must not be added again.",
    "No new small-factor or precession search is undertaken; only factorizations already named in§7A.1–7A.5 are retained."
  ],
  "prior_work_overlap": [
    {
      "steps": "C485–491; C733–746",
      "reused": "source-row projections, full regular/cumulative paths and native Cainan separation; not new numerical ages"
    },
    {
      "steps": "C749–760; C767",
      "reused": "typed rounding, whole residual fields, conservation and multiple-of5 compatibility"
    },
    {
      "steps": "C761–762",
      "reused": "SP53→55 versus52→50, conditional4411/4406 reconstruction; keep status unchanged"
    },
    {
      "steps": "C772–788",
      "reused": "finite Terah/Cainan supports and response of rounded paths"
    },
    {
      "steps": "C1151–1170",
      "reused": "complete post-Flood common begetting amplitudeu=100 with Nahor u/2 and explicit source masks"
    },
    {
      "steps": "File51a §7A.1–7A.5",
      "reused": "all target numerical spans are already source-stated. Proposed added explanatory work is their complete path reconstruction, residual and constraint dependency analysis; no novelty claim for the numbers."
    }
  ],
  "validation": {
    "checks": {
      "frozen_packet_source51a_hash_current": true,
      "frozen_packet_source18_hash_current": true,
      "all23_MT_literal_rounded_births": true,
      "all23_MT_literal_actual_strict_births": true,
      "complete_MT_has25_nodes24_edges": true,
      "late_91_39_to90_40_preserves130": true,
      "declared_Entry_Moses350_and430_minus80": true,
      "complete_cycle_family": true,
      "source_bridge_prefixes": true,
      "MT_full_five_block_partition": true,
      "post_Actual_to_Rounded129801_to130800": true,
      "Shem_death430_generated": true,
      "native_LXX_source_span3960": true,
      "SP_conditional_head_matches_transmitted": true,
      "SP_completed_branch_matches_secondary_only": true,
      "common_begetting_amplitude_predicts_post_partitions": true,
      "native_LXX_Cainan_ON_once": true,
      "finite_MT_variant_response": true
    },
    "passed": 18,
    "total": 18,
    "all_passed": true
  }
}