{
"status": "PASS: bounded source identity and source-cost audit; no numbered root actions or journal edits",
"created_utc": "2026-09-28T05:42:15.862923+00:00",
"scope": "Strategy4.1 coefficient5; matched Cainan-OFF MT/LXX ordinary Regular comparison, plus native forms and separately licensed finite variants.",
"main_conclusion": "The ordered row mask explains1250/650; the finite source choices explain405. Equating the row totals with the fivefold variant formula requires C=13u/10 and T=3u/5. The coefficient5 is an exact observed calibration between two sourced constructions, not a generator of the ancestral ages or their locations.",
"source_primitive_roles": [
{
"symbol": "u",
"value": 100,
"role": "Shared observed begetting difference on twelve named MT/LXX rows; Nahor carries half.",
"source": "File18 §§2.1.3–2.2,4.1–4.2; lines1223–1252,1692–1748.",
"status": "Difference of supplied selected rows; equality across locations is an observed/fitted pattern, not twelve independent historical trials."
},
{
"symbol": "T",
"value": 60,
"role": "Terah variant,130−70.",
"source": "File04 §2.4,lines427–446; File18 §1.3.1 Terah table,lines645–650.",
"status": "Repository textual harmonization205−75=130;130−70=60, explicitly structural inference."
},
{
"symbol": "C",
"value": 130,
"role": "Second Cainan Regular insertion.",
"source": "File18 §1.6.1–§1.6.2,lines1123–1147; nativeLXX§4.2.",
"status": "Selected begetting interval, distinct from his lifespan460 and from Terah’s numerically equal130. LXX already contains it."
},
{
"symbol": "S",
"value": 215,
"role": "Sojourn allocation difference with Exodus held.",
"source": "File00 §3.3.1,lines790–804; File18 §1.1.",
"status": "Primary Egypt215/430 comparison; not the subordinate whole-system Exodus215."
}
],
"named_row_changes": [
{
"name": "Adam",
"MT_b": 130,
"LXX_b": 230,
"difference": 100
},
{
"name": "Seth",
"MT_b": 105,
"LXX_b": 205,
"difference": 100
},
{
"name": "Enosh",
"MT_b": 90,
"LXX_b": 190,
"difference": 100
},
{
"name": "Kenan",
"MT_b": 70,
"LXX_b": 170,
"difference": 100
},
{
"name": "Mahalalel",
"MT_b": 65,
"LXX_b": 165,
"difference": 100
},
{
"name": "Jared",
"MT_b": 162,
"LXX_b": 162,
"difference": 0
},
{
"name": "Enoch",
"MT_b": 65,
"LXX_b": 165,
"difference": 100
},
{
"name": "Methuselah",
"MT_b": 187,
"LXX_b": 187,
"difference": 0
},
{
"name": "Lamech",
"MT_b": 182,
"LXX_b": 182,
"difference": 0
},
{
"name": "Noah",
"MT_b": 500,
"LXX_b": 500,
"difference": 0
},
{
"name": "Shem",
"MT_b": 100,
"LXX_b": 100,
"difference": 0
},
{
"name": "Arphaxad",
"MT_b": 35,
"LXX_b": 135,
"difference": 100
},
{
"name": "Shelah",
"MT_b": 30,
"LXX_b": 130,
"difference": 100
},
{
"name": "Eber",
"MT_b": 34,
"LXX_b": 134,
"difference": 100
},
{
"name": "Peleg",
"MT_b": 30,
"LXX_b": 130,
"difference": 100
},
{
"name": "Reu",
"MT_b": 32,
"LXX_b": 132,
"difference": 100
},
{
"name": "Serug",
"MT_b": 30,
"LXX_b": 130,
"difference": 100
},
{
"name": "Nahor",
"MT_b": 29,
"LXX_b": 79,
"difference": 50
},
{
"name": "Terah",
"MT_b": 70,
"LXX_b": 70,
"difference": 0
}
],
"early_support": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Enoch"
],
"late_support": [
"Arphaxad",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug"
],
"half_support": [
"Nahor"
],
"full_matched_birth_displacement": [
{
"name": "Adam",
"LXX_OFF_minus_MT_OFF": 1250,
"coefficient_of_u": "25/2"
},
{
"name": "Seth",
"LXX_OFF_minus_MT_OFF": 1150,
"coefficient_of_u": "23/2"
},
{
"name": "Enosh",
"LXX_OFF_minus_MT_OFF": 1050,
"coefficient_of_u": "21/2"
},
{
"name": "Kenan",
"LXX_OFF_minus_MT_OFF": 950,
"coefficient_of_u": "19/2"
},
{
"name": "Mahalalel",
"LXX_OFF_minus_MT_OFF": 850,
"coefficient_of_u": "17/2"
},
{
"name": "Jared",
"LXX_OFF_minus_MT_OFF": 750,
"coefficient_of_u": "15/2"
},
{
"name": "Enoch",
"LXX_OFF_minus_MT_OFF": 750,
"coefficient_of_u": "15/2"
},
{
"name": "Methuselah",
"LXX_OFF_minus_MT_OFF": 650,
"coefficient_of_u": "13/2"
},
{
"name": "Lamech",
"LXX_OFF_minus_MT_OFF": 650,
"coefficient_of_u": "13/2"
},
{
"name": "Noah",
"LXX_OFF_minus_MT_OFF": 650,
"coefficient_of_u": "13/2"
},
{
"name": "Shem",
"LXX_OFF_minus_MT_OFF": 650,
"coefficient_of_u": "13/2"
},
{
"name": "Arphaxad",
"LXX_OFF_minus_MT_OFF": 650,
"coefficient_of_u": "13/2"
},
{
"name": "Shelah",
"LXX_OFF_minus_MT_OFF": 550,
"coefficient_of_u": "11/2"
},
{
"name": "Eber",
"LXX_OFF_minus_MT_OFF": 450,
"coefficient_of_u": "9/2"
},
{
"name": "Peleg",
"LXX_OFF_minus_MT_OFF": 350,
"coefficient_of_u": "7/2"
},
{
"name": "Reu",
"LXX_OFF_minus_MT_OFF": 250,
"coefficient_of_u": "5/2"
},
{
"name": "Serug",
"LXX_OFF_minus_MT_OFF": 150,
"coefficient_of_u": "3/2"
},
{
"name": "Nahor",
"LXX_OFF_minus_MT_OFF": 50,
"coefficient_of_u": "1/2"
},
{
"name": "Terah",
"LXX_OFF_minus_MT_OFF": 0,
"coefficient_of_u": "0"
},
{
"name": "Abraham",
"LXX_OFF_minus_MT_OFF": 0,
"coefficient_of_u": "0"
}
],
"head_formula": {
"Creation": "(6+6+1/2)u=25u/2",
"Flood_Noah": "(6+1/2)u=13u/2",
"difference": "6u",
"center": "19u/2",
"radius": "3u",
"common_boundary": "MT/LXX shared Noah/Shem effective binding correction cancels; matched terminals and source count states retained."
},
"exact_identity_conditions": {
"required_equations": [
"25u/2 = 5(C+2T)",
"13u/2 = 5C"
],
"necessary_and_sufficient": [
"C=13u/10",
"T=3u/5"
],
"proof": "Second equation givesC=13u/10;subtracting gives6u=10T. Conversely substitution recovers both equations.",
"free_coefficient": "For nonzero u,C, a common κ satisfying25u/2=κ(C+2T),13u/2=κC exists iff6C=13T;thenκ=13u/(2C). The valueκ=5 additionally requiresC=13u/10.",
"S": "No restriction on S comes from the two head equalities; width remainsW=S+C+T.",
"count": "Two algebraically independent cross-layer conditions in the declared variable model; not a count of independent textual witnesses.",
"not_entailed": "Named support counts, binary switch laws and source ordering alone do not imply either numerical calibration."
},
"variant_field": {
"rows": [
{
"Terah": 0,
"Cainan": 0,
"Sojourn": 0,
"offset": 0,
"MT_Year6": 3901,
"MT_endpoint": 3899
},
{
"Terah": 1,
"Cainan": 0,
"Sojourn": 0,
"offset": 60,
"MT_Year6": 3961,
"MT_endpoint": 3959
},
{
"Terah": 0,
"Cainan": 1,
"Sojourn": 0,
"offset": 130,
"MT_Year6": 4031,
"MT_endpoint": 4029
},
{
"Terah": 1,
"Cainan": 1,
"Sojourn": 0,
"offset": 190,
"MT_Year6": 4091,
"MT_endpoint": 4089
},
{
"Terah": 0,
"Cainan": 0,
"Sojourn": 1,
"offset": 215,
"MT_Year6": 4116,
"MT_endpoint": 4114
},
{
"Terah": 1,
"Cainan": 0,
"Sojourn": 1,
"offset": 275,
"MT_Year6": 4176,
"MT_endpoint": 4174
},
{
"Terah": 0,
"Cainan": 1,
"Sojourn": 1,
"offset": 345,
"MT_Year6": 4246,
"MT_endpoint": 4244
},
{
"Terah": 1,
"Cainan": 1,
"Sojourn": 1,
"offset": 405,
"MT_Year6": 4306,
"MT_endpoint": 4304
}
],
"gap_word": [
60,
70,
60,
25,
60,
70,
60
],
"width": 405,
"conditions_for_this_order": "0<T<C and S>T+C; satisfied by60<130 and215>190.",
"four_Cainan_OFF_offsets": [
0,
60,
215,
275
],
"four_Cainan_OFF_width": 275,
"sources": "File07 §2.11.1a lines984–1016 explicitly lists all eight; File18 §1.1 lists four Sojourn/Terah states."
},
"support_masks": [
{
"block": "Adam through Arphaxad/Flood",
"T": 1,
"C": 1,
"S": 1
},
{
"block": "inserted Cainan through Terah",
"T": 1,
"C": 0,
"S": 1
},
{
"block": "Abraham through Joseph/Levi",
"T": 0,
"C": 0,
"S": 1
},
{
"block": "Aaron/Moses onward",
"T": 0,
"C": 0,
"S": 0
}
],
"support_qualifications": [
"Kohath/Amram have no direct regular-date anchors in this variant scheme.",
"Cainan’s inserted coordinate is constructed relative toShelah; it receives no extra self-shift.",
"The same variant state cancels from a paired MT/LXX comparison wherever masks agree. Unmatched labels addTΔt+CΔc+SΔs at shared upstream heads.",
"The ordinary common-row LXXOFF comparison is a declared theoretical leveling; nativeLXX retains its row and gives1380/780.",
"T/C/S masks are prefix incidence; the centenary row-change mask has internal locations. One does not determine the other."
],
"SP_side_check": {
"rows": [
{
"name": "Adam",
"MT_b": 130,
"SP_nominal_b": 130,
"SP_completed_primary_b": 130,
"completed_change": 0
},
{
"name": "Seth",
"MT_b": 105,
"SP_nominal_b": 105,
"SP_completed_primary_b": 105,
"completed_change": 0
},
{
"name": "Enosh",
"MT_b": 90,
"SP_nominal_b": 90,
"SP_completed_primary_b": 90,
"completed_change": 0
},
{
"name": "Kenan",
"MT_b": 70,
"SP_nominal_b": 70,
"SP_completed_primary_b": 70,
"completed_change": 0
},
{
"name": "Mahalalel",
"MT_b": 65,
"SP_nominal_b": 65,
"SP_completed_primary_b": 65,
"completed_change": 0
},
{
"name": "Jared",
"MT_b": 162,
"SP_nominal_b": 62,
"SP_completed_primary_b": 62,
"completed_change": -100
},
{
"name": "Enoch",
"MT_b": 65,
"SP_nominal_b": 65,
"SP_completed_primary_b": 65,
"completed_change": 0
},
{
"name": "Methuselah",
"MT_b": 187,
"SP_nominal_b": 67,
"SP_completed_primary_b": 67,
"completed_change": -120
},
{
"name": "Lamech",
"MT_b": 182,
"SP_nominal_b": 53,
"SP_completed_primary_b": 52,
"completed_change": -130
}
],
"pre_loss": -350,
"post_gain": 650,
"Creation_gain": 300,
"Flood_gain": 650,
"current_count_explanation": "Nominal100+120+129 becomes completed100+120+130 for the G2 primary path. The one-year distinction is used once; no upstream Gear extension."
},
"source_cost": [
{
"description": "Row generator",
"must_retain": "u plus all named nonzero/zero locations, Nahor1/2 relation, common row order, Cainan-leveling choice, shared bindings and terminal.",
"explains": "Whole20-boundary difference field, not only1250/650."
},
{
"description": "Variant generator",
"must_retain": "T,C,S, their finite binary states, nested supports and inserted-node convention.",
"explains": "Whole405 field; the275 restriction; which downstream dates move or remain fixed."
},
{
"description": "Combined fivefold summary",
"must_retain": "The two cross-layer identities as part of the model; S remains supplied.",
"explains": "Why the two proven source constructions admit one compact scalar expression at the selected values."
},
{
"description": "Conditional numeric reduction",
"must_retain": "IfT andC are expressed throughu, retain the coefficients3/5 and13/10 plus their source justification.",
"explains": "A coordinate compression; not a proof of lower global description cost or historical generation."
}
],
"prior_overlap": [
"C486: SP−350/+650 accounting. C739–741: whole inter-tradition fields and local support, includingSP129+1.",
"C772–777: complete finite variant cube and interval support; C778–788: state transfer and mode/rounding behavior.",
"C1178–1189: whole-genealogy row amplitudes, local supports,1250head and nativeCainan.",
"C1213: multiples-of-five row operations commute with rounding; this includesu,T,C,S but does not create the fivefold calibration.",
"The new audit is the explicit necessary/sufficient coefficient5 bridge and its source-cost interpretation. It is not a new1250/650/405 discovery."
],
"positive_explanation": [
"The long genealogy and the finite variant field describe different kinds of source structure. The first distributes repeated age changes over named generations; the second changes how an already formed chain is placed by three source-sanctioned choices.",
"Six early century changes create the600 drop from the Creation difference1250 to the Flood-side plateau650. The later six centuries and Nahor’s half-century explain the plateau itself. This makes the macro geometry a consequence of local placement, while preserving the intermediate staircase that the two totals conceal.",
"The Terah,Cainan and Sojourn choices independently have explicit source roles and generate their whole405 envelope. Their observed scales60/130 agree with the row scale100 in precisely the proportions needed for the fivefold summary. That agreement joins two existing constructions; it does not choose the ancestral ages, their order or the Sojourn value.",
"Thus the kernel is useful as a compact interface between two complete mechanisms. Regular/Cumulative differences still require the fuller row object: Terah repartition can preserve lifespan, whereas Cainan contributes130 or460 depending on the measure. A regular1250/650 formula cannot be exported unchanged into cumulative chronology."
],
"claim_limits": [
"No chronological source independence inferred from different symbols or source-file locations.",
"T is derived from a source-selected harmonization;C is a distinct person’s supplied age;their repeated130 does not merge their roles.",
"The sum/difference form950±300 is generated from the pair. Noah’s supplied lifespan950 is a numerical comparison requiring its own source role, not another proof of the samepair.",
"No source text reviewed here supplies a historical rule multiplying Terah/Cainan variants by five to create all ancestral ages.",
"No new target search, inverse operation, upstreamGear transport, source edits or external search."
],
"input_sha256": {
"Strategy": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/evidence/sources/Strategy.md",
"sha256": "9c9aa357f5483b3af1dbb5f0025ee514fa28160576a037be03037aa49bf01476"
},
"File18": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/evidence/sources/38-File_18.Chronological_Data_Tables-20260919-141048-.md",
"sha256": "68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5"
},
"File04": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/evidence/sources/34-File_04.Jacob_Jubilee_Standard_LXX_33_397_Sojourn-8-.md",
"sha256": "77d7b50e5db4cbc97e01e41bcbeb8b1d4344e839ddd38bdd118c675ac8eea4e4"
},
"File00": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/evidence/sources/35-File_00.Repository_Foundation_Axiom_Engine_Source_Map-9-.md",
"sha256": "ed718a9e579978a90eefb377911933312de10a3eae1221e59758158b994de64e"
},
"File07": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/evidence/sources/22-File_07.Creation_Seed_Decimal_Root-1-1-.md",
"sha256": "1aa4e02dd346c8e0879c8d196bd76c95c9069237fe41d1ca816175f84d3c162c"
},
"Capsule": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/evidence/sources/32-Restart_Capsule-20260914-154034-.md",
"sha256": "746d59eb554ae807017d1ea4d815b2136933f3b1a07a73060354d9876bf8fc93"
},
"Register": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/evidence/sources/33-State_Vocabulary_Register-20260914-154034-.md",
"sha256": "fe626d19a545195e8e3ac6fb8b762c281529226a3821e632bd981fff81c90ad1"
},
"Style": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/evidence/sources/26-490d_Repository_Style_Guide-20260908-220633-1-.md",
"sha256": "2e7993eac77ec119b27bfc9ace67e3d196d21d358a64c536a1dc8f60729e1abb"
},
"MainC1131": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/inherited/490d_How_Chronological_Families_Fit_Together_C1131.md",
"sha256": "c10be95a7f5a5a4559e6d92beaf0a85b4451d433b6ca8497a8deca0eac368139"
},
"OutcomeC1131": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/inherited/Research_Outcome_C1131.md",
"sha256": "b29df455f9d4efbf471629a97a385387e690400444024388b0fb0d2ff1c29d94"
},
"complete_rows": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/model/complete_source_row_packet.json",
"sha256": "1bd5961126532673e6fda1535befc5e64cf21d67d01a3c5e78d1a613bbb8ab59"
},
"five_model": {
"path": "/workspace/scratch/1b40da62dcbd/c1132_c1431/model/whole_genealogy_five_model.json",
"sha256": "00974b700a432f664a92f80cdbfdb8cef83e334d8f4ac3437aec4e3bb2921ac9"
}
},
"checks": {
"nineteen_common_rows": true,
"complete_u_mask": true,
"six_early_centuries": true,
"six_late_centuries_and_half": true,
"Creation_sum": true,
"Flood_comparison": true,
"literal_OFF_Creation": true,
"literal_OFF_Flood": true,
"native_Creation": true,
"native_Flood": true,
"T_provenance": true,
"coefficient_conditions": true,
"five_kernel": true,
"common_coefficient_condition": true,
"center_radius": true,
"eight_distinct_variants": true,
"eight_offsets": true,
"eight_gap_word": true,
"four_state_restriction": true,
"eight_source_Year6": true,
"width": true,
"SP_source_loss": true,
"SP_creation_offset": true,
"SP_Flood_offset": true
},
"check_count": 24
}
Evidence
regular kernel source cost.json
Linked sources and evidence
Edition and provenance
regular_kernel_source_cost.json
SHA-256 95050da2bd7b5e7bb0d7612b5b36cdf8e81a7e8d68f6493dd1824fe72cba3863
C480–C1634/Research_Cycles/C1132_C1431_Recovered/prep/regular_kernel_source_cost.json