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"title": "SP source-supported relations after the complete cap reconstruction",
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"excerpt": "| Patriarch / event | Birth BC | Death BC | Lifespan | Begetting age |\n|---|---:|---:|---:|---:|\n| Creation Week | 3906 | 3899 | 7 | — |\n| Adam | 3899 | 2969 | 930 | 130 |\n| Seth | 3769 | 2857 | 912 | 105 |\n| Enosh | 3664 | 2759 | 905 | 90 |\n| Kenan | 3574 | 2664 | 910 | 70 |\n| Mahalalel | 3504 | 2609 | 895 | 65 |\n| Jared | 3439 | 2477 | 962 | 162 |\n| Enoch | 3277 | 2912 | 365 | 65 |\n| Methuselah | 3212 | 2243 | 969 | 187 |\n| Lamech | 3025 | 2248 | 777 | 182 |\n| Noah | 2843 | 1893 | 950 | 500 |\n| Flood | 2243 | 2242 | 1 | — |"
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"excerpt": "| Patriarch / event | Birth BC | Death BC | Lifespan / count | Begetting age / binding |\n|---|---:|---:|---|---|\n| Creation Week | 4206 | 4199 | 7 | — |\n| Adam / preferred chain head | 4199 | 3269 | 930 | 130 |\n| Seth | 4069 | 3157 | 912 | 105 |\n| Enosh | 3964 | 3059 | 905 | 90 |\n| Kenan | 3874 | 2964 | 910 | 70 |\n| Mahalalel | 3804 | 2909 | 895 | 65 |\n| Jared | 3739 | 2893 | 847 inclusive | 62 |\n| Enoch | 3677 | 3312 | 365 | 65 |\n| Methuselah | 3612 | 2893 | 720 inclusive | 67 |\n| Lamech | 3545 | 2893 | 653 inclusive | 53rd year to primary Noah; full 53 to companion |\n| Noah — G2 primary | 3493 | 2543 | 950 | 500 to G2 primary Shem; other bindings in §3.2.1 |"
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{
"id": "remaining_years_reexpression",
"priority": "supporting",
"role": "Alternative local source coordinates, not compression",
"relations": [
"b_i = L_i − r_i",
"(930,912,905,910,895)−(800,807,815,840,830)=(130,105,90,70,65)",
"365−300=65"
],
"unknowns_constrained": [
"First five ages and Enoch65 if source lifespans and remaining-year entries are held"
],
"given": [
"Actual MT life and remaining-year columns; source-qualified shared early SP values"
],
"derived": [
"The begetting ages as differences of two held row components"
],
"premise_cost": "Ten held first-five component values do not explain five ages with fewer numerical premises; this is a complete reversible row description.",
"status": "Existing source decomposition; useful control against confusing recovery with explanatory reduction.",
"sources": [
{
"source": "File51a",
"section": "§3.4",
"line_start": 441,
"line_end": 463,
"excerpt": "### 3.4 Birth and Death Dates: Actual MT vs. Rounded (Remaining-Years Method)\nModal-state note: The rounded death-date layer is secondary and theoretical. Later references to rounded deaths such as Joseph 1806 BC, Jacob 1861 BC, or Methuselah 2456 BC inherit the `[MOD-5 THEORETICAL]` status unless explicitly reclassified.\n\nMethodology: To avoid chronological absurdities (e.g., Methuselah dying after the Flood), the rounded lifespan is computed by rounding the remaining years after begetting rather than the total lifespan. For example, Methuselah: rounded begetting (185) + rounded remaining (782 → 780) = 965, placing his death at the Flood (2456 BC), not 5 years after it. The MT does not provide remaining years from Arphaxad onward, so those are calculated as: lifespan − begetting age.\n\nMachine Guard [MOD-5 THEORETICAL]: All death dates in this table are derived from a secondary rounding operation (rounding the remaining-years value). They must not overwrite the primary baseline death-date nodes in the repository. All rounded death dates carry the tag [MOD-5 THEORETICAL] and exist as a distinct modal layer alongside the Actual MT death dates.\n\nMachine Guard [METHUSELAH BIFURCATION]: Regular chronology: round begetting and remaining independently, then sum (185 + 780 = 965). Cumulative chronology: round total lifespan directly (969 → 970). Both rules are applied uniformly to all patriarchs; Methuselah is the unique case where they diverge. Do not reconcile — preserve as modal states per domain.\n\nNote: 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 |"
}
],
"limitations": [
"Use actual columns only; theoretical rounded deaths remain separate.",
"File51a’s unrestricted Methuselah uniqueness sentence was qualified in C750 and is not imported.",
"No SP Enoch364 compression is activated."
]
},
{
"id": "jared_baseline_anatomy",
"priority": "medium",
"role": "One ancestral lifespan as a source biography",
"relations": [
"162+800=962",
"Jared and Adam share remaining800 in the actual MT ledger"
],
"unknowns_constrained": [
"Ancestral Jared life962 and therefore excess115 once capacity847 is held"
],
"given": [
"MT Jared begetting162 and remainder800; source cap capacity847"
],
"derived": [
"Jared life962",
"962−847=115"
],
"premise_cost": "The same biography is decomposed; no independent derivation of remainder800 or excess115 is supplied.",
"status": "Existing explicit source anatomy; excess is a consequence.",
"sources": [
{
"source": "File51a",
"section": "§8.2",
"line_start": 953,
"line_end": 960,
"excerpt": "\n### 8.2 The 960-Jared Cross-Tradition Connection\n| Source | 960 Connection |\n| --- | --- |\n| MT (rounded) | 160 begetting + 800 remaining = 960 lifespan |\n| MT (actual) | 162 + 800 = 962 ≈ 960 |\n| LXX | Adam is 960 years old when Jared is born (cumulative LXX begetting: 230+205+190+170+165 = 960) |\n"
},
{
"source": "File51a",
"section": "§3.4",
"line_start": 452,
"line_end": 461,
"excerpt": "| 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 |"
}
],
"limitations": [
"Rounded960 does not determine exact962.",
"Matching the scalar115 elsewhere cannot be used as a new source constraint without an explicit source link."
]
},
{
"id": "methuselah_flood_completion",
"priority": "highest",
"role": "Explicit additional path alignment relative to SP cap",
"relations": [
"187+182+600=969",
"Ancestral Methuselah dies at his tradition’s Flood"
],
"unknowns_constrained": [
"Ancestral Methuselah life969 and therefore excess249 once SP capacity720 is held"
],
"given": [
"MT/main LXX begettings187 and182; Noah-to-Flood600; source death-at-Flood alignment"
],
"derived": [
"969 baseline lifespan",
"969−720=249"
],
"premise_cost": "The alignment is an added source condition; it is not inferred from the SP clipped output.",
"status": "Existing explicit source path equation; strong next conditional-reconstruction candidate.",
"sources": [
{
"source": "File18",
"section": "§4A.2",
"line_start": 1772,
"line_end": 1772,
"excerpt": "Lamech now dies `29` years before the regular LXX Flood. The selected Methuselah `187` / Lamech `182` birth chain still puts Methuselah's death at the Flood: `187 + 182 + 600 = 969`. No regular birth date, Creation endpoint, Noah biography, Flood anchor, or Cainan/Terah/Sojourn operator is changed by the lifespan decision."
}
],
"limitations": [
"Do not activate188; it changes this path and remains nonoperative.",
"The relation is not independent evidence of the historical origin of969."
]
},
{
"id": "mt_lamech_remaining_years",
"priority": "supporting",
"role": "MT ancestral biography decomposition",
"relations": [
"182+595=777"
],
"unknowns_constrained": [
"MT Lamech777 and MT-to-SP excess124 if capacity653 is held"
],
"given": [
"MT begetting182 and remaining595"
],
"derived": [
"MT life777",
"777−653=124"
],
"premise_cost": "Two held components reproduce the biography; no independent age-origin theory results.",
"status": "Existing MT source anatomy; LXX use of777 remains appendix-only.",
"sources": [
{
"source": "File18",
"section": "Appendix B.1",
"line_start": 2470,
"line_end": 2470,
"excerpt": "The MT record and Smith's proposed LXX restoration are `182 + 595 = 777`. In this repository, applying MT `777` to the LXX is an appendix-only overlay, not the preferred original LXX lifespan. Smith's restoration is retained as an external reconstruction, not as a jointly attested original established here. The main LXX reconstruction retains attested `753` with restored `182` and does not claim Smith's support for that pair."
},
{
"source": "File51a",
"section": "§3.4",
"line_start": 461,
"line_end": 463,
"excerpt": "| 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 |"
}
],
"limitations": [
"Do not promote the LXX777 appendix overlay to the main LXX chain."
]
},
{
"id": "lamech_daniel_revelation_complement",
"priority": "medium",
"role": "Explicit cross-family structural constraint, marked inferred by source",
"relations": [
"483+777=1260",
"483=69×7;1260=42×30"
],
"unknowns_constrained": [
"MT Lamech777 if483,1260 and the source bridge are held"
],
"given": [
"Declared Daniel69-week measure483; Revelation42-month measure1260; explicit inferred identification of their complement with MT Lamech life"
],
"derived": [
"1260−483=777"
],
"premise_cost": "The identification of the complement with Lamech is an additional structural premise, not a consequence of the two numbers alone.",
"status": "Existing source-inferred bridge; conditional candidate, not textual or historical proof.",
"sources": [
{
"source": "File17",
"section": "§8.1",
"line_start": 694,
"line_end": 705,
"excerpt": "## 8. The `777` bridge: Daniel to Revelation\n\nActive state: Daniel-Revelation bridge state. `777` is MT Lamech’s lifespan and functions here as a component bridge into `1260`; it does not become a universal half-week operator.\n\n### 8.1 The `777`: Lamech’s lifespan\n\n| Component structure | Derivation |\n|---|---|\n| `483 + 777 = 1260` | Daniel’s 69 weeks + Lamech = Revelation’s half-week |\n| `770 + 490 = 1260` | alternate configuration |\n\nThis explains why `1260` accommodates multiple patterns without conflict. It has multiple valid decompositions."
},
{
"source": "File17",
"section": "§12.1",
"line_start": 978,
"line_end": 989,
"excerpt": "Active state: half-week variant register. The prophetic, Enochian, extended, and blessing endpoint forms are parallel states within the half-week family.\n\n### 12.1 The `1260`: prophetic half-week\n\n| Component structure | Derivation | Source |\n|---|---|---|\n| `360 + 720 + 180 = 1260` | Time + Times + Half-Time | Dan 7:25; Dan 12:7; Rev 12:14 |\n| `3.5 × 360 = 1260` | half of seven prophetic years | calculated |\n| `42 × 30 = 1260` | 42 months | Rev 11:2; Rev 13:5 |\n| `483 + 777 = 1260` | Daniel’s 69 weeks + Lamech | inferred |\n| `770 + 490 = 1260` | alternate configuration | inferred |\n"
}
],
"limitations": [
"The source expressly rejects promotion to a universal half-week operator.",
"No new endpoint or search domain is needed or authorized."
]
},
{
"id": "lamech_24_100_comparison",
"priority": "high",
"role": "Existing LXX/MT/SP lifespan constraints and their dependency",
"relations": [
"777−753=24",
"753−653=100",
"1656×70/69−1656=24",
"777−653=24+100=124"
],
"unknowns_constrained": [
"LXX life753 given MT777 and selected24 relation, or given SP653 and selected100 relation"
],
"given": [
"Attested LXX753 as current source input; comparison states777 and653; explicit structural association of24 gain and100 difference"
],
"derived": [
"Differences24 and100",
"MT-to-SP excess124 as their sum"
],
"premise_cost": "Reverse-solving the adopted support relations is an equivalent conditional description, not an independent creation of attested753.",
"status": "Existing source structural support with explicit historical and dependence ceiling.",
"sources": [
{
"source": "File18",
"section": "§4A.4",
"line_start": 1807,
"line_end": 1818,
"excerpt": "### 4A.4 Supporting lifespan relations: `24` and the SP century\n\n```text\n4114 − 2458 = 1656\n1656 × 70/69 = 1680 = 5 × 336\n1680 − 1656 = 24\n777 − 753 = 24\n753 − 653 = 100\n454 − 24 = 430\n```\n\nThe `777` in this main-body comparison is MT Lamech's unchanged lifespan; `753` is the adopted LXX lifespan and `653` is SP Lamech's lifespan. The `24` gain and the LXX–SP `100` difference give structural support to the choice of `753`. They do not imply that multiplying `753` by a Key yields `777`, or prove that SP was historically produced from the LXX. The cumulative `454 → 430` consequence remains controlled by §6D and uses the retained `753` input, rather than explaining that input independently of its selection."
},
{
"source": "File18",
"section": "§4A.1",
"line_start": 1746,
"line_end": 1756,
"excerpt": "Active state: author-adopted LXX main reconstruction, September 8 2026. `182` is the restored regular begetting input; `753` is the retained attested LXX lifespan in both Regular and Cumulative execution. This supersedes the former regular-`777` / cumulative-`753` dual-locality ruling. Unless specified otherwise, the displays below use the website `+215 Sojourn`, no-`+60 Terah`, native-LXX-Cainan frame. Appendix A retains the minimum-frame conversion. Appendix B preserves the MT-derived LXX `777` overlay, overlap geometry, and lesser corroborations outside the main chronology.\n\n### 4A.1 Source hierarchy and the component-wise reconstruction\n\nThe standard transmitted LXX record is `188 + 565 = 753`. **`753` itself is the attested/transmitted LXX lifespan in Genesis 5:31, not a reconstructed number.** This study retains it as the **preferred original LXX lifespan**, an author-adopted textual/structural conclusion supported especially by §4A.3. Its attestation is a textual fact; the judgment that it preserves the original LXX lifespan is distinct from that fact and does not establish the earliest Hebrew reading or a complete scribal transmission history.\n\nThe component-wise reconstruction pairs this retained `753` with the restored operative begetting age `182`, supported by the repository's MT/external-witness argument and source-selected birth chain. It gives `182 + 571 = 753`, with `571` calculated. No surviving manuscript witness jointly attesting `182/753`, or independently reading `571`, has been identified in the sources reviewed here. That qualification concerns the combined biography, not the attestation of `753`, and is not a claim that such a joint text could never have existed.\n\nSmith is an external reconstruction witness, not an endorsement of this combined selection. His different full-biography restoration and its source qualifications are retained in Appendix B.1/B.7. MT-like ancestry is the author's working transmission hypothesis, not a historical priority established by the numerical comparisons.\n\nClaim-status: attested LXX lifespan `753`; author-adopted judgment that it preserves the original LXX lifespan; restored begetting `182`; component-wise `182/753` reconstruction; calculated remainder `571`. Structural analysis supports retention of the attested lifespan but does not create joint manuscript attestation."
}
],
"limitations": [
"LXX753 itself is attested;182/753 is a component-wise reconstruction and571 is calculated.",
"Do not count124=24+100 as a further independent constraint.",
"No historical LXX→SP production is established."
]
},
{
"id": "early_mod5_fixation",
"priority": "low",
"role": "Rounding-domain restriction, not age generator",
"relations": [
"All first-five ages and Enoch65 are already multiples of5"
],
"unknowns_constrained": [
"Residue classes of early ages; no unique magnitudes"
],
"given": [
"Nearest-five policy and explicit source list of already-round begetting ages"
],
"derived": [
"These rows have zero rounding residual"
],
"premise_cost": "Congruence restrictions preserve many age assignments; they do not select the actual tuple.",
"status": "Existing rounding property; retain as a control only.",
"sources": [
{
"source": "File51a",
"section": "§2.1",
"line_start": 211,
"line_end": 211,
"excerpt": "The 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)."
}
],
"limitations": [
"Do not enumerate arbitrary alternative ages to find preferred endpoints."
]
}
],
"recommended_priority": [
"twin_65_half_adam",
"first_five_total_460",
"methuselah_flood_completion",
"lamech_24_100_comparison",
"lamech_daniel_revelation_complement"
],
"remaining_unknowns": {
"early_ages": "With Adam130 held, equal half-Adam flanks fix Mahalalel65 and Enoch65. First-five460 then fixes only Seth+Enosh+Kenan265, not105/90/70 individually.",
"jared_enoch_split": "The explicit Enoch relation supplies the missing value needed by the already established cap sum127; it does not come from cap outputs alone.",
"baseline_excess": "115,249,124 (or main-LXX100) remain differences of baseline inputs and capacities. The source supports particular baseline reconstructions but does not make the cap invertible.",
"historical_origin": "Source compatibility, conditional recovery, and explanatory compression remain distinct from an established transmission sequence."
},
"do_not_promote": [
{
"item": "File20 §2.2 exclusive4200/344 frame",
"reason": "Older exclusive comparison and transmitted BJ dependency cannot replace current native4199 source chain or count as independent age-generation evidence."
},
{
"item": "File53 §14A unified Enoch/compression display",
"reason": "Its70+294+1 accounting and optional364 compression are different source conventions; they do not replace actual365/65/300 or open a new cap state."
},
{
"item": "File51a rounded960",
"reason": "Nearest-five output does not uniquely identify actual962."
},
{
"item": "Other uses of115,249 or124",
"reason": "Matching tokens are not an admitted relation between the ancestral lifespan excess and another source object."
}
],
"prior_relation_status": {
"C953_C983": "Cap mechanism and its conditional inverse already proved; this inventory seeks declared premises beyond that cap, not a repeat of its arithmetic.",
"C733_C748": "Whole regular/cumulative source fields and ordered local differences already reconstructed.",
"C749_C770": "Complete rounding/residual behavior already explored."
},
"literal_arithmetic_checks": {
"shared_five_equal": true,
"first_five_sum": true,
"twin65_half130": true,
"remaining_reconstruction": true,
"jared_anatomy": true,
"methuselah_completion": true,
"lamech_anatomy": true,
"inferred_complement": true,
"lamech_difference_dependency": true
},
"all_checks_pass": true
}
Evidence
sp source relations.json
Linked sources and evidence
Edition and provenance
sp_source_relations.json
SHA-256 35f1150e6b9cd4e43fb4f8c2dbfae942535014f2f0dbde5c2f6ee81f46e3db25
C480–C1634/Research_Cycles/C1132_C1431_Recovered/prep/sp_source_relations.json