490d — C832–C851: sequential research record
Working continuation of C831 · 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.
C832 — Select complete-family transfer tests
Question. Can the established path grammar explain new source-controlled families without fitting their endpoints?
Sources. Strategy stagesD–H; C831 synthesis; local File58
Inputs
{
"first_family": "File58 complete ledger matrices and declared partitions",
"other_candidates": [
"File43/54 full Luke display",
"File52c complete paired-anchor field",
"File63 ordered carrier network"
],
"predecessor": "C831"
}
Results
{
"selection": {
"path": "model/RESEARCH_SELECTION.json",
"sha256": "57658fdf754e76e533371e0183608c0c10b33a58131b0dcfd0c92e85dfdc1709",
"bytes": 285
},
"source_snapshots": 41,
"primary": "a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530"
}
Finding. The next test moves from genealogy to a bounded list with multiple source-defined measurements. Complete-family transformations, not additional endpoint searches, will guide the cycle.
Reassessment. Freeze File58’s complete ledger and partition data before calculating its consequences.
C833 — Freeze the complete File58 list objects
Question. Which literal tables and declared orders are the inputs to the holdout?
Sources. File58 §§3–5,7,13
Inputs
{}
Results
{
"packet": {
"path": "model/list_inputs.json",
"sha256": "9884a95572290132effce69c3a16e362d9c298c9a9b4c6bded06545f449dd2f1",
"bytes": 14983
},
"literal_table_rows": {
"category": 8,
"leviticus": 3,
"feast_scale": 6,
"full_scale": 7,
"forward": 8,
"reverse": 8,
"esau": 9,
"clean_walk": 6
}
}
Finding. The complete category, sequence and partition tables are frozen with source line locators. Subsequent tests can distinguish source inputs from generated consequences.
Reassessment. Reconstruct the whole seven-day Sukkot count matrix.
C834 — Reconstruct a complete Sukkot species-by-day matrix
Question. Can the seven day totals be generated by one declining component and three constant components?
Sources. File58 §§3.1–3.2,7.1
Inputs
{
"uniform_daily_rams_lambs_goats": [
2,
14,
1
],
"status": "declared allocation reconstruction; marginal totals alone do not imply uniformity"
}
Results
{
"matrix": {
"path": "model/Sukkot_matrix.json",
"sha256": "2dd0f49ee2c98a58d388b4eb25ad26956588342e8058e1f8517abb1f9e4204a4",
"bytes": 642
},
"species": [
"bulls",
"rams",
"lambs",
"goats"
],
"day_rows": [
[
13,
2,
14,
1
],
[
12,
2,
14,
1
],
[
11,
2,
14,
1
],
[
10,
2,
14,
1
],
[
9,
2,
14,
1
],
[
8,
2,
14,
1
],
[
7,
2,
14,
1
]
],
"day_totals": [
30,
29,
28,
27,
26,
25,
24
],
"column_totals": [
70,
14,
98,
7
],
"rank": 2,
"generator": "row_d=(14−d,2,14,1), d=1…7"
}
Finding. The declared daily allocation has a rank-two generator: only the bull component changes. It recovers all seven totals and the complete189 species ledger. The uniform component allocation remains an input, not a deduction from margins alone.
Reassessment. Recover the whole Tishri category/species table as a linear measurement object.
C835 — Recover both complete Tishri margins
Question. Do event-category and species totals measure the same frozen count matrix?
Sources. File58 §3.1 literal category table
Inputs
{}
Results
{
"matrix": {
"path": "model/Tishri_count_matrix.json",
"sha256": "ccbb58ccd547dbe8e826eba227e09d3454451f998f4531f34677c06ee73375c2",
"bytes": 665
},
"category_totals": [
44,
6,
11,
10,
10,
189,
10
],
"species_totals": [
75,
18,
176,
11
],
"grand_total": 280
}
Finding. The two280 totals are different marginals of one seven-by-four matrix. Their agreement is forced by the shared ledger, while the chosen categories and entries remain source inputs.
Reassessment. Determine what the margins preserve and what they cannot recover.
C836 — Test whether the margins determine the ledger
Question. Can preserved category/species totals recover every internal cell?
Sources. C835; diagnostic only
Inputs
{}
Results
{
"diagnostic_changed_rows": {
"NewMoon": [
3,
1,
6,
1
],
"Trumpets": [
0,
1,
8,
1
]
},
"kernel_move": "a2×2 +1,−1,−1,+1 cell circulation",
"source_status": "not an admitted offering variant"
}
Finding. Both margins survive a nonzero cell circulation. Totals compress the ledger but do not reconstruct its source cells; the complete table supplies information beyond280.
Reassessment. Evaluate the source-admitted calendar/corpus overlay states.
C837 — Generate the finite calendar/corpus comparison matrix
Question. Do independent declared additions reconstruct all four source states?
Sources. File58 §4.3
Inputs
{}
Results
{
"states": {
"path": "model/Tishri_overlay_states.json",
"sha256": "6b9e2c3bfcfaf70af42bf0540baf3553326d37c0998a9450fee912eadec5ac0d",
"bytes": 387
},
"00": {
"species": [
75,
18,
176,
11
],
"total": 280
},
"01": {
"species": [
76,
20,
176,
13
],
"total": 285
},
"10": {
"species": [
75,
18,
178,
11
],
"total": 282
},
"11": {
"species": [
76,
20,
178,
13
],
"total": 287
},
"controls": "00 controls; fourth Sabbath and Leviticus16 are separate comparison choices"
}
Finding. The280/282/285/287 matrix is a two-choice additive configuration with independently stated supports. Calendar placement adds lambs; corpus inclusion adds a different animal vector.
Reassessment. Check the separate slaughtered subset and scaled overlay response.
C838 — Separate ledger selection from scale
Question. How do ritual disposition and shemitah scale interact with the finite overlay?
Sources. File58 §§4.3,5
Inputs
{}
Results
{
"complete_rite": 5,
"slaughtered_subset": 4,
"scaled_states": {
"00": 1960,
"01": 1995,
"10": 1974,
"11": 2009
},
"scaled_calendar_increment": 14,
"scaled_complete_rite_increment": 35,
"derived_slaughtered_totals": [
284,
286
]
}
Finding. Selecting displayed ritual animals or slaughtered animals changes the measured object by one goat. Scaling then carries that difference to seven; it cannot be suppressed by retaining the same ledger name.
Reassessment. Regenerate every forward festival boundary from its day generator.
C839 — Regenerate the full forward festival path
Question. Does one day generator recover every supplied cumulative and chronological row?
Sources. File58 §7.1
Inputs
{
"anchor": 1859,
"scale": 7
}
Results
{
"path": {
"path": "model/festival_forward_path.json",
"sha256": "b92c95b5b92dd58e80d9a6bbba6b1b8e0bae4b0de0da292d19d6bb68e552a67a",
"bytes": 340
},
"prefix_counts": [
0,
30,
59,
87,
114,
140,
165,
189,
199
],
"BC": [
1859,
1649,
1446,
1250,
1061,
879,
704,
536,
466
]
}
Finding. The complete forward path follows the descending day total and one appended Eighth-Day10. All eight source boundaries are forced once the source order, scale7, and1859 anchor are fixed.
Reassessment. Generate the complete declared reverse order through the same accumulation rule.
C840 — Regenerate the complete reverse-order festival path
Question. What relation joins the two declared orders at every boundary?
Inputs
{}
Results
{
"path": {
"path": "model/festival_reverse_path.json",
"sha256": "2a0416f26a90c2385b0ac39c1ea69d227783bc5d0804feadd08722dc4b6e0cbc",
"bytes": 287
},
"prefix_counts": [
0,
10,
34,
59,
85,
112,
140,
169,
199
],
"BC": [
1859,
1789,
1621,
1446,
1264,
1075,
879,
676,
466
],
"paired_formula": "reverse_prefix(k)=199−forward_prefix(8−k)",
"coordinate_pair_sum": 2325
}
Finding. Every reverse boundary is the complement of a corresponding forward boundary. This is a sequence-reversal relation on two paths, not a newly licensed formal Mirror operation.
Reassessment. Identify exactly where the two source orders share boundaries.
C841 — Resolve all shared boundaries of the two festival orders
Question. Which overlaps follow from the complete prefix sets?
Sources. C839–840
Inputs
{}
Results
{
"shared_boundaries": [
{
"count": 0,
"years": 0,
"BC": 1859,
"forward_step": 0,
"reverse_step": 0
},
{
"count": 59,
"years": 413,
"BC": 1446,
"forward_step": 2,
"reverse_step": 3
},
{
"count": 140,
"years": 980,
"BC": 879,
"forward_step": 5,
"reverse_step": 6
},
{
"count": 199,
"years": 1393,
"BC": 466,
"forward_step": 8,
"reverse_step": 8
}
],
"status": "complete dependent comparison of the two declared orders; no alternative-order search"
}
Finding. The two paths share only counts0,59,140,199, producing1859,1446,879,466. Their common internal boundaries occur at different step indices, so endpoint agreement does not identify the ordered paths.
Reassessment. Test scaling and order as separate linear operations.
C842 — Separate scale, order and accumulation
Question. Which operations commute, and which change the internal chronological field?
Sources. File58 declared order and×7; C839–841
Inputs
{}
Results
{
"scale_order_commutes": true,
"scale_accumulation_commutes": true,
"forward_prefix_years": [
210,
413,
609,
798,
980,
1155,
1323,
1393
],
"reverse_prefix_years": [
70,
238,
413,
595,
784,
980,
1183,
1393
]
}
Finding. Scaling commutes with both declared reordering and accumulation. Reordering preserves the total but changes the intermediate prefix field; that distinction is the same one needed for genealogical and Rounded paths.
Reassessment. Construct the complete sex-by-purity measurement table for Esau’s ledger.
C843 — Build the complete Esau joint-category table
Question. What cell structure lies beneath the equal490/60 marginals?
Sources. File58 §13.1 nine printed rows
Inputs
{}
Results
{
"joint_table": {
"path": "model/Esau_joint_measurements.json",
"sha256": "74bd41362ddc19e287e21419635e918f8fa091f10f6f059baf43cab8a13a8fbf",
"bytes": 1169
},
"joint_clean_unclean_by_female_male": [
[
440,
50
],
[
50,
10
]
],
"purity_totals": [
490,
60
],
"sex_totals": [
490,
60
]
}
Finding. The complete joint table is[[440,50],[50,10]]. Equal490/60 marginals arise because the two off-diagonal cells agree, while purity and sex remain different classifications.
Reassessment. Identify the exact constraint and freedom behind that equality.
C844 — Derive the equal-marginal constraint
Question. What exactly must be true for purity and sex totals to coincide?
Sources. C843
Inputs
{}
Results
{
"clean_minus_female": 0,
"unclean_minus_male": 0,
"fixed_margin_family": "[[490−t,t],[t,60−t]], 0≤t≤60",
"source_t": 50,
"constraint_count": 1,
"independence_determinant": 1900
}
Finding. The double490/60 display imposes one cross-category balance, b=c. Given those margins, one cell parameter remains; the source selects50. Distinct category definitions and equal marginals do not establish statistical independence.
Reassessment. Recover the exact rank of the nine-row measurement map.
C845 — Measure the information retained by the category projections
Question. How many independent totals do the four marginals supply?
Sources. File58 nine-row ledger; C843–844
Inputs
{}
Results
{
"incidence_matrix": [
[
1,
1,
1,
1,
1,
1,
0,
0,
0
],
[
0,
0,
0,
0,
0,
0,
1,
1,
1
],
[
1,
0,
1,
0,
1,
0,
1,
1,
0
],
[
0,
1,
0,
1,
0,
1,
0,
0,
1
]
],
"rank": 3,
"kernel_dimension_on_unrestricted_nine_counts": 6,
"row_relation": "clean+unclean=female+male"
}
Finding. The four totals contain three independent linear measurements of nine source counts. Six numerical directions are invisible to these marginals; species, order and individual counts remain necessary source data.
Reassessment. Regenerate the complete source-admitted clean category-order walk.
C846 — Regenerate the complete clean category-order walk
Question. Do declared category keys determine every source landing without selecting targets?
Sources. File58 §13.3
Inputs
{
"anchor": 1896,
"sort_keys": [
"male before female",
"goats sheep cattle"
]
}
Results
{
"ordered_counts": [
20,
20,
10,
200,
200,
40
],
"landings": [
1876,
1856,
1846,
1646,
1446,
1406
],
"source_rows_used": [
[
"Goats",
"male"
],
[
"Sheep",
"male"
],
[
"Cattle",
"male"
],
[
"Goats",
"female"
],
[
"Sheep",
"female"
],
[
"Cattle",
"female"
]
]
}
Finding. The predeclared male-first/species order yields all six source landings, including its intermediate boundaries. The result depends on category order in addition to the conserved490 total.
Reassessment. Explain the female cumulative register without turning it into one date walk.
C847 — Resolve the female register as a two-endpoint measurement
Question. How do400/430/470/490 arise when the chronological endpoints also change?
Sources. File58 §13.2
Inputs
{}
Results
{
"female_source_counts": [
200,
200,
30,
40,
20
],
"prefix_register": [
200,
400,
430,
470,
490
],
"chronology_heads": [
1846,
1876,
1876,
1896
],
"chronology_tails": [
1446,
1446,
1406,
1406
],
"span_changes": [
{
"head": 30,
"tail": 0,
"span": 30
},
{
"head": 0,
"tail": -40,
"span": 40
},
{
"head": 20,
"tail": 0,
"span": 20
}
]
}
Finding. The30,40,20 increments come respectively from an earlier head, a later tail, and an earlier head. This is a two-endpoint span register, not one chronology walk from a fixed anchor.
Reassessment. Test a second list’s declared regroupings against the same measurement grammar.
C848 — Transfer the projection model to the four-household ledger
Question. Do equal regrouped totals recover the ordered household inputs?
Sources. File58 §1.4 Genesis46 printed-household subtotal register
Inputs
{
"source_vector": [
33,
16,
14,
7
]
}
Results
{
"source_pair": [
49,
21
],
"source_bracket": [
40,
30
],
"source_prefix": [
33,
49,
63,
70
],
"invisible_regrouping_direction": [
1,
-1,
1,
-1
],
"diagnostic_prefix": [
34,
49,
64,
70
],
"scope": "printed source subtotals only; no person-count repair or chronology projection"
}
Finding. The same four counts produce49/21 and40/30 through two declared partitions. Both partitions miss one direction of change that the ordered prefix register detects. Retaining order adds information beyond shared totals.
Reassessment. State the precise extension of the path grammar established by the list holdout.
C849 — State the new list-family extension of the grammar
Question. What has transferred unchanged, and what must be added to the source object?
Sources. C833–848; Strategy stageH
Inputs
{}
Results
{
"transfer": {
"path": "model/list_transfer_summary.json",
"sha256": "62e4c18b5e59ca75bc8be2c620ee822cd8c4d7b978eb5ec526b76817b4e3614f",
"bytes": 762
}
}
Finding. The grammar transfers to lists when source rows retain category annotations and declared order. The new explanation identifies the constraints behind equal totals and the information those totals lose; it does not derive the textual counts or their historical intention.
Reassessment. Freeze the next complete File52c paired-anchor test before execution.
C850 — Freeze the full paired-anchor inverse field
Question. Can one digit-register rule explain every existing pair of File52c endpoints?
Sources. latest File52c §2.1 and AppendixA.2–A.3; inverse preparation audit
Inputs
{}
Results
{
"packet": {
"path": "model/inverse_inputs.json",
"sha256": "dbcb35bf6cfe88b318b4c8c327e97aa0be06583d5e945c43c9aac8b7f7b80911",
"bytes": 19844
},
"scope": "existing32 sources and64 endpoints; target columns excluded; original input durations only",
"hypothesis": "anchor dependence is generated by decimal borrow, core length and retained zero-placeholders"
}
Finding. The entire original paired field is the next fixed reconstruction target. No extra dates, target counts, or second-pass reversal are admitted.
Reassessment. Close the first20-step checkpoint, then test the paired field.
C851 — Close the first twenty-step explanatory checkpoint
Question. What did the complete list holdout add to the common grammar?
Sources. C832–850
Inputs
{}
Results
{
"checkpoint": {
"path": "deliverables/490d_Chronological_Families_Checkpoint_C851.md",
"sha256": "18816601d66beb94848c9353dd59c9d2cbc13c64b9fad842459de3a7d3e78369",
"bytes": 1453
}
}
Finding. The first transfer succeeds with one explicit enrichment: category predicates and declared order remain attached to source rows. Equal totals are now traced to exact constraints rather than treated as interchangeable objects.
Reassessment. Reconstruct the full paired-anchor field from its original digit registers.