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    {
      "id": "MT_PERSONS",
      "source": "File_02.md",
      "line_start": 659,
      "line_end": 716,
      "text": "### 6.2 Regular chronology: localized effect\n\nActive state:\nMT Minimum-Regular Noah/Shem pivot table.\n\nNode-class note:\nThe slash-pairs in this table are localized modal pairs, not collapsed date ranges and not unresolved typographical variants.\n\nIn regular chronology, the ±2 is localized. It affects only Noah and Shem without propagating through the remaining patriarchal chain.\n\n| Patriarch | Birth pair | Death pair | Lifespan |\n|---|---:|---:|---:|\n| Noah | 2843/2841 BC | 1893/1891 BC | 950 |\n| Shem | 2343/2341 BC | 1743/1741 BC | 600 |\n\nSource-control note:\nThe supplied source row `2845/2843 BC` and `1895/1893 BC` is preserved in the archive. The active `File_02` table uses `2843/2841 BC` and `1893/1891 BC` for Noah under current `File_00` / Restart Capsule v11.15 Noah-Shem pivot controls.\n\nArithmetic note:\nThe localized lifespan pairs check internally.\n\n$$2843-1893=950.$$\n\n$$2841-1891=950.$$\n\n$$2343-1743=600.$$\n\n$$2341-1741=600.$$\n\nEndpoint-state note:\nUnder the local MT Minimum-Regular Flood at `2243 BC`, the Noah birth pair gives the controlled 600/598 state:\n\n$$2843-2243=600.$$\n\n$$2841-2243=598.$$\n\nThis prepares the 598 ↔ 600 gear shift in §6.3 without retaining the prior `602` result as an active state.\n\nThe Shem birth pair gives the 100/98 state against the same Flood boundary:\n\n$$2343-2243=100.$$\n\n$$2341-2243=98.$$\n\nTransfer rule:\nThis table gives the localized Noah/Shem ±2 pair in the minimum-position MT regular state. It does not replace the MT Standard-Normal Flood at `2458 BC`.\n\nTo transfer the table into the other MT regular positions, apply the Universal Four-Position Matrix.\n\n| Position | Add to minimum-position Noah/Shem table |\n|---|---:|\n| Minimum-Regular | +0 |\n| Minimum-Regular +60 | +60 |\n| Standard-Normal | +215 |\n| Standard-Normal +60 | +275 |\n\nMachine-processing rule:\nRegular dates apply the ±2 ambiguity only to Noah and Shem.",
      "excerpt_sha256": "45b114f63ea4380febdaef22d664e23579dcecc53759f20c6a2a742cef885038"
    },
    {
      "id": "PERSON_BASES",
      "source": "File_18.md",
      "line_start": 1253,
      "line_end": 1282,
      "text": "\n#### 2.2.1 Noah and Shem `±2` anomaly\n\nActive state:\nRegular-localized Shem `±2`.\n\nGenesis 11:10 supplies the two-year distinction used in the regular Noah/Shem binding comparisons. This localized comparison permission does not restrict ordinary coherent Gear transport of the Flood; see §3.1.4. In Cumulative chronology, the `±2` propagates through the chain; see §6 and `File_02`.\n\n| Patriarch | Literal, in table | Idealistic `±2` | Source direction label |\n|---|---|---|---|\n| Noah | 2843–1893 BC | 2841–1891 BC | Earlier |\n| Shem | 2341–1741 BC | 2343–1743 BC | Later |\n\nThe literal dates represent the minimum baseline. The idealistic dates represent the alternative reading of Genesis 11:10. Both are valid.\n\nFor LXX, retain the independently sourced `±2` comparisons at its own native-Cainan positions:\n\n| Tradition | Patriarch | Literal | Idealistic `±2` |\n|---|---|---|---|\n| LXX | Noah | 3623–2673 BC | 3621–2671 BC |\n| LXX | Shem | 3121–2521 BC | 3123–2523 BC |\n\nThe corrected SP field additionally has a local one-year companion. Its native-frame G2 pairs are:\n\n| SP person | G2 primary biography | G2 lower-companion biography |\n|---|---|---|\n| Noah | 3493–2543 BC | 3492–2542 BC |\n| Shem | 2993–2393 BC | 2992–2392 BC |\n\nThese columns differ by one year and must not be labelled `±2`. The ordinary SP G1 Shem biography `2991–2391` remains the displayed Arphaxad-bound row, distinct from G2 `2993–2393` by two years. §3.2.1 gives all three Gears and the named bindings. MT and LXX do not inherit this SP-only adjacent rail.",
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      "id": "SP_FIELD",
      "source": "File_18.md",
      "line_start": 1571,
      "line_end": 1596,
      "text": "#### 3.2.1 SP Noah/Shem field and named bindings\n\nEach slash-pair below is ordered primary / lower companion. The companion is one year farther forward in time. The rows display ordinary Gear combined with SP-local person-station adjacency; they are not six independently attested source states or a new unrestricted execution generator.\n\n| Gear | Noah birth | Noah death | Shem birth | Shem death |\n|---|---|---|---|---|\n| G1 | 3491/3490 | 2541/2540 | 2991/2990 | 2391/2390 |\n| G2 | 3493/3492 | 2543/2542 | 2993/2992 | 2393/2392 |\n| G3 | 3495/3494 | 2545/2544 | 2995/2994 | 2395/2394 |\n\nAdd `215` for the reports’ equalized dates. Noah’s primary death column carries the inclusive/harmonic qualification and the lower column the ordinary-companion qualification. Matched birth/death endpoints preserve Noah `950` and Shem `600`; matched Noah/Shem births preserve `500`. The mixed G2 companion-Noah / primary-Shem path is `3492−2993=499`, the ordinal 500th-year alternative.\n\nThe native G2 post-Flood spans are `2893−2543=350` and `2892−2542=350`. The second uses Flood close and Noah’s companion death; it does not type the Flood close as a companion. The cross-pair `2893−2542=351` is not an unqualified `350`.\n\nThe following bindings preserve the prior usable stations while making their Gears explicit:\n\n| Shem station / binding | Birth BC | Death BC | Qualified relation |\n|---|---:|---:|---|\n| G2 primary, Noah/Flood comparison | 2993 | 2393 | G2 primary Noah `3493−500=2993`; `2993−100=2893`, Flood start. |\n| G2 companion, Noah/Flood comparison | 2992 | 2392 | G2 companion Noah `3492−500=2992`; ordinal `2992−99=2893`, Flood start. |\n| G1 primary, Arphaxad-bound | 2991 | 2391 | `2991−100=2891`, fixed Arphaxad; also `3493−502=2991` from G2 primary Noah. |\n| G1 companion, Noah-bound comparison | 2990 | 2390 | `3492−502=2990` from G2 companion Noah; it does not replace the full-100 Arphaxad-bound row. |\n\nG2 primary Shem `2993` is `102` from fixed Arphaxad `2891`. These comparisons retain their endpoint roles and bindings. Noah/Shem alone have the full qualified cross-Gear endpoint-comparison permission in this domain; other patriarchs retain coherent-Gear biographies. Qualified Noah↔Flood comparisons are allowed, while the Flood remains an event start/close structure.\n\nThe post-Flood begetting table selects the G1 primary / Arphaxad-bound Shem row:",
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    },
    {
      "id": "VARIANTS",
      "source": "File_18.md",
      "line_start": 620,
      "line_end": 627,
      "text": "\nTradition-scope clarification:\nThis multiplication is not MT-local. MT, SP, and LXX encounter the fork sequence at the same genealogical locations: the Sojourn / Egypt-position `+215` fork, the `+60 Terah` fork, and the 2nd Cainan `+130` boundary. The arithmetic status differs by tradition. MT / SP receive Cainan by restoration when that state is opened. LXX already contains Cainan in its regular baseline, so the LXX form is a native-Cainan boundary state unless a theoretical removal / reinsertion state is explicitly opened.\n\n| Epoch / boundary | Active variants | Possible explicit date states | Handling |\n|---|---|---:|---|\n| Adam → Arphaxad / Flood | `±215 Sojourn × +60 Terah × restored 2nd Cainan` where opened | eight states | Active only if restored 2nd Cainan is explicitly inserted. Arphaxad is synonymous with the Flood / Ark-exit conception boundary and is the first upstream row to absorb the Cainan hinge. |\n| 2nd Cainan → Terah | `±215 Sojourn × +60 Terah` | four states | 2nd Cainan, Shelah, Eber, Peleg, Reu, Serug, Nahor, and Terah remain four-position. |",
      "excerpt_sha256": "520ba2473d3664220f028a4d96d0f28e04397e164911a0c54a8fcdcd40237bfa"
    },
    {
      "id": "SP_LOCALITY",
      "source": "File_18.md",
      "line_start": 433,
      "line_end": 435,
      "text": "Machine Guard [FILE_18 SP NOAH/SHEM LOCALITY + FLOOD GEAR SEPARATION]:\n\nThe SP companion operator is primary minus one for Noah/Shem person-stations only. Native G2 Noah is `3493/3492`, Shem `2993/2992`, Noah death `2543/2542`, and Shem death `2393/2392`. G1 Shem `2991/2990` with deaths `2391/2390` remains available under named bindings; only `2991→2891` is the displayed full-100 Arphaxad-bound relation. Do not propagate the companion into Adam through Lamech or Arphaxad onward, and do not transfer it to MT/LXX. Native G2 Lamech is `3545→2893`, `653` inclusive. Flood `2893→2892` is a start→close event pair, not a companion pair. All three traditions retain ordinary Flood Gears and independent one-year Flood spans; §3.1.4 supplies the exact table. LXX is native Cainan ON in that comparison. Keep the G2 `654+654` midpoint to fixed Arphaxad separate from the G1 Lamech-death / Flood-start / Arphaxad coordinate convergence.",
      "excerpt_sha256": "57aacb11ce53ee625e98ab033b4c66199d654e0afc9b4be070baf07c8d96e677"
    },
    {
      "id": "LXX_REMOVAL",
      "source": "File_18.md",
      "line_start": 1140,
      "line_end": 1147,
      "text": "\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. |",
      "excerpt_sha256": "0eb1f430961a0680cff5801032d8bbdbd123030841e36d2a7543496eae896ca1"
    },
    {
      "id": "E_RULE",
      "source": "File_46.md",
      "line_start": 97,
      "line_end": 113,
      "text": "### L2. Prophetic Ratio (70/69)\n\nActive state: Key-of-23 Prophetic Expansion state.\n\n```markdown\n4830 × 70/69 = 4900\n```\n\nbecause `4830/69 = 70` and `70 × 70 = 4900`.\n\nTherefore:\n\n```markdown\n4836 BC → AD 65 = 4900\n```\n\nsince `4836 + 65 − 1 = 4900`.",
      "excerpt_sha256": "9ed16d0d17cc70c745ac4630155351a8b75aec2775cb59b2e3b02e40636c7d79"
    },
    {
      "id": "DUAL100",
      "source": "File_18.md",
      "line_start": 755,
      "line_end": 771,
      "text": "#### 1.3.5 Shem dual-`100` state\n\nTier: diagnostic modal-state support.\n\nActive state:\nRegular chronology; Shem `±2`; Noah-bound and Arphaxad-bound Shem states.\n\nShem carries two valid `100` states.\n\n| Shem state | Textual basis | Meaning | Handling |\n|---|---|---|---|\n| Noah-bound / Flood-bound `100` | Noah is `500` when Shem is born; Noah is `600` at the Flood | Shem is `100` at the Flood | Valid harmonic / structural state |\n| Arphaxad-bound / text-bound `100` | Genesis 11:10: Shem is `100` when he begets Arphaxad two years after the Flood | Shem is `100` at Arphaxad's birth | Valid textual state |\n\nThese states are not corrections of one another. They function like the Terah `70/130` begetting-state field: both readings are retained under named modal states.\n\nThe two-year difference is the Shem `±2` binding hinge. In Regular chronology this local binding distinction concerns Noah/Shem; ordinary coherent Flood Gear transport remains separately available (§3.1.4). In Cumulative chronology the anomaly may propagate through the cumulative chain where that state is opened.",
      "excerpt_sha256": "13e799de2148cb20f111736e59df30b616b05c4f621433e1f2219692046a6a54"
    },
    {
      "id": "MIRROR_COMPONENTS",
      "source": "File_09.md",
      "line_start": 2028,
      "line_end": 2065,
      "text": "Theological / calendrical hinge:\nThe repository Mirror is centered on the start of Jan 1, AD 1, traditionally associated with Christ's Day-8 circumcision and naming after the Dec 25, 1 BC birth placement. This is the Jan-1 hinge, not a July-1 hinge.\n\nProof-only coordinate notation:\nMeasure time in years from the start of Jan 1, AD 1. Then:\n\n```markdown\nA(AD y, Jan 1) = y − 1\nA(y BC, Jan 1) = −y\nA(AD y, n) = y − 3/4\nA(AD y, t) = y − 1/4\nA(y BC, n) = −y + 1/4\nA(y BC, t) = −y + 3/4\n```\n\nJanuary-centered BC source pair:\nFor a Tishri/Nisan pair:\n\n```markdown\nYt/(Y−1)n BC\n```\n\nThe two coordinates are:\n\n```markdown\nA(Yt BC) = −Y + 3/4\nA((Y−1)n BC) = −Y + 5/4\n```\n\nTherefore the internal pair width is:\n\n```markdown\n(−Y + 5/4) − (−Y + 3/4) = 1/2\n```\n\nand the pair-center is:\n\n```markdown",
      "excerpt_sha256": "40fa8ddcd665a2ac33eef2367ac976cadd047939ed48879e4f8ca3445e0cd668"
    }
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      "denominator": 529
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    "intercept": {
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      "denominator": 529
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    "intermediate_source_record_indices": [],
    "required_MT_Shem_death_Gear": 4
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    {
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    {
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    {
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      "whole_map_error": "24/529",
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    }
  ],
  "jointly_shifted_component_comparisons": [
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      "common_offset": "-1/4",
      "intermediate": "8079/4",
      "output": "7823/4",
      "same_fixed_pivots": false
    },
    {
      "common_offset": "1/4",
      "intermediate": "8081/4",
      "output": "7825/4",
      "same_fixed_pivots": false
    }
  ],
  "counts": {
    "source_excerpt_cards": 9,
    "direct_source_records_reconstructed": 18,
    "first_pivot_source_labels": 1,
    "second_pivot_source_labels": 2,
    "complete_record_labelled_paths": 2,
    "separate_Noah_biographies": 3,
    "plus2_intermediate_sources": 0,
    "fixed_pivot_component_assignments": 8,
    "preserved_fixed_pivot_assignments": 0,
    "joint_shifted_comparisons": 2,
    "new_protocol_prescriptions_established": 0
  },
  "interpretation": "The two actual pivots are SP companion Noah birth3620 and SP primary/LXX-OFF Noah death2756, in different contexts. The three path stations are different MT Shem-death source states, G2→G3→G1 with explicit Cainan/Terah changes. Each selected Noah biography remains950; pivot separation864 is cross-context. This is a sourced exact affine factorization, not a reviewed prescription for combined chronology or a single fixed-pivot seasonal action. The+2 partner lacks2022 and requires unavailable Gear4 for the analogous MT Shem-death state."
}
