490d — C482–C491: sequential research record

27 September 2026. Working continuation of C481. File52c’s latest supplied draft controls the rounded investigation. No canonical sources are changed. Second-order inversion remains deferred.

Each numbered entry records its question, declared inputs, exact results, finding, and reassessment. These are bounded research actions, not claims of independent discoveries. Parallel agents supplied source extraction and critical review; the main sequence was evaluated in order.

C482 — Cross-tradition transfer: freeze the evidence

Question. Can the complete C481 rounded two-path construction be instantiated from already supplied LXX and SP rows?

Source basis. File51a §§16.2,17.3–17.4; File18 §§6C–6D; C481 checkpoint

Frozen inputs

{
  "MT": {
    "rounded_R": 4106,
    "rounded_C": 14006,
    "rounded_F_R": 2456,
    "rounded_F_C": 4836
  },
  "LXX": {
    "rounded_R": 5486,
    "actual_R": 5494,
    "actual_C_completion": 14894
  },
  "SP_equalized": {
    "rounded_R_block": [
      4416,
      4411
    ],
    "actual_R": 4414,
    "actual_C_completion": 13396
  }
}

Results

{
  "MT": "complete supplied rounded path pair",
  "LXX": "rounded regular head supplied; cumulative rounded path not tabulated",
  "SP": "rounded regular block supplied; cumulative rounded path not tabulated"
}

Finding. A direct two-path transfer is not established by source lookup. Actual completion pairs can still test the frozen weighted constraint without constructing missing rounded rows.

Reassessment. Test the same weighted 12026 anchor on the supplied actual LXX and SP completion pairs.

C483 — Weighted-anchor transfer

Question. Do the supplied actual completion pairs preserve the C481 weighted anchor?

Source basis. File18 §§6B–6D; File22 §5.1; File52c §3.14

Frozen inputs

{
  "MT": [
    14004,
    4114
  ],
  "LXX_native_ON": [
    14894,
    5494
  ],
  "SP_equalized_OFF": [
    13396,
    4414
  ]
}

Results

{
  "MT": {
    "weighted_point": 12026,
    "difference_from_12026": 0,
    "residual_4C_plus_R_minus_5A": 0
  },
  "LXX_native_ON": {
    "weighted_point": 13014,
    "difference_from_12026": 988,
    "residual_4C_plus_R_minus_5A": 4940
  },
  "SP_equalized_OFF": {
    "weighted_point": "57998/5",
    "difference_from_12026": "-2132/5",
    "residual_4C_plus_R_minus_5A": -2132
  }
}

Finding. The 1:4 weighted operation transfers, but its value does not: LXX gives 13014 and SP gives 11599.6. The MT anchor is a particular input-dependent placement, not a universal cross-tradition constant.

Reassessment. Explain the failures through the actual regular/cumulative source differences rather than fit new anchors.

C484 — Why the anchor shifts

Question. Can source differences explain the weighted-anchor failures without adjustable parameters?

Source basis. File18 §§2.1.3,3.1,4.1,6B–6D; Strategy §§3.1–3.2

Frozen inputs

{
  "LXX": {
    "dC": 890,
    "dR": 1380,
    "regular_parts": [
      600,
      780
    ],
    "cumulative_parts": [
      430,
      460
    ]
  },
  "SP": {
    "dC": -608,
    "dR": 300,
    "regular_parts": [
      -350,
      650
    ],
    "cumulative_parts": [
      -115,
      -249,
      -124,
      -60,
      -60
    ]
  }
}

Results

{
  "LXX": {
    "regular_total": 1380,
    "cumulative_total": 890,
    "anchor_shift": 988
  },
  "SP": {
    "regular_total": 300,
    "cumulative_total": -608,
    "anchor_shift": "-2132/5"
  }
}

Finding. Regular and cumulative differences have different causes. LXX centenary repartitions move regular dates while preserving lifespans; SP shortens selected lives. The weighted failures are generated by these source changes.

Reassessment. Reconstruct the ordered local begetting and lifespan differences to see the shared mechanism directly.

C485 — Local repartitions explain LXX mode divergence

Question. Which Adam–Noah row operations generate regular and cumulative differences?

Source basis. File18 §2.1.3 rows1228–1237, §4.1 rows1697–1706

Frozen inputs

{
  "names": [
    "Adam",
    "Seth",
    "Enosh",
    "Kenan",
    "Mahalalel",
    "Jared",
    "Enoch",
    "Methuselah",
    "Lamech"
  ],
  "MT_b": [
    130,
    105,
    90,
    70,
    65,
    162,
    65,
    187,
    182
  ],
  "LXX_b": [
    230,
    205,
    190,
    170,
    165,
    162,
    165,
    187,
    182
  ],
  "MT_L": [
    930,
    912,
    905,
    910,
    895,
    962,
    365,
    969,
    777
  ],
  "LXX_L": [
    930,
    912,
    905,
    910,
    895,
    962,
    365,
    969,
    753
  ]
}

Results

{
  "rows": [
    {
      "row": "Adam",
      "delta_b": 100,
      "delta_remainder": -100,
      "delta_L": 0,
      "running_regular_delta": 100
    },
    {
      "row": "Seth",
      "delta_b": 100,
      "delta_remainder": -100,
      "delta_L": 0,
      "running_regular_delta": 200
    },
    {
      "row": "Enosh",
      "delta_b": 100,
      "delta_remainder": -100,
      "delta_L": 0,
      "running_regular_delta": 300
    },
    {
      "row": "Kenan",
      "delta_b": 100,
      "delta_remainder": -100,
      "delta_L": 0,
      "running_regular_delta": 400
    },
    {
      "row": "Mahalalel",
      "delta_b": 100,
      "delta_remainder": -100,
      "delta_L": 0,
      "running_regular_delta": 500
    },
    {
      "row": "Jared",
      "delta_b": 0,
      "delta_remainder": 0,
      "delta_L": 0,
      "running_regular_delta": 500
    },
    {
      "row": "Enoch",
      "delta_b": 100,
      "delta_remainder": -100,
      "delta_L": 0,
      "running_regular_delta": 600
    },
    {
      "row": "Methuselah",
      "delta_b": 0,
      "delta_remainder": 0,
      "delta_L": 0,
      "running_regular_delta": 600
    },
    {
      "row": "Lamech",
      "delta_b": 0,
      "delta_remainder": -24,
      "delta_L": -24,
      "running_regular_delta": 600
    }
  ],
  "Creation_to_Noah_MT": 1056,
  "Creation_to_Noah_LXX": 1656,
  "lifespan_delta": -24
}

Finding. Six +100 begetting moves each trade 100 from the remainder and conserve lifespan. Lamech is a separate −24 lifespan change with begetting182 fixed. One source row structure therefore produces two different chronological projections.

Reassessment. Apply the same row accounting to SP, including its completed-year boundary.

C486 — SP local reconstruction

Question. Does the same source-row accounting explain SP endpoint movement and its boundary exception?

Source basis. File18 §§2.1.3,3.1,3.2; lines1474–1488,1532–1534

Frozen inputs

{
  "begetting_deltas": [
    -100,
    -120,
    -129
  ],
  "primary_completed_year": -1,
  "lifespan_deltas": [
    -115,
    -249,
    -124,
    -60,
    -60
  ],
  "downstream_regular_shift": 650
}

Results

{
  "Adam_Noah_MT": 1056,
  "Adam_Noah_SP_primary": 706,
  "delta_regular_internal": -350,
  "delta_regular_Creation": 300,
  "delta_cumulative": -608,
  "SP_Lamech": "53rd year ->52 completed units;653 lifespan is inclusive"
}

Finding. SP uses the same two projections with different local data. Its −350 pre-Noah change plus +650 downstream placement gives +300 regular Creation, while five lifespan changes total−608 cumulatively. The inclusive Lamech convention must remain explicit.

Reassessment. Express this mechanism as a small linear source-row rule, with boundary terms kept separate.

C487 — A shared row grammar

Question. What common rule generates divergent regular and cumulative changes?

Source basis. Strategy §§3.2,5B; C485–C486

Frozen inputs

{
  "compatible_row": [
    "b",
    "r"
  ],
  "lifespan": "b+r",
  "regular_selector": [
    1,
    0
  ],
  "cumulative_selector": [
    1,
    1
  ]
}

Results

{
  "row_moves": {
    "repartition_100": {
      "regular_effect": 100,
      "cumulative_effect": 0,
      "remainder_effect": -100
    },
    "LXX_Lamech": {
      "regular_effect": 0,
      "cumulative_effect": -24,
      "remainder_effect": -24
    },
    "insert_Cainan": {
      "regular_effect": 130,
      "cumulative_effect": 460,
      "remainder_effect": 330
    }
  },
  "regular_formula": "anchor_R + sum(selected begetting intervals) + declared boundary terms",
  "cumulative_formula": "anchor_C + sum(selected lifespans) + declared phase terms",
  "projection_matrix": [
    [
      1,
      0
    ],
    [
      1,
      1
    ]
  ],
  "determinant": 1
}

Finding. A richer source row supports two distinct measurements. Repartition lies in the cumulative kernel; a lifespan-only change can leave the regular projection fixed. This explains family divergence without a universal map between their endpoints.

Reassessment. Test the admitted Cainan insertion as a concrete cross-mode vector.

C488 — Cainan as a cross-mode vector

Question. Which shared structures survive the admitted 130/460 insertion?

Source basis. Strategy §§3.2,4.4; File18 Cainan controls

Frozen inputs

{
  "delta_R": 130,
  "delta_C": 460,
  "MT_bridge": 9890
}

Results

{
  "bridge_change": 330,
  "weighted_point_change": 394,
  "restored_bridge": 10220,
  "Sothic_factor": 7,
  "finite_state_rule": "OFF -> ON once where admitted; native LXX starts ON"
}

Finding. One inserted row accounts for both130 and460, increases the cumulative–regular bridge by330, and sends9890 to10220=7×1460. It shifts the weighted point by394, so it is not a12026-preserving operation.

Reassessment. Check whether the rounded regular reversal construction survives native LXX inputs.

C489 — LXX rounded path transfer

Question. Does the admitted Noah refinement preserve the rounded reversal endpoint in native LXX?

Source basis. File51a §§2,17.3; File18 §4.1

Frozen inputs

{
  "rounded_creation": 5486,
  "rounded_Adam_Noah": 1650,
  "Noah_Flood": 600,
  "Conquest": 1406
}

Results

{
  "derived_rounded_Noah": 3836,
  "derived_rounded_Flood": 3236,
  "paths": {
    "primary": {
      "segments": [
        2250,
        1830
      ],
      "inverse_segments": [
        5220,
        3810
      ],
      "endpoint": 10436
    },
    "Noah_refinement": {
      "segments": [
        1650,
        600,
        1830
      ],
      "inverse_segments": [
        5610,
        600,
        3810
      ],
      "endpoint": 11426
    }
  }
}

Finding. LXX endpoints10436 and11426 differ990. The same path evaluator transfers, but MT’s equality under Noah refinement does not. The cumulative LXX branch remains uninstantiated, not silently approximated.

Reassessment. Test SP through its positively supplied block relations rather than an absent rounded path.

C490 — SP’s positive rounded contribution

Question. What supplied SP relationship can enter the shared grammar unchanged?

Source basis. File51a §17.4

Frozen inputs

{
  "creation_block": [
    4416,
    4411
  ],
  "conquest_block": [
    1406,
    1401
  ],
  "nativity_block": [
    6,
    1
  ],
  "MT_creation_block": [
    4111,
    4106
  ]
}

Results

{
  "conquest_widths": [
    3010,
    3010
  ],
  "nativity_widths": [
    4410,
    4410
  ],
  "SP_minus_MT": [
    305,
    305
  ],
  "Terah_plus60_comparison": [
    365,
    365
  ]
}

Finding. SP supplies a block translation: both members preserve3010=7×430 to Conquest and4410=9×490 to Nativity. This is a different positive realization of the common span-and-state grammar, without replacing4416/4411 by4406.

Reassessment. Complete the LXX lifespan reconstruction, then consolidate the cross-family result.

C491 — Close the cross-tradition source explanation

Question. Can every unit of LXX’s cumulative890 difference be traced to supplied lifespan rows?

Source basis. File18 §§2.2,4.1–4.2,6D; corrected339/339/330 triplet

Frozen inputs

{
  "Lamech": -24,
  "Arphaxad": 27,
  "Cainan": 460,
  "Shelah": 27,
  "Eber": 40,
  "Peleg": 100,
  "Reu": 100,
  "Serug": 100,
  "Nahor": 60
}

Results

{
  "row_deltas": {
    "Lamech": -24,
    "Arphaxad": 27,
    "Cainan": 460,
    "Shelah": 27,
    "Eber": 40,
    "Peleg": 100,
    "Reu": 100,
    "Serug": 100,
    "Nahor": 60
  },
  "postFlood_without_Cainan": 454,
  "all_deltas": 890,
  "endpoint_check": 890
}

Finding. The total is454+460−24=890. Alongside SP’s−608, this completes a source-row explanation of why the regular and cumulative families move differently. A common projection grammar is supported; a common12026 endpoint is not.

Reassessment. Return to the MT rounded/actual interface and derive its residual conservation from rows and endpoint selections.

Evidence

The accompanying evidence checkpoint contains the sequential journal, exact-arithmetic step scripts, source snapshots and SHA256 manifest. Latest step: C491. Assertions verify arithmetic or explicit scope decisions; they are not independent historical or statistical witnesses.