[
  {
    "step": 632,
    "title": "Freeze the calendar-half source family",
    "question": "What complete source packet is needed before testing File70’s three calendar bridges?",
    "inputs": {
      "restored_Creation_rail": [
        4251,
        4244,
        4237
      ],
      "standard_Creation_rail": [
        4121,
        4114,
        4107
      ],
      "exposure_nodes": [
        4238,
        4108
      ],
      "Joseph_birth_descent_elevation": [
        1915,
        1898,
        1885
      ],
      "Joseph_rail": [
        1885,
        1878,
        1871
      ],
      "regular_Cainan_difference": 130
    },
    "sources": [
      "File70 §§6.1–6.7; source state register"
    ],
    "opened_utc": "2026-09-28T00:56:25.987258+00:00",
    "predecessor_sha256": "C631:8da995fbc41dba4a3b78b59a6a6a316b712980b5052087bc963cd75e15db6351",
    "results": {
      "packet": {
        "path": "model/calendar_half_inputs.json",
        "sha256": "c3794e48f499ce37b49dfc94f7ead80771e50a487e4331f9c599e8e537886578",
        "bytes": 975
      },
      "primary_registers": {
        "Prophetic": [
          4238,
          1898,
          13,
          180
        ],
        "Priestly": [
          4237,
          1885,
          14,
          168
        ],
        "Enochian": [
          4251,
          1885,
          13,
          182
        ]
      }
    },
    "finding": "The complete packet fixes two Creation states, Joseph’s corresponding nodes, and the three13/14/13 half-year counts before calculation. The test can now explain the family from one labelled geometry.",
    "reassessment": "Generate the corresponding-node translation of the two seven-plus-seven rails.",
    "checks": {
      "source_section_present": true,
      "named_source_nodes": true
    },
    "closed_utc": "2026-09-28T00:56:25.988288+00:00",
    "sha256": "eeece7023cc8386382b385b9ec212f6eef1a499feaea2261e04d13592d5f4f4e"
  },
  {
    "step": 633,
    "title": "Generate the corresponding Creation–Joseph rail map",
    "question": "Do the two source seven-plus-seven rails require more than one translation?",
    "inputs": {
      "Creation": [
        4251,
        4244,
        4237
      ],
      "Joseph": [
        1885,
        1878,
        1871
      ]
    },
    "sources": [
      "File70 §6.3"
    ],
    "opened_utc": "2026-09-28T00:56:54.571747+00:00",
    "predecessor_sha256": "eeece7023cc8386382b385b9ec212f6eef1a499feaea2261e04d13592d5f4f4e",
    "results": {
      "corresponding_spans": [
        2366,
        2366,
        2366
      ],
      "rail_gaps": [
        [
          7,
          7
        ],
        [
          7,
          7
        ]
      ],
      "translation": 2366
    },
    "finding": "One translation of2366 carries all three source nodes and preserves the7+7 partition. The three matches are dependent coordinates of one rigid relation.",
    "reassessment": "Generate every cross-rail span to distinguish the special diagonals from the whole family.",
    "checks": {
      "translation": true,
      "shape": true
    },
    "closed_utc": "2026-09-28T00:56:54.571916+00:00",
    "sha256": "0546e755ab9dd83737899b935cd48b0288025b0ea9210c04ce267c96aa61c6e8"
  },
  {
    "step": 634,
    "title": "Generate the full cross-rail matrix",
    "question": "Does one indexed formula account for all nine span comparisons?",
    "inputs": {
      "head_difference": 2366,
      "rail_step": 7,
      "indices": [
        0,
        1,
        2
      ]
    },
    "sources": [
      "File70 §§6.3,6.5; derived completion of source geometry"
    ],
    "opened_utc": "2026-09-28T00:57:07.226648+00:00",
    "predecessor_sha256": "0546e755ab9dd83737899b935cd48b0288025b0ea9210c04ce267c96aa61c6e8",
    "results": {
      "span_matrix": [
        [
          2366,
          2373,
          2380
        ],
        [
          2359,
          2366,
          2373
        ],
        [
          2352,
          2359,
          2366
        ]
      ],
      "multiplicities": {
        "2352": 1,
        "2359": 2,
        "2366": 3,
        "2373": 2,
        "2380": 1
      },
      "formula": "D(i,j)=2366+7(j−i)",
      "source_selected_extremes": [
        2352,
        2366,
        2380
      ]
    },
    "finding": "The complete matrix has five span values with multiplicities1,2,3,2,1. Minimum, corresponding and maximum spans are2366−14,2366,2366+14; the other entries are generated comparisons, not additional source appointments.",
    "reassessment": "Explain the separate exposure span using its two thirteen-year flanks.",
    "checks": {
      "extremes": true,
      "frequency": true,
      "matrix_from_dates": true
    },
    "closed_utc": "2026-09-28T00:57:07.226929+00:00",
    "sha256": "3bef9066b0c13130bfd753799a43e2aaee36086aa9fcaf0f767da80df7c64879"
  },
  {
    "step": 635,
    "title": "Reconstruct the exposure bridge from its flanks",
    "question": "How does the13+2340+13 path relate to the corresponding2366 translation?",
    "inputs": {
      "path": [
        4251,
        4238,
        1898,
        1885
      ]
    },
    "sources": [
      "File70 §§6.1,6.4"
    ],
    "opened_utc": "2026-09-28T00:57:18.616719+00:00",
    "predecessor_sha256": "3bef9066b0c13130bfd753799a43e2aaee36086aa9fcaf0f767da80df7c64879",
    "results": {
      "partition": [
        13,
        2340,
        13
      ],
      "total": 2366,
      "calendar_difference": 26,
      "Joseph_ages": [
        17,
        30
      ]
    },
    "finding": "The source path supplies13-year flanks around2340, giving2366. The26 added years are exactly6.5 copies of the360-to364 calendar difference. Joseph’s ages17 and30 provide the same13-year lower flank.",
    "reassessment": "Compare all three calendar spans under their own calibrated Keys.",
    "checks": {
      "partition": true,
      "calendar_gain": true,
      "ages": true
    },
    "closed_utc": "2026-09-28T00:57:18.617072+00:00",
    "sha256": "d4fba769a5c3e22462d9fe6614b02309624c1ab71009705221d66170acf86e66"
  },
  {
    "step": 636,
    "title": "Normalize the three calendar registers",
    "question": "Do the three spans become one common output under their respective Keys?",
    "inputs": {
      "spans": [
        2340,
        2352,
        2366
      ],
      "days": [
        360,
        336,
        364
      ],
      "Keys": [
        "70/69",
        "25/23",
        "300/299"
      ]
    },
    "sources": [
      "File70 §6.7; C586 calendar calibration"
    ],
    "opened_utc": "2026-09-28T00:57:35.899669+00:00",
    "predecessor_sha256": "d4fba769a5c3e22462d9fe6614b02309624c1ab71009705221d66170acf86e66",
    "results": {
      "normalized_year_counts": [
        "13/2",
        7,
        "13/2"
      ],
      "Key_outputs": [
        "54600/23",
        "58800/23",
        "54600/23"
      ],
      "output_ratio": "13:14:13",
      "half_year_unit": "4200/23"
    },
    "finding": "The Prophetic and Enochian arms normalize to6.5 calendar years; the Priestly arm to7. Their outputs are13,14,13 copies of one calibrated half-year. The family preserves two count classes, not one undifferentiated result.",
    "reassessment": "Determine what equal transformed spans imply when their held heads differ.",
    "checks": {
      "normalization": true,
      "outputs": true,
      "two_classes": true
    },
    "closed_utc": "2026-09-28T00:57:35.899892+00:00",
    "sha256": "17fb6bac910067917df66b14db474b381af070138efcdb0c206f8674725e9eef"
  },
  {
    "step": 637,
    "title": "Carry normalized equality into anchored placement",
    "question": "Do equal Prophetic and Enochian outputs imply an identical dated endpoint here?",
    "inputs": {
      "Prophetic_head": 4238,
      "Enochian_head": 4251,
      "common_output": "54600/23"
    },
    "sources": [
      "File70 source endpoints; derived anchored-Key diagnostic"
    ],
    "opened_utc": "2026-09-28T00:57:45.785330+00:00",
    "predecessor_sha256": "17fb6bac910067917df66b14db474b381af070138efcdb0c206f8674725e9eef",
    "results": {
      "Prophetic_generated_endpoint": "42874/23",
      "Enochian_generated_endpoint": "43173/23",
      "endpoint_difference": 13,
      "frame_adjusted_Enochian_endpoint": "42874/23"
    },
    "finding": "The generated endpoints differ13 because the held heads differ13. Translating the Enochian output frame by−13 aligns them. Equal normalized spans explain the shape; source anchor differences explain its placement. These fractional outputs are diagnostics, not adopted event dates.",
    "reassessment": "Derive why the Priestly minimum has fourteen half-year units.",
    "checks": {
      "difference": true,
      "frame_relation": true
    },
    "closed_utc": "2026-09-28T00:57:45.785544+00:00",
    "sha256": "6913761b17e777dff8eec192689d88922a0dcae2329697f6ae654fe48fddd2c4"
  },
  {
    "step": 638,
    "title": "Explain the Priestly minimum by factor structure",
    "question": "Why does subtracting the14-year rail width from13×182 produce14×168?",
    "inputs": {
      "corresponding_count": 13,
      "Enochian_half": 182,
      "rail_width": 14
    },
    "sources": [
      "File70 §§6.2–6.5"
    ],
    "opened_utc": "2026-09-28T00:57:56.936051+00:00",
    "predecessor_sha256": "6913761b17e777dff8eec192689d88922a0dcae2329697f6ae654fe48fddd2c4",
    "results": {
      "corresponding_factorization": [
        14,
        169
      ],
      "minimum_factorization": [
        14,
        168
      ],
      "Priestly_half": 168,
      "identity": "13×182−14=14(169−1)=14×168"
    },
    "finding": "The Priestly minimum follows from182=14×13 and168=13²−1. The common14-year width turns the corresponding vector into fourteen Priestly halves. This explains the change from13 to14 calendar units through the rail geometry.",
    "reassessment": "Test whether the combined half-calendar conditions select a unique count or a congruence family.",
    "checks": {
      "factorization": true,
      "minimum": true,
      "difference_of_squares": true
    },
    "closed_utc": "2026-09-28T00:57:56.936249+00:00",
    "sha256": "48e03ab500abe657bfcd30dd81ee12ec3744e5ab24b2d6c021bf1052845dc452"
  },
  {
    "step": 639,
    "title": "Solve the two-calendar compatibility equation",
    "question": "What count family permits an Enochian corresponding span and a Priestly minimum fourteen years shorter?",
    "inputs": {
      "equation": "182m−14=168n",
      "positive_integer_counts": true
    },
    "sources": [
      "Derived from File70 §6 source geometry"
    ],
    "opened_utc": "2026-09-28T00:58:22.881303+00:00",
    "predecessor_sha256": "48e03ab500abe657bfcd30dd81ee12ec3744e5ab24b2d6c021bf1052845dc452",
    "results": {
      "reduced_equation": "13m−12n=1",
      "general_solution": "m=1+12q; n=1+13q",
      "examples_m_n": [
        [
          1,
          1
        ],
        [
          13,
          14
        ],
        [
          25,
          27
        ],
        [
          37,
          40
        ]
      ],
      "source_choice_q": 1
    },
    "finding": "The pair of calendar requirements has an infinite integer family. Its source member is m=13,n=14; the smaller m=n=1 also fits the two-calendar equation. The exposure condition must supply any stronger selection.",
    "reassessment": "Add the fixed thirteen-year exposure flanks and solve the complete three-calendar system.",
    "checks": {
      "examples": true,
      "source_member": true,
      "not_unique_pair": true
    },
    "closed_utc": "2026-09-28T00:58:22.881481+00:00",
    "sha256": "2d75bc9bfb77ad832fbb24b55007d44225e7432b192eeef77c2166cdfd940f33"
  },
  {
    "step": 640,
    "title": "Solve the complete three-calendar congruence family",
    "question": "Do the fixed fourteen-year rail and thirteen-year flanks select the source count triple as the smallest positive solution?",
    "inputs": {
      "conditions": [
        "T=182m",
        "T−14=168n",
        "T−26=180p"
      ],
      "counts": "positive integers"
    },
    "sources": [
      "File70 §6 geometry; derived integer compatibility theorem"
    ],
    "opened_utc": "2026-09-28T00:58:46.567888+00:00",
    "predecessor_sha256": "2d75bc9bfb77ad832fbb24b55007d44225e7432b192eeef77c2166cdfd940f33",
    "results": {
      "m_residue_mod180": [
        13
      ],
      "general_T": "2366+32760q",
      "general_counts": "m=13+180q; n=14+195q; p=13+182q",
      "examples": [
        {
          "q": 0,
          "T": 2366,
          "m": 13,
          "n": 14,
          "p": 13
        },
        {
          "q": 1,
          "T": 35126,
          "m": 193,
          "n": 209,
          "p": 195
        },
        {
          "q": 2,
          "T": 67886,
          "m": 373,
          "n": 404,
          "p": 377
        }
      ],
      "least_positive_solution": [
        2366,
        13,
        14,
        13
      ]
    },
    "finding": "With the source offsets fixed, the full system has T=2366+32760q. Its least positive solution is exactly the source2366 and13/14/13 half-count triple. This is a conditional local minimality result, not a claim of a globally minimal chronology.",
    "reassessment": "Relate the congruence period to the calendar lattice, then test the source no-Cainan companion.",
    "checks": {
      "fundamental_residue": true,
      "all_three_equations": true,
      "least_positive": true
    },
    "closed_utc": "2026-09-28T00:58:46.568078+00:00",
    "sha256": "623fd5df259934d6c3ff7cec267048b2c6c0b361546a0a0f59ddddd9c1f4a956"
  },
  {
    "step": 641,
    "title": "Identify the calendar compatibility period",
    "question": "Why is the full congruence period32760, and how does it meet the earlier common-volume family?",
    "inputs": {
      "half_calendars": [
        168,
        180,
        182
      ],
      "full_calendars": [
        336,
        360,
        364
      ]
    },
    "sources": [
      "C640; File12 calendar definitions; C575"
    ],
    "opened_utc": "2026-09-28T00:58:58.617439+00:00",
    "predecessor_sha256": "623fd5df259934d6c3ff7cec267048b2c6c0b361546a0a0f59ddddd9c1f4a956",
    "results": {
      "half_calendar_lcm": 32760,
      "full_calendar_lcm": 65520,
      "previous_volume_coefficient": 327600,
      "ratios": [
        2,
        10
      ]
    },
    "finding": "The period32760 is the least common multiple of the three half-calendars. Doubling gives65520 for full calendars; the earlier327600 common-volume coefficient is ten half-periods. The numerical link comes from the same calendar denominators, with units retained.",
    "reassessment": "Execute the no-Cainan rail companion and locate which calendar divisibilities it preserves.",
    "checks": {
      "period": true,
      "previous_volume": true,
      "counts_increment": true
    },
    "closed_utc": "2026-09-28T00:58:58.617609+00:00",
    "sha256": "aca507fc8cb4d8a7ff368876b5cf8e91a3c68205120bedafce3f964c098b542e"
  },
  {
    "step": 642,
    "title": "Reconstruct the no-Cainan companion",
    "question": "Which relations survive when the Creation rail alone moves130?",
    "inputs": {
      "standard_Creation": [
        4121,
        4114,
        4107
      ],
      "Joseph": [
        1885,
        1878,
        1871
      ],
      "standard_exposure": 4108
    },
    "sources": [
      "File70 §§6.1,6.6"
    ],
    "opened_utc": "2026-09-28T00:59:33.175668+00:00",
    "predecessor_sha256": "aca507fc8cb4d8a7ff368876b5cf8e91a3c68205120bedafce3f964c098b542e",
    "results": {
      "span_family": [
        2210,
        2222,
        2236,
        2250
      ],
      "corresponding_spans": [
        2236,
        2236,
        2236
      ],
      "calendar_half_counts": [
        "221/18",
        "1111/84",
        "86/7"
      ],
      "shift_from_restored": 130
    },
    "finding": "Removing130 preserves both7+7 rails and all their relative diagonals, giving2236 as the corresponding translation. It changes the calendar counts to nonintegers, so the restored state’s13/14/13 specialization is not automatic from rail shape alone.",
    "reassessment": "Ask whether the fixed standard state and three-calendar conditions select130 as the least nonnegative correction.",
    "checks": {
      "companion": true,
      "shape": true,
      "counts_changed": true
    },
    "closed_utc": "2026-09-28T00:59:33.175833+00:00",
    "sha256": "bfffe3745aa25cf6e552ea3071d48994bddd5bd76620a6756efff51414405fdc"
  },
  {
    "step": 643,
    "title": "Solve the source-state correction congruence",
    "question": "Given the standard2236 vector, what correction first enters the complete calendar-compatible class?",
    "inputs": {
      "standard_vector": 2236,
      "compatible_class": "2366+32760q",
      "permitted_test": "nonnegative integer correction to Creation rail only"
    },
    "sources": [
      "C640,C642; File70 regular Cainan comparison"
    ],
    "opened_utc": "2026-09-28T00:59:50.845969+00:00",
    "predecessor_sha256": "bfffe3745aa25cf6e552ea3071d48994bddd5bd76620a6756efff51414405fdc",
    "results": {
      "correction_class": "130+32760q",
      "least_nonnegative": 130,
      "examples": [
        130,
        32890,
        65650
      ],
      "source_regular_Cainan": 130
    },
    "finding": "With the standard vector and the14/26 offsets fixed, the least nonnegative correction satisfying all three calendar conditions is130. This recovers the supplied regular-Cainan increment conditionally; it does not infer an insertion history or change the frozen MT state.",
    "reassessment": "Use the supplied Enoch close to reconstruct the Priestly minimum’s internal partition.",
    "checks": {
      "least": true,
      "compatible": true
    },
    "closed_utc": "2026-09-28T00:59:50.846140+00:00",
    "sha256": "2d76bad693f618f2534e23e922c8d6ae92c4cca38f6b11bd4c7b6dc807d3a113"
  },
  {
    "step": 644,
    "title": "Recover the Enoch partition of the Priestly minimum",
    "question": "What additional placement does the appendix’s supplied Enoch close contribute?",
    "inputs": {
      "path": [
        4237,
        3257,
        1885
      ],
      "Enoch_status": "pre-existing secondary source comparison; no Gear transport"
    },
    "sources": [
      "File70 Appendix D.2–D.4"
    ],
    "opened_utc": "2026-09-28T01:00:01.628554+00:00",
    "predecessor_sha256": "2d76bad693f618f2534e23e922c8d6ae92c4cca38f6b11bd4c7b6dc807d3a113",
    "results": {
      "partition": [
        980,
        1372
      ],
      "jubilee49_coefficients": [
        20,
        28
      ],
      "primitive196_coefficients": [
        5,
        7
      ],
      "whole": 2352
    },
    "finding": "The supplied Enoch close partitions2352 as980+1372, or20+28 jubilee49 units. The reduced ratio is5:7. The total follows from the rail geometry; this particular internal cut depends on the separately supplied3257 role.",
    "reassessment": "Test the corresponding Enoch head to identify which part of the partition is role-specific.",
    "checks": {
      "partition": true,
      "total": true,
      "ratio": true
    },
    "closed_utc": "2026-09-28T01:00:01.628730+00:00",
    "sha256": "c26f666a0f60b1a78231c0ab16fe7c353022d0aa312dbcfb172e373a516d55a2"
  },
  {
    "step": 645,
    "title": "Test the Enoch partition role",
    "question": "Does the supplied Enoch head give the same internal partition as its close?",
    "inputs": {
      "head": 3264,
      "close": 3257,
      "outer": [
        4237,
        1885
      ]
    },
    "sources": [
      "File70 Appendix D.1–D.4",
      "C644"
    ],
    "opened_utc": "2026-09-28T01:03:53.595962+00:00",
    "predecessor_sha256": "c26f666a0f60b1a78231c0ab16fe7c353022d0aa312dbcfb172e373a516d55a2",
    "results": {
      "head_partition": [
        973,
        1379
      ],
      "close_partition": [
        980,
        1372
      ],
      "head_49_coefficients": [
        "139/7",
        "197/7"
      ]
    },
    "finding": "Replacing the supplied close with the head transfers seven years between the two arms and preserves2352. The5:7 partition belongs to the close role; it is not a property of any Enoch placement.",
    "reassessment": "Recover the complete two-node Enoch comparison from its seven-year rails.",
    "checks": {
      "head": true,
      "transfer": true,
      "total": true
    },
    "closed_utc": "2026-09-28T01:03:53.596210+00:00",
    "sha256": "5051984995800a79412c616ea15b3a8e1034afce5a7ba02b08e6e0c5e5898ca9"
  },
  {
    "step": 646,
    "title": "Generate the Creation–Enoch rail square",
    "question": "Can one translation recover all four admitted Creation–Enoch spans?",
    "inputs": {
      "upper": [
        4244,
        4237
      ],
      "lower": [
        3264,
        3257
      ]
    },
    "sources": [
      "File70 Appendix D.1"
    ],
    "opened_utc": "2026-09-28T01:04:02.788349+00:00",
    "predecessor_sha256": "5051984995800a79412c616ea15b3a8e1034afce5a7ba02b08e6e0c5e5898ca9",
    "results": {
      "matrix": [
        [
          980,
          987
        ],
        [
          973,
          980
        ]
      ],
      "translation": 980,
      "rail": 7
    },
    "finding": "The four comparisons are one seven-year rail translated by980: corresponding980s and crossed973/987. This reuses the same rail generator as the larger calendar family.",
    "reassessment": "Ask whether the source’s nested14/140/980 spans share one normalized shape.",
    "checks": {
      "whole_matrix": true,
      "entries": true
    },
    "closed_utc": "2026-09-28T01:04:02.788514+00:00",
    "sha256": "e43acebadfd5a87cfe91676d5933ebd599a2af327f809f6ec2b87cd1f3b4a4bc"
  },
  {
    "step": 647,
    "title": "Normalize the nested bilateral spans",
    "question": "What structure is shared by the source’s14,140 and980 layers?",
    "inputs": {
      "widths": [
        14,
        140,
        980
      ],
      "halves": [
        7,
        70,
        490
      ]
    },
    "sources": [
      "File70 Appendix D.5"
    ],
    "opened_utc": "2026-09-28T01:04:13.636096+00:00",
    "predecessor_sha256": "e43acebadfd5a87cfe91676d5933ebd599a2af327f809f6ec2b87cd1f3b4a4bc",
    "results": {
      "normalized_halves": [
        [
          1,
          1
        ],
        [
          1,
          1
        ],
        [
          1,
          1
        ]
      ],
      "scale_from14": [
        1,
        10,
        70
      ]
    },
    "finding": "The three layers share the bilateral1|1 shape at scales1,10,70. This establishes nested geometric scale, without creating an appointment at an unsupplied midpoint.",
    "reassessment": "Test the more informative five-node Creation–Terah refinement rather than stopping at bilateral similarity.",
    "checks": {
      "halves": true,
      "scales": true
    },
    "closed_utc": "2026-09-28T01:04:13.636323+00:00",
    "sha256": "eebd35943fcf34a0390ba6b207d01d4c46454ddf6e2ca10563c2efe7cab6071d"
  },
  {
    "step": 648,
    "title": "Recover the five-node Creation refinement",
    "question": "Can one small template reproduce both standard and restored Creation refinements?",
    "inputs": {
      "standard": [
        4121,
        4115,
        4114,
        4108,
        4107
      ],
      "restored": [
        4251,
        4245,
        4244,
        4238,
        4237
      ],
      "template": [
        7,
        1,
        0,
        -6,
        -7
      ]
    },
    "sources": [
      "File70 §§2.3,3.2; A.3"
    ],
    "opened_utc": "2026-09-28T01:04:26.557313+00:00",
    "predecessor_sha256": "eebd35943fcf34a0390ba6b207d01d4c46454ddf6e2ca10563c2efe7cab6071d",
    "results": {
      "generated": [
        [
          4121,
          4115,
          4114,
          4108,
          4107
        ],
        [
          4251,
          4245,
          4244,
          4238,
          4237
        ]
      ],
      "gaps": [
        6,
        1,
        6,
        1
      ],
      "component_translation": [
        130,
        130,
        130,
        130,
        130
      ]
    },
    "finding": "Both Creation states are the same five-position template centered at4114 or4244; regular Cainan changes every coordinate by130 and leaves the6|1|6|1 refinement intact.",
    "reassessment": "Test the complete Terah refinement against this template.",
    "checks": {
      "standard": true,
      "restored": true,
      "translation": true
    },
    "closed_utc": "2026-09-28T01:04:26.557526+00:00",
    "sha256": "55f515ca546e718d153b292e3e2f70d5c297ee2da5b2e4998114b15c6dd4cec4"
  },
  {
    "step": 649,
    "title": "Map Creation’s entire refinement to Terah",
    "question": "Does the tenfold scale preserve all four subdivisions and five roles?",
    "inputs": {
      "creation": [
        4121,
        4115,
        4114,
        4108,
        4107
      ],
      "terah": [
        2296,
        2236,
        2226,
        2166,
        2156
      ],
      "centers": [
        4114,
        2226
      ]
    },
    "sources": [
      "File70 §§2.3,3.2,4.2; A.2–A.3"
    ],
    "opened_utc": "2026-09-28T01:04:38.874545+00:00",
    "predecessor_sha256": "55f515ca546e718d153b292e3e2f70d5c297ee2da5b2e4998114b15c6dd4cec4",
    "results": {
      "mapped": [
        2296,
        2236,
        2226,
        2166,
        2156
      ],
      "terah_gaps": [
        60,
        10,
        60,
        10
      ],
      "normalized_roles": [
        7,
        1,
        0,
        -6,
        -7
      ]
    },
    "finding": "One affine map carries the complete Creation6|1|6|1 refinement into Terah60|10|60|10. The correspondence is between structural positions; the source’s biographical and comparison roles remain distinct.",
    "reassessment": "Determine which broader three-node families are projections of this refined template.",
    "checks": {
      "all_five": true,
      "refinement": true
    },
    "closed_utc": "2026-09-28T01:04:38.874736+00:00",
    "sha256": "982f58d3ce265d83088399737601350b1e213352f64319e8dd8df35e5c84138d"
  },
  {
    "step": 650,
    "title": "Locate the common coarse rail",
    "question": "Which supplied triples share the same bilateral projection?",
    "inputs": {
      "triples": [
        [
          4121,
          4114,
          4107
        ],
        [
          4251,
          4244,
          4237
        ],
        [
          2296,
          2226,
          2156
        ],
        [
          1929,
          1922,
          1915
        ],
        [
          1885,
          1878,
          1871
        ]
      ],
      "centers": [
        4114,
        4244,
        2226,
        1922,
        1878
      ],
      "steps": [
        7,
        7,
        70,
        7,
        7
      ]
    },
    "sources": [
      "File70 §§3–6; A.3,A.5,A.6"
    ],
    "opened_utc": "2026-09-28T01:04:52.873999+00:00",
    "predecessor_sha256": "982f58d3ce265d83088399737601350b1e213352f64319e8dd8df35e5c84138d",
    "results": {
      "normalized": [
        [
          1,
          0,
          -1
        ],
        [
          1,
          0,
          -1
        ],
        [
          1,
          0,
          -1
        ],
        [
          1,
          0,
          -1
        ],
        [
          1,
          0,
          -1
        ]
      ],
      "refinement_projection": [
        0,
        2,
        4
      ]
    },
    "finding": "All five supplied triples normalize to1|0|-1. Creation and Terah additionally share the five-node refinement; Jacob and Joseph establish the coarse rail only. A shared outer shape does not supply missing inner events.",
    "reassessment": "Consolidate the first20 steps into an explanation of geometry versus selected calendar placement.",
    "checks": {
      "all_triples": true,
      "projection": true
    },
    "closed_utc": "2026-09-28T01:04:52.874257+00:00",
    "sha256": "e4c24280b4d4426f3ceec817198a956ebe03ed332b45f3e95d2b601944e35429"
  },
  {
    "step": 651,
    "title": "Consolidate the rail and refinement families",
    "question": "What is the shortest supported explanation after the first20 steps?",
    "inputs": {
      "families": [
        "calendar rails",
        "five-position Creation–Terah refinement",
        "coarse Jacob/Joseph rails"
      ],
      "scope": "source-conditioned geometry"
    },
    "sources": [
      "C632–C650",
      "Research Strategy"
    ],
    "opened_utc": "2026-09-28T01:05:24.402267+00:00",
    "predecessor_sha256": "e4c24280b4d4426f3ceec817198a956ebe03ed332b45f3e95d2b601944e35429",
    "results": {
      "artifact": {
        "path": "deliverables/C651_Interim_Synthesis.md",
        "sha256": "ff98f9808fb24b7648ba2eeb7f8e0a1a23508c84f34e2dae154bb7f095f750ab",
        "bytes": 1119
      },
      "completed_range": [
        632,
        651
      ],
      "core_rules": [
        "Dij=T+7(j−i)",
        "R(c,u)=c+u(7,1,0,−6,−7)",
        "T=2366+32760q"
      ]
    },
    "finding": "Twenty sequential steps now explain two whole-family generators and distinguish their inherited shapes from the source-selected placements. Further scalar boundary searches are lower priority than the prepared reflection and cumulative families.",
    "reassessment": "Reconstruct the source’s Jacob-centered reflection as a complete event-role object.",
    "checks": {
      "range": true,
      "calendar": true,
      "refinement": true
    },
    "closed_utc": "2026-09-28T01:05:24.402497+00:00",
    "sha256": "45e5a551cfa6f6c155c1c4932f71c7c08997ccbf79e0d2110994f1269d2d9e77"
  },
  {
    "step": 652,
    "title": "Generate Jacob’s death-centered reflection",
    "question": "Does one reflection recover every supplied paired node?",
    "inputs": {
      "center": 1859,
      "path": [
        1936,
        1929,
        1859,
        1789,
        1782
      ],
      "secondary_role": "1789 traditional Judah death"
    },
    "sources": [
      "File70 §5.3; A.5 JB001–016"
    ],
    "opened_utc": "2026-09-28T01:05:56.462713+00:00",
    "predecessor_sha256": "45e5a551cfa6f6c155c1c4932f71c7c08997ccbf79e0d2110994f1269d2d9e77",
    "results": {
      "reflected": [
        1782,
        1789,
        1859,
        1929,
        1936
      ],
      "gaps": [
        7,
        70,
        70,
        7
      ],
      "centered": [
        77,
        70,
        0,
        -70,
        -77
      ]
    },
    "finding": "Reflection about Jacob1859 reverses the full source path, with offsets77,70,0,−70,−77. The70|70 body and seven-year wings are one symmetric object; the traditional Judah role remains secondary.",
    "reassessment": "Compare this death-centered object with Jacob’s biographical70|7|70 path.",
    "checks": {
      "reflection": true,
      "gaps": true
    },
    "closed_utc": "2026-09-28T01:05:56.463188+00:00",
    "sha256": "f1a71412af35345e94de061a755c6f5c33b1db5869be9e93a2775ca2382f45d3"
  },
  {
    "step": 653,
    "title": "Separate Jacob’s two symmetric objects",
    "question": "How do the biographical and death-centered patterns connect?",
    "inputs": {
      "biography": [
        2006,
        1936,
        1929,
        1859
      ],
      "death_centered": [
        1936,
        1929,
        1859,
        1789,
        1782
      ]
    },
    "sources": [
      "File70 §5.3; A.5"
    ],
    "opened_utc": "2026-09-28T01:06:09.168697+00:00",
    "predecessor_sha256": "f1a71412af35345e94de061a755c6f5c33b1db5869be9e93a2775ca2382f45d3",
    "results": {
      "biography_gaps": [
        70,
        7,
        70
      ],
      "biography_center": "3865/2",
      "reflection": [
        1859,
        1929,
        1936,
        2006
      ],
      "centers_separation": "147/2"
    },
    "finding": "Jacob’s lifespan path is a different symmetric object:70|7|70 around1932.5, while the later reflection is centered at his death1859. They share sourced nodes1936/1929/1859 but cannot be collapsed into one center.",
    "reassessment": "Test the30/40 subdivision family to see what its junction equality depends on.",
    "checks": {
      "gaps": true,
      "symmetry": true,
      "total": true
    },
    "closed_utc": "2026-09-28T01:06:09.168994+00:00",
    "sha256": "adbcfc15390dec89a47f87874a4910b7fc6d90e3dd55e9aec748e1315f527dc8"
  },
  {
    "step": 654,
    "title": "Reconstruct the secondary30/40 junction",
    "question": "Which equation generates the source’s30|30|40|40 arrangement?",
    "inputs": {
      "H": 1929,
      "D": 1859,
      "a": 30,
      "b": 40,
      "source_path": [
        1959,
        1929,
        1899,
        1859,
        1819
      ]
    },
    "sources": [
      "File70 §5.4; secondary schematic comparison"
    ],
    "opened_utc": "2026-09-28T01:06:20.396425+00:00",
    "predecessor_sha256": "adbcfc15390dec89a47f87874a4910b7fc6d90e3dd55e9aec748e1315f527dc8",
    "results": {
      "path": [
        1959,
        1929,
        1899,
        1859,
        1819
      ],
      "junction_from_below": 1899,
      "gaps": [
        30,
        30,
        40,
        40
      ],
      "whole": 140
    },
    "finding": "The shared1899 junction follows exactly from H−D=a+b=70. The whole path then has width2(a+b)=140. Its schematic30-day premise supplies the junction; choosing29 would give1900 instead.",
    "reassessment": "Reconstruct Joseph’s complete supplied age rail and determine what is retained from Creation.",
    "checks": {
      "source_path": true,
      "junction": true,
      "dependency": true
    },
    "closed_utc": "2026-09-28T01:06:20.396626+00:00",
    "sha256": "14c2e962db65235ffc3310e40dbdab2dd2684788aed34f81121ae669703b86b4"
  },
  {
    "step": 655,
    "title": "Generate Joseph’s age-position family",
    "question": "Does one birth anchor and the supplied ages recover the economic rail?",
    "inputs": {
      "birth": 1915,
      "ages": [
        17,
        30,
        37,
        44
      ],
      "source_dates": [
        1898,
        1885,
        1878,
        1871
      ]
    },
    "sources": [
      "File70 §§5.5–5.6; A.6 P001–011"
    ],
    "opened_utc": "2026-09-28T01:06:31.798023+00:00",
    "predecessor_sha256": "14c2e962db65235ffc3310e40dbdab2dd2684788aed34f81121ae669703b86b4",
    "results": {
      "dates": [
        1898,
        1885,
        1878,
        1871
      ],
      "gaps": [
        13,
        7,
        7
      ],
      "creation_components": [
        13,
        1
      ],
      "Joseph_components": [
        13,
        14
      ]
    },
    "finding": "Joseph’s17/30/37/44 ages generate1898/1885/1878/1871 and13|7|7. The13-year opening is retained in the Creation comparison while the following1 becomes14; the complete paths are not uniform scalar copies.",
    "reassessment": "Use the authorized local Noah variant rows to test the same separation of shape and placement.",
    "checks": {
      "dates": true,
      "gaps": true,
      "not_uniform": true
    },
    "closed_utc": "2026-09-28T01:06:31.798295+00:00",
    "sha256": "f41734dd9a81bfaae1a8cd1624ac912b6aaf30ce4f62e79917dfaa9629c65b02"
  },
  {
    "step": 656,
    "title": "Reconstruct the local Noah/Shem variant field",
    "question": "Which spacings survive the admitted local gear and lifespan comparisons?",
    "inputs": {
      "Noah_G1": [
        2296,
        2236,
        2166,
        2106
      ],
      "Noah_G2": [
        2298,
        2238,
        2168,
        2108
      ],
      "Shem_G1": [
        2146,
        2086,
        2016,
        1956
      ],
      "role": "alternative death coordinates, not successive deaths"
    },
    "sources": [
      "File70 §§4.3–4.5; A.7"
    ],
    "opened_utc": "2026-09-28T01:06:45.144102+00:00",
    "predecessor_sha256": "f41734dd9a81bfaae1a8cd1624ac912b6aaf30ce4f62e79917dfaa9629c65b02",
    "results": {
      "gaps": [
        [
          60,
          70,
          60
        ],
        [
          60,
          70,
          60
        ],
        [
          60,
          70,
          60
        ]
      ],
      "G2_minus_G1": [
        2,
        2,
        2,
        2
      ],
      "Shem_minus_Noah": [
        -150,
        -150,
        -150,
        -150
      ]
    },
    "finding": "The admitted alternative-date rows have one60|70|60 shape. The local Noah gear change translates it by2; the Shem comparison translates it by−150. No operation is extended to Creation or the later patriarchs.",
    "reassessment": "Determine how the supplied Joseph endpoint completes the local Noah400 comparison.",
    "checks": {
      "shape": true,
      "local_gear": true,
      "Shem": true
    },
    "closed_utc": "2026-09-28T01:06:45.144356+00:00",
    "sha256": "573c841d309b176b75aa17fa814703a74033852f7c2c22193021ccfc72237158"
  },
  {
    "step": 657,
    "title": "Complete the admitted Noah–Joseph comparison",
    "question": "How much of the400 comparison follows from the variant field?",
    "inputs": {
      "G2_variants": [
        2298,
        2238,
        2168,
        2108
      ],
      "Joseph_age17": 1898
    },
    "sources": [
      "File70 §§4.3–4.5; A.7"
    ],
    "opened_utc": "2026-09-28T01:06:55.557944+00:00",
    "predecessor_sha256": "573c841d309b176b75aa17fa814703a74033852f7c2c22193021ccfc72237158",
    "results": {
      "comparison_gaps": [
        60,
        70,
        60,
        210
      ],
      "total": 400,
      "variant_width": 190,
      "endpoint_arm": 210
    },
    "finding": "The source’s400 comparison is the190-wide alternative-date field plus the210 arm to Joseph1898. Its equality to a400 Affliction duration does not identify their event pairs, and the variant positions are not successive Noah deaths.",
    "reassessment": "Move to the cumulative4900 body and recover all its supplied cuts with one index.",
    "checks": {
      "gaps": true,
      "sum": true
    },
    "closed_utc": "2026-09-28T01:06:55.558129+00:00",
    "sha256": "bf11078192859834c0850ef1427d5eee9d34d171b17c11b810850d27fac015f4"
  },
  {
    "step": 658,
    "title": "Generate the cumulative4900 cuts",
    "question": "Can one70-year index recover the principal source junctions?",
    "inputs": {
      "head": 5436,
      "tail": 536,
      "indices": [
        0,
        49,
        50,
        69,
        70
      ],
      "source_nodes": [
        5436,
        2006,
        1936,
        606,
        536
      ]
    },
    "sources": [
      "File70 §9.1A; A.13.3 CM019–027"
    ],
    "opened_utc": "2026-09-28T01:07:10.286093+00:00",
    "predecessor_sha256": "bf11078192859834c0850ef1427d5eee9d34d171b17c11b810850d27fac015f4",
    "results": {
      "indexed_nodes": {
        "0": 5436,
        "49": 2006,
        "50": 1936,
        "69": 606,
        "70": 536
      },
      "cut_pairs": [
        [
          49,
          21
        ],
        [
          50,
          20
        ],
        [
          69,
          1
        ]
      ],
      "duration": 4900
    },
    "finding": "One rule x(k)=5436−70k recovers the source’s regular Jacob, cumulative Jacob/Levi, captivity and restoration positions. The49|21,50|20 and69|1 divisions are alternate cuts of one70-unit body.",
    "reassessment": "Test the1400 rectangle embedded in this indexed body.",
    "checks": {
      "all_nodes": true,
      "whole": true
    },
    "closed_utc": "2026-09-28T01:07:10.286398+00:00",
    "sha256": "319effa6a74d7ef5f55e635be6dc604f49c00c44ecb6023ac705019357f6c7dc"
  },
  {
    "step": 659,
    "title": "Generate the cumulative1400 rectangle",
    "question": "Are the four source spans independent or generated by matching70-year rails?",
    "inputs": {
      "upper": [
        2006,
        1936
      ],
      "lower": [
        606,
        536
      ]
    },
    "sources": [
      "File70 A.13.4 CM028–030; C658"
    ],
    "opened_utc": "2026-09-28T01:07:20.033807+00:00",
    "predecessor_sha256": "319effa6a74d7ef5f55e635be6dc604f49c00c44ecb6023ac705019357f6c7dc",
    "results": {
      "matrix": [
        [
          1400,
          1470
        ],
        [
          1330,
          1400
        ]
      ],
      "formula": "1400+70(j−i)",
      "rail_indices": [
        [
          49,
          50
        ],
        [
          69,
          70
        ]
      ]
    },
    "finding": "The1400 rectangle is the existing rail generator at spacing70. Its crossed1330/1470 spans follow from matching rails; the second1400 is a dependent corresponding comparison.",
    "reassessment": "Recover the source’s490|910 lower subdivision and locate Exodus within the same index.",
    "checks": {
      "matrix": true,
      "translation": true
    },
    "closed_utc": "2026-09-28T01:07:20.034008+00:00",
    "sha256": "ab2f1743e5cdeb2823d0646105d6079a963e48e58ec52d3aeffc29f5e803cd1e"
  },
  {
    "step": 660,
    "title": "Insert Exodus into the indexed cumulative body",
    "question": "What does the supplied Exodus1446 add to the4900 index?",
    "inputs": {
      "path": [
        5436,
        1936,
        1446,
        536
      ],
      "unit": 70
    },
    "sources": [
      "File70 §9.1A; A.13.3–4"
    ],
    "opened_utc": "2026-09-28T01:07:30.631859+00:00",
    "predecessor_sha256": "ab2f1743e5cdeb2823d0646105d6079a963e48e58ec52d3aeffc29f5e803cd1e",
    "results": {
      "indices": [
        0,
        50,
        57,
        70
      ],
      "gaps": [
        3500,
        490,
        910
      ],
      "unit_gaps": [
        50,
        7,
        13
      ]
    },
    "finding": "Exodus is index57 in the same source-conditioned lattice. The lower1400 is7|13 units, embedded in the complete50|7|13 partition of4900. The supplied Exodus role selects the cut; the other measures follow.",
    "reassessment": "Reconstruct the larger cumulative spine in its175-year unit.",
    "checks": {
      "indices": true,
      "parts": true,
      "closure": true
    },
    "closed_utc": "2026-09-28T01:07:30.632091+00:00",
    "sha256": "d03ee8c3087e7136879e8122d35a78baab6a12bd969dee9c4f699ee71128600e"
  },
  {
    "step": 661,
    "title": "Reconstruct the77-unit cumulative spine",
    "question": "Does one175-year path reproduce the entire supplied Creation-to-restoration spine?",
    "inputs": {
      "nodes": [
        14011,
        5436,
        1936,
        536
      ],
      "coefficients": [
        49,
        20,
        8
      ],
      "unit": 175
    },
    "sources": [
      "File70 §§1.4,5.8,9.1A; A.13.1 CM001–010"
    ],
    "opened_utc": "2026-09-28T01:07:42.014697+00:00",
    "predecessor_sha256": "d03ee8c3087e7136879e8122d35a78baab6a12bd969dee9c4f699ee71128600e",
    "results": {
      "generated": [
        14011,
        5436,
        1936,
        536
      ],
      "durations": [
        8575,
        3500,
        1400
      ],
      "total": 13475,
      "49_units": 275
    },
    "finding": "The full macro spine is49|20|8 in175-year units, totaling77 units or13475. The shared175 unit connects its anatomy to the earlier Abraham/covenant work without requiring every intermediate event to occupy the same role.",
    "reassessment": "Test what changes when the Jacob junction uses its exact phase instead of its whole-year display.",
    "checks": {
      "all_nodes": true,
      "coeff_sum": true,
      "alternate_measure": true
    },
    "closed_utc": "2026-09-28T01:07:42.014904+00:00",
    "sha256": "a0d84f8c925b253872722f59fc06113ea48519323f052803bc8e72618789290e"
  },
  {
    "step": 662,
    "title": "Resolve phase at the cumulative Jacob junction",
    "question": "Which macro properties survive replacing the displayed1936 with exact1936.5?",
    "inputs": {
      "outer": [
        5436,
        536
      ],
      "display": 1936,
      "exact": "3873/2"
    },
    "sources": [
      "File70 §§5.8,9.1A; exact-phase caution"
    ],
    "opened_utc": "2026-09-28T01:07:52.736421+00:00",
    "predecessor_sha256": "a0d84f8c925b253872722f59fc06113ea48519323f052803bc8e72618789290e",
    "results": {
      "display_arms": [
        3500,
        1400
      ],
      "exact_arms": [
        "6999/2",
        "2801/2"
      ],
      "change": [
        "-1/2",
        "1/2"
      ]
    },
    "finding": "The half-year phase transfers0.5 from the upper arm to the lower arm. The4900 body survives, but its20|8 split in175 units belongs to the whole-year display. A conserved total does not authorize discarding phase.",
    "reassessment": "Recover the source’s complete first-to-last triple correspondence.",
    "checks": {
      "exact": true,
      "total": true,
      "transfer": true
    },
    "closed_utc": "2026-09-28T01:07:52.736915+00:00",
    "sha256": "2daea098ec6cbf63a88a5a4f3bf3e42fed80faa0830ac55466b90b427df6a78b"
  },
  {
    "step": 663,
    "title": "Recover the cumulative first-to-last triple",
    "question": "Does the12075 correspondence apply to the whole supplied triple?",
    "inputs": {
      "creation": [
        14011,
        14004,
        13997
      ],
      "household": [
        1936,
        1929,
        1922
      ],
      "companion_role": "13997 source lower comparison node"
    },
    "sources": [
      "File70 §§1.4,5.8; A.13.1"
    ],
    "opened_utc": "2026-09-28T01:08:04.258801+00:00",
    "predecessor_sha256": "2daea098ec6cbf63a88a5a4f3bf3e42fed80faa0830ac55466b90b427df6a78b",
    "results": {
      "corresponding_spans": [
        12075,
        12075,
        12075
      ],
      "cross_matrix": [
        [
          12075,
          12082,
          12089
        ],
        [
          12068,
          12075,
          12082
        ],
        [
          12061,
          12068,
          12075
        ]
      ],
      "P_output": 12250,
      "175_coefficients": [
        69,
        70
      ]
    },
    "finding": "The supplied first-to-last triples form one7-year rail translated by12075. Its Prophetic conversion69→70 in175 units recovers12250, now within a complete coordinate family rather than an isolated duration.",
    "reassessment": "Fit Jacob’s147|490 biography and household boundary into the retained-path explanation.",
    "checks": {
      "all_three": true,
      "P": true,
      "anatomy": true
    },
    "closed_utc": "2026-09-28T01:08:04.259107+00:00",
    "sha256": "d625a36937a8aa68f064015a7f062f60ab5519646a7a91c2906c0c194117bbae"
  },
  {
    "step": 664,
    "title": "Recover the13-jubilee household path",
    "question": "How does Jacob’s lifespan partition the cumulative path to Exodus?",
    "inputs": {
      "nodes": [
        2083,
        1936,
        1446
      ],
      "roles": [
        "cumulative Jacob birth",
        "whole-year Jacob-death/Levi-birth boundary",
        "Exodus"
      ]
    },
    "sources": [
      "File70 §§5.8,9.1A; A.13"
    ],
    "opened_utc": "2026-09-28T01:08:15.256726+00:00",
    "predecessor_sha256": "d625a36937a8aa68f064015a7f062f60ab5519646a7a91c2906c0c194117bbae",
    "results": {
      "gaps": [
        147,
        490
      ],
      "49_coefficients": [
        3,
        10
      ],
      "total": 637
    },
    "finding": "The source household boundary partitions637 as147+490, or3|10 jubilee units. Its corporate reading concerns the boundary of Jacob’s household; it does not date every son’s birth to1936. File70’s macro and biographical families are linked through retained junction roles.",
    "reassessment": "Open Supplement A’s native720/30 family as a test of the same retained-component mechanism.",
    "checks": {
      "gaps": true,
      "jubilees": true,
      "total": true
    },
    "closed_utc": "2026-09-28T01:08:15.256986+00:00",
    "sha256": "57bef4b00bb583fe9e1f92091e9ed4b8628859c2d91d3fb2cb87336c800a3afb"
  },
  {
    "step": 665,
    "title": "Derive the native core from carrier and flank",
    "question": "What minimal source inputs generate the720/30 family?",
    "inputs": {
      "carrier": 720,
      "flank": 30
    },
    "sources": [
      "Supplement A §§1.1–1.2"
    ],
    "opened_utc": "2026-09-28T01:08:30.974042+00:00",
    "predecessor_sha256": "57bef4b00bb583fe9e1f92091e9ed4b8628859c2d91d3fb2cb87336c800a3afb",
    "results": {
      "core": 690,
      "flank_coefficients": {
        "core": 23,
        "carrier": 24,
        "native_bracket": 25,
        "expanded_core": 25
      }
    },
    "finding": "The crossed core690 is23 flanks of30. The carrier is24 flanks, and both the native two-flank bracket and E-expanded core are25 flanks. Their shared750 is forced by core=23×flank, while their component roles differ.",
    "reassessment": "Generate all native, P and E core/flank/bracket states together.",
    "checks": {
      "core": true,
      "forced_equality": true
    },
    "closed_utc": "2026-09-28T01:08:30.976261+00:00",
    "sha256": "1aeb72d2ecd8dc9dd6ded191817336a2590dc2700aed7b90d530052f84cb6a71"
  },
  {
    "step": 666,
    "title": "Generate the complete retained-flank table",
    "question": "Can one formula produce every native and converted bracket column?",
    "inputs": {
      "core": 690,
      "flank": 30,
      "operators": [
        "identity",
        "P",
        "E"
      ]
    },
    "sources": [
      "Supplement A §§1.1–1.2"
    ],
    "opened_utc": "2026-09-28T01:08:43.934003+00:00",
    "predecessor_sha256": "1aeb72d2ecd8dc9dd6ded191817336a2590dc2700aed7b90d530052f84cb6a71",
    "results": {
      "columns": [
        "core",
        "gain",
        "one_flank",
        "two_flanks"
      ],
      "rows": [
        [
          690,
          0,
          720,
          750
        ],
        [
          700,
          10,
          730,
          760
        ],
        [
          750,
          60,
          780,
          810
        ]
      ]
    },
    "finding": "Applying each Key to the core while retaining30-unit flanks generates the full source table:690/720/750,700/730/760 and750/780/810. The gain belongs to the core; a whole-bracket conversion is a different operation.",
    "reassessment": "Measure the exact difference between retained-flank and whole-bracket conversion.",
    "checks": {
      "source_table": true,
      "gains": true
    },
    "closed_utc": "2026-09-28T01:08:43.934579+00:00",
    "sha256": "13f081be334a5e06920e021097c80171ecc6103e09c820fb6f6241482071ebd6"
  },
  {
    "step": 667,
    "title": "Explain retained-part conversion algebraically",
    "question": "What term distinguishes converting a core from converting its entire bracket?",
    "inputs": {
      "core": 690,
      "flanks": [
        30,
        30
      ],
      "operators": [
        "P",
        "E"
      ]
    },
    "sources": [
      "C666",
      "C631 retained-part synthesis"
    ],
    "opened_utc": "2026-09-28T01:08:54.665397+00:00",
    "predecessor_sha256": "13f081be334a5e06920e021097c80171ecc6103e09c820fb6f6241482071ebd6",
    "results": {
      "rows": [
        {
          "retained": 760,
          "whole": "17500/23",
          "excess": "20/23",
          "flank_gain": "20/23"
        },
        {
          "retained": 810,
          "whole": "18750/23",
          "excess": "120/23",
          "flank_gain": "120/23"
        }
      ],
      "general_difference": "2(k−1)f"
    },
    "finding": "Whole conversion adds exactly2(k−1)f more than core conversion with retained flanks. This is the same retained-subdivision distinction that explains the earlier partial-E and whole-J routes: matching totals never establish identical internal paths.",
    "reassessment": "Reconstruct the native alternating ladder from its two rail parameters.",
    "checks": {
      "P_excess": true,
      "E_excess": true,
      "identity": true
    },
    "closed_utc": "2026-09-28T01:08:54.665748+00:00",
    "sha256": "65ceaa2a2d6692224d37483637d748381cb2e0a3bee2146ee8594dc7d403a603"
  },
  {
    "step": 668,
    "title": "Generate the whole alternating720/30 ladder",
    "question": "Can the source’s ten coordinates be recovered without separate date fitting?",
    "inputs": {
      "head": 4326,
      "core": 690,
      "flank": 30,
      "source": [
        4326,
        4296,
        3606,
        3576,
        2886,
        2856,
        2166,
        2136,
        1446,
        1416
      ]
    },
    "sources": [
      "Supplement A §1.3; admitted source ladder only"
    ],
    "opened_utc": "2026-09-28T01:09:07.681958+00:00",
    "predecessor_sha256": "65ceaa2a2d6692224d37483637d748381cb2e0a3bee2146ee8594dc7d403a603",
    "results": {
      "generated_nodes": [
        4326,
        4296,
        3606,
        3576,
        2886,
        2856,
        2166,
        2136,
        1446,
        1416
      ],
      "gaps": [
        30,
        690,
        30,
        690,
        30,
        690,
        30,
        690,
        30
      ],
      "same_rail_steps": [
        [
          720,
          720,
          720,
          720
        ],
        [
          720,
          720,
          720,
          720
        ]
      ],
      "width": 2910
    },
    "finding": "The ten supplied positions are two720-step rails separated by30. Their interleaving generates the alternating30|690 path and2910 outer width. Source, dependency and generated-companion roles remain attached to the original positions; no new SKL transport is inferred.",
    "reassessment": "Extract the six-node1470 cell and explain its alternative partitions.",
    "checks": {
      "whole_ladder": true,
      "gaps": true,
      "width": true
    },
    "closed_utc": "2026-09-28T01:09:07.682365+00:00",
    "sha256": "ebb63304f38feeb2026c85d30e53b38622a7cd2260ae47abc076d873610e9378"
  },
  {
    "step": 669,
    "title": "Explain every native1470 partition",
    "question": "Why do the source’s690+780 and720+750 measures agree?",
    "inputs": {
      "cell": [
        3606,
        3576,
        2886,
        2856,
        2166,
        2136
      ],
      "core": 690,
      "flank": 30
    },
    "sources": [
      "Supplement A §§1.4–1.5,2.3"
    ],
    "opened_utc": "2026-09-28T01:09:20.114961+00:00",
    "predecessor_sha256": "ebb63304f38feeb2026c85d30e53b38622a7cd2260ae47abc076d873610e9378",
    "results": {
      "total": 1470,
      "partitions": [
        [
          690,
          780
        ],
        [
          720,
          750
        ]
      ],
      "flank_units": 49,
      "center": 2871,
      "central_rail_center": 2871
    },
    "finding": "All three1470 expressions reduce to2c+3f=49f. The six-node cell and its central30 rail share midpoint2871. These are decompositions of one supplied object, not independent appearances of1470.",
    "reassessment": "Compare the cell’s48+1 month anatomy with the supplied intercalation ledger.",
    "checks": {
      "total": true,
      "partitions": true,
      "center": true
    },
    "closed_utc": "2026-09-28T01:09:20.115201+00:00",
    "sha256": "20f6d5b48f396e9af79d36e701509405ceaf30acfd6869ce31f401e8d8756404"
  },
  {
    "step": 670,
    "title": "Connect the1470 cell with calendrical intercalation",
    "question": "Which part of the shared1470 is the same anatomy, and which part retains distinct units?",
    "inputs": {
      "cell_units": [
        48,
        1
      ],
      "month_days": 30,
      "ledger": [
        6,
        2190,
        1470
      ],
      "civil_year_days": "1461/4"
    },
    "sources": [
      "Supplement A §2.2; File12 calendrical physics"
    ],
    "opened_utc": "2026-09-28T01:09:30.920569+00:00",
    "predecessor_sha256": "20f6d5b48f396e9af79d36e701509405ceaf30acfd6869ce31f401e8d8756404",
    "results": {
      "final_block": 1470,
      "ledger_days": 14610,
      "year_equivalent": "1461/4",
      "cell_30_units": 49
    },
    "finding": "The supplied intercalation final block has the same48+1 anatomy:4×360+30=1470 days. Its full ledger6×2190+1470=40×365.25 is a distinct calendrical realization; it does not turn the chronological1470-year cell into days.",
    "reassessment": "Consolidate File70’s indexed paths and Supplement A’s retained-flank family before phase analysis.",
    "checks": {
      "final": true,
      "ledger": true,
      "year_equivalent": true
    },
    "closed_utc": "2026-09-28T01:09:30.921473+00:00",
    "sha256": "77c4d361acbd2c726dbc617df8e8fe7c8aa3cc812c751cb2342a1855981e4bfa"
  },
  {
    "step": 671,
    "title": "Consolidate the retained-path explanation",
    "question": "What new mechanism connects biography, cumulative paths and calendar flanks?",
    "inputs": {
      "completed_range": [
        652,
        671
      ],
      "precision": [
        "phase test holds outer nodes fixed",
        "2083/1936/1446 path uses whole-year displays"
      ]
    },
    "sources": [
      "C652–C670",
      "Reviewer C652–C664"
    ],
    "opened_utc": "2026-09-28T01:09:53.093395+00:00",
    "predecessor_sha256": "77c4d361acbd2c726dbc617df8e8fe7c8aa3cc812c751cb2342a1855981e4bfa",
    "results": {
      "artifact": {
        "path": "deliverables/C671_Interim_Synthesis.md",
        "sha256": "2a41c2f375f92b22f0b043d23cd38cd2a3e48eaaa15807d6e901f8eda3ebf527",
        "bytes": 988
      },
      "mechanisms": [
        "reflection",
        "indexed path",
        "retained core and flanks"
      ]
    },
    "finding": "Forty steps now provide a connected explanatory grammar. The next productive question is how phase and center coordinates account for the source’s40/70/120 fields and Actual/Rounded closure.",
    "reassessment": "Derive the complete micro phase table from center, width and phase offsets.",
    "checks": {
      "range": true,
      "core_flank": true,
      "spine": true
    },
    "closed_utc": "2026-09-28T01:09:53.093672+00:00",
    "sha256": "c0fea8a69bfff9cd2fbde9e529de06cd0c6154e22d7db324869023ecc68124f0"
  },
  {
    "step": 672,
    "title": "Generate the complete phase bracket",
    "question": "Can center, width and suffix offset recover all eight supplied endpoints?",
    "inputs": {
      "base_center": 2871,
      "widths": [
        34,
        40
      ],
      "phase_offsets": {
        "n": 0,
        "t": "1/2"
      },
      "BC_label_rule": "coord(tY)=Y−1/2"
    },
    "sources": [
      "Supplement A §§4.1,4.3"
    ],
    "opened_utc": "2026-09-28T01:10:25.916112+00:00",
    "predecessor_sha256": "c0fea8a69bfff9cd2fbde9e529de06cd0c6154e22d7db324869023ecc68124f0",
    "results": {
      "phase_rows": [
        {
          "width": 34,
          "phase": "n",
          "coordinates": [
            2888,
            2854
          ],
          "labels": [
            2888,
            2854
          ]
        },
        {
          "width": 34,
          "phase": "t",
          "coordinates": [
            "5777/2",
            "5709/2"
          ],
          "labels": [
            2889,
            2855
          ]
        },
        {
          "width": 40,
          "phase": "n",
          "coordinates": [
            2891,
            2851
          ],
          "labels": [
            2891,
            2851
          ]
        },
        {
          "width": 40,
          "phase": "t",
          "coordinates": [
            "5783/2",
            "5703/2"
          ],
          "labels": [
            2892,
            2852
          ]
        }
      ],
      "formula": "x=C+epsilon±w/2"
    },
    "finding": "One center/width/phase formula generates all eight before/after positions. Corresponding suffix widths are34 and40; Tishri and Nisan centers remain separated by half a year in exact coordinates.",
    "reassessment": "Test whether one global affine date map can perform this entire phase change.",
    "checks": {
      "source_labels": true,
      "fixed_phase": true
    },
    "closed_utc": "2026-09-28T01:10:25.916432+00:00",
    "sha256": "7678cbcaa6477f93b68fab8add528ac5f16f45cd92d2602992138e0fc1a48d50"
  },
  {
    "step": 673,
    "title": "Test one-map compression of the phase family",
    "question": "Can one affine function change34 to40 while preserving every half-year phase separation?",
    "inputs": {
      "width_change": [
        34,
        40
      ],
      "phase_change": [
        "1/2",
        "1/2"
      ]
    },
    "sources": [
      "C672",
      "Supplement A §4.3"
    ],
    "opened_utc": "2026-09-28T01:10:37.837145+00:00",
    "predecessor_sha256": "7678cbcaa6477f93b68fab8add528ac5f16f45cd92d2602992138e0fc1a48d50",
    "results": {
      "required_width_slope": "20/17",
      "required_phase_slope": 1,
      "false_global_phase_gap": "10/17",
      "role_specific_rule": "C+epsilon+(20/17)(x−C−epsilon)"
    },
    "finding": "A single affine date map is impossible: width demands slope20/17, while the preserved phase separation demands slope1. The valid expression dilates around each phase’s own center. This explains why the full object needs a phase coordinate.",
    "reassessment": "Compare the scalar34.5 Key input with the coordinate34-to40 construction.",
    "checks": {
      "incompatible": true,
      "phase_miss": true,
      "phase_specific": true
    },
    "closed_utc": "2026-09-28T01:10:37.837450+00:00",
    "sha256": "acb88dbed3d675e012284caf3a98ebde7ef4e3ebf8c24677937e2a5ce1694f19"
  },
  {
    "step": 674,
    "title": "Unify the micro Key outputs",
    "question": "How do35,37.5 and40 relate to the source’s34.5 input?",
    "inputs": {
      "source_scalar": "69/2",
      "normalization_residual": "5/2"
    },
    "sources": [
      "Supplement A §§4.1,4.3"
    ],
    "opened_utc": "2026-09-28T01:10:47.985243+00:00",
    "predecessor_sha256": "acb88dbed3d675e012284caf3a98ebde7ef4e3ebf8c24677937e2a5ce1694f19",
    "results": {
      "P_output": 35,
      "E_output": "75/2",
      "output_gap": "5/2",
      "normalized": 40,
      "affine_continuation": 40
    },
    "finding": "The normalization residual2.5 equals the gap between E and P outputs. The source-defined40 therefore equals2E(34.5)−P(34.5). This compresses the two-stage calculation without promoting it to a new universal Key.",
    "reassessment": "Relate the scalar completion to the whole before/after phase envelopes.",
    "checks": {
      "keys": true,
      "residual": true,
      "completion": true
    },
    "closed_utc": "2026-09-28T01:10:47.985485+00:00",
    "sha256": "2441183bdc17f95c6de29513d0ee9f899375f5fc6731f27a16d936adc0c4e126"
  },
  {
    "step": 675,
    "title": "Recover all phase-envelope measurements",
    "question": "Which widths belong to each suffix or cross-phase measurement?",
    "inputs": {
      "corresponding_widths": [
        34,
        40
      ],
      "phase_offset": "1/2"
    },
    "sources": [
      "Supplement A §4.3; C672–C674"
    ],
    "opened_utc": "2026-09-28T01:10:59.990616+00:00",
    "predecessor_sha256": "2441183bdc17f95c6de29513d0ee9f899375f5fc6731f27a16d936adc0c4e126",
    "results": {
      "columns": [
        "inner_cross",
        "same_suffix",
        "outer_cross"
      ],
      "rows": [
        [
          "67/2",
          34,
          "69/2"
        ],
        [
          "79/2",
          40,
          "81/2"
        ]
      ],
      "coordinate_width_gain": 6,
      "scalar_normalization_gain": "11/2"
    },
    "finding": "The full phase table is33.5/34/34.5 before and39.5/40/40.5 after. Outward endpoint motion adds6 to every matched measurement, whereas34.5→40 adds5.5 because it changes measurement class. Those two statements are compatible once the measured objects are named.",
    "reassessment": "Resolve the source’s recovered35 row using exact phase coordinates.",
    "checks": {
      "rows": true,
      "uniform_gain": true,
      "different_class": true
    },
    "closed_utc": "2026-09-28T01:10:59.990859+00:00",
    "sha256": "80b6104a4a9454c430bb592a91bf17c53d61c2ec2c1a6df99ecafc6badf7b7ae"
  },
  {
    "step": 676,
    "title": "Reconstruct the recovered35 phase pair",
    "question": "What exact coordinates result from withdrawing2.5 at both normalized endpoints?",
    "inputs": {
      "T_coordinates": [
        "5783/2",
        "5703/2"
      ],
      "N_coordinates": [
        2891,
        2851
      ],
      "withdrawal": "5/2"
    },
    "sources": [
      "Supplement A §4.3; derived phase-resolution test"
    ],
    "opened_utc": "2026-09-28T01:11:12.299801+00:00",
    "predecessor_sha256": "80b6104a4a9454c430bb592a91bf17c53d61c2ec2c1a6df99ecafc6badf7b7ae",
    "results": {
      "from_T_coordinates": [
        2889,
        2854
      ],
      "from_T_labels": [
        "2889n",
        "2854n"
      ],
      "from_N_coordinates": [
        "5777/2",
        "5707/2"
      ],
      "from_N_labels": [
        "2889t",
        "2854t"
      ]
    },
    "finding": "Withdrawing2.5 from both normalized endpoints recovers width35 and changes the displayed suffix: the Tishri coordinates land on Nisan labels, and vice versa. The apparent integer-label ambiguity is resolved by the exact half-year convention.",
    "reassessment": "Generate the two40 brackets and their common120 field.",
    "checks": {
      "T_to_N": true,
      "N_to_T": true,
      "widths": true
    },
    "closed_utc": "2026-09-28T01:11:12.300041+00:00",
    "sha256": "e4e7f7c186a8300250e317a5d0021a4a8dfc136572995d93966ea4ae6ac8d330"
  },
  {
    "step": 677,
    "title": "Generate the120 field from two40 brackets",
    "question": "Does the supplied80 translation determine the entire enclosing field?",
    "inputs": {
      "lower_bracket": [
        2891,
        2851
      ],
      "translation": 80
    },
    "sources": [
      "Supplement A §4.4"
    ],
    "opened_utc": "2026-09-28T01:11:27.519699+00:00",
    "predecessor_sha256": "e4e7f7c186a8300250e317a5d0021a4a8dfc136572995d93966ea4ae6ac8d330",
    "results": {
      "upper": [
        2971,
        2931
      ],
      "ordered_field": [
        2971,
        2931,
        2891,
        2851
      ],
      "gaps": [
        40,
        40,
        40
      ],
      "center": 2911,
      "center_shift": 40
    },
    "finding": "Translating the40 bracket by80 generates three consecutive40 intervals across a120 envelope. Its center2911 is40 above the lower bracket’s center2871. The repeated40s are consequences of the supplied width and translation.",
    "reassessment": "Insert the separately supplied70-wide Enoch body at this common center.",
    "checks": {
      "upper": true,
      "field_gaps": true,
      "center": true
    },
    "closed_utc": "2026-09-28T01:11:27.520076+00:00",
    "sha256": "ef0b559f087799e8c71d4e2f7907fc4954945b043c34aa5aa477203bbbf23941"
  },
  {
    "step": 678,
    "title": "Derive the nested25|35|35|25 field",
    "question": "What follows once the source70 and120 bodies share center2911?",
    "inputs": {
      "center": 2911,
      "outer_width": 120,
      "Enoch_width": 70,
      "source_Enoch": [
        2946,
        2876
      ]
    },
    "sources": [
      "Supplement A §4.5"
    ],
    "opened_utc": "2026-09-28T01:11:43.642567+00:00",
    "predecessor_sha256": "ef0b559f087799e8c71d4e2f7907fc4954945b043c34aa5aa477203bbbf23941",
    "results": {
      "nodes": [
        2971,
        2946,
        2911,
        2876,
        2851
      ],
      "gaps": [
        25,
        35,
        35,
        25
      ],
      "margin": 25,
      "Key_decomposition": [
        25,
        35,
        35,
        25
      ]
    },
    "finding": "The two source widths and their common center force25|35|35|25. Each35 is P(34.5), each25 is E(23), but their sum is a retained-component construction rather than a newly defined whole120 Key image.",
    "reassessment": "Distinguish the source’s scalar1470 closure from its coordinate1475 envelope.",
    "checks": {
      "source_Enoch": true,
      "gaps": true,
      "keys": true
    },
    "closed_utc": "2026-09-28T01:11:43.642795+00:00",
    "sha256": "6a61820ebb7e0772f460ab3438ba227612a57983e352c71197f9ccf96669d696"
  },
  {
    "step": 679,
    "title": "Resolve the1470 versus1475 closure",
    "question": "Why do the source’s scalar and coordinate closures differ by five?",
    "inputs": {
      "center": 2871,
      "start_offsets": [
        -13,
        13
      ],
      "outward_arm": "1449/2",
      "scalar_arm": "1449/2"
    },
    "sources": [
      "Supplement A §4.2"
    ],
    "opened_utc": "2026-09-28T01:11:57.905972+00:00",
    "predecessor_sha256": "6a61820ebb7e0772f460ab3438ba227612a57983e352c71197f9ccf96669d696",
    "results": {
      "scalar_total": 1470,
      "coordinate_half_width": "1475/2",
      "coordinate_endpoints": [
        "7217/2",
        "4267/2"
      ],
      "coordinate_total": 1475,
      "Tishri_labels": [
        3609,
        2134
      ]
    },
    "finding": "P converts the scalar724.5 arm to735, giving1470. The coordinate construction instead starts13 away from center before adding724.5, giving737.5 per side and1475 overall. The five-year difference is fully accounted for by different constructions.",
    "reassessment": "Reconstruct the exterior-core opening of the ten-node ladder.",
    "checks": {
      "scalar": true,
      "coordinate": true,
      "labels": true
    },
    "closed_utc": "2026-09-28T01:11:57.906263+00:00",
    "sha256": "2568b44913d699faf86fa9b7c21f4d19e1e9139c2ff93f4aeb2f84ebd44cc2f9"
  },
  {
    "step": 680,
    "title": "Generate the exterior Prophetic opening",
    "question": "Does converting only the two outer cores recover the supplied2930 ladder?",
    "inputs": {
      "native": [
        4326,
        4296,
        3606,
        3576,
        2886,
        2856,
        2166,
        2136,
        1446,
        1416
      ],
      "outer_core_gain": 10
    },
    "sources": [
      "Supplement A §3.2"
    ],
    "opened_utc": "2026-09-28T01:12:11.959476+00:00",
    "predecessor_sha256": "2568b44913d699faf86fa9b7c21f4d19e1e9139c2ff93f4aeb2f84ebd44cc2f9",
    "results": {
      "opened_ladder": [
        4336,
        4306,
        3606,
        3576,
        2886,
        2856,
        2166,
        2136,
        1436,
        1406
      ],
      "gaps": [
        30,
        700,
        30,
        690,
        30,
        690,
        30,
        700,
        30
      ],
      "widths": [
        2910,
        2930
      ],
      "centers": [
        2871,
        2871
      ]
    },
    "finding": "Two ten-year core gains produce the complete source2930 ladder while preserving the six inner nodes, every30 flank and midpoint2871. This is selective opening, not P applied to the whole2910 span.",
    "reassessment": "Add the source’s final five-year boundary displacements and identify the conserved quantity.",
    "checks": {
      "source": true,
      "gaps": true,
      "selective": true
    },
    "closed_utc": "2026-09-28T01:12:11.959697+00:00",
    "sha256": "7258bcf80daec442b6b73da230c778d113d247ac031687675dcc1cbde8a0b143"
  },
  {
    "step": 681,
    "title": "Complete the conserved-center2940 corridor",
    "question": "What invariant joins all three source-selected outer endpoint pairs?",
    "inputs": {
      "pairs": [
        [
          4326,
          1416
        ],
        [
          4336,
          1406
        ],
        [
          4341,
          1401
        ]
      ],
      "final_outward_displacement": 5,
      "source_local_components": [
        2,
        3
      ]
    },
    "sources": [
      "Supplement A §5.1"
    ],
    "opened_utc": "2026-09-28T01:12:24.068500+00:00",
    "predecessor_sha256": "7258bcf80daec442b6b73da230c778d113d247ac031687675dcc1cbde8a0b143",
    "results": {
      "endpoint_sums": [
        5742,
        5742,
        5742
      ],
      "centers": [
        2871,
        2871,
        2871
      ],
      "widths": [
        2910,
        2930,
        2940
      ],
      "width_increments": [
        20,
        10
      ]
    },
    "finding": "Opposed endpoint changes preserve U+L=5742 while widening2910→2930→2940. The final five-year displacement is the source’s local2+3 construction; it supplies generated extremities4341/1401, not new canonical Creation/Conquest anchors or upstream Gear permission.",
    "reassessment": "Express translation and symmetric opening in center/width coordinates.",
    "checks": {
      "conservation": true,
      "widths": true,
      "increments": true
    },
    "closed_utc": "2026-09-28T01:12:24.068917+00:00",
    "sha256": "d32d88df01582cdc941379c82608f496ef61a931430306f6dc332bed2584b4d9"
  },
  {
    "step": 682,
    "title": "Separate translation from opening",
    "question": "Can one coordinate rule explain both the120 construction and the2940 closure?",
    "inputs": {
      "changes": {
        "translate80": [
          80,
          80
        ],
        "open10": [
          10,
          -10
        ],
        "open5": [
          5,
          -5
        ]
      }
    },
    "sources": [
      "C677,C680,C681"
    ],
    "opened_utc": "2026-09-28T01:12:36.616587+00:00",
    "predecessor_sha256": "d32d88df01582cdc941379c82608f496ef61a931430306f6dc332bed2584b4d9",
    "results": {
      "effects": {
        "translate80": {
          "center_change": 80,
          "width_change": 0
        },
        "open10": {
          "center_change": 0,
          "width_change": 20
        },
        "open5": {
          "center_change": 0,
          "width_change": 10
        }
      },
      "general_rule": "delta_c=(delta_U+delta_L)/2; delta_w=delta_U−delta_L"
    },
    "finding": "Center and width provide a common language for two different mechanisms: translation moves the center while retaining width; symmetric opening widens the body while retaining center. The new sources instantiate both, so no single undifferentiated date shift explains the family.",
    "reassessment": "Continue the admitted alternating ladder across the BC/AD boundary using civil elapsed time.",
    "checks": {
      "translation": true,
      "opening": true,
      "final": true
    },
    "closed_utc": "2026-09-28T01:12:36.616956+00:00",
    "sha256": "a351a7a5c3fee6a9423402b95d80d68802fbbf922aa1712a0a73b450b4762a68"
  },
  {
    "step": 683,
    "title": "Reconstruct the civil alternating continuation",
    "question": "Does the native30|690 cell close consistently across the missing year zero?",
    "inputs": {
      "civil_nodes": [
        "1446BC",
        "1416BC",
        "726BC",
        "696BC",
        "6BC",
        "AD25"
      ],
      "elapsed_coordinate": "BC B -> 1−B; AD A -> A"
    },
    "sources": [
      "Supplement A §5.2"
    ],
    "opened_utc": "2026-09-28T01:12:48.529185+00:00",
    "predecessor_sha256": "a351a7a5c3fee6a9423402b95d80d68802fbbf922aa1712a0a73b450b4762a68",
    "results": {
      "elapsed_coordinates": [
        -1445,
        -1415,
        -725,
        -695,
        -5,
        25
      ],
      "gaps": [
        30,
        690,
        30,
        690,
        30
      ],
      "total": 1470,
      "direct_civil": 1470
    },
    "finding": "The admitted continuation preserves30|690|30|690|30 and totals1470 under civil BC+AD−1. Its comparison terminals retain their source roles. The rounded mirror convention is a separate coordinate rule and is not substituted here.",
    "reassessment": "Relate the source’s750 civil brackets and final three-year completion.",
    "checks": {
      "gaps": true,
      "closure": true
    },
    "closed_utc": "2026-09-28T01:12:48.529476+00:00",
    "sha256": "b6d0d5c514db2773c492b86870cea98b88ed11072baf93ebf603ba450c8fb770"
  },
  {
    "step": 684,
    "title": "Connect civil brackets with the micro gain",
    "question": "How do the supplied750 brackets and AD27→30 completion arise?",
    "inputs": {
      "civil_pairs": [
        [
          726,
          25
        ],
        [
          724,
          27
        ]
      ],
      "micro_input": "69/2",
      "AD_start": 27
    },
    "sources": [
      "Supplement A §§5.3–5.4"
    ],
    "opened_utc": "2026-09-28T01:13:00.121864+00:00",
    "predecessor_sha256": "b6d0d5c514db2773c492b86870cea98b88ed11072baf93ebf603ba450c8fb770",
    "results": {
      "civil_widths": [
        750,
        750
      ],
      "coordinate_translation": 2,
      "E_micro_gain": 3,
      "completed_AD_label": 30
    },
    "finding": "Both supplied civil pairs have width750 and differ by a uniform two-year forward translation. The separate AD27→30 completion uses the micro E-gain3. Equal durations and later completion are connected operations with separately supplied anchors.",
    "reassessment": "Close the three-calendar calibration triangle at the micro input34.5.",
    "checks": {
      "widths": true,
      "gain": true,
      "completion": true
    },
    "closed_utc": "2026-09-28T01:13:00.122209+00:00",
    "sha256": "16f3165d0ad36e19154aa17131c11fbedf5e7f7ece0ca2f8ed67e20274403d66"
  },
  {
    "step": 685,
    "title": "Close the three-calendar micro triangle",
    "question": "Do all three existing Keys yield one calibrated volume at34.5?",
    "inputs": {
      "seed": "69/2",
      "calendar_lengths": [
        336,
        360,
        364
      ],
      "operators": [
        "E",
        "P",
        "J"
      ]
    },
    "sources": [
      "Supplement A §6; C631 common calibration"
    ],
    "opened_utc": "2026-09-28T01:13:12.649245+00:00",
    "predecessor_sha256": "16f3165d0ad36e19154aa17131c11fbedf5e7f7ece0ca2f8ed67e20274403d66",
    "results": {
      "converted_counts": [
        "75/2",
        35,
        "450/13"
      ],
      "calendar_volumes": [
        12600,
        12600,
        12600
      ],
      "common_volume": 12600
    },
    "finding": "At the micro seed34.5, all three calibrated routes meet at12600:336×E(s)=360×P(s)=364×J(s). The Priestly route completes the source’s P/J comparison using the already established common-calibration identity.",
    "reassessment": "Explain the exact twentyfold relation between the micro seed and the native690 core.",
    "checks": {
      "three_routes": true,
      "P_count": true,
      "E_count": true
    },
    "closed_utc": "2026-09-28T01:13:12.649489+00:00",
    "sha256": "2c656f9311602fd91e4ee680c5b909212683e2edf9709eb4e20b875e5be41f55"
  },
  {
    "step": 686,
    "title": "Unify the690 core and34.5 micro seed",
    "question": "Which parts of the two source constructions are exact scalar copies?",
    "inputs": {
      "micro_seed": "69/2",
      "scale": 20,
      "native_core": 690
    },
    "sources": [
      "Supplement A §§1,4,6"
    ],
    "opened_utc": "2026-09-28T01:13:24.014732+00:00",
    "predecessor_sha256": "2c656f9311602fd91e4ee680c5b909212683e2edf9709eb4e20b875e5be41f55",
    "results": {
      "micro_native_P_E": [
        "69/2",
        35,
        "75/2"
      ],
      "twentyfold": [
        690,
        700,
        750
      ],
      "twentyfold_normalized40": 800,
      "retained_bracket810_over20": "81/2"
    },
    "finding": "The native/P/E core sequence690→700/750 is exactly twenty times34.5→35/37.5. The normalized40 would scale to800, so it remains a separate completion. The810/20=40.5 comparison is numerical and does not establish an endpoint map.",
    "reassessment": "Trace the micro seed’s364-volume into the existing Actual/Rounded macro interface.",
    "checks": {
      "scaled": true,
      "normalization_distinct": true,
      "ratio": true
    },
    "closed_utc": "2026-09-28T01:13:24.015216+00:00",
    "sha256": "88a82a98769ff14a54acb300b8d0a816e66ef4160810b361291aead4fe825ba7"
  },
  {
    "step": 687,
    "title": "Connect micro volume to the Actual/Rounded span",
    "question": "Which equation explains the matching12558→12600 structure across scales?",
    "inputs": {
      "micro_count": "69/2",
      "calendar": 364,
      "Actual_pair": [
        14004,
        1446
      ],
      "Rounded_pair": [
        14006,
        1406
      ]
    },
    "sources": [
      "Supplement A §6; File52c latest; C631 Actual/Rounded interface"
    ],
    "opened_utc": "2026-09-28T01:13:40.622784+00:00",
    "predecessor_sha256": "88a82a98769ff14a54acb300b8d0a816e66ef4160810b361291aead4fe825ba7",
    "results": {
      "micro_volume_days": 12558,
      "Actual_elapsed_years": 12558,
      "J_completed_numeric": 12600,
      "Rounded_elapsed_years": 12600,
      "identity": "J(364s)=360P(s)"
    },
    "finding": "The micro volume34.5×364 and Actual cumulative interval share the numerical input12558. Their12600 completion follows from364J=360P. This is a common conversion structure across distinct units; the Rounded14006/1406 pair supplies its own endpoint realization.",
    "reassessment": "Determine why the alternative12740 register is a different calendar choice.",
    "checks": {
      "shared_input": true,
      "completion": true,
      "identity": true
    },
    "closed_utc": "2026-09-28T01:13:40.623049+00:00",
    "sha256": "332b3727acd8634833ea09bc05e689c5955eb17f94f698ba4696e00946bdaf58"
  },
  {
    "step": 688,
    "title": "Explain the two completed volume registers",
    "question": "What operation distinguishes12600 from12740 at the same35 count?",
    "inputs": {
      "count": 35,
      "calendar_lengths": [
        360,
        364
      ],
      "root_volume": 12558
    },
    "sources": [
      "Supplement A §6"
    ],
    "opened_utc": "2026-09-28T01:13:50.854956+00:00",
    "predecessor_sha256": "332b3727acd8634833ea09bc05e689c5955eb17f94f698ba4696e00946bdaf58",
    "results": {
      "volumes": [
        12600,
        12740
      ],
      "difference": 140,
      "calendar_ratio": "91/90",
      "cross_products": [
        4586400,
        4586400
      ],
      "root_outputs": [
        12600,
        12740
      ]
    },
    "finding": "The12600/12740 pair uses the same completed count35 with360/364 calendar lengths. Their ratio91/90 and shared cross-product follow from this construction; the product is a register equality, not an additional chronology or independent witness.",
    "reassessment": "Account for the PhaseNorm40 volume and its residual relative to12600.",
    "checks": {
      "outputs": true,
      "difference": true,
      "cross_products": true
    },
    "closed_utc": "2026-09-28T01:13:50.855260+00:00",
    "sha256": "6a57b724fbf99b68c4140eb5feef5e5089bec76a4cf0b92c0e3e3e75c48f3ba4"
  },
  {
    "step": 689,
    "title": "Explain the normalized13440 register",
    "question": "What added quantity separates PhaseNorm40 from the calibrated micro completion?",
    "inputs": {
      "E_count": "75/2",
      "normalized_count": 40,
      "Priestly_calendar": 336
    },
    "sources": [
      "Supplement A §§4.3,6"
    ],
    "opened_utc": "2026-09-28T01:14:01.247385+00:00",
    "predecessor_sha256": "6a57b724fbf99b68c4140eb5feef5e5089bec76a4cf0b92c0e3e3e75c48f3ba4",
    "results": {
      "calibrated_volume": 12600,
      "normalized_volume": 13440,
      "residual_volume": 840,
      "identity": "40×336 = E(34.5)×336 + 2.5×336"
    },
    "finding": "The normalized13440 body adds exactly840 to12600, because the source’s2.5 residual is measured in336-day units. This explains the extra completion without assigning it to a new event or applying another Key.",
    "reassessment": "Compare these scalar registers with the source’s retained2940 cumulative partition.",
    "checks": {
      "volumes": true,
      "additivity": true,
      "residual_count": true
    },
    "closed_utc": "2026-09-28T01:14:01.247647+00:00",
    "sha256": "445aa97ebd598e316fcc5451eea28d34d0ea5b4ef6486afe7a2b983ac1915aa2"
  },
  {
    "step": 690,
    "title": "Reconstruct the three cumulative completion paths",
    "question": "Can one retained2940 component generate the12600/12740/13440 family?",
    "inputs": {
      "source_head": 14006,
      "hinge": 4346,
      "tail": 1406,
      "upper": 9660,
      "retained_lower": 2940
    },
    "sources": [
      "Supplement A §10.2; inherited source family"
    ],
    "opened_utc": "2026-09-28T01:14:17.581267+00:00",
    "predecessor_sha256": "445aa97ebd598e316fcc5451eea28d34d0ea5b4ef6486afe7a2b983ac1915aa2",
    "results": {
      "paths": [
        {
          "upper": 9660,
          "lower": 2940,
          "total": 12600,
          "head": 14006
        },
        {
          "upper": 9800,
          "lower": 2940,
          "total": 12740,
          "head": 14146
        },
        {
          "upper": 10500,
          "lower": 2940,
          "total": 13440,
          "head": 14846
        }
      ],
      "calendar_bodies": [
        12600,
        12740,
        13440
      ],
      "upper_gain": [
        0,
        140,
        840
      ]
    },
    "finding": "Holding4346→1406 fixed while converting only the9660 upper arm generates all three source totals12600/12740/13440. The generated heads14006/14146/14846 retain their existing status. This realizes the micro register family through retained macro components, not one whole-span conversion.",
    "reassessment": "Consolidate the micro-to-Rounded bridge and decide which anchored routes best explain its placement.",
    "checks": {
      "source_paths": true,
      "heads": true,
      "gains": true
    },
    "closed_utc": "2026-09-28T01:14:17.581549+00:00",
    "sha256": "095d04922354663bba3291939fc2ccf9d76a4e0bc263e88c8a8d95761eacc34c"
  },
  {
    "step": 691,
    "title": "Consolidate phase and calendar completion",
    "question": "What causal chain now connects fine phase structure to the Round chronology?",
    "inputs": {
      "completed_range": [
        672,
        691
      ],
      "chain": [
        "phase scalar",
        "common calibration",
        "unit-qualified12558",
        "retained macro realization"
      ]
    },
    "sources": [
      "C672–C690",
      "Supplement A §§4–6,10"
    ],
    "opened_utc": "2026-09-28T01:14:40.195450+00:00",
    "predecessor_sha256": "095d04922354663bba3291939fc2ccf9d76a4e0bc263e88c8a8d95761eacc34c",
    "results": {
      "artifact": {
        "path": "deliverables/C691_Interim_Synthesis.md",
        "sha256": "87a846f67f4e545ba4a1bbaf0dbddfe3ad0804a57346e5ee646055e5a63e463a",
        "bytes": 1253
      },
      "completed_steps": 60
    },
    "finding": "Sixty steps now connect the local calendar geometry to the Rounded cumulative family through a common calibrated structure and a retained-component realization. The next explanatory need is the source-conditioned placement of the4346 hinge.",
    "reassessment": "Reconstruct both supplied regular-MT routes to4346 as anchored maps.",
    "checks": {
      "count": true,
      "calibration": true,
      "retained_completion": true
    },
    "closed_utc": "2026-09-28T01:14:40.195907+00:00",
    "sha256": "b780bd8176a9db84bb8d43f7ea3ef05e9d38fd8bbb69eb48d7de922745e35ac3"
  }
]