{
  "step": "C434",
  "source_excerpt_cards": [
    {
      "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.",
      "excerpt_sha256": "bdc7bf81662ed18805fc57aae6ec26d2026111cca6b3f7262366c1c14c067dd5"
    },
    {
      "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:",
      "excerpt_sha256": "f756f840110723b596d44f3bbbe7f3f3b2541dd0cd6716d42683490363ed3250"
    },
    {
      "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": "FLOOD_GEAR_SCOPE",
      "source": "File_18.md",
      "line_start": 1540,
      "line_end": 1552,
      "text": "#### 3.1.4 Ordinary Flood Gears, fixed Arphaxad, and the SP midpoint\n\nThis table uses the full-430 comparison frame, Terah `+60` OFF, MT/SP second Cainan OFF, and LXX native second Cainan ON. The LXX G2 Creation head is `5494`, consistent with `5494−3238=2256`; Cainan-OFF `5364` must not be paired with native-ON Flood `3238`.\n\n| Tradition | G3 Flood start→close | G2 Flood start→close | G1 Flood start→close | Fixed Arphaxad |\n|---|---|---|---|---:|\n| MT | 2460→2459 | 2458→2457 | 2456→2455 | 2456 |\n| LXX — native Cainan ON | 3240→3239 | 3238→3237 | 3236→3235 | 3236 |\n| SP | 3110→3109 | 3108→3107 | 3106→3105 | 3106 |\n\nEvery row has the ladder `G3 start → G2 start → G1 start → G1 close = 2+2+1 = 5`. At this layer LXX is MT `+780`, including Arphaxad. Each Flood close arises from that Gear’s one-year event span, independently of SP Noah/Shem primary→companion. At held Sojourn, Terah, and Cainan settings, regular Arphaxad onward through Moses does not move with Gear; the separately scoped variant mechanisms retain their own permissions.\n\nSubtract `215` from this table for the corresponding minimum/native frames. The native SP starts G3/G2/G1 are `2895/2893/2891`, with closes `2894/2892/2890`; fixed Arphaxad is `2891`.",
      "excerpt_sha256": "99eb07c7c52ecdde9818217457ff47358e05ab8a8ef3f06330ced9e4dcec8b15"
    },
    {
      "id": "E_RATIO_CORRECTED",
      "source": "File_46.md",
      "line_start": 117,
      "line_end": 133,
      "text": "### L3. Priestly Ratio (25/23)\n\nActive state: Key-of-23 Priestly Expansion state.\n\n```markdown\n4830 × 25/23 = 5250\n```\n\nbecause `4830/23 = 210` and `210 × 25 = 5250`.\n\nTherefore:\n\n```markdown\n5256 BC → 6 BC = 5256 − 6 = 5250\n```\n\nThe source associates this operator with Luke (the Luke / Priestly expansion); the association is developed in §4.2.",
      "excerpt_sha256": "2b4e25ac5e9ffe7eb57254349fb12c984f1f3a40ce88464cde7eb712869897cf"
    },
    {
      "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"
    }
  ],
  "source_G1_SP_bases": {
    "Noah birth": {
      "primary": 3491,
      "companion": 3490
    },
    "Noah death": {
      "primary": 2541,
      "companion": 2540
    },
    "Shem birth": {
      "primary": 2991,
      "companion": 2990
    },
    "Shem death": {
      "primary": 2391,
      "companion": 2390
    }
  },
  "domain": {
    "labelled_records": 528,
    "coordinate_count": 373,
    "meaning_of_absent": "Absent only from the frozen regular Noah/Shem/Flood register; not a repository-wide negative."
  },
  "source_formula": {
    "N": "3706+2(g-1)+60T",
    "H": "N-500",
    "P": "N+130-215-1=N-86",
    "Q": "N-950",
    "exact_identity": "25(215-130+1)+23(950)=48(500)=24000",
    "factorization": "E_Q composed with E_P equals E_H squared",
    "integer_parameter": "P=H+23*18; Q=H-25*18",
    "input": "H-1058",
    "intermediate": "H-1186",
    "output": "H-1250"
  },
  "cases": [
    {
      "gear": 1,
      "Terah60": 0,
      "coordinates": {
        "N": 3706,
        "H": 3206,
        "P": 3620,
        "Q": 2756,
        "input": 2148,
        "intermediate": 2020,
        "output": 1956
      },
      "source_record_indices": {
        "N": [
          177,
          433
        ],
        "H": [
          209,
          449
        ],
        "P": [
          188
        ],
        "Q": [
          193,
          441
        ],
        "input": [
          271
        ],
        "intermediate": [
          363
        ],
        "output": [
          169
        ]
      },
      "selected_SP_support_records": {
        "N": 177,
        "H": 209,
        "P": 188,
        "Q": 193,
        "P_own_death": 204
      },
      "gains": [
        128,
        64
      ],
      "gaps": [
        1472,
        1600,
        736,
        800
      ],
      "affine_slope": [
        625,
        529
      ],
      "affine_intercept": [
        -307776,
        529
      ],
      "whole_map_identity": true,
      "complete_source_path": true,
      "labelled_actual_pivot_paths": 2,
      "missing_in_fixed_register": [],
      "formal_MT_station_states": {
        "input": {
          "gear": 2,
          "Cainan": 1,
          "Terah60": 1,
          "full430": 1
        },
        "intermediate": {
          "gear": 3,
          "Cainan": 0,
          "Terah60": 1,
          "full430": 1
        },
        "output": {
          "gear": 1,
          "Cainan": 0,
          "Terah60": 0,
          "full430": 1
        }
      },
      "inadmissible_formal_states_are_not_source_records": true
    },
    {
      "gear": 2,
      "Terah60": 0,
      "coordinates": {
        "N": 3708,
        "H": 3208,
        "P": 3622,
        "Q": 2758,
        "input": 2150,
        "intermediate": 2022,
        "output": 1958
      },
      "source_record_indices": {
        "N": [
          273,
          465
        ],
        "H": [
          305,
          481
        ],
        "P": [
          284
        ],
        "Q": [
          289,
          473
        ],
        "input": [
          367
        ],
        "intermediate": [],
        "output": [
          265
        ]
      },
      "selected_SP_support_records": {
        "N": 273,
        "H": 305,
        "P": 284,
        "Q": 289,
        "P_own_death": 300
      },
      "gains": [
        128,
        64
      ],
      "gaps": [
        1472,
        1600,
        736,
        800
      ],
      "affine_slope": [
        625,
        529
      ],
      "affine_intercept": [
        -307968,
        529
      ],
      "whole_map_identity": true,
      "complete_source_path": false,
      "labelled_actual_pivot_paths": 0,
      "missing_in_fixed_register": [
        "intermediate"
      ],
      "formal_MT_station_states": {
        "input": {
          "gear": 3,
          "Cainan": 1,
          "Terah60": 1,
          "full430": 1
        },
        "intermediate": {
          "gear": 4,
          "Cainan": 0,
          "Terah60": 1,
          "full430": 1
        },
        "output": {
          "gear": 2,
          "Cainan": 0,
          "Terah60": 0,
          "full430": 1
        }
      },
      "inadmissible_formal_states_are_not_source_records": true
    },
    {
      "gear": 3,
      "Terah60": 0,
      "coordinates": {
        "N": 3710,
        "H": 3210,
        "P": 3624,
        "Q": 2760,
        "input": 2152,
        "intermediate": 2024,
        "output": 1960
      },
      "source_record_indices": {
        "N": [
          369,
          497
        ],
        "H": [
          401,
          513
        ],
        "P": [
          380
        ],
        "Q": [
          385,
          505
        ],
        "input": [],
        "intermediate": [],
        "output": [
          361
        ]
      },
      "selected_SP_support_records": {
        "N": 369,
        "H": 401,
        "P": 380,
        "Q": 385,
        "P_own_death": 396
      },
      "gains": [
        128,
        64
      ],
      "gaps": [
        1472,
        1600,
        736,
        800
      ],
      "affine_slope": [
        625,
        529
      ],
      "affine_intercept": [
        -308160,
        529
      ],
      "whole_map_identity": true,
      "complete_source_path": false,
      "labelled_actual_pivot_paths": 0,
      "missing_in_fixed_register": [
        "input",
        "intermediate"
      ],
      "formal_MT_station_states": {
        "input": {
          "gear": 4,
          "Cainan": 1,
          "Terah60": 1,
          "full430": 1
        },
        "intermediate": {
          "gear": 5,
          "Cainan": 0,
          "Terah60": 1,
          "full430": 1
        },
        "output": {
          "gear": 3,
          "Cainan": 0,
          "Terah60": 0,
          "full430": 1
        }
      },
      "inadmissible_formal_states_are_not_source_records": true
    },
    {
      "gear": 1,
      "Terah60": 1,
      "coordinates": {
        "N": 3766,
        "H": 3266,
        "P": 3680,
        "Q": 2816,
        "input": 2208,
        "intermediate": 2080,
        "output": 2016
      },
      "source_record_indices": {
        "N": [
          179,
          435
        ],
        "H": [
          211,
          451
        ],
        "P": [
          190
        ],
        "Q": [
          195,
          443
        ],
        "input": [],
        "intermediate": [],
        "output": [
          171
        ]
      },
      "selected_SP_support_records": {
        "N": 179,
        "H": 211,
        "P": 190,
        "Q": 195,
        "P_own_death": 206
      },
      "gains": [
        128,
        64
      ],
      "gaps": [
        1472,
        1600,
        736,
        800
      ],
      "affine_slope": [
        625,
        529
      ],
      "affine_intercept": [
        -313536,
        529
      ],
      "whole_map_identity": true,
      "complete_source_path": false,
      "labelled_actual_pivot_paths": 0,
      "missing_in_fixed_register": [
        "input",
        "intermediate"
      ],
      "formal_MT_station_states": {
        "input": {
          "gear": 2,
          "Cainan": 1,
          "Terah60": 2,
          "full430": 1
        },
        "intermediate": {
          "gear": 3,
          "Cainan": 0,
          "Terah60": 2,
          "full430": 1
        },
        "output": {
          "gear": 1,
          "Cainan": 0,
          "Terah60": 1,
          "full430": 1
        }
      },
      "inadmissible_formal_states_are_not_source_records": true
    },
    {
      "gear": 2,
      "Terah60": 1,
      "coordinates": {
        "N": 3768,
        "H": 3268,
        "P": 3682,
        "Q": 2818,
        "input": 2210,
        "intermediate": 2082,
        "output": 2018
      },
      "source_record_indices": {
        "N": [
          275,
          467
        ],
        "H": [
          307,
          483
        ],
        "P": [
          286
        ],
        "Q": [
          291,
          475
        ],
        "input": [],
        "intermediate": [],
        "output": [
          267
        ]
      },
      "selected_SP_support_records": {
        "N": 275,
        "H": 307,
        "P": 286,
        "Q": 291,
        "P_own_death": 302
      },
      "gains": [
        128,
        64
      ],
      "gaps": [
        1472,
        1600,
        736,
        800
      ],
      "affine_slope": [
        625,
        529
      ],
      "affine_intercept": [
        -313728,
        529
      ],
      "whole_map_identity": true,
      "complete_source_path": false,
      "labelled_actual_pivot_paths": 0,
      "missing_in_fixed_register": [
        "input",
        "intermediate"
      ],
      "formal_MT_station_states": {
        "input": {
          "gear": 3,
          "Cainan": 1,
          "Terah60": 2,
          "full430": 1
        },
        "intermediate": {
          "gear": 4,
          "Cainan": 0,
          "Terah60": 2,
          "full430": 1
        },
        "output": {
          "gear": 2,
          "Cainan": 0,
          "Terah60": 1,
          "full430": 1
        }
      },
      "inadmissible_formal_states_are_not_source_records": true
    },
    {
      "gear": 3,
      "Terah60": 1,
      "coordinates": {
        "N": 3770,
        "H": 3270,
        "P": 3684,
        "Q": 2820,
        "input": 2212,
        "intermediate": 2084,
        "output": 2020
      },
      "source_record_indices": {
        "N": [
          371,
          499
        ],
        "H": [
          403,
          515
        ],
        "P": [
          382
        ],
        "Q": [
          387,
          507
        ],
        "input": [],
        "intermediate": [],
        "output": [
          363
        ]
      },
      "selected_SP_support_records": {
        "N": 371,
        "H": 403,
        "P": 382,
        "Q": 387,
        "P_own_death": 398
      },
      "gains": [
        128,
        64
      ],
      "gaps": [
        1472,
        1600,
        736,
        800
      ],
      "affine_slope": [
        625,
        529
      ],
      "affine_intercept": [
        -313920,
        529
      ],
      "whole_map_identity": true,
      "complete_source_path": false,
      "labelled_actual_pivot_paths": 0,
      "missing_in_fixed_register": [
        "input",
        "intermediate"
      ],
      "formal_MT_station_states": {
        "input": {
          "gear": 4,
          "Cainan": 1,
          "Terah60": 2,
          "full430": 1
        },
        "intermediate": {
          "gear": 5,
          "Cainan": 0,
          "Terah60": 2,
          "full430": 1
        },
        "output": {
          "gear": 3,
          "Cainan": 0,
          "Terah60": 1,
          "full430": 1
        }
      },
      "inadmissible_formal_states_are_not_source_records": true
    }
  ],
  "used_source_records": [
    {
      "record_index": 169,
      "record": {
        "tradition": "MT",
        "gear": 1,
        "role": "Shem death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 1956
      }
    },
    {
      "record_index": 171,
      "record": {
        "tradition": "MT",
        "gear": 1,
        "role": "Shem death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 2016
      }
    },
    {
      "record_index": 177,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Noah birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3706
      }
    },
    {
      "record_index": 179,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Noah birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3766
      }
    },
    {
      "record_index": 188,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Noah birth",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 0,
        "full430": 0,
        "center": 3620
      }
    },
    {
      "record_index": 190,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Noah birth",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 1,
        "full430": 0,
        "center": 3680
      }
    },
    {
      "record_index": 193,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Noah death",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 2756
      }
    },
    {
      "record_index": 195,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Noah death",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 2816
      }
    },
    {
      "record_index": 204,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Noah death",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 0,
        "full430": 0,
        "center": 2670
      }
    },
    {
      "record_index": 206,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Noah death",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 1,
        "full430": 0,
        "center": 2730
      }
    },
    {
      "record_index": 209,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Shem birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3206
      }
    },
    {
      "record_index": 211,
      "record": {
        "tradition": "SP",
        "gear": 1,
        "role": "Shem birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3266
      }
    },
    {
      "record_index": 265,
      "record": {
        "tradition": "MT",
        "gear": 2,
        "role": "Shem death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 1958
      }
    },
    {
      "record_index": 267,
      "record": {
        "tradition": "MT",
        "gear": 2,
        "role": "Shem death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 2018
      }
    },
    {
      "record_index": 271,
      "record": {
        "tradition": "MT",
        "gear": 2,
        "role": "Shem death",
        "rail": null,
        "Cainan": 1,
        "Terah60": 1,
        "full430": 1,
        "center": 2148
      }
    },
    {
      "record_index": 273,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Noah birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3708
      }
    },
    {
      "record_index": 275,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Noah birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3768
      }
    },
    {
      "record_index": 284,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Noah birth",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 0,
        "full430": 0,
        "center": 3622
      }
    },
    {
      "record_index": 286,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Noah birth",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 1,
        "full430": 0,
        "center": 3682
      }
    },
    {
      "record_index": 289,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Noah death",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 2758
      }
    },
    {
      "record_index": 291,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Noah death",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 2818
      }
    },
    {
      "record_index": 300,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Noah death",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 0,
        "full430": 0,
        "center": 2672
      }
    },
    {
      "record_index": 302,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Noah death",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 1,
        "full430": 0,
        "center": 2732
      }
    },
    {
      "record_index": 305,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Shem birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3208
      }
    },
    {
      "record_index": 307,
      "record": {
        "tradition": "SP",
        "gear": 2,
        "role": "Shem birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3268
      }
    },
    {
      "record_index": 361,
      "record": {
        "tradition": "MT",
        "gear": 3,
        "role": "Shem death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 1960
      }
    },
    {
      "record_index": 363,
      "record": {
        "tradition": "MT",
        "gear": 3,
        "role": "Shem death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 2020
      }
    },
    {
      "record_index": 367,
      "record": {
        "tradition": "MT",
        "gear": 3,
        "role": "Shem death",
        "rail": null,
        "Cainan": 1,
        "Terah60": 1,
        "full430": 1,
        "center": 2150
      }
    },
    {
      "record_index": 369,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Noah birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3710
      }
    },
    {
      "record_index": 371,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Noah birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3770
      }
    },
    {
      "record_index": 380,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Noah birth",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 0,
        "full430": 0,
        "center": 3624
      }
    },
    {
      "record_index": 382,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Noah birth",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 1,
        "full430": 0,
        "center": 3684
      }
    },
    {
      "record_index": 385,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Noah death",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 2760
      }
    },
    {
      "record_index": 387,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Noah death",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 2820
      }
    },
    {
      "record_index": 396,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Noah death",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 0,
        "full430": 0,
        "center": 2674
      }
    },
    {
      "record_index": 398,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Noah death",
        "rail": "companion",
        "Cainan": 1,
        "Terah60": 1,
        "full430": 0,
        "center": 2734
      }
    },
    {
      "record_index": 401,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Shem birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3210
      }
    },
    {
      "record_index": 403,
      "record": {
        "tradition": "SP",
        "gear": 3,
        "role": "Shem birth",
        "rail": "primary",
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3270
      }
    },
    {
      "record_index": 433,
      "record": {
        "tradition": "LXX",
        "gear": 1,
        "role": "Noah birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3706
      }
    },
    {
      "record_index": 435,
      "record": {
        "tradition": "LXX",
        "gear": 1,
        "role": "Noah birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3766
      }
    },
    {
      "record_index": 441,
      "record": {
        "tradition": "LXX",
        "gear": 1,
        "role": "Noah death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 2756
      }
    },
    {
      "record_index": 443,
      "record": {
        "tradition": "LXX",
        "gear": 1,
        "role": "Noah death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 2816
      }
    },
    {
      "record_index": 449,
      "record": {
        "tradition": "LXX",
        "gear": 1,
        "role": "Shem birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3206
      }
    },
    {
      "record_index": 451,
      "record": {
        "tradition": "LXX",
        "gear": 1,
        "role": "Shem birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3266
      }
    },
    {
      "record_index": 465,
      "record": {
        "tradition": "LXX",
        "gear": 2,
        "role": "Noah birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3708
      }
    },
    {
      "record_index": 467,
      "record": {
        "tradition": "LXX",
        "gear": 2,
        "role": "Noah birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3768
      }
    },
    {
      "record_index": 473,
      "record": {
        "tradition": "LXX",
        "gear": 2,
        "role": "Noah death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 2758
      }
    },
    {
      "record_index": 475,
      "record": {
        "tradition": "LXX",
        "gear": 2,
        "role": "Noah death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 2818
      }
    },
    {
      "record_index": 481,
      "record": {
        "tradition": "LXX",
        "gear": 2,
        "role": "Shem birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3208
      }
    },
    {
      "record_index": 483,
      "record": {
        "tradition": "LXX",
        "gear": 2,
        "role": "Shem birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3268
      }
    },
    {
      "record_index": 497,
      "record": {
        "tradition": "LXX",
        "gear": 3,
        "role": "Noah birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3710
      }
    },
    {
      "record_index": 499,
      "record": {
        "tradition": "LXX",
        "gear": 3,
        "role": "Noah birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3770
      }
    },
    {
      "record_index": 505,
      "record": {
        "tradition": "LXX",
        "gear": 3,
        "role": "Noah death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 2760
      }
    },
    {
      "record_index": 507,
      "record": {
        "tradition": "LXX",
        "gear": 3,
        "role": "Noah death",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 2820
      }
    },
    {
      "record_index": 513,
      "record": {
        "tradition": "LXX",
        "gear": 3,
        "role": "Shem birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1,
        "center": 3210
      }
    },
    {
      "record_index": 515,
      "record": {
        "tradition": "LXX",
        "gear": 3,
        "role": "Shem birth",
        "rail": null,
        "Cainan": 0,
        "Terah60": 1,
        "full430": 1,
        "center": 3270
      }
    }
  ],
  "counts": {
    "pivot_comparisons": 6,
    "whole_map_identities": 6,
    "sourced_inputs": 2,
    "sourced_intermediates": 1,
    "sourced_outputs": 6,
    "complete_coordinate_paths": 1,
    "labelled_actual_pivot_paths": 2
  },
  "boundary_proof": {
    "input": "S_MT(g+1, C1, T+1, F1)",
    "intermediate": "S_MT(g+2, C0, T+1, F1)",
    "output": "S_MT(g, C0, T, F1)",
    "allowed_gear": [
      1,
      2,
      3
    ],
    "allowed_T": [
      0,
      1
    ],
    "consequence": "T=0 and g=1; full-register membership shows no alternative role/alias rescue."
  },
  "controls": {
    "companion_removed_effective_H_error": [
      25,
      48
    ],
    "displacement_required_for_502_with_Q_fixed": [
      -2246,
      25
    ],
    "fixed_H_intermediate_2056_absent": true,
    "source_midpoint_shift": 36,
    "modal_502_is_not_rejected": true
  },
  "provenance_correction": {
    "prior": "C432 E_RULE card pointed to File_46 lines97-113: P=70/69.",
    "corrected": "File_46 L3, lines117-133: E=25/23.",
    "effect": "Excerpt locator correction only. Earlier E calculations already used25/23."
  },
  "limits": [
    "Source-qualified affine comparison, not a combined chronology prescription.",
    "SP primary Noah-death retains the inclusive/harmonic qualification.",
    "P and Q cross contexts; their864 gap is not one Noah lifespan.",
    "Regular Gears remain Noah/Shem/Flood only; formal G4/G5 and T2 are rejected.",
    "LXX OFF aliases are theoretical, not native-Cainan dates or independent witnesses.",
    "Existing phase/component limits are inherited; no new seasonal claim.",
    "SKL supplement retained for awareness only.",
    "No wider-input census is performed: C435 remains unexecuted."
  ]
}