490d — C732–C791: sequential research record
Working continuation of C731 · 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.
C732 — Select the ordered cross-tradition family
Question. Can one row-to-boundary rule explain the full MT/LXX/SP displacement fields and their rounded residuals?
Sources. Research Strategy §§3,5B–G; C731 checkpoint; File18; File51a
Inputs
{
"source_manifest_sha256": "60159f91fa858a5651da5b097c2e7b5523835ded3757374fed59943b67f4727f",
"predecessor": "C731",
"comparison": "whole ordered boundary fields; not repeated endpoint totals"
}
Results
{
"selection": {
"path": "model/RESEARCH_SELECTION.json",
"sha256": "f839f7769dfae2e351c0a66baeadae3b71bee524b05302bb3a933706e12b8bbc",
"bytes": 397
},
"source_snapshots": 41,
"primary_File52c": "a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530"
}
Finding. The new cycle will test ordered support and operation compatibility across entire source families. Previous aggregate sums are retained as baseline evidence; the new target is reconstruction of every intermediate boundary and residual.
Reassessment. Freeze the shared source-row alignment and choose the first complete displacement field.
C733 — Derive the full mode-bridge recurrence
Question. What row quantity generates the change in cumulative-minus-regular displacement between adjacent named boundaries?
Sources. File18 MT regular/cumulative rows; File61 root vector; Research Strategy §5B
Inputs
{
"definition": "G_i=C_i−R_i",
"regular_edge": "R_i−R_(i+1)=b_eff_i",
"cumulative_edge": "C_i−C_(i+1)=L_i",
"local_MT_example": {
"regular": [
2166,
2066,
2006
],
"cumulative": [
2435,
2260,
2080
],
"lifespans": [
175,
180
],
"effective_begetting": [
100,
60
]
}
}
Results
{
"mode_bridge": [
269,
194,
74
],
"bridge_increments": [
75,
120
],
"row_remainders": [
75,
120
],
"general_rule": "G_i−G_(i+1)=L_i−b_eff_i"
}
Finding. The mode bridge has a local generator: lifespan minus the effective regular edge. Telescoping these row contributions reconstructs the whole bridge once the terminal displacement is supplied. Declared binding corrections belong in b_eff rather than being hidden in a global conversion.
Reassessment. Apply this recurrence to every shared MT boundary, retaining source roles and terminal frame.
C734 — Reconstruct the entire MT mode-bridge field
Question. Does one terminal displacement and the row remainder rule recover every Adam-to-Abraham boundary?
Sources. File18 §§2.1.3,2.2,6A
Inputs
{
"packet_sha256": "37dd27bbe2eb9d0b7606d75620de499b0ab3493d7188ec814f4f443adb6af9b2",
"regular_frame": "+215 full430",
"cumulative_frame": "Moses/Nisan centers; AdamYear6 role retained",
"Noah_edge_correction": 2
}
Results
{
"names": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Jared",
"Enoch",
"Methuselah",
"Lamech",
"Noah",
"Shem",
"Arphaxad",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham"
],
"center_mode_bridge": [
9892,
9092,
8285,
7470,
6630,
5800,
5000,
4700,
3918,
3323,
2875,
2375,
1972,
1569,
1139,
930,
723,
523,
404,
269
],
"row_generators": [
800,
807,
815,
840,
830,
800,
300,
782,
595,
448,
500,
403,
403,
430,
209,
207,
200,
119,
135
],
"terminal_bridge": 269,
"head_role": "9892 pairs cumulativeYear6 with regularCreation-completion; not the established9890 completion bridge"
}
Finding. The same remainder-plus-binding rule reconstructs all20 MT mode comparisons from terminal269. The mixed Adam-label displacement9892 is explicitly a center-profile quantity; it is not silently substituted for the established completion bridge9890.
Reassessment. Change the entire cumulative profile to its source lower-envelope members and test what is preserved.
C735 — Transport the whole bridge to the lower envelope
Question. Does the chosen completion profile preserve the row-generating law?
Sources. File18 §6A envelopes; C734; C731 Actual bridge
Inputs
{
"cumulative_profile_shift": -2,
"regular_frame": "+215",
"scope": "all selected cumulative lower-envelope members, not newGeartransport"
}
Results
{
"lower_profile": [
9890,
9090,
8283,
7468,
6628,
5798,
4998,
4698,
3916,
3321,
2873,
2373,
1970,
1567,
1137,
928,
721,
521,
402,
267
],
"center_to_lower": [
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2
],
"terminal": 267,
"completion_head": 9890
}
Finding. Selecting the lower-envelope member translates the entire MT bridge by−2 and preserves every adjacent generator. It recovers9890 at Creation and267 at Abraham. This is a source-defined profile choice, not an adjustment fitted independently at each node.
Reassessment. Transfer the same full-field recurrence to nativeLXX, retaining its insertedCainan row.
C736 — Transfer the full bridge to native LXX
Question. Does the MT row-to-boundary rule reconstruct the nativeLXX profile without removingCainan?
Sources. File18 §§4.1,6D; C733–C735
Inputs
{
"source_names": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Jared",
"Enoch",
"Methuselah",
"Lamech",
"Noah",
"Shem",
"Arphaxad",
"Cainan2",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah"
],
"Cainan": "nativeON",
"terminal_lower_pair": [
2433,
2166
],
"Lamech": "182/753"
}
Results
{
"names": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Jared",
"Enoch",
"Methuselah",
"Lamech",
"Noah",
"Shem",
"Arphaxad",
"Cainan2",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham"
],
"lower_mode_bridge": [
9400,
8700,
7993,
7278,
6538,
5808,
5008,
4808,
4026,
3455,
3007,
2507,
2177,
1847,
1517,
1147,
938,
731,
531,
402,
267
],
"row_generators": [
700,
707,
715,
740,
730,
800,
200,
782,
571,
448,
500,
330,
330,
330,
370,
209,
207,
200,
129,
135
],
"source_center_checks": {
"Adam": 14896,
"Lamech": 8048,
"Cainan2": 5280,
"Peleg": 3856
}
}
Finding. The identical rule generates all21 nativeLXX comparisons, including theCainan330 remainder contribution. Four separately printed cumulative nodes confirm the reconstructed chain. The resulting Creation bridge9400 belongs to the nativeLXX state, rather than being forced toMT9890.
Reassessment. Transfer the same rule toSP while keeping its inclusive and primaryNoah correction explicit.
C737 — Transfer the full bridge to SP
Question. Does the same recurrence preserve SP’s local counting conventions throughout the field?
Sources. File18 §§3.1–3.2,6C; C733–C736
Inputs
{
"Cainan": "OFF",
"terminal_lower_pair": [
2433,
2166
],
"edge_corrections": {
"Noah": 2,
"Lamech": -1
},
"Lamech_count": "53rd year52completed;653inclusive lifespan ledger"
}
Results
{
"names": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Jared",
"Enoch",
"Methuselah",
"Lamech",
"Noah",
"Shem",
"Arphaxad",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham"
],
"lower_mode_bridge": [
8982,
8182,
7375,
6560,
5720,
4890,
4105,
3805,
3152,
2551,
2103,
1603,
1300,
997,
727,
618,
511,
411,
342,
267
],
"row_generators": [
800,
807,
815,
840,
830,
785,
300,
653,
601,
448,
500,
303,
303,
270,
109,
107,
100,
69,
75
],
"source_center_checks": {
"Adam": 13398,
"Peleg": 3436,
"Terah": 2580
}
}
Finding. All20 SP comparisons follow from the same recurrence with its two declared edge corrections. The Creation bridge8982 arises from the full source profile. The653 inclusive lifespan ledger and52 completed regular interval remain distinct inputs, rather than an unexplained one-year repair.
Reassessment. Compare the three complete profiles on their shared named boundaries and locate their source differences.
C738 — Unify the three complete mode profiles
Question. Can one implementation reconstruct all native profiles while preserving their distinct row membership?
Inputs
{
"traditions": [
"MT",
"LXX",
"SP"
],
"common_terminal": {
"regular": 2166,
"cumulative_center": 2435,
"lower": 2433
}
}
Results
{
"artifact": {
"path": "model/native_mode_fields.json",
"sha256": "bc9bbd34af7478bd21d03d23dba6c926c4f741271bc6ebb761337a71e06652b4",
"bytes": 10042
},
"native_row_counts": {
"MT": 20,
"LXX": 21,
"SP": 20
},
"head_G": {
"MT": 9890,
"LXX": 9400,
"SP": 8982
}
}
Finding. A single source-aware constructor now carries all61 native node comparisons. TheLXX-onlyCainan row stays explicit; an absent row is not replaced with a zero-life patriarch. These fields support direct cross-tradition comparisons without another global fit.
Reassessment. Compute the entire inter-tradition displacement profiles on the common named nodes.
C739 — Recover the complete inter-tradition displacement fields
Question. Where do regular and cumulative differences actually change along the shared genealogy?
Sources. File18 source fields; C738
Inputs
{
"shared_nodes": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Jared",
"Enoch",
"Methuselah",
"Lamech",
"Noah",
"Shem",
"Arphaxad",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham"
],
"reference": "MT; commonfull430regular andlowercumulativeprofile"
}
Results
{
"artifact": {
"path": "model/tradition_displacement_profiles.json",
"sha256": "a30d1703e4ddaa7670451a1e32597fde8825da57aace1430526d3a8f688fb4f2",
"bytes": 2056
},
"profiles": {
"LXX": {
"R": [
1380,
1280,
1180,
1080,
980,
880,
880,
780,
780,
780,
780,
780,
550,
450,
350,
250,
150,
50,
0,
0
],
"C_lower": [
890,
890,
890,
890,
890,
890,
890,
890,
890,
914,
914,
914,
427,
400,
360,
260,
160,
60,
0,
0
],
"G": [
-490,
-390,
-290,
-190,
-90,
10,
10,
110,
110,
134,
134,
134,
-123,
-50,
10,
10,
10,
10,
0,
0
]
},
"SP": {
"R": [
300,
300,
300,
300,
300,
300,
400,
400,
520,
650,
650,
650,
550,
450,
350,
250,
150,
50,
0,
0
],
"C_lower": [
-608,
-608,
-608,
-608,
-608,
-608,
-493,
-493,
-244,
-120,
-120,
-120,
-120,
-120,
-60,
-60,
-60,
-60,
-60,
0
],
"G": [
-908,
-908,
-908,
-908,
-908,
-908,
-893,
-893,
-764,
-770,
-770,
-770,
-670,
-570,
-410,
-310,
-210,
-110,
-60,
0
]
}
}
}
Finding. The complete displacement fields expose plateaus and change points hidden byCreation totals. At every shared node, the bridge displacement equals cumulative displacement minus regular displacement; each mode retains its own source-driven shape.
Reassessment. Use adjacent differences to recover the exact support of theLXX row changes, including thecollapsedCainanedge.
C740 — Recover LXX local changes from its boundary profile
Question. Can adjacent differences identify the contributing rows and distinguish aninsertedrowfromalifespanchange?
Sources. C739; File18 §§2,4,6D
Inputs
{
"shared_edge": "Arphaxad→Shelah spansLXXCainan2",
"profile": "LXXminusMT"
}
Results
{
"nonzero_edge_changes": {
"R": {
"Adam": 100,
"Seth": 100,
"Enosh": 100,
"Kenan": 100,
"Mahalalel": 100,
"Enoch": 100,
"Arphaxad": 230,
"Shelah": 100,
"Eber": 100,
"Peleg": 100,
"Reu": 100,
"Serug": 100,
"Nahor": 50
},
"C_lower": {
"Lamech": -24,
"Arphaxad": 487,
"Shelah": 27,
"Eber": 40,
"Peleg": 100,
"Reu": 100,
"Serug": 100,
"Nahor": 60
},
"G": {
"Adam": -100,
"Seth": -100,
"Enosh": -100,
"Kenan": -100,
"Mahalalel": -100,
"Enoch": -100,
"Lamech": -24,
"Arphaxad": 257,
"Shelah": -73,
"Eber": -60,
"Nahor": 10
}
},
"collapsed_Arphaxad_components": {
"regular": [
100,
130
],
"cumulative": [
27,
460
],
"bridge": [
-73,
330
]
}
}
Finding. Finite differences recover the entireLXX change support. At the sharedArphaxad→Shelah edge, regular230 splits into100+130 and cumulative487 into27+460. KeepingCainan as a native row distinguishes insertion from the adjacent biography change; collapsing them would lose that explanation.
Reassessment. Recover theSP support with its separateLamech completed-year correction.
C741 — Recover SP local changes from its boundary profile
Question. Which source rows and counting terms generateSP’s entire displacement staircase?
Sources. C739; File18 §§3.1–3.2,6C
Inputs
{
"profile": "SPminusMT",
"Lamech_regular": "53counted versus52completed"
}
Results
{
"nonzero_edge_changes": {
"R": {
"Jared": -100,
"Methuselah": -120,
"Lamech": -130,
"Arphaxad": 100,
"Shelah": 100,
"Eber": 100,
"Peleg": 100,
"Reu": 100,
"Serug": 100,
"Nahor": 50
},
"C_lower": {
"Jared": -115,
"Methuselah": -249,
"Lamech": -124,
"Eber": -60,
"Terah": -60
},
"G": {
"Jared": -15,
"Methuselah": -129,
"Lamech": 6,
"Arphaxad": -100,
"Shelah": -100,
"Eber": -160,
"Peleg": -100,
"Reu": -100,
"Serug": -100,
"Nahor": -50,
"Terah": -60
}
},
"Lamech_regular_decomposition": [
-129,
-1
]
}
Finding. TheSP profile localizes its regular130-yearLamech difference as129 from the nominal age plus one completed-year correction. Cumulative support remains the five lifespan changes. The whole staircase therefore explains both the shared plateaus and the different mode response.
Reassessment. Test the entire post-ShelahLXX/SP family where births agree but cumulative coordinates differ.
C742 — Explain equal births with unequal cumulative boundaries
Question. Why does the entireLXX/SP birthsuffix coincide while itscumulativeprofilediverges?
Sources. File18 §§3–4,6C–D; C738
Inputs
{
"nodes": [
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham"
],
"native_Cainan": [
"LXXON",
"SPOFF"
],
"regular_frame": "commonfull430"
}
Results
{
"regular_differences": [
0,
0,
0,
0,
0,
0,
0,
0
],
"cumulative_differences": [
547,
520,
420,
320,
220,
120,
60,
0
],
"lifespan_changes": [
27,
100,
100,
100,
100,
60,
60
]
}
Finding. All eightLXX/SP birthpositionsShelah throughAbraham coincide. Their cumulative differences547→520→420→320→220→120→60→0 are exactly generated by the local lifespan changes. This is a complete positive example of shared regular geometry with divergent cumulative realization.
Reassessment. Insert the single admittedCainan row intoSP and test how far the shared birthsuffix extends.
C743 — Recover the shared Cainan-ON birthsuffix
Question. Does theadmittedSP insertion align the completeNoah-to-Abraham birthpath with nativeLXX?
Sources. File18 Cainan restoration§1.3; §§3–4; C742
Inputs
{
"names": [
"Noah",
"Shem",
"Arphaxad",
"Cainan2",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham"
],
"SP_regular_insertion": 130,
"scope": "single source-authorized insertion aboveShelah; noGeartransport"
}
Results
{
"SP_ON_births": [
3838,
3336,
3236,
3101,
2971,
2841,
2707,
2577,
2445,
2315,
2236,
2166
],
"native_LXX_births": [
3838,
3336,
3236,
3101,
2971,
2841,
2707,
2577,
2445,
2315,
2236,
2166
],
"all_differences": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
]
}
Finding. The single admittedSPCainan insertion aligns every one of the12Noah-to-Abraham birthpositions with nativeLXX. This is a whole-path agreement produced by shared downstream begetting rows and the inserted130 interval, while the source lifespans remain different.
Reassessment. Compare deaths across the newly shared birthpath to identify exactly what the agreementdoesnotpreserve.
C744 — Explain death differences within identical birthpaths
Question. What remains different afterSPCainan-ON births align with nativeLXX?
Sources. File18 source rows; C743
Inputs
{
"shared_births": "C743",
"Cainan_inserted_lifespan": 460,
"nodes": [
"Noah",
"Shem",
"Arphaxad",
"Cainan2",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah"
]
}
Results
{
"death_comparison": [
{
"name": "Noah",
"SP_death": 2888,
"LXX_death": 2888,
"LXX_minus_SP_death": 0
},
{
"name": "Shem",
"SP_death": 2736,
"LXX_death": 2736,
"LXX_minus_SP_death": 0
},
{
"name": "Arphaxad",
"SP_death": 2798,
"LXX_death": 2771,
"LXX_minus_SP_death": -27
},
{
"name": "Cainan2",
"SP_death": 2641,
"LXX_death": 2641,
"LXX_minus_SP_death": 0
},
{
"name": "Shelah",
"SP_death": 2538,
"LXX_death": 2511,
"LXX_minus_SP_death": -27
},
{
"name": "Eber",
"SP_death": 2437,
"LXX_death": 2337,
"LXX_minus_SP_death": -100
},
{
"name": "Peleg",
"SP_death": 2468,
"LXX_death": 2368,
"LXX_minus_SP_death": -100
},
{
"name": "Reu",
"SP_death": 2338,
"LXX_death": 2238,
"LXX_minus_SP_death": -100
},
{
"name": "Serug",
"SP_death": 2215,
"LXX_death": 2115,
"LXX_minus_SP_death": -100
},
{
"name": "Nahor",
"SP_death": 2167,
"LXX_death": 2107,
"LXX_minus_SP_death": -60
},
{
"name": "Terah",
"SP_death": 2091,
"LXX_death": 2031,
"LXX_minus_SP_death": -60
}
]
}
Finding. With the whole birthpath fixed, each death difference is exactly the negative lifespan difference. Noah,Shem and insertedCainan deaths coincide; the other differences follow locally. Birthpath agreement therefore transfers a specific projection of the sources, not every chronological measure.
Reassessment. Compare matchedCainan cumulativefields to locate the maximal translation blocks.
C745 — Locate matched-Cainan translation blocks
Question. Does the familiar430 cumulative alignment extend through the whole matched-state genealogy?
Inputs
{
"comparison": "nativeLXXON minus admittedMTON",
"insertion_support": "Adam throughArphaxad",
"cumulative_insertion": 460
}
Results
{
"matched_profile": [
430,
430,
430,
430,
430,
430,
430,
430,
430,
454,
454,
454,
427,
400,
360,
260,
160,
60,
0,
0
],
"constant_blocks": [
{
"from": "Adam",
"through": "Lamech",
"displacement": 430
},
{
"from": "Noah",
"through": "Arphaxad",
"displacement": 454
},
{
"from": "Shelah",
"through": "Shelah",
"displacement": 427
},
{
"from": "Eber",
"through": "Eber",
"displacement": 400
},
{
"from": "Peleg",
"through": "Peleg",
"displacement": 360
},
{
"from": "Reu",
"through": "Reu",
"displacement": 260
},
{
"from": "Serug",
"through": "Serug",
"displacement": 160
},
{
"from": "Nahor",
"through": "Nahor",
"displacement": 60
},
{
"from": "Terah",
"through": "Abraham",
"displacement": 0
}
]
}
Finding. The430 alignment is exactly theAdam-throughLamech plateau. Noah-throughArphaxad differs454, and later blocks follow their own source rows. MatchingCainan removes insertion from the comparison but does not turn the entire genealogy into one translation.
Reassessment. Test pointwise composition of thethree native comparisonfields with all source modes retained.
C746 — Verify composition on the full shared genealogy
Question. Do MT→SP→LXX comparisons compose node-by-node in both modes and the modebridge?
Sources. C738–C745; Research Strategy §5D
Inputs
{
"shared_nodes": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Jared",
"Enoch",
"Methuselah",
"Lamech",
"Noah",
"Shem",
"Arphaxad",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham"
],
"modes": [
"R",
"C_lower",
"G"
],
"excluded_from_shared_grid": "nativeLXX-onlyCainan retained in itsownpath"
}
Results
{
"composition_residuals": {
"R": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"C_lower": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"G": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
]
},
"typed_comparisons": 60
}
Finding. All60 typed shared-node comparisons compose exactly. This is consistency of a common source-coordinate representation, not independent confirmation from60matches. The native inserted row remains visible rather than being invented in the othertraditions.
Reassessment. Test why matchingCreation totals alone cannot recover the ordered source structure.
C747 — Test the information supplied by intermediate boundaries
Question. Could the same aggregate lifespan difference conceal a different source-row order?
Sources. C742; Research Strategy §5B
Inputs
{
"source_deltas": [
27,
100,
100,
100,
100,
60,
60
],
"diagnostic": "swap firsttwo row differences; no newsource state"
}
Results
{
"source_profile": [
547,
520,
420,
320,
220,
120,
60,
0
],
"diagnostic_profile": [
547,
447,
420,
320,
220,
120,
60,
0
],
"profile_difference": [
0,
-73,
0,
0,
0,
0,
0,
0
]
}
Finding. Swapping just two row contributions preserves the547total and terminal but changes theEber comparison by73. The supplied intermediate boundary therefore contains information that theCreation or outer total cannot recover. This is a diagnostic of explanatory sufficiency, not an admitted variant.
Reassessment. State the exact reconstruction relation between local row changes and thewholeboundaryprofile.
C748 — Identify the ordered reconstruction operator
Question. Does the complete boundary profile determine itslocalcontributionsuniquely once theterminal is fixed?
Sources. C742,C747; Research Strategy §5F
Inputs
{
"local_vector": [
27,
100,
100,
100,
100,
60,
60
],
"terminal": 0,
"operator": "uppertriangularsuffixsum"
}
Results
{
"suffix_matrix": [
[
1,
1,
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1,
1,
1
],
[
0,
0,
1,
1,
1,
1,
1
],
[
0,
0,
0,
1,
1,
1,
1
],
[
0,
0,
0,
0,
1,
1,
1
],
[
0,
0,
0,
0,
0,
1,
1
],
[
0,
0,
0,
0,
0,
0,
1
]
],
"profile": [
547,
520,
420,
320,
220,
120,
60,
0
],
"recovered_rows": [
27,
100,
100,
100,
100,
60,
60
],
"determinant": 1,
"rank": 7
}
Finding. The suffix-sum matrix is triangular with unit diagonal. With terminal fixed, every ordered boundary determines exactly one local row vector, recovered by adjacent differences. This gives theStrategy a small linear mechanism for whole-family explanation, while total-only evaluation loses theordering.
Reassessment. Test thewhole rounded-row family for compatibility between lifespan projection androunding.
C749 — Freeze the three rounding domains
Question. Which row operations and domains may be compared?
Sources. File51a §§3.4,16.1–16.2; File18 regular tables
Inputs
{}
Results
{
"packet": {
"path": "model/rounding_inputs.json",
"sha256": "1c34bdf733d5822070359212b1fc1bedd09747e2ea47ae613a45570546f1aaf4",
"bytes": 50661
},
"row_counts": {
"MT_native_OFF": 26,
"LXX_native_ON": 27,
"SP_native_OFF": 26
},
"operations": [
"Q(b) regular births",
"Q(b)+Q(r) theoretical regular lifespan",
"Q(L) cumulative lifespan"
],
"restrictions": [
"SP inclusive counts retain count type",
"Jacob b=91 belongs to Joseph collateral",
"four final b inputs withheld"
]
}
Finding. Rounded is three typed row operations, followed by path accumulation. A missing or collateral begetting input cannot become a trunk edge.
Reassessment. Reconstruct both MT lifespan operators over every admitted row.
C750 — Reconstruct every MT rounded lifespan
Question. Where do the two lifespan operations diverge?
Sources. File51a §3.4 and §16.1 literal tables
Inputs
{}
Results
{
"parts": [
930,
910,
905,
910,
895,
960,
365,
965,
775,
950,
600,
440,
435,
465,
240,
235,
230,
150,
205,
175,
180,
145
],
"whole": [
930,
910,
905,
910,
895,
960,
365,
970,
775,
950,
600,
440,
435,
465,
240,
240,
230,
150,
205,
175,
180,
145,
135,
135,
135,
120
],
"nonzero_defects": {
"Methuselah": -5,
"Reu": -5
}
}
Finding. Methuselah and Reu both give parts-minus-total = −5. The source tables agree; the unrestricted uniqueness sentence about Methuselah needs qualification.
Reassessment. Record the first 20-step checkpoint, including the common regular comparison frame.
C751 — First twenty-step explanatory checkpoint
Question. What generalizes, and what frame must remain explicit?
Sources. C733–750
Inputs
{
"regular_frame": "common full430 comparison",
"native_Cainan": {
"MT": "OFF",
"LXX": "ON",
"SP": "OFF"
}
}
Results
{
"checkpoint": {
"path": "deliverables/490d_Chronological_Families_Checkpoint_C751.md",
"sha256": "6865f3a55c73e0a3b0d2d6964597a26f6c4cbe5a46484ffd85a542ca18784464",
"bytes": 1313
},
"SP_frame_check": {
"full430": 8982,
"native215": 9197
}
}
Finding. The comparison now has an explicit frame and a whole-field explanation. Proceed with the residual operator rather than surveying more endpoints.
Reassessment. Derive the complete finite rounding defect law.
C752 — Derive the finite rounding defect law
Question. Can one residue table explain every parts-versus-total defect?
Sources. C749–750; File51a rounding rules
Inputs
{}
Results
{
"table_b_rows_r_columns": [
[
0,
0,
0,
0,
0
],
[
0,
0,
-5,
0,
0
],
[
0,
-5,
-5,
0,
0
],
[
0,
0,
0,
5,
5
],
[
0,
0,
0,
5,
0
]
],
"formula": "K(b,r)=Q(b)+Q(r)-Q(b+r)",
"periodicity": "Q(x+5k)=Q(x)+5k"
}
Finding. Every compatible integer row belongs to one of 25 residue classes; defects are only −5,0,+5. Methuselah and Reu share class(2,2).
Reassessment. Check whether the three traditions add new defect classes within the admitted domains.
C753 — Transfer the defect law across traditions
Question. Which ordinary rows have nonzero defects in each tradition?
Sources. File18 rows; File51a rules
Inputs
{}
Results
{
"defects": {
"MT_native_OFF": {
"Methuselah": {
"K": -5,
"residues": [
2,
2
]
},
"Reu": {
"K": -5,
"residues": [
2,
2
]
}
},
"LXX_native_ON": {
"Methuselah": {
"K": -5,
"residues": [
2,
2
]
},
"Lamech": {
"K": -5,
"residues": [
2,
1
]
},
"Reu": {
"K": -5,
"residues": [
2,
2
]
}
},
"SP_native_OFF": {
"Reu": {
"K": -5,
"residues": [
2,
2
]
}
}
},
"inclusive_rows_not_ordinary_biographies": {
"MT_native_OFF": [],
"LXX_native_ON": [],
"SP_native_OFF": [
"Jared",
"Methuselah",
"Lamech"
]
}
}
Finding. LXX adds main Lamech(182+571=753), class(2,1), with defect−5. SP ordinary Reu also has−5. Inclusive SP rows remain ledger diagnostics.
Reassessment. Reconstruct the full MT cumulative rounding field.
C754 — Reconstruct the complete MT residual field
Question. Do all 26 literal cumulative boundaries follow row rounding?
Sources. File51a §16.1–16.2
Inputs
{
"terminal": 1406
}
Results
{
"field": {
"path": "model/MT_rounding_field.json",
"sha256": "58f0d98b8bcc3918c2dc9c79ce018326db0166ed7d1efbc21773b62e63ecdcde",
"bytes": 1359
},
"D": [
0,
0,
2,
2,
2,
2,
4,
4,
3,
5,
5,
5,
3,
1,
0,
-1,
-2,
-2,
-4,
-4,
-4,
-4,
-2,
0,
-2,
0
]
}
Finding. All 26 printed MT boundaries follow one suffix-sum residual field. Endpoint cancellation coexists with internal displacements from−4 to+5.
Reassessment. Recover the local residuals from the boundary field and identify unchanged intervals.
C755 — Invert and classify the MT residual field
Question. Which entire interval families survive rounding exactly?
Sources. C754
Inputs
{}
Results
{
"recovered_e": [
0,
-2,
0,
0,
0,
-2,
0,
1,
-2,
0,
0,
2,
2,
1,
1,
1,
0,
2,
0,
0,
0,
-2,
-2,
2,
-2,
0
],
"equal_residual_classes": {
"-4": [
"Terah",
"Abraham",
"Isaac",
"Jacob"
],
"-2": [
"Serug",
"Nahor",
"Levi",
"Amram"
],
"-1": [
"Reu"
],
"0": [
"Adam",
"Seth",
"Peleg",
"Kohath",
"Moses",
"terminal1406"
],
"1": [
"Eber"
],
"2": [
"Enosh",
"Kenan",
"Mahalalel",
"Jared"
],
"3": [
"Lamech",
"Shelah"
],
"4": [
"Enoch",
"Methuselah"
],
"5": [
"Noah",
"Shem",
"Arphaxad"
]
},
"interval_rule": "rounded(i,j)-actual(i,j)=D_i-D_j"
}
Finding. Every pair within one residual class preserves its interval. These are consequences of one field, not independent numerical hits. Adjacent differences recover every row residual.
Reassessment. Transfer the full residual operator to LXX and isolate changed row support.
C756 — Transfer the cumulative residual field to LXX
Question. Which changed rows explain every LXX-versus-MT rounding difference?
Sources. File18 LXX main rows; File51a rounding rule
Inputs
{}
Results
{
"fields": {
"path": "model/all_rounding_fields.json",
"sha256": "6ce58f06e5687e621578a52663a0d6f32b50d3b1cd1ad74ff2cc4225a359c6fe",
"bytes": 7609
},
"row_support": {
"Lamech": 4,
"Arphaxad": -2,
"Shelah": -2
},
"nonzero_boundary_differences": {
"Noah": -4,
"Shem": -4,
"Arphaxad": -4,
"Shelah": -2
}
}
Finding. Three LXX residual changes generate the complete comparison: Lamech+4, Arphaxad−2, Shelah−2. Their total cancels, but the Noah–Arphaxad plateau changes−4 and Shelah−2.
Reassessment. Test SP support and explain its changed head residual.
C757 — Transfer the residual field to SP
Question. Why does SP gain three at the cumulative head?
Sources. File18 SP inclusive lifespan ledger; C756
Inputs
{}
Results
{
"row_support": {
"Methuselah": -1,
"Lamech": 4
},
"boundary_differences": {
"Adam": 3,
"Seth": 3,
"Enosh": 3,
"Kenan": 3,
"Mahalalel": 3,
"Jared": 3,
"Enoch": 3,
"Methuselah": 3,
"Lamech": 4
},
"head_actual_rounded": [
13398,
13401
]
}
Finding. SP rounding changes the cumulative head by+3, entirely from Methuselah−1 and Lamech+4 relative to MT residuals. The inclusive ledger remains the input type.
Reassessment. Determine cross-tradition interval families preserved by rounding.
C758 — Classify cross-tradition interval preservation
Question. When does rounding preserve a difference between traditions?
Sources. C754–757
Inputs
{}
Results
{
"comparison_classes": {
"LXX_native_ON": {
"-4": [
"Noah",
"Shem",
"Arphaxad"
],
"-2": [
"Shelah"
],
"0": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Jared",
"Enoch",
"Methuselah",
"Lamech",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham",
"Isaac",
"Jacob",
"Levi",
"Kohath",
"Amram",
"Moses"
]
},
"SP_native_OFF": {
"0": [
"Noah",
"Shem",
"Arphaxad",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham",
"Isaac",
"Jacob",
"Levi",
"Kohath",
"Amram",
"Moses"
],
"3": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Jared",
"Enoch",
"Methuselah"
],
"4": [
"Lamech"
]
}
},
"criterion": "DeltaD_i=DeltaD_j iff the cross-tradition interval difference is unchanged by rounding"
}
Finding. Equal comparison-residual plateaus identify complete preserved interval families. Cross-tradition compatibility follows from two local field values, without a new list of isolated matches.
Reassessment. Test whether admitted Cainan insertion preserves these residual fields.
C759 — Test Cainan residual neutrality
Question. Does insertion change existing rounding discrepancies?
Sources. File18 Cainan; C754–758
Inputs
{
"Cainan": {
"b": 130,
"r": 330,
"L": 460
}
}
Results
{
"results": {
"MT_native_OFF": {
"all_common_residuals_equal": true,
"new_node_D": 3,
"Shelah_D": 3
},
"LXX_native_ON": {
"all_common_residuals_equal": true,
"new_node_D": 1,
"Shelah_D": 1
},
"SP_native_OFF": {
"all_common_residuals_equal": true,
"new_node_D": 3,
"Shelah_D": 3
}
},
"duration_residuals": [
0,
0,
0
]
}
Finding. Cainan insertion changes admitted durations but preserves every corresponding residual. Its new boundary inherits the local plateau; zero row residual does not imply zero boundary displacement.
Reassessment. Prove rounding compatibility with admitted multiples-of-five changes.
C760 — Prove rounding equivariance for admitted shifts
Question. Which state changes commute with componentwise rounding?
Sources. File51a variants; C752
Inputs
{
"admitted_amounts": [
60,
130,
215,
460
]
}
Results
{
"identity": "For k=5m, Q(n+k)=5 floor((n+5m+2)/5)=Q(n)+5m. Thus row residuals and corresponding boundary residuals persist under compatible admitted changes.",
"checked_amounts": {
"60": true,
"130": true,
"215": true,
"460": true
},
"scope": "compatible coordinates or rows; insertion retains topology; finite source states only"
}
Finding. Rounding compatibility is an equivariance under multiples of five. It explains why several variants preserve residual profiles without making all chronology operations interchangeable.
Reassessment. Test counted-versus-completed input order where the shift is not a multiple of five.
C761 — Resolve SP counting before rounding
Question. How does the local 53rd-year versus 52-completed distinction affect rounding?
Sources. File18 §3.1; File51a §17
Inputs
{
"counted": 53,
"completed": 52
}
Results
{
"Q53": 55,
"Q52": 50,
"raw_separation": 1,
"rounded_separation": 5,
"round_then_subtract_one": 54
}
Finding. The raw one-unit distinction becomes a five-unit rounding distinction:55 versus50. Rounding then subtracting one gives54, a different construction. Counting convention must be resolved at the input.
Reassessment. Test the complete SP regular diagnostic while keeping its source status conditional.
C762 — Test the conditional SP lower-block reconstruction
Question. Can one local input distinction generate the transmitted five-unit separation?
Sources. File51a §17; File18 SP begetting rows
Inputs
{
"terminal_Jacob": 2006,
"Noah_additional_binding": "omitted in this strict begetting diagnostic"
}
Results
{
"diagnostics": {
"counted53": {
"raw": 4413,
"rounded": 4411
},
"completed52": {
"raw": 4412,
"rounded": 4406
}
},
"status": "conditional reconstruction, not established derivation of File51a blocks"
}
Finding. The strict branch calculation gives4411 versus4406, matching the transmitted and secondary blocks. The match identifies a possible mechanism; it does not promote this diagnostic to the primary SP path.
Reassessment. Separate terminal branch selection from row rounding in the SP cumulative head.
C763 — Separate SP rounding from terminal branch selection
Question. Can the Strategy13406 head be reconstructed by explicit typed increments?
Sources. File51a §16.2 Aaron variant; Strategy cumulative SP/J rectangle; C757
Inputs
{
"SP_lower_actual": 13396,
"Moses_center": 13398,
"rounded_Moses": 13401,
"rounded_Aaron_increment": 5
}
Results
{
"chain": [
13396,
13398,
13401,
13406
],
"increments": [
2,
3,
5
],
"status": "conditional cross-tradition application of the source rounding/branch rules",
"distinction": "rounded Aaron125-minus-Moses120 is not exact Actual Tishri phase+3.5"
}
Finding. The Strategy head13406 has a transparent conditional reconstruction: +2 endpoint selection, +3 SP row-rounding residual, +5 rounded Aaron branch. The arithmetic explains the supplied+10 without proving that derivation was intended.
Reassessment. Check the complete SP/J rectangle with this head and label its generated status.
C764 — Attach the residual decomposition to the Strategy rectangle
Question. What part of the SP equal-gain rectangle is now explained?
Sources. Strategy §4.3; C763
Inputs
{
"regular_head": 4206,
"cumulative_head": 13406,
"origin": 1446,
"target": 1406
}
Results
{
"native_spans": [
2760,
11960
],
"expanded_spans": [
2800,
12000
],
"gains": [
40,
40
],
"preserved_gap": [
9200,
9200
],
"new_explanation": "conditional cumulative-head provenance+2/+3/+5",
"remaining_input": "the regular4206 branch and application status remain source-controlled"
}
Finding. The existing rectangle survives exactly. This cycle adds a row-based explanation for its cumulative-head offset, not a new independent rectangle or permission to tune other heads.
Reassessment. Test how lifespan splitting changes the whole accumulated comparison.
C765 — Accumulate the splitting defect as a field
Question. What happens if rounded theoretical lifespans are accumulated instead of rounded whole lives?
Sources. C750–753; diagnostic operator comparison only
Inputs
{}
Results
{
"fields": {
"path": "model/splitting_defect_fields.json",
"sha256": "4321928895655ea15e0338966a6568fec38a15d73b1a07847a5736d4d60f8590",
"bytes": 1740
},
"head_defects": {
"MT_native_OFF": -10,
"LXX_native_ON": -15
},
"scope": "operator diagnostic over local biographies; not a licensed replacement cumulative chronology"
}
Finding. Parts-rounding and total-rounding differ over whole fields: MT head−10, LXX−15 on the common admitted biography domain. A constant endpoint correction cannot reproduce their internal jumps.
Reassessment. Derive how two rounding fields modify the regular–cumulative bridge.
C766 — Join rounding to the mode bridge
Question. Does bridge rounding follow the difference of the two boundary residuals?
Sources. File51a §3.1 strict regular and §16.2 cumulative tables
Inputs
{}
Results
{
"source_packet": {
"path": "model/variant_inputs.json",
"sha256": "637ee29c7bcb34fbdf313690535d3f2035837e6f77940bc0580e5a90295f8cf0",
"bytes": 187357
},
"bridge": {
"path": "model/MT_rounding_bridge.json",
"sha256": "8b8c6c130a8aaf156453fe1b74b3ffa72d29a9529134efc1678b7f8234a8732f",
"bytes": 2560
},
"common_nodes": 22,
"Adam": {
"name": "Adam",
"G_actual": 9894,
"G_rounded": 9900,
"delta_G": 6,
"D_C_minus_D_R": 6
}
}
Finding. On the literal strict regular comparison, rounded G−actual G equals D_C−D_R at every common node. Rounding modifies the mode bridge through two fields, not one date offset.
Reassessment. Check the local bridge-generator identity from adjacent differences.
C767 — Recover rounded bridge changes locally
Question. Do changes in adjacent bridge gaps equal row rounding differences?
Sources. C766; File51a strict comparison
Inputs
{}
Results
{
"local_changes": [
{
"name": "Adam",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Seth",
"field_difference": -2,
"row_prediction": -2
},
{
"name": "Enosh",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Kenan",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Mahalalel",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Jared",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Enoch",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Methuselah",
"field_difference": 3,
"row_prediction": 3
},
{
"name": "Lamech",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Noah",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Shem",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Arphaxad",
"field_difference": 2,
"row_prediction": 2
},
{
"name": "Shelah",
"field_difference": 2,
"row_prediction": 2
},
{
"name": "Eber",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Peleg",
"field_difference": 1,
"row_prediction": 1
},
{
"name": "Reu",
"field_difference": 3,
"row_prediction": 3
},
{
"name": "Serug",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Nahor",
"field_difference": 1,
"row_prediction": 1
},
{
"name": "Terah",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Abraham",
"field_difference": 0,
"row_prediction": 0
},
{
"name": "Isaac",
"field_difference": 0,
"row_prediction": 0
}
],
"scope": "21 consecutive strict regular edges Adam→Jacob; Jacob/Joseph collateral is not continued to Levi"
}
Finding. The rounded bridge itself is generated locally by e(L)−e(b). This joins source rows, mode choice, and rounding in one recurrence.
Reassessment. Test direct rounding of date labels against the source-derived field.
C768 — Compare row rounding with date-grid rounding
Question. Can rounding already calculated dates reproduce the source chronology?
Sources. File51a §16.2; C754–757
Inputs
{
"grid_anchor": 1406
}
Results
{
"diagnostic": {
"path": "model/date_grid_diagnostic.json",
"sha256": "ac040f2ee4e2718dc6af24e48a39d46edbff3525e3a215e0f5ab2e1a1b8bd876",
"bytes": 2216
},
"mismatch_counts": {
"MT_native_OFF": 11,
"LXX_native_ON": 7,
"SP_native_OFF": 17
},
"MT_examples": {
"Noah": {
"grid": 6381,
"row": 6386
},
"Abraham": {
"grid": 2436,
"row": 2431
}
}
}
Finding. A nearest1/6 date-grid projection fails at11 of26 MT boundaries. Rounded chronology depends on the source path, not just the final Actual date.
Reassessment. Test subdivision dependence over an informative complete source subpath.
C769 — Measure the effect of retained subdivisions
Question. Does whole-chain cancellation justify rounding arbitrary subpath totals?
Sources. File51a cumulative Enoch and Terah boundaries
Inputs
{}
Results
{
"subpath": "Enoch→Terah",
"actual_span": 5852,
"row_rounded_span": 5860,
"once_rounded_total": 5850,
"defect": 10,
"field_span_change": 8
}
Finding. The source subpath5852 becomes5860 by row rounding but5850 by rounding its total. Retained subdivision is part of the construction, even when the full12600 total cancels.
Reassessment. State the minimal recoverable object linking Actual and Rounded.
C770 — Identify a recoverable shared source object
Question. What must accompany Rounded to preserve the original family?
Sources. C754–769
Inputs
{}
Results
{
"reconstruction": "Actual boundary = Rounded boundary − D; actual row = rounded row − e",
"affine_obstruction": {
"fixed_dates": [
1406,
1526
],
"moved_date": [
1663,
1661
]
},
"retained_data": [
"ordered source rows",
"typed path and terminal",
"mode selector",
"rounding residual field"
]
}
Finding. Rounded plus its residual field recovers Actual exactly. Rounded alone loses information; no one affine date map works, since two fixed dates force identity while Amram moves.
Reassessment. Integrate the 40-step checkpoint and move to finite variant configurations.
C771 — Forty-step synthesis checkpoint
Question. Which common mechanism now explains the Rounded family?
Sources. C732–770
Inputs
{}
Results
{
"checkpoint": {
"path": "deliverables/490d_Chronological_Families_Checkpoint_C771.md",
"sha256": "4c032c5d12943f45cc600e2db12f4d16ad34f83fea9776731e994d301a974820",
"bytes": 1493
}
}
Finding. The general object is an ordered source path with mode-specific row measurements and a recoverable rounding field. Finite variants are the next discriminating test.
Reassessment. Reconstruct the finite variant masks against literal source examples.
C772 — Define the finite source configuration
Question. What is the smallest regular birth-state formula consistent with the declared variant domains?
Sources. File18 §§1.3–1.6; model/variant_inputs.json
Inputs
{
"s": "0/1 minimum/full430",
"t": "0/1 baseline/+60 Terah",
"c": "0/1 Cainan OFF/ON"
}
Results
{
"rule": {
"path": "model/variant_rule.json",
"sha256": "58ac54c59156d94eeedd4313111bbd2ec5edcb91af5eab442f2e2251878fb5b5",
"bytes": 516
},
"masks": {
"Adam–Arphaxad": [
1,
1,
1
],
"Shelah–Terah": [
1,
1,
0
],
"Abraham–Joseph/Levi": [
1,
0,
0
],
"Aaron/Moses terminal": [
0,
0,
0
]
}
}
Finding. Three finite choices have nested supports. The rule predicts placements within each source domain while preserving native LXX Cainan and unassigned regular births.
Reassessment. Recover the four literal Terah states before extending the rule.
C773 — Recover all four Terah birth states
Question. Does the finite rule reproduce each literal birth/death/begetting combination?
Sources. File18 lines643–648
Inputs
{}
Results
{
"generated": [
[
2021,
1816,
70,
1951
],
[
2081,
1876,
130,
1951
],
[
2236,
2031,
70,
2166
],
[
2296,
2091,
130,
2166
]
],
"literal": [
[
2021,
1816,
70,
1951
],
[
2081,
1876,
130,
1951
],
[
2236,
2031,
70,
2166
],
[
2296,
2091,
130,
2166
]
]
}
Finding. All four Terah states follow one supported birth shift with lifespan205 retained. Abraham is insensitive to the Terah switch but responds to the Sojourn placement.
Reassessment. Recover all four inserted-Cainan states without applying its own insertion twice.
C774 — Recover every inserted-Cainan position
Question. Does Cainan have four placements while upstream common rows have eight?
Sources. File18 lines634–639
Inputs
{}
Results
{
"generated": [
[
2481,
2611,
2151
],
[
2421,
2551,
2091
],
[
2266,
2396,
1936
],
[
2206,
2336,
1876
]
]
}
Finding. Cainan is an inserted node at Shelah+130. Its four placements use the two downstream position choices; it does not receive an additional own-Cainan130 shift.
Reassessment. Generate the complete finite configuration for all three traditions.
C775 — Generate all admitted common-row birth configurations
Question. Do the same support masks produce the three complete comparison families?
Sources. C738 native Cainan/common430 field; C772–774
Inputs
{}
Results
{
"configurations": {
"path": "model/finite_birth_configurations.json",
"sha256": "07d7a5fab5ff11110f3aaf177b82c3e529f129261e4bb8a35a8a23ac05885591",
"bytes": 11074
},
"placement_counts": {
"MT": {
"Adam": 8,
"Shelah": 4,
"Abraham": 2
},
"LXX": {
"Adam": 8,
"Shelah": 4,
"Abraham": 2
},
"SP": {
"Adam": 8,
"Shelah": 4,
"Abraham": 2
}
},
"SP_minimum_full_heads": [
4199,
4414
]
}
Finding. Each tradition has eight admitted state labels, restricting to eight upstream, four middle, and two Abraham placements. Native SP215 and equalized full430 remain distinct selections.
Reassessment. Test reversible finite switching and its direction-dependent increments.
C776 — Test the finite switch algebra
Question. Do variant switches commute without becoming unlimited translations?
Sources. C772–775
Inputs
{}
Results
{
"state_count": 8,
"switch_amount_rule": "weight*(1−2*current_bit)*support_mask",
"domain": "finite source labels; not repeated positive additions"
}
Finding. The three switches commute and undo themselves on binary state labels. Their numeric direction changes on return; this supplies a bounded configuration rather than an unrestricted translation rule.
Reassessment. Use support differences to predict entire interval responses.
C777 — Derive the whole interval-response law
Question. Which switches can affect a given interval?
Sources. C772–776
Inputs
{}
Results
{
"formula": "delta span =215 ds(S_i−S_j)+60 dt(T_i−T_j)+130 dc(H_i−H_j)",
"examples": {
"Adam→Arphaxad": {
"000": 1658,
"001": 1658,
"010": 1658,
"011": 1658,
"100": 1658,
"101": 1658,
"110": 1658,
"111": 1658
},
"Arphaxad→Shelah": {
"000": 35,
"001": 165,
"010": 35,
"011": 165,
"100": 35,
"101": 165,
"110": 35,
"111": 165
},
"Terah→Abraham": {
"000": 70,
"001": 70,
"010": 130,
"011": 130,
"100": 70,
"101": 70,
"110": 130,
"111": 130
}
},
"dependent_comparisons": 4560
}
Finding. Intervals inside one support block are invariant; intervals crossing a hinge detect exactly that hinge. The entire finite family follows one incidence rule.
Reassessment. Test matched configurations on the newly aligned SP/LXX birth suffix.
C778 — Transfer SP/LXX birth agreement across admitted states
Question. Does the complete aligned suffix remain equal under matched Sojourn/Terah choices?
Inputs
{}
Results
{
"matched_states": {
"001": {
"equal": true,
"Noah": 3623,
"Abraham": 1951
},
"011": {
"equal": true,
"Noah": 3683,
"Abraham": 1951
},
"101": {
"equal": true,
"Noah": 3838,
"Abraham": 2166
},
"111": {
"equal": true,
"Noah": 3898,
"Abraham": 2166
}
},
"native_minimum_sequence": [
3623,
3121,
3021,
2886,
2756,
2626,
2492,
2362,
2230,
2100,
2021,
1951
]
}
Finding. The twelve-node SP-with-Cainan/LXX birth agreement holds throughout all four matched placement states. Shared masks explain the transfer; no new date fitting is needed.
Reassessment. Explain why this birth agreement does not force a unique cumulative lift.
C779 — Build the Terah source triangle
Question. Can the same regular+60 have distinct cumulative meanings?
Sources. File18 §§3.2.2,6A,6C
Inputs
{}
Results
{
"triangle": {
"path": "model/Terah_triangle.json",
"sha256": "f5792e3ef1a0018a7ea9e91582ec3697efb813685b26b6dd93d7c7a23d5c9a4a",
"bytes": 450
},
"states": {
"SP_textual": {
"b": 70,
"r": 75,
"L": 145,
"regular_head": 2021,
"regular_death": 1876,
"cumulative_head": 2580
},
"MT_LXX_baseline": {
"b": 70,
"r": 135,
"L": 205,
"regular_head": 2021,
"regular_death": 1816,
"cumulative_head": 2640
},
"common_alternative": {
"b": 130,
"r": 75,
"L": 205,
"regular_head": 2081,
"regular_death": 1876,
"cumulative_head": 2640
}
},
"status": "SP textual145 and MT/LXX205 literal; SP common130/205 biography is a compatible derived construction, not official cumulative replacement"
}
Finding. SP textual, MT/LXX baseline, and the common alternative form one row triangle. Their regular and cumulative projections distinguish which component changed.
Reassessment. Test path independence around the triangle in both projections.
C780 — Test both Terah projection paths
Question. Do the two-step and direct row changes agree without identifying their meanings?
Sources. C779
Inputs
{}
Results
{
"row_changes": [
[
0,
60
],
[
60,
-60
],
[
60,
0
]
],
"regular_cumulative_changes": [
[
0,
60
],
[
60,
0
],
[
60,
60
]
]
}
Finding. The projected route(0,60)+(60,0) equals(60,60). MT/LXX+60 preserves life205, while the compatible SP145→205 route changes life. A regular shift alone cannot specify its cumulative realization.
Reassessment. Distinguish the secondary Rounded cumulative+60 block from raw Terah repartition.
C781 — Separate the secondary cumulative block translation
Question. Does the source Rounded cumulative+60 block come from raw MT Terah repartition?
Sources. File51a §23.7; C779–780
Inputs
{
"source_blocks": [
[
14011,
14006
],
[
14071,
14066
]
]
}
Results
{
"raw_lifespan_change": 0,
"secondary_block_change": [
60,
60
],
"scope": "source-admitted displayed macro block; no unlicensed full-genealogy extension"
}
Finding. Both operations are legitimate in their stated domains, but their outputs differ: raw lifespan-preserving Terah change gives0 cumulative shift; the secondary display block explicitly moves60. Their provenance must accompany the variant name.
Reassessment. Compare Cainan support across regular and cumulative representations.
C782 — Compare Cainan support across modes
Question. Do regular130 and cumulative460 act on the same surviving rows?
Sources. File18 §1.6; C738,C775
Inputs
{}
Results
{
"support_fields": {
"path": "model/Cainan_support_modes.json",
"sha256": "45dea3de086384345794270c68de649963f39290b90c0f57302f31f2e59f9e3f",
"bytes": 5989
}
}
Finding. Cainan insertion has one upstream support and two mode weights. Its effect on the gap is330 on that prefix and0 downstream; the inserted node is represented separately.
Reassessment. Determine which regular state choices are forgotten by the raw lifespan projection.
C783 — Identify the cumulative restriction of the regular state cube
Question. Must eight regular configurations produce eight different raw cumulative chains?
Sources. File18 raw MT/LXX Terah and Cainan rules
Inputs
{}
Results
{
"raw_MT_LXX_cumulative_classes": {
"0": [
"000",
"010",
"100",
"110"
],
"1": [
"001",
"011",
"101",
"111"
]
},
"forgotten_choices": [
"Sojourn regular placement",
"Terah life205-preserving repartition"
],
"retained_choice": "Cainan lifespan460 insertion",
"SP_scope": "official145 retained; ideal205 is separately tagged"
}
Finding. For the admitted raw MT/LXX lifespan projection, the eight regular labels collapse to two cumulative executions. Mode choice forgets some source-position data; it does not erase the source-state labels themselves.
Reassessment. Test the complete residual vectors under all admitted matched configurations.
C784 — Transfer full residual vectors through finite variants
Question. Does rounding retain its coordinate discrepancies throughout the admitted MT configuration?
Sources. File51a 23 regular and26 cumulative paired rows; C760,C772
Inputs
{}
Results
{
"residuals": {
"path": "model/variant_residual_vectors.json",
"sha256": "8ec539b81d93e426a3dbfa143ea51f46d05c08288af75e4b302b27093a9040b8",
"bytes": 4203
},
"basis": "row-level Q(n+5k)=Q(n)+5k; coordinate calculation is its consequence"
}
Finding. All existing23 regular and26 cumulative MT residual coordinates persist under their compatible admitted state moves. This transfers the whole field, while keeping raw cumulative Terah/Sojourn choices forgotten.
Reassessment. Evaluate the new Cainan coordinate on both Actual and Rounded rails.
C785 — Distinguish zero row residual from zero coordinate residual
Question. What residual does the inserted MT Cainan boundary inherit?
Sources. File51a paired rows; File18 Cainan130/460
Inputs
{
"regular_Shelah": [
2421,
2421
],
"cumulative_Shelah": [
4393,
4396
]
}
Results
{
"regular_Cainan": [
2551,
2551
],
"cumulative_Cainan": [
4853,
4856
],
"residuals": [
0,
3
]
}
Finding. The inserted local durations are already round, but the cumulative Cainan coordinate inherits Shelah’s+3 residual:4853→4856. Local exactness and coordinate exactness are different properties.
Reassessment. Check Terah triangle compatibility with both rounding selectors.
C786 — Verify rounding on the complete Terah triangle
Question. Does the distinction between the Terah lifts survive rounding?
Sources. C779–780; Q5 rule
Inputs
{}
Results
{
"rounded_states": {
"SP_textual": {
"rounded_b": 70,
"rounded_r": 75,
"rounded_L": 145,
"K": 0
},
"MT_LXX_baseline": {
"rounded_b": 70,
"rounded_r": 135,
"rounded_L": 205,
"K": 0
},
"common_alternative": {
"rounded_b": 130,
"rounded_r": 75,
"rounded_L": 205,
"K": 0
}
}
}
Finding. Rounding fixes every component in the Terah triangle. It preserves the distinction between a repartition and a lifespan change, so rounding cannot justify conflating their cumulative effects.
Reassessment. Recover cumulative divergence on the SP/LXX aligned birth suffix.
C787 — Accumulate cumulative divergence behind equal births
Question. What complete cumulative field accompanies the aligned SP/LXX birth suffix?
Sources. C743–744,C778; File18 lifespan rows
Inputs
{}
Results
{
"field": {
"path": "model/aligned_birth_divergence.json",
"sha256": "aacfd29fd88f42ab72b7891609b9758e925732f16ba5f373eb0eb36f4a7cef4a",
"bytes": 1802
},
"lifespan_differences": [
0,
0,
27,
0,
27,
100,
100,
100,
100,
60,
60,
0
],
"cumulative_differences": [
574,
574,
574,
547,
547,
520,
420,
320,
220,
120,
60,
0
]
}
Finding. The same twelve birth labels coexist with a cumulative difference rising to574 upstream. Death differences are the negative local lifespan changes; cumulative differences are their running sums. This is a complete example of what each representation retains or forgets.
Reassessment. Test whether the aligned birth family survives row rounding.
C788 — Transfer the aligned family through rounding
Question. Do equal births remain equal while cumulative divergence changes locally?
Sources. C787; File18 rows and Q5 rule
Inputs
{}
Results
{
"rounded_begetting_differences": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"rounded_lifespan_differences": [
0,
0,
25,
0,
25,
100,
100,
100,
100,
60,
60,
0
],
"rounded_cumulative_differences": [
570,
570,
570,
545,
545,
520,
420,
320,
220,
120,
60,
0
],
"scope": "derived row-rounding comparison with matched source bindings/anchor"
}
Finding. The aligned birth family survives rounding because its source begetting rows agree. Its cumulative divergence changes574→570 through Arphaxad and Shelah27→25, preserving the explanation by different measurements of the same rows.
Reassessment. Condense the result into an explicit representation map.
C789 — Specify the shared representation map
Question. Which information is retained and lost in each chronological view?
Sources. C733–788
Inputs
{}
Results
{
"representations": {
"path": "model/representation_map.json",
"sha256": "8eb698f7338398ef742ed093e5f8353af30929952d84b8a6d2eb2e928e4d3e23",
"bytes": 705
},
"recovery_requirement": "source type + path + anchor + residuals for rounded reconstruction"
}
Finding. These families are related representations of structured source data. Their differences are explained by selectors and retained information; a universal date-to-date map is unnecessary and unsupported.
Reassessment. Record independent review qualifications and prepare the BJ transfer.
C790 — Select the next whole-family transfer and freeze its inputs
Question. Does BJ offer a discriminating extension of the path grammar?
Sources. File53 index/deletion tables; File20 biological/surface paths; review C749–770
Inputs
{}
Results
{
"packet": {
"path": "model/jubilees_inputs.json",
"sha256": "7be3a9155dfb8145760cfb5a0780c71484186ccb70c5026044ea0c2bcd42486a",
"bytes": 47193
},
"selected_tests": [
"distinguish index deletion from duration deletion",
"retain the source57 and endpoint roles",
"test the complete biological/surface path",
"connect retained-component2450 path"
],
"review_qualifications": [
"common430 profile versus nativeSP215",
"derived LXX/SP rounding",
"conditional SP+10 route",
"grid means labels ending1 or6",
"insertion preserves existing order while adding membership"
]
}
Finding. BJ tests topology, duration weights, and role selection on complete supplied objects. It can extend the grammar without inventing a BJ cumulative lifespan or broadening boundary searches.
Reassessment. Close the 60-step checkpoint before executing BJ transfer.
C791 — Sixty-step synthesis checkpoint
Question. What do finite variants add to the common explanation?
Sources. C772–790
Inputs
{}
Results
{
"checkpoint": {
"path": "deliverables/490d_Chronological_Families_Checkpoint_C791.md",
"sha256": "1791215de10167594a972b3e5d146f2b4b7909bb9ffc7aff04efa75719c935df",
"bytes": 1562
}
}
Finding. Finite variants fit as bounded choices acting on source-defined supports. Cross-mode behavior depends on the source row lift, not just the variant name.
Reassessment. Reconstruct the complete BJ index object.