490d — C732–C751: 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.