[
  {
    "step": 482,
    "title": "Cross-tradition transfer: freeze the evidence",
    "question": "Can the complete C481 rounded two-path construction be instantiated from already supplied LXX and SP rows?",
    "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
      }
    },
    "sources": [
      "File51a §§16.2,17.3–17.4",
      "File18 §§6C–6D",
      "C481 checkpoint"
    ],
    "opened_utc": "2026-09-27T22:37:27.114819+00:00",
    "predecessor_sha256": "C481:4d7a97cf35348c8ea23a23079b0682f739bb5b4b0cc734e24e7b9bc6e0b19455",
    "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.",
    "checks": {
      "primary_52c_preserved": true,
      "no_missing_rows_imputed": true
    },
    "closed_utc": "2026-09-27T22:37:27.114992+00:00",
    "sha256": "1895d9835b6b584fec00642b47f194b86f46c2081240f97586f415f571f4857b"
  },
  {
    "step": 483,
    "title": "Weighted-anchor transfer",
    "question": "Do the supplied actual completion pairs preserve the C481 weighted anchor?",
    "inputs": {
      "MT": [
        14004,
        4114
      ],
      "LXX_native_ON": [
        14894,
        5494
      ],
      "SP_equalized_OFF": [
        13396,
        4414
      ]
    },
    "sources": [
      "File18 §§6B–6D",
      "File22 §5.1",
      "File52c §3.14"
    ],
    "opened_utc": "2026-09-27T22:37:52.573459+00:00",
    "predecessor_sha256": "1895d9835b6b584fec00642b47f194b86f46c2081240f97586f415f571f4857b",
    "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.",
    "checks": {
      "MT": true,
      "LXX": true,
      "SP": true
    },
    "closed_utc": "2026-09-27T22:37:52.573685+00:00",
    "sha256": "2d8648e433b1c5b5e236b77fae7662d91e5431ed83423f0be5710a5700868c5d"
  },
  {
    "step": 484,
    "title": "Why the anchor shifts",
    "question": "Can source differences explain the weighted-anchor failures without adjustable parameters?",
    "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
        ]
      }
    },
    "sources": [
      "File18 §§2.1.3,3.1,4.1,6B–6D",
      "Strategy §§3.1–3.2"
    ],
    "opened_utc": "2026-09-27T22:38:12.777807+00:00",
    "predecessor_sha256": "2d8648e433b1c5b5e236b77fae7662d91e5431ed83423f0be5710a5700868c5d",
    "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.",
    "checks": {
      "LXX": true,
      "SP": true
    },
    "closed_utc": "2026-09-27T22:38:12.778112+00:00",
    "sha256": "eec39f6501d594bed3b861d4106437d5e83aa91adeb73e53b653e045999d7f75"
  },
  {
    "step": 485,
    "title": "Local repartitions explain LXX mode divergence",
    "question": "Which Adam–Noah row operations generate regular and cumulative differences?",
    "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
      ]
    },
    "sources": [
      "File18 §2.1.3 rows1228–1237, §4.1 rows1697–1706"
    ],
    "opened_utc": "2026-09-27T22:38:31.325826+00:00",
    "predecessor_sha256": "eec39f6501d594bed3b861d4106437d5e83aa91adeb73e53b653e045999d7f75",
    "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.",
    "checks": {
      "six_repartitions": true,
      "regular600": true,
      "cumulative_minus24": true
    },
    "closed_utc": "2026-09-27T22:38:31.326136+00:00",
    "sha256": "934f0c51380606bedec92a8a87e13b5ef21fa6a726ba4fde385bb0948e79a0ae"
  },
  {
    "step": 486,
    "title": "SP local reconstruction",
    "question": "Does the same source-row accounting explain SP endpoint movement and its boundary exception?",
    "inputs": {
      "begetting_deltas": [
        -100,
        -120,
        -129
      ],
      "primary_completed_year": -1,
      "lifespan_deltas": [
        -115,
        -249,
        -124,
        -60,
        -60
      ],
      "downstream_regular_shift": 650
    },
    "sources": [
      "File18 §§2.1.3,3.1,3.2; lines1474–1488,1532–1534"
    ],
    "opened_utc": "2026-09-27T22:38:56.215706+00:00",
    "predecessor_sha256": "934f0c51380606bedec92a8a87e13b5ef21fa6a726ba4fde385bb0948e79a0ae",
    "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.",
    "checks": {
      "regular": true,
      "cumulative": true
    },
    "closed_utc": "2026-09-27T22:38:56.215891+00:00",
    "sha256": "96196b18b7ce0e7439090355632d626dfe6d82abae5ef9f28f24ecb2eb925993"
  },
  {
    "step": 487,
    "title": "A shared row grammar",
    "question": "What common rule generates divergent regular and cumulative changes?",
    "inputs": {
      "compatible_row": [
        "b",
        "r"
      ],
      "lifespan": "b+r",
      "regular_selector": [
        1,
        0
      ],
      "cumulative_selector": [
        1,
        1
      ]
    },
    "sources": [
      "Strategy §§3.2,5B",
      "C485–C486"
    ],
    "opened_utc": "2026-09-27T22:39:11.631579+00:00",
    "predecessor_sha256": "96196b18b7ce0e7439090355632d626dfe6d82abae5ef9f28f24ecb2eb925993",
    "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.",
    "checks": {
      "repartition_kernel": true,
      "insertion": true
    },
    "closed_utc": "2026-09-27T22:39:11.631755+00:00",
    "sha256": "cf03e97da2b1013fa5cbae893db9813e84e6a7d80e85f5acb0531ac9f1c5b81f"
  },
  {
    "step": 488,
    "title": "Cainan as a cross-mode vector",
    "question": "Which shared structures survive the admitted 130/460 insertion?",
    "inputs": {
      "delta_R": 130,
      "delta_C": 460,
      "MT_bridge": 9890
    },
    "sources": [
      "Strategy §§3.2,4.4",
      "File18 Cainan controls"
    ],
    "opened_utc": "2026-09-27T22:39:26.289098+00:00",
    "predecessor_sha256": "cf03e97da2b1013fa5cbae893db9813e84e6a7d80e85f5acb0531ac9f1c5b81f",
    "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.",
    "checks": {
      "bridge": true,
      "weighted_shift": true
    },
    "closed_utc": "2026-09-27T22:39:26.289320+00:00",
    "sha256": "81ce12908cdbb31a2fea6cbebbe635805da6fc1db08b73041dcb9737a0999cf3"
  },
  {
    "step": 489,
    "title": "LXX rounded path transfer",
    "question": "Does the admitted Noah refinement preserve the rounded reversal endpoint in native LXX?",
    "inputs": {
      "rounded_creation": 5486,
      "rounded_Adam_Noah": 1650,
      "Noah_Flood": 600,
      "Conquest": 1406
    },
    "sources": [
      "File51a §§2,17.3",
      "File18 §4.1"
    ],
    "opened_utc": "2026-09-27T22:39:48.590457+00:00",
    "predecessor_sha256": "81ce12908cdbb31a2fea6cbebbe635805da6fc1db08b73041dcb9737a0999cf3",
    "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.",
    "checks": {
      "primary": true,
      "refinement": true,
      "difference": true
    },
    "closed_utc": "2026-09-27T22:39:48.590669+00:00",
    "sha256": "9fecbe41b9475fec06582eae9bd92e70ed09f6cd679dd7350c149cd24898f1b5"
  },
  {
    "step": 490,
    "title": "SP’s positive rounded contribution",
    "question": "What supplied SP relationship can enter the shared grammar unchanged?",
    "inputs": {
      "creation_block": [
        4416,
        4411
      ],
      "conquest_block": [
        1406,
        1401
      ],
      "nativity_block": [
        6,
        1
      ],
      "MT_creation_block": [
        4111,
        4106
      ]
    },
    "sources": [
      "File51a §17.4"
    ],
    "opened_utc": "2026-09-27T22:40:02.227524+00:00",
    "predecessor_sha256": "9fecbe41b9475fec06582eae9bd92e70ed09f6cd679dd7350c149cd24898f1b5",
    "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.",
    "checks": {
      "conquest": true,
      "nativity": true,
      "state_shift": true
    },
    "closed_utc": "2026-09-27T22:40:02.227840+00:00",
    "sha256": "27dc1bcb3a0ec7aedd0095603ad0b3c1ed826497488a575b040e8107c3e225ff"
  },
  {
    "step": 491,
    "title": "Close the cross-tradition source explanation",
    "question": "Can every unit of LXX’s cumulative890 difference be traced to supplied lifespan rows?",
    "inputs": {
      "Lamech": -24,
      "Arphaxad": 27,
      "Cainan": 460,
      "Shelah": 27,
      "Eber": 40,
      "Peleg": 100,
      "Reu": 100,
      "Serug": 100,
      "Nahor": 60
    },
    "sources": [
      "File18 §§2.2,4.1–4.2,6D; corrected339/339/330 triplet"
    ],
    "opened_utc": "2026-09-27T22:40:15.843136+00:00",
    "predecessor_sha256": "27dc1bcb3a0ec7aedd0095603ad0b3c1ed826497488a575b040e8107c3e225ff",
    "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.",
    "checks": {
      "total": true,
      "postFlood": true,
      "regular_independent": true
    },
    "closed_utc": "2026-09-27T22:40:15.843363+00:00",
    "sha256": "09851060f453b478462087352850941d9c1e72097fcda695304666ec74bf6567"
  },
  {
    "step": 492,
    "title": "Resolve regular rounded-to-actual residual",
    "question": "Is the regular +8 shift all rounding?",
    "inputs": {
      "Actual_minus_Rounded_begetting_residuals": {
        "Jared": 2,
        "Methuselah": 2,
        "Lamech": 2,
        "Eber": -1,
        "Reu": 2,
        "Nahor": -1
      },
      "Rounded_MT": 4106,
      "Rounded_LXX": 5486,
      "selected_Shem_difference": 2
    },
    "sources": [
      "File51a §§2.1,3.1–3.3",
      "File18 §§4.1–4.2",
      "File52c §3.14"
    ],
    "opened_utc": "2026-09-27T22:41:26.339629+00:00",
    "predecessor_sha256": "09851060f453b478462087352850941d9c1e72097fcda695304666ec74bf6567",
    "results": {
      "begetting_residual_sum": 6,
      "MT_heads": [
        4106,
        4112,
        4114
      ],
      "LXX_heads": [
        5486,
        5492,
        5494
      ]
    },
    "finding": "No. Six row residuals sum+6; the selected standard versus strict Shem convention supplies the additional+2. The same decomposition applies to the supplied MT and LXX regular heads; it does not authorize upstream Gear transport.",
    "reassessment": "Resolve the cumulative −2 separately before calling the combined shift a conservation law.",
    "checks": {
      "sum": true,
      "heads": true
    },
    "closed_utc": "2026-09-27T22:41:26.339946+00:00",
    "sha256": "4d36a3fc6fe3930ede92f3f0de459daeb2be77c5c9c50b10d4927126ffefdced"
  },
  {
    "step": 493,
    "title": "Cumulative residuals and completion selection",
    "question": "Does cumulative rounding itself create the −2 change used in C481?",
    "inputs": {
      "MT_26_lifespans": [
        930,
        912,
        905,
        910,
        895,
        962,
        365,
        969,
        777,
        950,
        600,
        438,
        433,
        464,
        239,
        239,
        230,
        148,
        205,
        175,
        180,
        147,
        137,
        133,
        137,
        120
      ],
      "terminal_anchor": 1406,
      "actual_completion": 14004
    },
    "sources": [
      "File51a §§16.1–16.2",
      "File22 §5.1"
    ],
    "opened_utc": "2026-09-27T22:41:47.928076+00:00",
    "predecessor_sha256": "4d36a3fc6fe3930ede92f3f0de459daeb2be77c5c9c50b10d4927126ffefdced",
    "results": {
      "actual_sum": 12600,
      "rounded_sum": 12600,
      "positive_rounding": 12,
      "negative_rounding": -12,
      "Moses_line_heads": [
        14006,
        14006
      ],
      "completion_offset": -2
    },
    "finding": "Cumulative rounding preserves12600 and the14006 Moses-line head exactly. The−2 is the selected lower completion endpoint14004, not a cumulative rounding error. The bridge uses both row residuals and explicit endpoint selection.",
    "reassessment": "Combine the two separately explained shifts and test which endpoint alternatives preserve the anchor.",
    "checks": {
      "total": true,
      "residuals": true
    },
    "closed_utc": "2026-09-27T22:41:47.928329+00:00",
    "sha256": "191fcfd19b8f4216ab56a16ed411f0e8f1405b5a2eb2e1412f960d17370da41e"
  },
  {
    "step": 494,
    "title": "The exact residual conservation law",
    "question": "Which declared endpoint changes preserve the weighted anchor?",
    "inputs": {
      "rounded": [
        14006,
        4106
      ],
      "actual_completion": [
        14004,
        4114
      ],
      "strict_comparison": [
        14006,
        4112
      ],
      "Year6_pair": [
        14006,
        4116
      ]
    },
    "sources": [
      "File51a §§3,16",
      "File22 §§5.1,7.1",
      "File52c §3.14"
    ],
    "opened_utc": "2026-09-27T22:42:02.281825+00:00",
    "predecessor_sha256": "191fcfd19b8f4216ab56a16ed411f0e8f1405b5a2eb2e1412f960d17370da41e",
    "results": {
      "states": {
        "rounded": {
          "weighted_point": 12026,
          "shift_from_12026": 0
        },
        "actual_completion": {
          "weighted_point": 12026,
          "shift_from_12026": 0
        },
        "strict_comparison": {
          "weighted_point": "60136/5",
          "shift_from_12026": "6/5"
        },
        "Year6_pair": {
          "weighted_point": 12028,
          "shift_from_12026": 2
        }
      },
      "kernel": "4 delta_C + delta_R = 0",
      "selected_vector": [
        -2,
        8
      ],
      "general_integer_kernel": "t*(1,-4)"
    },
    "finding": "The actual completion selection lies exactly in the kernel. Strict and Year6 alternatives give shifts6/5 and2. The conserved anchor is therefore a precise relation between selected states, not invariance under every actual/rounded convention.",
    "reassessment": "Formalize the rounded path evaluator so convergence and nonconvergence can be explained by one rule.",
    "checks": {
      "completion": true,
      "strict": true,
      "year6": true
    },
    "closed_utc": "2026-09-27T22:42:02.282051+00:00",
    "sha256": "6046d8b0bd0ffcab38d96bd1834e20f236c87b3bf140ab959f4be75644722ebb"
  },
  {
    "step": 495,
    "title": "Rounded chronology as path evaluation",
    "question": "Can one rule explain both convergence and the LXX miss?",
    "inputs": {
      "anchor": 1406,
      "paths": {
        "MT_regular": [
          1650,
          1050
        ],
        "MT_cumulative": [
          9170,
          3430
        ],
        "LXX_regular": [
          2250,
          1830
        ]
      }
    },
    "sources": [
      "File52c §3.3",
      "C489"
    ],
    "opened_utc": "2026-09-27T22:42:21.243193+00:00",
    "predecessor_sha256": "6046d8b0bd0ffcab38d96bd1834e20f236c87b3bf140ab959f4be75644722ebb",
    "results": {
      "rule": "V_a(path)=a+sum I(segment); chi(path)=sum(I(segment)-segment)",
      "paths": {
        "MT_regular": {
          "raw_total": 2700,
          "reversal_gain": 7920,
          "evaluated_endpoint": 12026
        },
        "MT_cumulative": {
          "raw_total": 12600,
          "reversal_gain": -1980,
          "evaluated_endpoint": 12026
        },
        "LXX_regular": {
          "raw_total": 4080,
          "reversal_gain": 4950,
          "evaluated_endpoint": 10436
        }
      },
      "composition": "chi(P followed by Q)=chi(P)+chi(Q), for an admitted concatenation"
    },
    "finding": "Path gains are additive over retained segment lists. The MT regular gain7920 and cumulative gain−1980 offset their original9900 difference; LXX has different gains. Forgetting the partition discards necessary input.",
    "reassessment": "Measure the exact effect of only the source-admitted Noah and Shem refinements.",
    "checks": {
      "MT_convergence": true,
      "LXX_miss": true
    },
    "closed_utc": "2026-09-27T22:42:21.243412+00:00",
    "sha256": "8a4cd775dc33fc52edf7cde89eb38e1dff9f3e623e580d94d57784d9a342abdf"
  },
  {
    "step": 496,
    "title": "Refinement defects",
    "question": "When do documented refinements preserve the reversed path value?",
    "inputs": {
      "MT_regular_Noah": [
        1650,
        [
          1050,
          600
        ]
      ],
      "MT_cumulative_Shem": [
        9170,
        [
          8570,
          600
        ]
      ],
      "MT_cumulative_Noah": [
        9170,
        [
          7620,
          1550
        ]
      ],
      "LXX_regular_Noah": [
        2250,
        [
          1650,
          600
        ]
      ]
    },
    "sources": [
      "File52c §3.3",
      "C489"
    ],
    "opened_utc": "2026-09-27T22:42:34.936653+00:00",
    "predecessor_sha256": "8a4cd775dc33fc52edf7cde89eb38e1dff9f3e623e580d94d57784d9a342abdf",
    "results": {
      "defects": {
        "MT_regular_Noah": 0,
        "MT_cumulative_Shem": 990,
        "MT_cumulative_Noah": 990,
        "LXX_regular_Noah": 990
      },
      "definition": "delta_refinement=sum I(parts)-I(sum parts)"
    },
    "finding": "The MT regular refinement has defect0; both cumulative refinements and the LXX regular refinement have defect990. Thus12026 versus13016 and10436 versus11426 are outcomes of the same path rule, not separate arbitrary anchors.",
    "reassessment": "Test whether appending the documented Conquest-to-Nativity leg gives a uniform backbone continuation.",
    "checks": {
      "raw_lengths_preserved": true,
      "defects": true
    },
    "closed_utc": "2026-09-27T22:42:34.936928+00:00",
    "sha256": "3bc4c41817c5a53cc1f35b997be3e74536789539edd1e7d6c9897faab3af971a"
  },
  {
    "step": 497,
    "title": "One shared tail links12026 and14726",
    "question": "How does the documented1400 leg connect the two backbone anchors?",
    "inputs": {
      "Conquest": 1406,
      "Nativity": 6,
      "primary_reversed_sum": 10620
    },
    "sources": [
      "File52c §§3.3–3.4"
    ],
    "opened_utc": "2026-09-27T22:42:47.572297+00:00",
    "predecessor_sha256": "3bc4c41817c5a53cc1f35b997be3e74536789539edd1e7d6c9897faab3af971a",
    "results": {
      "tail": 1400,
      "reversed_tail": 4100,
      "net_anchor_change": 2700,
      "Conquest_backbone": 12026,
      "Nativity_backbone": 14726,
      "Nativity_span": 14720,
      "E_span": 16000
    },
    "finding": "Appending the shared1400 leg changes the reconstructed endpoint by4100−1400=2700. Both primary paths therefore continue together from12026 to14726. The backbone’s14720 span then expands to16000.",
    "reassessment": "Identify the decimal gain law that explains the990 and2700 increments.",
    "checks": {
      "continuation": true,
      "expansion": true
    },
    "closed_utc": "2026-09-27T22:42:47.572502+00:00",
    "sha256": "a7622ff34f06565ea4ce69b1787c1e6ffff17cb40d448a0b624d37c4e3f21ac9"
  },
  {
    "step": 498,
    "title": "Decimal gains explain the path increments",
    "question": "Which algebraic properties of decimal reversal generate the observed increments?",
    "inputs": {
      "three_digit_core": "10*(100a+10b+c)",
      "two_digit_core": "100*(10a+b)",
      "source_segments": [
        1650,
        1050,
        9170,
        3430,
        1400
      ]
    },
    "sources": [
      "File52c §1.2",
      "C481",
      "C495–C497"
    ],
    "opened_utc": "2026-09-27T22:43:04.561288+00:00",
    "predecessor_sha256": "a7622ff34f06565ea4ce69b1787c1e6ffff17cb40d448a0b624d37c4e3f21ac9",
    "results": {
      "gains": {
        "1650": 3960,
        "1050": 3960,
        "9170": -1980,
        "3430": 0,
        "1400": 2700
      },
      "three_digit_gain": "990*(c-a)",
      "two_digit_gain": "900*(b-a)",
      "general_invariant": "digit sum mod9; with10^k placeholders, gain divisible by9*10^k",
      "not_23_preserving_example": {
        "input": 230,
        "inverse": 320,
        "inverse_mod23": 21
      }
    },
    "finding": "The primary990 increments and the2700 tail increment are decimal-place effects. Reversal does not by itself preserve the23-lattice; its conjunction with the Key families still requires particular source inputs.",
    "reassessment": "Determine the exact compatible scaling and translation rules for the rounded path module.",
    "checks": {
      "gains": true,
      "negative23": true
    },
    "closed_utc": "2026-09-27T22:43:04.561498+00:00",
    "sha256": "80b38f1933d3c37d67d4e2333ccff17c6e0df5268b132a6a2c803e23a6f197f4"
  },
  {
    "step": 499,
    "title": "Where path evaluation is compatible with affine geometry",
    "question": "Which operations commute with the path evaluator without losing segmentation?",
    "inputs": {
      "parts": [
        1650,
        1050
      ],
      "anchor": 1406,
      "test_translation": 215,
      "decimal_scale": 10
    },
    "sources": [
      "File52c §1.2",
      "Strategy §§5C–5F",
      "C495"
    ],
    "opened_utc": "2026-09-27T22:43:19.757713+00:00",
    "predecessor_sha256": "80b38f1933d3c37d67d4e2333ccff17c6e0df5268b132a6a2c803e23a6f197f4",
    "results": {
      "translated_endpoint": 12241,
      "scaled_endpoint": 120260,
      "original_endpoint": 12026,
      "whole_span_inverse": 7200,
      "segmented_inverse_sum": 10620,
      "general_rules": [
        "all dates and anchor translated together: V shifts by same t",
        "all durations and anchor scaled by10^k: V scales by10^k",
        "I(s+t) need not equal I(s)+I(t)"
      ]
    },
    "finding": "The module respects a change of origin and decimal rescaling when the entire declared object moves. It does not respect erasing segmentation. These are mathematical compatibility rules, not permission to translate source chronologies outside their admitted domains.",
    "reassessment": "Connect the actual field to the three calendar Keys through their common measure.",
    "checks": {
      "translation": true,
      "scale": true,
      "nonadditive": true
    },
    "closed_utc": "2026-09-27T22:43:19.757928+00:00",
    "sha256": "ce6d76fb4adda85cc41fc08521f6dbacb1b1aeffd236bf259317221b9aae69fa"
  },
  {
    "step": 500,
    "title": "The calendar family’s common measure",
    "question": "Do the three Keys share a conserved quantity despite producing different year counts?",
    "inputs": {
      "ratios": {
        "E": "25/23",
        "P": "70/69",
        "J": "300/299"
      },
      "year_lengths": {
        "E": 336,
        "P": 360,
        "J": 364
      },
      "source_seed": 12558
    },
    "sources": [
      "Strategy §3.3",
      "File52c §3.15",
      "C481"
    ],
    "opened_utc": "2026-09-27T22:43:36.399128+00:00",
    "predecessor_sha256": "ce6d76fb4adda85cc41fc08521f6dbacb1b1aeffd236bf259317221b9aae69fa",
    "results": {
      "E": {
        "calibration": "8400/23",
        "seed_output": 13650,
        "modeled_day_volume": 4586400
      },
      "P": {
        "calibration": "8400/23",
        "seed_output": 12740,
        "modeled_day_volume": 4586400
      },
      "J": {
        "calibration": "8400/23",
        "seed_output": 12600,
        "modeled_day_volume": 4586400
      }
    },
    "finding": "All three use K=8400/23 and give the same modeled day-volume4586400 for seed12558. The reusable rule is K_d(s)=(K/d)s. This explains common measurement, not every selected chronological placement.",
    "reassessment": "Find the common integral input domain and apply it to the Jared–Noah–Flood field.",
    "checks": {
      "calibration": true,
      "volume": true
    },
    "closed_utc": "2026-09-27T22:43:36.399427+00:00",
    "sha256": "d42d5541b7b56a6b572d1f47c84cc3c164902a1d8468fc4199f99ad243a12eab"
  },
  {
    "step": 501,
    "title": "The three-Key integral domain",
    "question": "Why does the middle member admit all three integral calendar outputs?",
    "inputs": {
      "Jared": 8372,
      "Noah_G1": 8970,
      "Flood_G2": 9568,
      "Creation": 7912
    },
    "sources": [
      "File52c §3.15",
      "C500"
    ],
    "opened_utc": "2026-09-27T22:43:53.341661+00:00",
    "predecessor_sha256": "d42d5541b7b56a6b572d1f47c84cc3c164902a1d8468fc4199f99ad243a12eab",
    "results": {
      "common_input_lattice": 897,
      "rows": {
        "Jared": {
          "E": 9100,
          "P": "25480/3",
          "J": 8400,
          "all_integral": false
        },
        "Noah_G1": {
          "E": 9750,
          "P": 9100,
          "J": 9000,
          "all_integral": true
        },
        "Flood_G2": {
          "E": 10400,
          "P": "29120/3",
          "J": 9600,
          "all_integral": false
        },
        "Creation": {
          "E": 8600,
          "P": "24080/3",
          "J": "103200/13",
          "all_integral": false
        }
      },
      "JNF_mod3_coefficients": [
        2,
        0,
        1
      ]
    },
    "finding": "The common integral span domain is897Z, since897=lcm(23,69,299). For598m, E and J are integral for all integer m; P additionally needs3|m. Of14,15,16 only Noah’s15 qualifies. This explains the three-Key middle role from the existing progression.",
    "reassessment": "Use those outputs to derive the shared2926 endpoint and assess which placement assumptions remain.",
    "checks": {
      "lattice": true,
      "middle_only": true
    },
    "closed_utc": "2026-09-27T22:43:53.341906+00:00",
    "sha256": "3ad039dfc81a6b222c3776f8f9384647015ccaf55a0585aaa31e4e508fecbee3"
  }
]