490d — C1132–C1231: sequential research record

Working continuation of C1131 · packet date20260928.

Each completed step retains its question, declared inputs, exact results, finding, and reassessment. These are bounded research actions, not a count of independent discoveries. Canonical sources remain unchanged; second decimal inversion remains deferred.

C1132 — Inventory source relations behind the SP inputs

Question. Which explicit supplied relations constrain the SP ages and lifespan excesses that the cap leaves undetermined?

Sources. File18 §§2.1.3,3.1,4A.2–4A.4; File51a §8.3; File47 §8.4; File20 §7A.10; C1131 continuation

Inputs

{}

Results

{
  "relation_inventory": {
    "path": "model/source_relation_inventory.json",
    "sha256": "66f58b98e2c90a3596f86253eb2bc7d5563086f6cc4f844d80343b97a316e1c4",
    "bytes": 1106
  },
  "candidate_families": 5
}

Finding. Explicit source relations constrain the age packet beyond the cap: two half/equality relations and the first-five460 total. Methuselah has a source Flood equation; Lamech753 remains supplied despite supporting differences.

Reassessment. Freeze one joint age-variable model and determine exactly what these relations recover.

C1133 — Form the joint SP age constraints

Question. How many free age coordinates remain after the explicit source relations and inherited cap equations?

Sources. C1132; File18 §3.1; File51a §8.3

Inputs

{
  "variables": [
    "Adam",
    "Seth",
    "Enosh",
    "Kenan",
    "Mahalalel",
    "Jared",
    "Enoch",
    "Methuselah",
    "Lamech"
  ]
}

Results

{
  "age_constraints": {
    "path": "model/SP_age_constraints.json",
    "sha256": "a424c44212d21411e61116d36dad64234cf5602e9c4578c3989ac79f8ab308fd",
    "bytes": 1226
  },
  "rank": 6,
  "free_coordinates": 3
}

Finding. The six retained relations have rank6 on nine ages, leaving three free coordinates. They reduce the local input model without uniquely recovering the whole age sequence.

Reassessment. Describe the three remaining freedoms explicitly to see which source values are still needed.

C1134 — Parametrize the unresolved age family

Question. What does every age sequence satisfying the six retained constraints look like?

Sources. C1133

Inputs

{}

Results

{
  "parametrization": {
    "path": "model/SP_age_parametrization.json",
    "sha256": "de7e3be7439f8607d97083bb28d39c658f2d44e702d9f70cc9e47c15a0f2128f",
    "bytes": 646
  },
  "source_parameters": [
    65,
    105,
    70
  ]
}

Finding. All solutions are controlled by the shared65 scale and two interior ages. Adam and Jared follow from that scale; Enosh follows from the460 total and the two retained interior ages. This is conditional reconstruction, not proof of historical choice.

Reassessment. Identify how the same three freedoms appear in birth positions and the Flood-cap output.

C1135 — Track the remaining freedoms through source positions

Question. Which birth coordinates can change while the newly constrained age relations remain true?

Sources. C1134; C954; C972

Inputs

{}

Results

{
  "birth_directions": {
    "path": "model/SP_unresolved_birth_directions.json",
    "sha256": "06c8549a24f007d713d04909118201f454eefd03e7b5188a2463cfbf41972610",
    "bytes": 595
  },
  "changing_row_indices": [
    1,
    2,
    3,
    4,
    6
  ]
}

Finding. The unresolved source freedom changes internal births while retaining Adam and Jared positions, Methuselah and Lamech positions, and the named active cap capacities. The460 source total fixes a whole segment but not its interior.

Reassessment. Determine whether ordinary positivity and the active cap support reduce the remaining65-scale freedom.

C1136 — Bound the residual age freedom by the whole cap

Question. Do positivity and all nine cap inequalities identify the shared age scale?

Sources. C1134–C1135; File18 §3.1.3

Inputs

{}

Results

{
  "inequality_model": {
    "path": "model/SP_age_cap_inequalities.json",
    "sha256": "3bc99eb9d464d5649ce7756d19131a50985dbb4272fa69301647bc5b2bbbee5e",
    "bytes": 980
  },
  "integer_scale_range": [
    48,
    126
  ]
}

Finding. The full cap permits a broad positive-age scale interval; explicit alternatives at48 and126 retain every capped lifespan. Its source value65 needs additional information.

Reassessment. Test the source-motivated five-year grid and observed early-age order with65 retained.

C1137 — Test whether the early rounded grid fixes the interior

Question. Do the first-five460 total, retained65 scale, five-year grid and descending order recover105,90,70?

Sources. C1134; File51a §8.3; File18 §3.1

Inputs

{
  "scale": 65,
  "grid": 5,
  "order": "130>Seth>Enosh>Kenan>65"
}

Results

{
  "early_grid_fibre": {
    "path": "model/SP_early_grid_fibre.json",
    "sha256": "fe333c9392687892aa535da1858fa1fb571bf4bb53e83babb93ea0a5c4aa94b6",
    "bytes": 606
  },
  "solutions": [
    [
      95,
      90,
      80
    ],
    [
      100,
      85,
      80
    ],
    [
      100,
      90,
      75
    ],
    [
      100,
      95,
      70
    ],
    [
      105,
      85,
      75
    ],
    [
      105,
      90,
      70
    ],
    [
      110,
      80,
      75
    ],
    [
      110,
      85,
      70
    ],
    [
      115,
      80,
      70
    ],
    [
      120,
      75,
      70
    ]
  ],
  "count": 10
}

Finding. The natural five-year grid and strict early-age order still permit multiple internal allocations. The actual105,90,70 is retained as source data rather than forced by460 and65.

Reassessment. Determine how much one extra internal source age would identify within this complete bounded family.

C1138 — Locate the remaining source information in the grid family

Question. Which single retained interior age, if any, identifies the printed sequence?

Sources. C1137

Inputs

{}

Results

{
  "single_age_fibres": {
    "path": "model/SP_grid_single_measurements.json",
    "sha256": "a71a44cba2970798613a05ef054fc169c326a4f021b63764c9a30ec17d4e5e7a",
    "bytes": 482
  },
  "counts": {
    "Seth": 2,
    "Enosh": 3,
    "Kenan": 5
  },
  "rejected_hypothesis": "Enosh90 alone was tested for uniqueness; it leaves3 candidates"
}

Finding. Each single source age leaves multiple grid allocations: Seth105 leaves2, Enosh90 leaves3, and Kenan70 leaves5. The tested single-age uniqueness hypothesis fails even within the selected grid/order conditions.

Reassessment. Compare finite-grid identification with an unrestricted rational source-coordinate basis.

C1139 — Complete the age reconstruction with a stated source basis

Question. Which retained source coordinates close the unconstrained linear age model?

Sources. C1133–C1134; File18 §3.1

Inputs

{}

Results

{
  "age_basis": {
    "path": "model/SP_age_basis_completion.json",
    "sha256": "b4a86d46e1fe491032030e01dbd19b5f4be75570e41dd6ec824d20c3883fe9de",
    "bytes": 1248
  },
  "rank": 9,
  "reconstructed": [
    130,
    105,
    90,
    70,
    65,
    62,
    65,
    67,
    52
  ]
}

Finding. The shared65 age and two interior ages provide an exact full-rank reconstruction after the six stated relations are retained. The distinction between a rational model and a bounded grid explains their different identification costs.

Reassessment. Audit the full input cost so reverse cap recovery is not counted as a new independent source explanation.

C1140 — Separate source constraints from reverse measurement

Question. Does the age parametrization reduce the whole source packet or only one conditional representation?

Sources. C1133–C1139; Strategy §§5B,5D,6

Inputs

{}

Results

{
  "information_cost": {
    "path": "model/SP_age_information_cost.json",
    "sha256": "53203ef61c17ad91efec986f1a744f660ce0ee9fefaa08f0b9722ad688850f5e",
    "bytes": 729
  },
  "source_age_constraints": 3,
  "conditional_cap_constraints": 3
}

Finding. The age analysis supplies a useful reconstruction order, but cap values must be counted when used backward. The genuinely additional source-age structure is the two half/equality relations and the460 total; the chosen interior ages remain unexplained.

Reassessment. Examine whether the source Methuselah-Flood equation explains a baseline lifespan discarded by the SP cap.

C1141 — Recover the Methuselah baseline from its source death relation

Question. Can a retained MT/LXX local birth chain account for the lifespan discarded by SP clipping?

Sources. File18 §4A.2; C1140

Inputs

{
  "MT_Methuselah_begetting": 187,
  "MT_Lamech_begetting": 182,
  "Noah_to_Flood": 600
}

Results

{
  "baseline_constraint": {
    "path": "model/Methuselah_baseline_constraint.json",
    "sha256": "3e0ae70dac9acb4008d9ddabe4369fad9fe0a997274246020ac165e5ecee9f9e",
    "bytes": 319
  },
  "life": 969,
  "discarded_excess": 249
}

Finding. The supplied MT/LXX death-at-Flood condition recovers969 from187,182 and600, hence the249 excess above SP720. This connects traditions through a local condition while retaining its three source inputs.

Reassessment. Derive the249 difference directly from the two begetting changes and the inclusive convention.

C1142 — Explain the Methuselah249 reduction by local changes

Question. Which pieces of the retained source shift produce249 rather than250?

Sources. C1141; File18 §§2.1.3,3.1

Inputs

{}

Results

{
  "local_reduction": {
    "path": "model/Methuselah_reduction_decomposition.json",
    "sha256": "9613acc437399d19ecf7d394e9e7031aab6d0633eac1ad3bb00846c643bcb5fc",
    "bytes": 299
  },
  "reduction": 249
}

Finding. The249 reduction is120+130−1: two local age changes and one count-convention difference. Using the ordinal53 label gives129 at that stage, but the completed52 primary path must not receive a second correction.

Reassessment. Place all nine ancestral rows on the same capacity-and-slack comparison.

C1143 — Express the SP changes as capacity reductions against baseline slack

Question. Does one positive-part formula explain all three clipped rows and the six unchanged lives?

Sources. File18 §§2.1.3,3.1.3; C1142; C953–C970

Inputs

{}

Results

{
  "slack_transfer": {
    "path": "model/SP_capacity_slack_transfer.json",
    "sha256": "7f737584f8e0dd53f2a57af2a4fa39e337666e91bbc66594a19bc6f82f4d2e25",
    "bytes": 696
  },
  "capacity_reductions": [
    350,
    350,
    350,
    350,
    350,
    350,
    250,
    250,
    130
  ],
  "slack": [
    727,
    615,
    517,
    422,
    367,
    235,
    670,
    1,
    6
  ],
  "life_reductions": [
    0,
    0,
    0,
    0,
    0,
    115,
    0,
    249,
    124
  ]
}

Finding. A single threshold law generates the whole SP reduction field: only capacity loss exceeding pre-existing baseline slack reduces a life. Jared crosses by115, Methuselah by249, Lamech by124; the other six retain slack.

Reassessment. Separate the role of age-change location from its total350 capacity reduction.

C1144 — Locate each capacity-loss step in the genealogy

Question. Why does a shared350 loss affect some rows differently and shrink downstream?

Sources. C1143; File18 §§2.1.3,3.1

Inputs

{}

Results

{
  "step_locations": {
    "path": "model/SP_capacity_step_locations.json",
    "sha256": "d66ca2af1e2770ef2b872ecf735a4a81562fedba81a4977961c395fd244f7c70",
    "bytes": 544
  },
  "local_losses": [
    0,
    0,
    0,
    0,
    0,
    100,
    0,
    120,
    130
  ]
}

Finding. The350 loss is the cumulative effect of three located changes100,120,130. Its downstream levels350,250,130 follow their positions, so the complete cap response depends on an ordered source change vector, not just its total.

Reassessment. Test whether moving a fixed loss to a different source row preserves the cap output.

C1145 — Test the information carried by loss placement

Question. Can an unchanged total350 produce a different complete lifespan field?

Sources. C1144; Strategy §6

Inputs

{}

Results

{
  "placement_counterexample": {
    "path": "model/SP_loss_placement_counterexample.json",
    "sha256": "761b4d186e53aa9ba06e42fd3cd7c00d5e751ac739537c9ce31c982bbaa7ac73",
    "bytes": 940
  },
  "lifespan_difference": [
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    20,
    0
  ]
}

Finding. A diagnostic exchange of100 and120 preserves the outer350 loss but changes Methuselah’s capped life by20. The source locations carry explanatory information that an endpoint total discards.

Reassessment. Determine which baseline lifespan relations the new threshold explanation still leaves unresolved.

C1146 — Classify the remaining baseline-life explanations

Question. Which existing source relations identify a discarded excess, and which merely re-express supplied biography?

Sources. prep/sp_source_relations.md; File51a §3.4; File18 §4A; File17 §§8.1,12.1

Inputs

{
  "source_inventory_sha256": "35f1150e6b9cd4e43fb4f8c2dbfae942535014f2f0dbde5c2f6ee81f46e3db25"
}

Results

{
  "baseline_status": {
    "path": "model/baseline_explanation_status.json",
    "sha256": "54e0af53e6738024ef0b04038ba931ad897a5ea2ae2d8886c6c457ee6ac9e2da",
    "bytes": 703
  }
}

Finding. Methuselah has an explicit local alignment equation. Jared and MT Lamech can be recovered from their retained biography components. Calculated LXX571 cannot independently explain753, and the prophetic complement requires a separate inferred identification.

Reassessment. Test the relational content of the complete777/753/653 Lamech triple without assigning historical priority.

C1147 — Measure the information in the Lamech triple

Question. What do the two stated differences24 and100 determine about the three source lives?

Sources. File18 §4A.4; C1146

Inputs

{}

Results

{
  "triple_constraints": {
    "path": "model/Lamech_triple_constraints.json",
    "sha256": "61fae319a4c2351f7e4ee251e9cc765554e0854c54013fb75e77ca26e72cd598",
    "bytes": 504
  },
  "rank": 2,
  "common_translation_freedom": true
}

Finding. The24 and100 relations fix two differences but leave a common lifespan translation free. Holding653 reconstructs753 and777 conditionally; the124 comparison follows and adds no third independent relation.

Reassessment. Translate the cap result into remaining-year measurements to connect it to conserved-lifespan repartition.

C1148 — Express the clipped rows in begetting and remainder coordinates

Question. How do the three SP lifespan changes split between birth intervals and remaining years?

Sources. File18 §§2.1.3,3.1; C1143

Inputs

{}

Results

{
  "clipped_row_decomposition": {
    "path": "model/SP_clipped_row_decomposition.json",
    "sha256": "ec2429915a537f5878593c1d589d17cbcc927e5285357521d3a43bfad7a7e0db",
    "bytes": 684
  },
  "MT_remainders": [
    800,
    782,
    595
  ],
  "SP_algebraic_remainders": [
    785,
    653,
    601
  ]
}

Finding. The changes split as Jared−100/−15, Methuselah−120/−129 and Lamech−130/−124 in begetting/remainder coordinates. Both components can change when life is clipped, unlike a conserved-lifespan repartition.

Reassessment. Ask which shared Flood-boundary relations survive this change of row coordinates.

C1149 — Derive adjacent-cap remainder relations

Question. When does a clipped ancestor’s remaining count equal the next capacity or next lifespan?

Sources. C1148; File18 §3.1.3

Inputs

{}

Results

{
  "adjacent_cap_relations": {
    "path": "model/SP_cap_remainder_relations.json",
    "sha256": "6c303c3e35f6e67041ad8bb85aff9b5d33d0bc089a1ef7c4e918d56cbce80f9d",
    "bytes": 598
  }
}

Finding. A clipped row’s algebraic remainder equals the next capacity. Adjacent clipped rows therefore share a remainder/life equality; across uncapped Enoch the equality is with capacity785, leaving the actual365 distinct.

Reassessment. Use this source-local distinction to formulate a compact connection from the SP mechanism to the wider row grammar.

C1150 — State what the SP source analysis has explained

Question. What positive connection can now replace the open-ended search for every individual age?

Sources. C1132–C1149; Strategy §§1,5B,6; selection_audit review message

Inputs

{}

Results

{
  "SP_explanatory_note": {
    "path": "deliverables/SP_Source_Choices_Interim.md",
    "sha256": "f8d6c70379638fc4ee9356e646f96993e7c07f1f834340eeef4018446b5f6c65",
    "bytes": 2431
  },
  "C1139_clarification": "No retained-coordinate-count advantage established for the actual grid tuple; both models use scale plus two interior ages."
}

Finding. The SP investigation has a bounded explanatory result: source age relations plus a located capacity-loss/slack law. Unresolved individual ages remain explicit, and the next constructive extension is the post-Flood component structure.

Reassessment. Adopt the complete post-Flood source packet and identify a common row-operation basis.

C1151 — Adopt the complete post-Flood relational packet

Question. Which full ordered source field will test the extension beyond Flood clipping?

Sources. File18 §§2.2,3.2.1,4.2; prep/postflood_source_packets.md

Inputs

{
  "packet_sha256": "514d9bb85d0b0da636197a33c50f6bf8c6da5474cf425eb9500f8f95b8f5e23c"
}

Results

{
  "postflood_rows": {
    "path": "model/postflood_rows.json",
    "sha256": "a0ff44bb5f3bc7719a261916b06d853f671442e15a331d688ac3ad20fc60d426",
    "bytes": 6240
  },
  "rows": 28
}

Finding. The complete28-row source packet preserves native Cainan, SP officialTerah145, corrected LXX339/339/330 and calculated-remainder provenance. It provides a fixed family for testing shared component constraints.

Reassessment. Define a unique two-component row-change basis and distinguish its conserved quantities.

C1152 — Define the row-operation basis

Question. Can every compatible change in begetting, remainder and lifespan be written with two explicit operations?

Sources. Strategy §§3.2,5B; C1151

Inputs

{}

Results

{
  "row_basis": {
    "path": "model/row_operation_basis.json",
    "sha256": "d5890c1fc31751f0260af97c1b982841593fe6ecf28fd42cf503922eb04be8e2",
    "bytes": 385
  },
  "basis_matrix": [
    [
      1,
      0
    ],
    [
      -1,
      1
    ],
    [
      0,
      1
    ]
  ],
  "rank": 2
}

Finding. Two row operations describe every compatible source change uniquely: transfer between begetting and remainder while preserving life, then change remainder and life together while preserving begetting. Their equal-amplitude combination preserves remainder.

Reassessment. Place the complete post-Flood inter-tradition changes in this basis.

C1153 — Encode every post-Flood row change in the common basis

Question. Does the same pair of operations cover the entire source packet including its exceptions?

Sources. C1151–C1152

Inputs

{}

Results

{
  "complete_operations": {
    "path": "model/postflood_row_operations.json",
    "sha256": "ce50515189f1475e712c55d19ed24a1ae8404803ccad6213e8e4cd37e227799b",
    "bytes": 1809
  },
  "rows": 18,
  "operation_pairs": [
    [
      0,
      -60
    ],
    [
      0,
      0
    ],
    [
      50,
      0
    ],
    [
      50,
      60
    ],
    [
      100,
      -60
    ],
    [
      100,
      0
    ],
    [
      100,
      27
    ],
    [
      100,
      40
    ],
    [
      100,
      100
    ]
  ]
}

Finding. All18 shared-row transformations fit the same R/A basis. The exceptional Eber,Nahor andTerah rows receive explicit source coefficients; they are not hidden inside a uniform-century claim.

Reassessment. Test whether three shared amplitudes generate those located coefficients across the whole packet.

C1154 — Construct the shared-amplitude post-Flood dictionary

Question. Can the located operations be generated by one century, one sixty and one early-life increment?

Sources. C1153; prep/postflood_source_packets.json

Inputs

{
  "amplitudes": [
    "u=100",
    "t=60",
    "a=27"
  ]
}

Results

{
  "amplitude_dictionary": {
    "path": "model/postflood_amplitude_dictionary.json",
    "sha256": "3bba40cef2d38a6ebc31e2206c567e328bd0cf20b85aeff0f4f44daaf4a57d98",
    "bytes": 3645
  },
  "rank": 3,
  "outputs": 36
}

Finding. The whole36-coordinate change packet lies in a rank3 source-labelled model with amplitudes100,60,27. Repeated changes share parameters, but their named supports remain part of the description.

Reassessment. Determine which observations actually recover the three amplitudes.

C1155 — Recover amplitudes from a minimal local observation set

Question. Which three source differences identify the shared dictionary parameters?

Sources. C1154

Inputs

{}

Results

{
  "local_parameter_recovery": {
    "path": "model/postflood_local_parameter_recovery.json",
    "sha256": "a9277fb71ba857920e95d12af2670e7b6193a9dea00ee394681db9ee7fc7761c",
    "bytes": 419
  },
  "parameters": [
    100,
    60,
    27
  ]
}

Finding. One century begetting difference, the officialTerah lifespan difference and one early LXX life difference recover all three amplitudes. Other rows test the already fitted support pattern rather than introducing new parameter values.

Reassessment. Compare the information visible through regular and cumulative measurements.

C1156 — Compare regular and cumulative parameter visibility

Question. Which parts of the shared source change are invisible in each chronological measurement?

Sources. C1154; Strategy §§3.1–3.2

Inputs

{}

Results

{
  "projection_visibility": {
    "path": "model/postflood_projection_visibility.json",
    "sha256": "817997b009590c22ea121ef6263e5a8436ee996461cd9bcca741b2ace15aa4c8",
    "bytes": 325
  },
  "ranks": [
    1,
    1,
    3
  ]
}

Finding. The same source dictionary has different visible information in each mode: regular ages see only100, SP life differences only60, and the full LXX life field sees all three amplitudes. This explains aligned births alongside different cumulative structures.

Reassessment. Determine what is lost when the complete lifespan fields are reduced to their outer totals.

C1157 — Measure amplitude information retained by whole totals

Question. Which source parameters disappear when the ordered fields are summed?

Sources. C1156; C1154

Inputs

{}

Results

{
  "total_measurements": {
    "path": "model/postflood_total_measurements.json",
    "sha256": "005cfbe0c33d8d6f5d03d6b178ed8e0afbed34a7a74e61b900ddbf64faf729c6",
    "bytes": 303
  },
  "measurement_rows": [
    [
      "13/2",
      0,
      0
    ],
    [
      0,
      -2,
      0
    ],
    [
      4,
      0,
      2
    ]
  ],
  "life_total_rank": 2
}

Finding. The totals are6.5u,−2t and4u+2a. The two lifespan totals have rank2 and cannot separateu froma; LXX’s total also cancels its two opposite t contributions. Ordered rows preserve information absent from their sum.

Reassessment. Ask whether combining regular and cumulative outer totals recovers the amplitudes under fixed source supports.

C1158 — Recover the shared amplitudes from complementary totals

Question. Do the regular and two cumulative totals jointly determine the fixed-support model?

Sources. C1157

Inputs

{}

Results

{
  "total_parameter_recovery": {
    "path": "model/postflood_total_parameter_recovery.json",
    "sha256": "b7cbee8e9ee57c6f28bdf47561a51e5ccc5813084a78f29fef11b3d65d7a2bc1",
    "bytes": 377
  },
  "determinant": -26,
  "parameters": [
    100,
    60,
    27
  ]
}

Finding. The three complementary totals recover100,60,27 exactly within the fixed-support model. Their success depends on the located source patterns; totals alone cannot justify that pattern.

Reassessment. Demonstrate the source-location information that this recovery still requires.

C1159 — Separate amplitude recovery from row-support recovery

Question. Can the same total data conceal a different internal life field?

Sources. C1158; Strategy §6

Inputs

{}

Results

{
  "support_counterexample": {
    "path": "model/postflood_support_counterexample.json",
    "sha256": "653291f11ca05bc926527501af839c04f4434d5a277eb033ea4c686ca8d3acd6",
    "bytes": 582
  },
  "same_total": 454
}

Finding. Exchanging the27 and40 increments at Arphaxad andEber preserves454 and every regular age while changing two lives and an internal cumulative boundary. The complete source support therefore remains essential.

Reassessment. Examine the repeated early remainder block as a source relation within that support.

C1160 — Identify the complete early remainder block

Question. What common row relation joins Arphaxad andShelah across the three traditions?

Sources. C1151; File18 §§2.2,3.2.1,4.2

Inputs

{}

Results

{
  "early_remainder_block": {
    "path": "model/postflood_early_remainder_block.json",
    "sha256": "23053bb32fd37dee359f22da33f10026d82015860d95b4f10fc261847999bd8e",
    "bytes": 721
  },
  "remainder_values": {
    "MT_native_OFF": 403,
    "SP_native_OFF_official145": 303,
    "LXX_native_ON": 330
  }
}

Finding. Each tradition preserves an equal-remainder Arphaxad/Shelah pair:403,303 or330. Their five-year begetting difference is matched by a five-year lifespan difference. This is a relational block carried through both measurements.

Reassessment. Determine how many independent coordinates describe the complete cross-tradition early block.

C1161 — Parametrize the early six-row source block

Question. How much of the Arphaxad/Shelah field follows from equal remainders and shared changes?

Sources. C1160; C1154

Inputs

{}

Results

{
  "early_block_model": {
    "path": "model/postflood_early_block_rank.json",
    "sha256": "9beab9334ccc6dfe598b19d29df22d6e27f16d09864886912b193b39a474fec6",
    "bytes": 1173
  },
  "rank": 5,
  "outputs": [
    35,
    438,
    30,
    433,
    135,
    438,
    130,
    433,
    135,
    465,
    130,
    460
  ]
}

Finding. Five coordinates describe the twelve early b/L values once the equal-remainder and shared-change relations are held. The source35/30 difference and common403 remainder have distinct roles from the100 and27 transformation amplitudes.

Reassessment. Compare the late Peleg/Reu/Serug block, where the conserved quantity changes.

C1162 — Parametrize the late remainder-preserving block

Question. What shared rule generates the Peleg/Reu/Serug rows across MT,SP andLXX?

Sources. C1151; C1152

Inputs

{}

Results

{
  "late_block_model": {
    "path": "model/postflood_late_block_rank.json",
    "sha256": "10c554b5f058f61a1fab50938cb7c20c949b0777afa8963a5e1428ab70238a1a",
    "bytes": 1889
  },
  "rank": 7,
  "outputs": [
    30,
    239,
    32,
    239,
    30,
    230,
    130,
    239,
    132,
    239,
    130,
    230,
    130,
    339,
    132,
    339,
    130,
    330
  ]
}

Finding. The late block has seven free coordinates in this model: six baseline components and one shared century. MT→SP preserves each life; SP→LXX preserves the raised begetting age; the combined MT→LXX move preserves the original remainder.

Reassessment. Check that the intermediate rows in this factorization are actual suppliedSP rows.

C1163 — Identify a source-realized two-stage row factorization

Question. Does the late conserved-remainder operation pass through the suppliedSP biography?

Sources. C1162; File18 §§2.2,3.2.1,4.2

Inputs

{}

Results

{
  "source_triangles": {
    "path": "model/postflood_late_source_triangles.json",
    "sha256": "504ebfd746ae2abdfad8dfce687da3726454b0699c71b81682eaf63d7c32e95e",
    "bytes": 1230
  }
}

Finding. For all three late rows, the intermediate R100 result is the suppliedSP row, and the following A100 result is the suppliedLXX row. This gives a concrete connection between three source families while leaving historical direction open.

Reassessment. Extend the source-realized factorization to all nine common post-Flood rows.

C1164 — Factor the complete post-Flood triangle throughSP

Question. Can the same source-realized composition explain early blocks and exceptional rows too?

Sources. C1153; C1163

Inputs

{}

Results

{
  "complete_source_triangle": {
    "path": "model/postflood_complete_source_triangle.json",
    "sha256": "a644d72f2230a2074ea533eee0f3cf78937af3db7b77691b405c5c074bd9f0de",
    "bytes": 1967
  },
  "SP_to_LXX_life_changes": [
    0,
    27,
    27,
    100,
    100,
    100,
    100,
    60,
    60
  ]
}

Finding. Every common post-Flood row admits the source-realized triangle. SP andLXX share the begetting measurement, so their final edge changes only remainder and lifespan:27/27, four100s, two60s, and the unchangedShem row.

Reassessment. Express that final edge as a disjoint three-amplitude source pattern.

C1165 — Compress the SP-to-LXX lifespan edge by its disjoint supports

Question. Which part of the three-tradition pattern is common to every final-edge row?

Sources. C1164; C1154

Inputs

{}

Results

{
  "disjoint_life_pattern": {
    "path": "model/SP_LXX_disjoint_life_pattern.json",
    "sha256": "01a75dc646299050788ad3967c1ae427f21c540b567488b8b056b0edaedc0d64",
    "bytes": 865
  },
  "rank": 3,
  "source_total": 574
}

Finding. The final lifespan edge is a disjoint4/2/2 pattern with amplitudes100,60,27. It explains a common regular birth path alongside a cumulative surplus574, with no need to assign a different birth transformation to each row.

Reassessment. Determine how the pattern propagates through the complete cumulative path rather than just its total.

C1166 — Propagate the disjoint source pattern through the whole cumulative field

Question. Does the three-amplitude model retain its meaning at every ordered boundary?

Sources. C1165; inherited U reconstruction

Inputs

{}

Results

{
  "cumulative_pattern": {
    "path": "model/SP_LXX_cumulative_amplitude_pattern.json",
    "sha256": "e636ce7c4b437dc61d4ef11a76b1bad546c0c272bd29adbd0a9549f778710d4d",
    "bytes": 805
  },
  "rank": 3,
  "complete_field": [
    574,
    574,
    547,
    520,
    420,
    320,
    220,
    120,
    60
  ]
}

Finding. The same three amplitudes generate all nine cumulative differences574,574,547,520,420,320,220,120,60. Repeated and changing plateaus follow the exact source support; the cumulative representation retains all three parameters.

Reassessment. Separate the triangle’s operator consistency from genuinely additional source constraints.

C1167 — Audit the source triangle’s dependent agreements

Question. Which parts of the three-route agreement explain source structure rather than restate subtraction?

Sources. C1164–C1166; Strategy §5D

Inputs

{}

Results

{
  "triangle_dependency_audit": {
    "path": "model/postflood_triangle_dependency_audit.json",
    "sha256": "317aab7f9adab28520c4e945715e4382cab042135c1e1e0987ba8f4c71b20c44",
    "bytes": 876
  }
}

Finding. The triangle closure itself is forced subtraction. Its useful content is the repeated source-supported coefficient pattern and the actualSP intermediate rows; these organize the family without multiplying its evidence.

Reassessment. Restore nativeCainan through its complete source biography and determine which information the repeated330 block shares.

C1168 — Restore nativeCainan as a labelled member of the early block

Question. What is numerically shared by Cainan andShelah, and what remains a distinct source premise?

Sources. File18 §§1.6.1,4.2; C1160–C1161

Inputs

{}

Results

{
  "native_Cainan_block": {
    "path": "model/native_Cainan_early_block.json",
    "sha256": "8f34af9bc7db2a7446cb5d8e8caf4bbf4e402117c0ad3ce0c4af0abe271f8835",
    "bytes": 487
  },
  "shared_vector": [
    130,
    330,
    460
  ]
}

Finding. NativeCainan extends the early330-remainder block and numerically repeatsShelah’s130/330/460 biography. That equality can share numeric parameters while Cainan’s existence, name and position remain independent source structure.

Reassessment. Compute the parameter count of the whole native post-Flood family under the declared relations.

C1169 — Measure the complete native post-Flood model dimension

Question. How many free numeric coordinates generate all28 source rows under the stated dictionary and Cainan relation?

Sources. C1154; C1168

Inputs

{}

Results

{
  "native_joint_model": {
    "path": "model/postflood_native_joint_model.json",
    "sha256": "17da9d5fcad0baf115b8fa23a2e47b303607a8d6cedbbfae7efb96cfcf4b1d54",
    "bytes": 12227
  },
  "outputs": 56,
  "rank": 21
}

Finding. The complete28-row native family has56 b/L outputs generated by21 numeric coordinates in the declared model. This includes the18 baseline values; the three-amplitude claim does not erase their input cost.

Reassessment. Assess what the MT equal-remainder relation contributes if it is included in the baseline itself.

C1170 — Include the baseline early-remainder relation

Question. Does the MT Arphaxad/Shelah constraint reduce the complete family model rather than only a projection?

Sources. C1160; C1169

Inputs

{}

Results

{
  "restricted_native_model": {
    "path": "model/postflood_native_with_early_relation.json",
    "sha256": "e2d25c8794d995a9ca16bbcad5b65a9c753686c1ab310eeb5a36c6418897a732",
    "bytes": 427
  },
  "rank": 20
}

Finding. Including the shared MT403 remainder as a relation reduces the declared whole-family dimension from21 to20. The reduction applies to all native outputs coherently; it does not make403 or the remaining baseline ages self-explanatory.

Reassessment. Test another explicit repeated baseline value and keep its numerical role separate from shared operators.

C1171 — Keep baseline equalities distinct from transformation equalities

Question. How do the repeated MT ages and lives constrain the complete native family?

Sources. File18 §2.2; C1169–C1170

Inputs

{}

Results

{
  "baseline_equalities": {
    "path": "model/postflood_baseline_equalities.json",
    "sha256": "6382fce0b770c956c180be8131004b9c5048295a016096aaf672bd619fb29f86",
    "bytes": 1085
  },
  "constraint_rank": 4,
  "family_rank": 17
}

Finding. Four independent named baseline equalities reduce this declared native-family model to17 numeric freedoms. Baseline repetitions and shared transformation amplitudes have different explanatory roles and should remain separately costed.

Reassessment. Check whether minimizing rank alone would actually satisfy the Strategy’s compression goal.

C1172 — Reject rank alone as an explanation score

Question. Could a formally smaller numeric dimension conceal a larger description of the source family?

Sources. C1171; Strategy §6

Inputs

{}

Results

{
  "rank_counterexample": {
    "path": "model/rank_only_compression_counterexample.json",
    "sha256": "b54c1d3fc222a1ffb0f88d10a1ba8d4eb9df7b7f3e9d7c9e5c5c2ca7b4857d1a",
    "bytes": 469
  }
}

Finding. A one-dimensional fitted ray can encode every observed value only by placing all56 values in its coefficients. This shows why lower rank is not itself the Strategy’s desired compression; source rules, masks and exceptional choices must be counted.

Reassessment. Establish the algebraic domain of the row moves before using them as a shared operation grammar.

C1173 — State the domain of compatible row moves

Question. When is a two-operation row transformation a valid nonnegative biography calculation?

Sources. C1152; Strategy §§5B,5C,5G

Inputs

{}

Results

{
  "row_domains": {
    "path": "model/row_operation_domains.json",
    "sha256": "eaa724a2a5031a17aa72a8193ddeac33905c82448cef49c67467df70d7e698c6",
    "bytes": 436
  }
}

Finding. The normal form is an integer-coordinate identity, but nonnegative intermediate biographies impose order-sensitive domains. Source admission is an additional requirement beyond those inequalities.

Reassessment. Exhibit a complete positive endpoint for which one formal order leaves the nonnegative domain.

C1174 — Test order against the biography domain

Question. Can commuting formulas fail to define both source-compatible intermediate paths?

Sources. C1173

Inputs

{
  "row": [
    1,
    1,
    2
  ],
  "d": 2,
  "e": 1
}

Results

{
  "order_counterexample": {
    "path": "model/row_order_domain_counterexample.json",
    "sha256": "b7317aad0bab6daf107563c28761bb167acc40b4845d3452487bdd43095d171f",
    "bytes": 363
  }
}

Finding. The formulas commute on unrestricted coordinates, yet R-first produces a negative remainder in this diagnostic while A-first remains valid. A common endpoint therefore does not authorize every intermediate route.

Reassessment. Check how the complete source packet uses the domain-qualified operations.

C1175 — Check source-row normal forms against their domains

Question. Are the normal forms for all18 observed post-Flood changes numerically admissible, and which intermediate rows are actually supplied?

Sources. C1151–C1153; C1173–C1174

Inputs

{}

Results

{
  "normal_form_domain_check": {
    "path": "model/postflood_normal_form_domain_check.json",
    "sha256": "4d32cccf4e0881fbccf346590dae80e1d6861768549e59f3ad905f2ce5f46f61",
    "bytes": 4396
  },
  "rows": 18
}

Finding. All18 selected R-first normal forms stay nonnegative. The intermediate matches a suppliedSP row only where its lifespan is unchanged; Eber andTerah retain an additional source life change. Mathematical admissibility and source realization are now distinguished row by row.

Reassessment. Summarize the whole post-Flood connection in a compact source-labelled reconstruction.

C1176 — Write the post-Flood family explanation

Question. How can the complete three-tradition relation be presented without a catalogue of isolated totals?

Sources. C1151–C1175; Strategy §1

Inputs

{}

Results

{
  "postflood_explanation": {
    "path": "deliverables/PostFlood_Row_Grammar_Interim.md",
    "sha256": "254b621a11ea8c7c249b554a9e629f8d567f958585ab449489aa50931c1de69f",
    "bytes": 2866
  }
}

Finding. The new explanation connects complete source blocks through conserved row components and their chronological projections. It gives the positive mechanism before the parameter and provenance qualifications.

Reassessment. Prepare the full pre/post-Flood row packet to test whether the same operators extend across the entire shared genealogy.

C1177 — Freeze the complete labelled genealogy for the next extension

Question. Can the pre- and post-Flood rows be tested together without losing count and source tags?

Sources. File18 §§2–4; prep/operator_extension_proposals.json

Inputs

{
  "proposal_packet_sha256": "1421aa3dbef2f870ef256672b2abd931a3562dc997a22a606507ce3e6c58ec5e"
}

Results

{
  "complete_source_rows": {
    "path": "model/complete_source_row_packet.json",
    "sha256": "1bd5961126532673e6fda1535befc5e64cf21d67d01a3c5e78d1a613bbb8ab59",
    "bytes": 17795
  },
  "counts": {
    "MT": 19,
    "SP": 19,
    "LXX": 20
  },
  "next_domain": "ordinary rows plus separately tagged SP inclusive counts; no inferred physical remainder for those counts"
}

Finding. The58-row native packet preserves ordinary biographies, SP inclusive exceptions, nominal versus completed Lamech intervals and nativeCainan. It enables a full pre/post-Flood operator comparison under explicit types.

Reassessment. Check how the source-supported century operation changes its conserved quantity across the Flood.

C1178 — Connect the pre-Flood and post-Flood century changes

Question. Does the same100 amplitude act through different conserved components on declared source blocks?

Sources. C1152; C1163; C1177

Inputs

{}

Results

{
  "cross_Flood_century": {
    "path": "model/century_operation_across_Flood.json",
    "sha256": "0db5b3b9f3418e6025a6203479f93c9308b44961bbef0c627715807711b64182",
    "bytes": 1305
  }
}

Finding. The six pre-Flood LXX century changes preserve lifespan; the three later changes preserve remainder. The shared100 amplitude connects the blocks through the same row grammar while their different conserved quantities explain different cumulative effects.

Reassessment. Identify the additional source coefficient needed for a complete whole-genealogy model.

C1179 — Specify the whole-genealogy extension before execution

Question. Which extra local source change must join the post-Flood dictionary to cover MT andLXX completely?

Sources. C1178; File18 §4A; C1154

Inputs

{}

Results

{
  "whole_genealogy_next_model": {
    "path": "model/whole_genealogy_extension_question.json",
    "sha256": "826ee1186994592063674adc6bdb4c228acf9a60b905f281e5bdecfbba031b8e",
    "bytes": 546
  },
  "extra_life_coefficient": [
    {
      "name": "Lamech",
      "delta_b": 0,
      "delta_L": -24
    }
  ]
}

Finding. Lamech’s−24 is the only additional pre-Flood lifespan change needed. The proposed complete model will compare four shared coefficients against the less constrained five-parameter alternative, keeping its fitted Eber relation visible.

Reassessment. Assess the first block’s gains against its unresolved source burdens before the required full Strategy reread.

C1180 — Cost the first block’s explanatory gains

Question. Which results reduce a declared source model and which are consistency or new encodings?

Sources. C1132–C1179; Strategy §§1,6

Inputs

{}

Results

{
  "first_block_cost_ledger": {
    "path": "model/block1_explanation_cost_ledger.json",
    "sha256": "b8f39e95f57c25b33b0f24a4fc1a0964f14851020f0058316f5ca5dd00fc2a21",
    "bytes": 1408
  },
  "explanatory_families": 8
}

Finding. The block advances the source-generation question through located threshold behavior and a complete row-operation grammar. It leaves inherited magnitudes and source roles visible, rejects rank-only scoring, and sets up a full-genealogy test.

Reassessment. Close the50-action checkpoint, then reread every section of the Strategy before selecting C1182.

C1181 — Close the first50-action research block

Question. Is the current result coherent enough for the required fresh Strategy assessment?

Sources. C1132–C1180; model/block1_explanation_cost_ledger.json

Inputs

{}

Results

{
  "block_checkpoint": {
    "path": "deliverables/Block_01_C1132_C1181_Checkpoint.json",
    "sha256": "0f2e2674251526b7c75c73576ed59a87cb346b1b3b56b7377bbe6510791efd02",
    "bytes": 1142
  },
  "completed_in_block": 50,
  "cycle_completed": 50,
  "remaining_authorized": 250
}

Finding. The first50 actions provide a coherent SP source-choice analysis and post-Flood family reconstruction. A full fresh Strategy review is required now before any further numbered action.

Reassessment. Reread Strategy completely, reassess the whole first block, then choose C1182 as the best continuation toward the common chronological grammar.

C1182 — Extend the row grammar across the whole shared genealogy

Question. Does the five-amplitude model reconstruct every MT to LXX common-row change?

Sources. C1179; model/complete_source_row_packet.json; File18

Inputs

{
  "parameters": [
    "u",
    "lambda",
    "a",
    "e",
    "n"
  ],
  "values": [
    100,
    -24,
    27,
    40,
    60
  ]
}

Results

{
  "model": {
    "path": "model/whole_genealogy_five_model.json",
    "sha256": "00974b700a432f664a92f80cdbfdb8cef83e334d8f4ac3437aec4e3bb2921ac9",
    "bytes": 3399
  },
  "rank": 5,
  "matched_rows": 19
}

Finding. Five source-labelled amplitudes reconstruct all38 common-row begetting/lifespan changes. The same century coefficient acts before and after the Flood through different row operations.

Reassessment. Test the explicit e+n=u restriction rather than silently reducing the parameter count.

C1183 — Expose the extra premise in the four-amplitude model

Question. What is lost when Eber40 and Nahor60 are tied to the century100?

Sources. C1182; C1154

Inputs

{
  "relation": "e+n=u"
}

Results

{
  "model": {
    "path": "model/whole_genealogy_four_model.json",
    "sha256": "db6857df003663117809841c614779640cb386f165c4c8281cc8c8f03d5f8595",
    "bytes": 2952
  },
  "rank5_to_rank4": [
    5,
    4
  ]
}

Finding. The four-amplitude form is exact only after adding the fitted relation40+60=100. It is a useful compression, but not an independent derivation of these source numerals.

Reassessment. Find a small transparent observation set that recovers the five coefficients without totals.

C1184 — Recover amplitudes from local named observations

Question. Which five source differences identify the unrestricted model?

Sources. C1182

Inputs

{}

Results

{
  "recovery": {
    "path": "model/whole_genealogy_local_recovery.json",
    "sha256": "02ec326eb620855f03d145bedfec53dc2653efb6ee52b3679550b22c9c3d893b",
    "bytes": 608
  },
  "observations": {
    "Adam:b": 100,
    "Lamech:L": -24,
    "Arphaxad:L": 27,
    "Eber:L": 40,
    "Nahor:L": 60
  }
}

Finding. Adam’s begetting difference and four named lifespan differences recover the five amplitudes directly. The four-parameter version predicts a relation among these five already-known observations.

Reassessment. Determine exactly what the two chronology head differences conceal.

C1185 — Compare complete row recovery with two head differences

Question. Can regular and cumulative totals distinguish the same five coefficients?

Sources. C1182

Inputs

{}

Results

{
  "head_information": {
    "path": "model/whole_genealogy_head_information.json",
    "sha256": "855645f2d27bb371e76a02f8b5dcc6b46e64ebdaa303b4c33eb8bf74b49071c6",
    "bytes": 487
  },
  "head_differences": [
    1250,
    430
  ],
  "rank": 2,
  "lost_dimensions": 3
}

Finding. The two heads see12.5u and3u+lambda+2a+e+n. Their values1250 and430 leave three coefficient directions invisible, even though all local row changes are recoverable from five named observations.

Reassessment. Check whether the four-amplitude restriction restores that missing information.

C1186 — Test head identification after shared-amplitude compression

Question. Do two chronology heads identify the four-amplitude form?

Sources. C1183; C1185

Inputs

{}

Results

{
  "head_information": {
    "path": "model/whole_genealogy_four_head_information.json",
    "sha256": "2d00c6ef8bd02475535fe9a95771d4a08f65d68553083e88eac824606c664423",
    "bytes": 378
  },
  "kernel": [
    [
      0,
      -2,
      1,
      0
    ],
    [
      0,
      0,
      0,
      1
    ]
  ]
}

Finding. Even the four-amplitude form leaves two directions hidden from the heads: the sixty-year allocation and the trade between Lamech’s correction and the paired early increments. Complete fields are needed to locate them.

Reassessment. Restore native Cainan and distinguish insertion information from coefficient compression.

C1187 — Restore native LXX insertion after matched-row comparison

Question. What does Cainan add that no common-row coefficient can supply?

Sources. C1182; C1168; model/complete_source_row_packet.json

Inputs

{}

Results

{
  "native_insertion": {
    "path": "model/whole_genealogy_native_insertion.json",
    "sha256": "47ae760f92ed9eb575696dfb014115d80ff1215ca9b548fe188be5faaec1b50c",
    "bytes": 658
  },
  "native_heads": [
    1380,
    890
  ]
}

Finding. Native Cainan adds130 to the Regular and460 to the Cumulative head difference, producing1380 and890. Its numbers match Shelah, but its existence and ordered position are separate source information.

Reassessment. Find a whole-field observation that distinguishes an insertion from a redistributed total.

C1188 — Distinguish insertion from redistribution at the named boundary

Question. Can the same head change conceal different internal birth paths?

Sources. C1187; C1167

Inputs

{}

Results

{
  "witness": {
    "path": "model/insertion_redistribution_witness.json",
    "sha256": "d11e0e5d562cd187b3e4c49bff508fa3f70b2630d3d9df40c68ece1782c086b0",
    "bytes": 495
  },
  "equal_terminal_total": 395
}

Finding. An added130 can be hidden in a neighbouring interval if only the total is observed. The new Cainan-labelled boundary and its incidence recover the structural distinction.

Reassessment. Summarize the whole-genealogy row grammar before moving to Rounded information loss.

C1189 — Write the complete-genealogy explanatory bridge

Question. How should a reader understand the common operations without mistaking compression for origin?

Sources. C1152; C1182–C1188; C1143

Inputs

{}

Results

{
  "explanation": {
    "path": "deliverables/Whole_Genealogy_Row_Grammar_Interim.md",
    "sha256": "7614f3f07386d2d738fa9bdf7834f3147bb2c128722949f2263bed4841130c35",
    "bytes": 2203
  }
}

Finding. The complete genealogy is now described by a small vocabulary of located row operations, alongside explicit cap and insertion mechanisms. This turns the numerical comparisons into a readable family connection.

Reassessment. Establish the exact finite fibre of a Rounded row with its lifespan retained.

C1190 — Specify the joint Rounded-row observation

Question. What exact data remain after begetting and remaining years are rounded separately?

Sources. C1189; File51a; File52c_latest.md; C1131 inherited rounding analysis

Inputs

{
  "Q": "nearest multiple of5 on integer nonnegative durations"
}

Results

{
  "observation": {
    "path": "model/joint_rounding_observation.json",
    "sha256": "dda331935947e8bcd63cba12aa5afc9ec31aa3a07ca64995199c8529d7452d77",
    "bytes": 540
  },
  "cells": {
    "0": [
      0,
      1,
      2
    ],
    "5": [
      3,
      4,
      5,
      6,
      7
    ],
    "10": [
      8,
      9,
      10,
      11,
      12
    ]
  }
}

Finding. Joint Rounded observations restrict two hidden residuals to a bounded line u+v=L−B−R. Nonnegative durations truncate the cell at zero; current derived remainders do not supply independent evidence.

Reassessment. Derive and verify the exact size of that bounded line for interior cells.

C1191 — Count the exact residual fibre

Question. How many original decompositions share B,R,L away from zero?

Sources. C1190

Inputs

{}

Results

{
  "fibre_count": {
    "path": "model/joint_rounding_fibre_count.json",
    "sha256": "675aded4ec0b4aa373b5fb41a62a59b066ba872990fb481b07f80f5fd2ee610f",
    "bytes": 388
  },
  "counts": {
    "-5": 0,
    "-4": 1,
    "-3": 2,
    "-2": 3,
    "-1": 4,
    "0": 5,
    "1": 4,
    "2": 3,
    "3": 2,
    "4": 1,
    "5": 0
  }
}

Finding. Interior joint fibres have5−|z| members for |z|<=4. A singleton occurs only at z=±4, where both residuals must be the same extreme ±2.

Reassessment. Apply this criterion to the complete55-row ordinary source domain.

C1192 — Compute joint Rounded fibres on all ordinary source rows

Question. Which rows remain exactly identifiable when exact life and both rounded parts are retained?

Sources. C1191; model/complete_source_row_packet.json

Inputs

{}

Results

{
  "fibres": {
    "path": "model/ordinary_joint_rounding_fibres.json",
    "sha256": "1cb4a13c33bfabf1020e463c99bd040a92121ec0f3ae9f96e5447592ad059df7",
    "bytes": 14320
  },
  "ordinary_rows": 55,
  "singletons": [
    "MT:Methuselah",
    "MT:Reu",
    "SP:Reu",
    "LXX:Methuselah",
    "LXX:Reu"
  ]
}

Finding. Five of55 ordinary rows have singleton joint fibres: MT/LXX Methuselah, MT/LXX Reu, and SP Reu. This conditional uniqueness comes from two same-sign extreme residuals, not from new source testimony.

Reassessment. Compare each singleton with the ambiguity when only one rounded component is retained.

C1193 — Measure the gain from the second rounded component

Question. How does a singleton arise from combining two individually ambiguous observations?

Sources. C1192

Inputs

{}

Results

{
  "intersections": {
    "path": "model/joint_rounding_singleton_intersections.json",
    "sha256": "64be39ff48facb6d403eb3b77ed1258eb586e644ea46e6f4acc71aa1d8ad18ce",
    "bytes": 1372
  },
  "rows": 5
}

Finding. Each singleton combines two five-choice observations whose candidate sets touch at one endpoint. The gain is genuine conditional information, although these current observations share the same source derivation.

Reassessment. Use LXX Lamech to show a nearby non-singleton and preserve the main753 state.

C1194 — Inspect the main LXX Lamech joint ambiguity

Question. Do the rounded components identify182 and571 when life753 is known?

Sources. C1192; File18 main LXX753

Inputs

{}

Results

{
  "ambiguity": {
    "path": "model/LXX_Lamech_joint_rounding_ambiguity.json",
    "sha256": "fadf71b03bb34e6c537cd1466cce62070877a8d0061e127067d395ea05a8ae01",
    "bytes": 446
  },
  "pairs": [
    [
      181,
      572
    ],
    [
      182,
      571
    ]
  ]
}

Finding. With life753 and rounded parts180/570, both181+572 and182+571 remain possible. The current182/571 pair still needs its source assignment; the753 state remains primary.

Reassessment. Determine the total amount of conditional ambiguity across all55 rows.

C1195 — Summarize the full joint observation ambiguity

Question. How much rowwise ambiguity remains before any cross-row constraints are introduced?

Sources. C1192

Inputs

{}

Results

{
  "summary": {
    "path": "model/ordinary_joint_rounding_ambiguity_summary.json",
    "sha256": "43d77706b99348a303441412447f3e223d6ddb7189c1f94240874ff6c964f417",
    "bytes": 403
  },
  "histogram": {
    "1": 5,
    "2": 1,
    "3": 13,
    "4": 6,
    "5": 30
  },
  "products": {
    "MT": 22781250000,
    "SP": 2531250000,
    "LXX": 210937500000
  }
}

Finding. The joint observations narrow every row to at most five possibilities but leave50 of55 rows ambiguous. Their product counts formal decompositions only, before source-labelled cross-row relations are imposed.

Reassessment. Test whether source-equal remaining years create additional recovery in the early post-Flood block.

C1196 — Intersect Rounded fibres with the early equal-remainder relation

Question. Does Arphaxad/Shelah equal remaining life select their exact source decomposition?

Sources. C1192; C1160

Inputs

{}

Results

{
  "intersections": {
    "path": "model/early_pair_rounding_relation.json",
    "sha256": "5c76d1a7978ba62189b3f22166a016fb9443399c0063a6ba53cdce442783599a",
    "bytes": 987
  },
  "counts": [
    [
      "MT",
      9,
      3
    ],
    [
      "SP",
      9,
      3
    ],
    [
      "LXX",
      25,
      5
    ]
  ]
}

Finding. The equal-remainder premise sharply reduces paired ambiguity but does not identify the exact early values. Its five-year begetting difference follows from the exact lifespan difference once the shared remainder is imposed.

Reassessment. Test the late block where Reu supplies a conditional singleton.

C1197 — Test late-block recovery under shared century operations

Question. Do the exact Reu recovery and shared source operations determine Peleg and Serug?

Sources. C1192; C1162; C1171

Inputs

{}

Results

{
  "late_block": {
    "path": "model/late_block_joint_rounding_recovery.json",
    "sha256": "7b23de1d3ad4c27eb643636c854a02745d7b03a84e9a3920e9f00a86d6309ed4",
    "bytes": 333
  },
  "remaining_common_choices": [
    28,
    29,
    30,
    31
  ]
}

Finding. Reu is conditionally fixed at32, while Peleg and Serug can jointly take28,29,30 or31 in MT, with the century counterparts in SP/LXX. The shared row grammar narrows the block but does not generate the source30.

Reassessment. Identify the exact missing kind of input rather than search for a new numerical target.

C1198 — State the residual information needed to recover an ordinary row

Question. Which one additional coordinate resolves any remaining joint fibre?

Sources. C1190–C1197

Inputs

{}

Results

{
  "recovery": {
    "path": "model/joint_rounding_residual_recovery.json",
    "sha256": "0783a2d7611a7e7908a1a1d4fd35ccb0353d9e71b1a0cffd1690be45463a06f5",
    "bytes": 4132
  },
  "rows": 55
}

Finding. One exact residual per ambiguous row supplies what joint rounding removed. Singleton rows need no extra residual, but reading a stored source residual back is reconstruction, not a new discovery.

Reassessment. Connect the joint fibre to the failure of separate rounding to preserve b+r=L.

C1199 — Derive the row rounding carry from the hidden residual sum

Question. How does the joint observation control the difference between rounded life and rounded parts?

Sources. C1191; C1192

Inputs

{}

Results

{
  "carry_bridge": {
    "path": "model/joint_rounding_carry_bridge.json",
    "sha256": "09df548a9ff72ded568e716ef1fca3f0cb17d025f60f6662d99181bdcbd7b46e",
    "bytes": 4134
  },
  "branches": {
    "-4": -5,
    "-3": -5,
    "-2": 0,
    "-1": 0,
    "0": 0,
    "1": 0,
    "2": 0,
    "3": 5,
    "4": 5
  }
}

Finding. The same residual sum that measures joint ambiguity determines the carry between rounded lifespan and rounded parts. Carry is−5 for z≤−3, zero for |z|≤2, and+5 for z≥3.

Reassessment. Check whether the carry by itself retains the exact joint recovery information.

C1200 — Separate carry information from exact residual information

Question. Can knowing the carry replace knowing the exact lifespan in joint recovery?

Sources. C1199

Inputs

{}

Results

{
  "carry_information": {
    "path": "model/rounding_carry_information.json",
    "sha256": "92e6d16905b18c5ee3305c094f7ef6fc0af0339cb3dc69ba596d574bf7f12d12",
    "bytes": 365
  },
  "pair_counts": {
    "-5": 3,
    "0": 19,
    "5": 3
  }
}

Finding. A carry stores only a branch: its three classes contain3,19 and3 residual pairs. Even an extreme carry leaves three possible exact decompositions when exact life is absent.

Reassessment. Combine this result with the cap, which removes excess lifespan rather than a small rounding residual.

C1201 — Write the joint Rounded-row explanatory bridge

Question. What does joint recovery add to the family picture?

Sources. C1190–C1200; C1189

Inputs

{}

Results

{
  "explanation": {
    "path": "deliverables/Joint_Rounded_Row_Information.md",
    "sha256": "f582659b5226cb2d9115eaaa9d572eff7f17c63c37f2e3cd4d8d088500a669fa",
    "bytes": 1863
  }
}

Finding. Joint Rounded observations now have a concrete information account: bounded residual fibres explain both conditional recovery and the local carry between different rounded constructions.

Reassessment. Derive the composite cap-plus-round fibre with source capacities held.

C1202 — Derive the composite cap-plus-round inverse set

Question. What original lifespans can produce a fixed rounded capped value when capacity is known?

Sources. C1201; C1143; C1131 cap analysis

Inputs

{}

Results

{
  "fibre_law": {
    "path": "model/cap_round_fibre_law.json",
    "sha256": "4ff7af76d04d05a1559f9918457b5a1ea19a6369cf01f0740073105104291fbf",
    "bytes": 2166
  }
}

Finding. At the rounded capacity, a finite rounding cell joins an unbounded cap tail. The rounded capped output can therefore forget even whether clipping occurred.

Reassessment. Apply the threshold formula to the three SP clipped capacities.

C1203 — Calculate the SP composite fibre thresholds

Question. How far below each exact cap can an uncapped life imitate its rounded clipped output?

Sources. C1202; C1143

Inputs

{}

Results

{
  "thresholds": {
    "path": "model/SP_cap_round_fibre_thresholds.json",
    "sha256": "0e5375ce43907dc1ce63d0b6d0786a30ed3ddaa91d3fbf3682294d53aea30dbb",
    "bytes": 752
  },
  "minimum_inputs": [
    843,
    718,
    653
  ]
}

Finding. Jared’s845 output permits any life at least843; Methuselah’s720 permits at least718; Lamech’s655 permits at least653. Rounded output alone does not recover the original962/969/777 ledger or generally the clipping status.

Reassessment. Determine how a known clipping branch changes the information needed for reconstruction.

C1204 — Separate the two loss types by the known cap branch

Question. Are rounding residual and cap excess independent missing quantities on every row?

Sources. C1202; C1203

Inputs

{}

Results

{
  "branch_information": {
    "path": "model/cap_round_branch_information.json",
    "sha256": "496cab05f8d37f8f3f5ac004911fb79736ca2e4435da321932625405a2f45d59",
    "bytes": 2128
  }
}

Finding. The two loss registers are not two independent unknowns per row. A known clipped row has y=c, fixing its rounding residual; a known unclipped row has zero excess and needs only its rounding residual.

Reassessment. Verify reconstruction of all nine baseline lives using the branch-appropriate register.

C1205 — Recover the baseline from branch-appropriate loss data

Question. Do the three excesses and six ordinary residuals reconstruct the complete ledger?

Sources. C1204

Inputs

{}

Results

{
  "recovery": {
    "path": "model/SP_composite_loss_recovery.json",
    "sha256": "0a7fb945140282fae094852f57bddd8f2ce60ab0bfaa766ad35a5618e246fa81",
    "bytes": 1119
  },
  "recovered": [
    930,
    912,
    905,
    910,
    895,
    962,
    365,
    969,
    777
  ]
}

Finding. The declared register exactly recovers all nine baseline lives. This is an information-preserving enlargement of the cap-and-round construction, not an inverse of its output alone.

Reassessment. Test whether the single total488 can replace the three located excesses.

C1206 — Test total-loss recovery of the clipped baseline

Question. Can total reduction488 identify the three lost source lifespans?

Sources. C1205; C1143

Inputs

{}

Results

{
  "ambiguity": {
    "path": "model/SP_total_excess_ambiguity.json",
    "sha256": "38552129de7b83e606e002bd913c6a5b105c31a1b2f1a1aa3161f1477465bceb",
    "bytes": 476
  },
  "same_total": 488
}

Finding. Total488 gives one equation for three removed amounts. Moving one year between Jared and Methuselah preserves every capped output and the total while changing the baseline ledger.

Reassessment. Determine what extra located measurements would resolve the loss distribution.

C1207 — Identify the missing located measurements for cap recovery

Question. How many extra independent excess measurements supplement the total?

Sources. C1206

Inputs

{}

Results

{
  "measurement_completion": {
    "path": "model/SP_excess_measurement_completion.json",
    "sha256": "4fc6202631b89ebf6649113e942494dbf1adf1a0b8e97840042b384ef675a920",
    "bytes": 515
  },
  "recovered": [
    115,
    249,
    124
  ]
}

Finding. After the total is retained, two independent located excesses recover the third. The source must still provide those measurements or equivalent baseline facts.

Reassessment. Relate rounded reduction to exact cap excess using the residual identity.

C1208 — Explain the change from exact to rounded cap reduction

Question. Why does total488 become485 under row rounding?

Sources. C1204; C1143; C1131 inherited cap-round result

Inputs

{}

Results

{
  "loss_identity": {
    "path": "model/cap_round_loss_identity.json",
    "sha256": "238adb4d7804f3f7873b3ee15c3ac61e23e8c1f7b8bf0615c2b7b462b5c3cb14",
    "bytes": 1794
  },
  "exact_total": 488,
  "rounded_total": 485
}

Finding. Rounded reduction equals exact removed life plus the difference of the two rounding errors. The three SP cap losses115/249/124 become115/250/120, explaining488→485 without a second cap rule.

Reassessment. Check what commutes when both the cap and its input are rounded consistently.

C1209 — State the exact cap-round commutation condition

Question. When does rounding commute with the cap?

Sources. C1208; C1131 inherited cap-round theorem

Inputs

{}

Results

{
  "commutation_scope": {
    "path": "model/cap_round_commutation_scope.json",
    "sha256": "3a28ca3976b2b3e0c3db3acc855fbab20e1484a32e4cf271b3787b19eb686a3f",
    "bytes": 450
  }
}

Finding. Cap and rounding commute when both quantities are rounded by the same monotone rule. Keeping the capacity exact on only one route changes the operation; it is not a counterexample to that theorem.

Reassessment. Test whether rounding preserves the strict fact that a life exceeded capacity.

C1210 — Distinguish cap commutation from strict clipping visibility

Question. Can exact clipping disappear after rounding, and can an unrounded cap change the result?

Sources. C1209; C1203

Inputs

{}

Results

{
  "witnesses": {
    "path": "model/cap_round_visibility_witnesses.json",
    "sha256": "9444cd743e2f3d518f91e21500c8d2c52c5d0ac6005ce952b1b6969fb8a4d77c",
    "bytes": 414
  }
}

Finding. A one-year excess can disappear inside a rounded cell. Separately, L14 and c11 yield10 when the cap is rounded consistently but11 when only the input is rounded. C1209’s12/11 example did not distinguish the routes; this one does.

Reassessment. State the strict clipping criterion in terms of rounded-cell thresholds.

C1211 — Determine the threshold for visible rounded clipping

Question. How large must a life be for its cap reduction to remain visible after rounding?

Sources. C1210; C1203

Inputs

{}

Results

{
  "visibility": {
    "path": "model/cap_round_strict_visibility.json",
    "sha256": "2a81074b2f3001decdb18bf7167d22e03ff71e1a0520a12704f08f3800f0b0b3",
    "bytes": 736
  },
  "thresholds": [
    848,
    723,
    658
  ]
}

Finding. Visible rounded clipping begins at Q(c)+3. For the SP capacities the thresholds are848,723 and658; the actual baseline lives exceed them comfortably, so all three reductions remain visible.

Reassessment. Summarize cap and rounding as distinct kinds of information loss before returning to cross-family transformations.

C1212 — Write the cap-and-round information bridge

Question. How can the two operations agree forward while remaining non-invertible?

Sources. C1202–C1211; C1143

Inputs

{}

Results

{
  "explanation": {
    "path": "deliverables/Cap_and_Round_Information.md",
    "sha256": "228c06a4b52ef3e54734d8e061292c124824d661fc306bc2a2d662d7cbd03a80",
    "bytes": 1893
  }
}

Finding. The cap-to-Rounded interface now has both a forward rule and an exact account of its lost information. This completes the bounded information analysis and returns attention to source mechanisms feeding larger chronology relations.

Reassessment. Check which whole-genealogy row operations are preserved by nearest-five rounding.

C1213 — Test row operations that translate by the five-year lattice

Question. Which changes pass through nearest-five rounding without changing their amplitude?

Sources. C1182; C1199; prep/review1182_1201 pending independent review

Inputs

{}

Results

{
  "equivariance": {
    "path": "model/round_lattice_equivariance.json",
    "sha256": "cd4cba7a1d4f52780ea7a1406c86691f7f48b8dbaefa232792e71ca96049ced1",
    "bytes": 504
  }
}

Finding. All translations by multiples of five pass through rounding exactly, including the century, half-century, forty and sixty changes. The signed carry notation uses an algebraic extension, not negative source durations.

Reassessment. Locate the only whole-genealogy amplitudes outside that lattice.

C1214 — Compute the Rounded common-row change field

Question. Where do the five source amplitudes change after rounding?

Sources. C1182; C1213

Inputs

{}

Results

{
  "rounded_field": {
    "path": "model/whole_genealogy_rounded_changes.json",
    "sha256": "59c733198e1c6b2dca7c08d425e2a4764198b31dcf334d79cc93652e6fc96cd3",
    "bytes": 3065
  },
  "changed_rows": [
    "Lamech",
    "Arphaxad",
    "Shelah"
  ]
}

Finding. Only Lamech and the Arphaxad/Shelah pair change their lifespan-difference amplitudes:−24 becomes−20, while each27 becomes25. Every common-row begetting difference survives exactly.

Reassessment. Determine why the whole Cumulative head difference nevertheless stays unchanged.

C1215 — Explain the exact cancellation in the Rounded head difference

Question. Why do local rounding changes preserve the total430?

Sources. C1214

Inputs

{}

Results

{
  "cancellation": {
    "path": "model/whole_genealogy_rounded_head_cancellation.json",
    "sha256": "3d45a7d600eda8d3b759b2b612bd9ca5267b4804fb9b58fa83e23698e46fce33",
    "bytes": 436
  },
  "located_errors": [
    {
      "name": "Lamech",
      "difference_error": 4
    },
    {
      "name": "Arphaxad",
      "difference_error": -2
    },
    {
      "name": "Shelah",
      "difference_error": -2
    }
  ]
}

Finding. The Rounded Cumulative total remains430 because Lamech contributes+4 and Arphaxad/Shelah contribute−2 each. The cancellation explains the shared head while predicting an internal displacement field.

Reassessment. Reconstruct the internal rounding-displacement field rather than stop at its zero total.

C1216 — Reconstruct the hidden interior effect of head cancellation

Question. Which cumulative boundaries move even though the head error is zero?

Sources. C1215

Inputs

{}

Results

{
  "interior_field": {
    "path": "model/whole_genealogy_rounding_interior_field.json",
    "sha256": "6d567b190a9b6394b05ca6e81b64f7eefde7f8e2021b4b92f407e75e25fa0c2d",
    "bytes": 916
  },
  "nonzero_boundaries": [
    {
      "boundary": "Noah",
      "difference_error": -4
    },
    {
      "boundary": "Shem",
      "difference_error": -4
    },
    {
      "boundary": "Arphaxad",
      "difference_error": -4
    },
    {
      "boundary": "Shelah",
      "difference_error": -2
    }
  ]
}

Finding. The head cancellation hides a−4 comparison shift at Noah, Shem and Arphaxad, followed by−2 at Shelah. Adjacent differences recover the three local rounding changes exactly.

Reassessment. Check compatibility with separately rounded remaining years and identify the carry change.

C1217 — Locate the row where the rounding carry itself changes

Question. Does rounded lifespan change always equal rounded begetting plus remaining-year changes?

Sources. C1214; C1199

Inputs

{}

Results

{
  "carry_change": {
    "path": "model/whole_genealogy_rounded_carry_change.json",
    "sha256": "9e64605b3c1b687ca5656ad9eb06a5cfe846fd29f54ea82de3a48bd97031fdc8",
    "bytes": 1422
  },
  "nonzero": [
    {
      "name": "Lamech",
      "carry_change": 5
    }
  ]
}

Finding. Lamech alone changes the carry, by+5. Its Rounded lifespan adjustment is−20, while its rounded remaining-year adjustment is−25; keeping the carry reconciles both constructions.

Reassessment. Summarize the whole-row route into Rounded chronology and select the next larger family connection.

C1218 — Lift source translations to Rounded values plus residuals

Question. How can a non-grid row change act coherently on the Rounded representation?

Sources. C1213–C1217; prep/round_joint_fibres.md

Inputs

{}

Results

{
  "translation": {
    "path": "model/rounded_residual_translation.json",
    "sha256": "f9e2b0fdc53f2c54c40d63f1de6d2aaa0aa0eef6eb8f7fe79eb7cde3bd98fdee",
    "bytes": 936
  },
  "examples": [
    {
      "x": 777,
      "d": -24,
      "Q_x": 775,
      "rho": 2,
      "rounded_shift": -20,
      "new_rounded": 755,
      "new_residual": -2
    },
    {
      "x": 595,
      "d": -24,
      "Q_x": 595,
      "rho": 0,
      "rounded_shift": -25,
      "new_rounded": 570,
      "new_residual": 1
    },
    {
      "x": 438,
      "d": 27,
      "Q_x": 440,
      "rho": -2,
      "rounded_shift": 25,
      "new_rounded": 465,
      "new_residual": 0
    },
    {
      "x": 433,
      "d": 27,
      "Q_x": 435,
      "rho": -2,
      "rounded_shift": 25,
      "new_rounded": 460,
      "new_residual": 0
    }
  ]
}

Finding. The retained residual determines how an off-grid change crosses rounded cells. This single rule explains why the same−24 change produces−20 in Lamech’s rounded lifespan and−25 in his rounded remainder.

Reassessment. Verify the lifted rule across every ordinary existing tradition comparison.

C1219 — Verify the lifted rule on all ordinary tradition changes

Question. Does one residual law cover all35 common-row comparisons and all three measurements?

Sources. C1218; model/complete_source_row_packet.json

Inputs

{}

Results

{
  "all_translations": {
    "path": "model/all_ordinary_lifted_translations.json",
    "sha256": "2758dc3c28556dbcad313c1eb49e12d357695a36b441e826377b20681d96a5ce",
    "bytes": 20768
  },
  "measurement_checks": 105
}

Finding. The lifted rule reconstructs all105 rounded measurements across35 ordinary existing row comparisons. It unifies source shifts with Rounded representation while preserving the native insertion and inclusive-row distinctions.

Reassessment. Test composition so that the rule applies to a sequence of source changes.

C1220 — Prove coherence of consecutive rounded-residual translations

Question. Does the lifted action depend on how an admitted total shift is decomposed?

Sources. C1218; C1219

Inputs

{}

Results

{
  "composition": {
    "path": "model/rounded_translation_composition.json",
    "sha256": "75a28f7bb3d4a6f20397c95c1ee5d51b30d61bd6dc6d190fbb0db940da93dba8",
    "bytes": 384
  },
  "diagnostic_cases": 25
}

Finding. The lifted translations compose exactly because they retain the full original value. Their coherence is mathematical; source authorization of each intermediate state remains separate.

Reassessment. Determine precisely when the residual may be dropped without breaking a universal shift rule.

C1221 — Characterize source shifts that descend to rounded cells

Question. When can the Rounded value alone determine the Rounded shifted value for every input?

Sources. C1213; C1220

Inputs

{}

Results

{
  "criterion": {
    "path": "model/rounded_cell_shift_criterion.json",
    "sha256": "4c2cbdaadd6fd462334918a11e56c5bcae951522a91a8675add093e2ff9ebb15",
    "bytes": 1385
  }
}

Finding. Only multiples of five act on all Rounded cells without residual information. The off-grid27 and−24 changes therefore need source residues; their successful finite examples do not define a universal rounded-only rule.

Reassessment. Conclude the second block’s local-to-Rounded bridge and begin the Strategy’s equal-gain source provenance.

C1222 — Write the source-change to Rounded-path synthesis

Question. What has the full-row test established beyond endpoint agreement?

Sources. C1213–C1221; C1189

Inputs

{}

Results

{
  "synthesis": {
    "path": "deliverables/Source_Changes_to_Rounded_Paths.md",
    "sha256": "9629485664a6702d46147cf21859dfd7a987ccbba15aee8da413d1846b06a230",
    "bytes": 1632
  }
}

Finding. The full-row test explains both stable totals and shifted internal boundaries through located residuals. It supplies the mechanism needed to carry source families into Rounded representations.

Reassessment. Bind the source-appointed nodes and wrappers of the SP rectangle before substituting cap reductions.

C1223 — Bind the source nodes of the SP equal-gain rectangle

Question. Which node classes and placements must remain distinct before the row mechanisms are substituted?

Sources. Strategy §4.3; File18 §§3.1,6C.1; File22; prep/family_synthesis_candidates.json

Inputs

{}

Results

{
  "source_nodes": {
    "path": "model/SP_rectangle_source_nodes.json",
    "sha256": "73d96eaab3a4be396ee556bf510367945b9a26048dc881a7653e8d321fd91c23",
    "bytes": 1113
  }
}

Finding. The rectangle uses the Regular week opening4206 and Cumulative decade opening13406. Their underlying4199 and13396 endpoints have different wrappers; these supplied source roles must remain visible.

Reassessment. Generate the Regular head from the located source begetting changes and declared frame shift.

C1224 — Derive the Regular rectangle radius from source row changes

Question. Can the reconstructed source changes account for the Regular2760 input?

Sources. C1223; C1143; C1157; File22 Actual4114

Inputs

{}

Results

{
  "regular_provenance": {
    "path": "model/SP_rectangle_regular_provenance.json",
    "sha256": "2f8b03fe5ba73a792a2d88f7055f234c51f0dab12223a1293ccf05731dcd1893",
    "bytes": 343
  },
  "radius": 2760
}

Finding. The Regular input2760 decomposes into the MT baseline radius, post-Flood+650, pre-Flood−350, the declared−215 frame change and the seven-year wrapper. The row grammar explains the two genealogical changes; frame and wrapper remain source premises.

Reassessment. Generate the Cumulative radius using the cap loss and post-Flood life changes.

C1225 — Derive the Cumulative rectangle radius from the cap

Question. Can the new cap mechanism explain the Cumulative11960 input?

Sources. C1223; C1143; C1157; File22 Actual14004

Inputs

{}

Results

{
  "cumulative_provenance": {
    "path": "model/SP_rectangle_cumulative_provenance.json",
    "sha256": "b4e710d1dcc79ad4e3027ef0ccb10ff8072422c99e855b58b9a6643bcd2ee467",
    "bytes": 361
  },
  "radius": 11960
}

Finding. The Cumulative input11960 is now traced through the cap-generated488 and the separate Eber/Terah120 reduction, followed by its supplied decade opening. This explains the source mechanism behind the existing endpoint.

Reassessment. Apply the established Keys to the two fully sourced radii and classify what is new.

C1226 — Close the source-to-Key rectangle

Question. Do the two source-generated radii produce the same40-year gain?

Sources. C1224; C1225; Strategy §4.3

Inputs

{}

Results

{
  "rectangle": {
    "path": "model/SP_rectangle_source_to_keys.json",
    "sha256": "2915b2ba9d1a46ccd7d9d007050f8822558866bd9ac4f478d7e5a612fd262477",
    "bytes": 444
  },
  "gains": [
    40,
    40
  ],
  "gap": 9200
}

Finding. The reconstructed inputs give the established40/40 gains to Conquest1406, preserving9200, whose25/23 expansion is10000. The advance is the genealogy-to-cap-to-Key explanation, not another independent occurrence of those numbers.

Reassessment. Determine which supplied placements are essential to the equal-gain equality.

C1227 — Audit the wrapper contribution to equal gains

Question. Does the equality follow from the two genealogical endpoints before their wrappers are applied?

Sources. C1223–C1226

Inputs

{}

Results

{
  "wrapper_audit": {
    "path": "model/SP_rectangle_wrapper_residual.json",
    "sha256": "9e3470448d64f0c911e014dd204e25ae4d7bc479ae9e914445477ab1967f3468",
    "bytes": 353
  },
  "unwrapped_balance": 61,
  "wrapper_balance": -61
}

Finding. Before the wrappers, the equal-gain balance is61 rather than zero. The distinct+7 and+10 source openings contribute−61 and complete the equality. The cap mechanism explains the life reduction but does not independently generate the chosen node roles.

Reassessment. Test whether the equal-gain claim is stable under a common relocation of its target anchor.

C1228 — Distinguish common translation from a changed held anchor

Question. Is equal gain automatic for another comparison anchor?

Sources. C1227; Strategy §4.3

Inputs

{}

Results

{
  "anchor_dependence": {
    "path": "model/SP_rectangle_anchor_dependence.json",
    "sha256": "79f6de07f587cb73249f1bc7555e484298cff70ca7200a7c88fb9f3c98ceba84",
    "bytes": 612
  },
  "conditional_anchor": 1446
}

Finding. For these fixed source heads, equal gain selects1446 algebraically. Moving only the comparison anchor breaks the equality; translating the complete frame preserves it. The source’s Exodus identification is separate from the equation.

Reassessment. Present the entire source-to-rectangle dependency chain with its explanatory limits.

C1229 — Write the Strategy rectangle from the row mechanisms

Question. Can the larger relation now be explained as one connected construction?

Sources. C1223–C1228; C1143; C1154

Inputs

{}

Results

{
  "explanation": {
    "path": "deliverables/Source_Rows_to_SP_Equal_Gain_Rectangle.md",
    "sha256": "26de2697e7a6c74c6b60fff95888ed90aa329d5e386cc19f8a425cf909036285",
    "bytes": 2058
  }
}

Finding. The Strategy rectangle is now a connected source-row, cap, placement and Key construction. Its inherited numerical closure is explained alongside the remaining absolute and node-role premises.

Reassessment. Review the second block’s net explanatory gain and choose the next complete source family.

C1230 — Assess the second block before the required Strategy reread

Question. Which gains advance explanation, and which proposed work should now stop?

Sources. C1182–C1229; prep/family_synthesis_candidates.json; prep/review1182_1201.json

Inputs

{}

Results

{
  "ledger": {
    "path": "model/block2_explanation_cost_ledger.json",
    "sha256": "0520b903d46fd6e56955a0a4a36b6c6b2b9c2d0eb3433e2d55efcb1354493b60",
    "bytes": 1564
  },
  "next_candidate": "File51a §7A Moses-centred complete family"
}

Finding. The second block has connected complete genealogies to Rounded information and the Strategy rectangle. The next useful move is a full source-appointed Moses-centred family, rather than more generic rank or fibre enumeration.

Reassessment. Close the100-action checkpoint, then reread the entire Strategy before selecting C1232.

C1231 — Close the second fifty-action checkpoint

Question. What completed results and unresolved premises should the next full Strategy review assess?

Sources. C1182–C1230; Strategy.md

Inputs

{}

Results

{
  "checkpoint": {
    "path": "deliverables/Block_02_C1182_C1231_Checkpoint.json",
    "sha256": "5bbee6cd906bd6183bf6db9f8156f0b3d5771af1f0b716c98b0437c72656b8b7",
    "bytes": 1422
  },
  "completed_actions": 100,
  "remaining_actions": 200
}

Finding. The second50 actions are closed, with exact artifacts and appended clarifications retained. A fresh full Strategy review must now decide the next action.

Reassessment. Read the complete Strategy and reassess the larger family explanation before beginning C1232.