Selection audit for C832–C931
This is an independent preparation memo, not a numbered research action or a canonical amendment. It reads the Strategy, C831 checkpoint/synthesis, all C482–C831 titles/findings, and the selected File43/54/58 source sections. Agent proposals for the inverse and additional carrier family are identified as proposals below. Root alone chooses and executes numbered actions.
Best next whole-family test
Begin with File58's complete bounded list families. This is a substantive domain transfer expressly anticipated by Strategy Stage H, using an operator grammar already established from genealogies. None of the four available cycle journals C482–C831 invokes File58 or reconstructs its list fields. This is new to those cycles; it does not establish that no earlier C01–C479 analysis ever mentioned its values. Its source's own arithmetic is already explored, so call it a held-out domain transfer relative to the current path grammar, not a virgin discovery or an independent statistical test.
The resulting explanatory question is clear: can incidence, ordered accumulation, retained partitions, and the declared scaling operation explain a complete sacrificial/list field without importing a chronological date at every boundary? The input category definitions and the animal-year interpretation are still premises. The generic ability to sum a list is not itself evidence of hidden design.
Ranked selection
| Priority | Complete object | New explanatory content | Already completed and not new |
|---|---|---|---|
| 1 | File58 Numbers Tishri ledger, complete seven-day Sukkot matrix, eight-part forward/reverse field; Genesis32 nine-number list and category maps | Transfer the fixed linear/path grammar to ritual counts; derive all intermediate values from the ordered generator; identify exactly which category equality is additional and which agreements follow automatically | Source arithmetic totals280,182,189,1274,1323,1960 are supplied; rechecking them alone adds little |
| 2 | Latest File52c's complete32-source paired-anchor inverse field, all64 already supplied endpoints | Explain anchor displacement through digit positions, carries/borrows, core length and retained placeholders across the whole frozen domain, including misses | C495–499 path additivity/refinement/decimal gains; C512–520 nine-hit and selected companion fields; no second reversal, target scan, or new statistical count |
| 3 | File43 full78-row dual genealogy display and File54's declared Luke/Round/BJ interfaces | Source-role/index generator covers an entire further literal object; derive finite Key-return support and common49/70 boundaries, preserving different meanings of names, intervals and envelope heads | C587–607 already reconstruct File68/69 Enoch/NT cells and complete49-row four-rail matrix. C808–809 already establish5326−2876=2450 and birth-head alternative2520 |
| 4 | File63 §§7.7–7.9 ordered11960→12000→12005→12075 path and source/output squares, subject to packet check | Explain the complete40 | 5 |
| 5 | Operator relations on these concrete transferred objects | A small reusable compiler from typed list/path data to measures; show which operations commute and what information each projection loses | Broad claims that one path object organizes all finite lists; an inventory with no further prediction; global minimality claims |
Do not reopen the bulk Covenant60/61/62 families as an untouched domain. C532–573 already cover their principal complete objects. Any new packet must name its exact previously untested source section and discriminate an additional question.
File58: strongest concrete tests
A. Distinguish the generator from its marginals
File58 §§3 and7 provide the complete seven Sukkot rows. With day d=1,…,7, the four-species row is (14−d,2,14,1), hence its total is31−d. This rank-two row family generates the ordered day totals30,29,28,27,26,25,24, the species totals70,14,98,7, and their189 total. These totals are different projections of one matrix, not independent confirmations. The extra eighth-day row (1,1,7,1) is separately sourced, not obtained by continuing the descending bull rule to d=8.
The full seven-category Numbers table is a second complete source object. A day-resolved22-day field can be generated only with the fixed calendar schedule and per-event row inputs explicitly declared. Daily and Sabbath additions, New Moon/Trumpets coincidence, and the seven festival rows have distinct incidence supports. This can explain280 as a whole field rather than a favorable total, but it must not turn fixed-week364 and lunar-four-Sabbath states into one chronology.
B. Explain the dual Genesis32 equality with a joint table
In source order, use the nine displayed values:
200,20,200,20,30,40,10,20,10
corresponding to female/male goats, female/male sheep, female camels, female/male cattle, and female/male donkeys. Unnumbered camel offspring are outside the printed-number ledger.
| Joint category | Female | Male | Purity total |
|---|---|---|---|
| Clean | 440 | 50 | 490 |
| Unclean | 50 | 10 | 60 |
| Sex total | 490 | 60 | 550 |
The equality of purity and sex marginals is exactly the equality of the two off-diagonal cells50=50. It is not a statement that the predicates coincide. The4×9 marginal-incidence map has rank3 and kernel dimension6; the corresponding map on the four joint cells has one-dimensional kernel generated by (1,−1,−1,1). This describes precisely what the marginal totals forget. Do not label the category predicates statistically independent: their definitions differ, but no probability model was supplied.
A diagnostic perturbation in a kernel direction can preserve all marginals while altering the ordered source field. Keep it explicitly unadmitted, used only to show why totals cannot identify the printed list. One such diagnostic suffices; do not enumerate arbitrary perturbed lists.
C. Test every source-ordered intermediate boundary
The female projection in source order gives200,400,430,470,490. The clean male-first permutation gives increments20,20,10,200,200,40; unclean framing gives20,30,10. These are different source-declared ordered objects. Each uses every row in its partition once. Their date projections use supplied anchors and remain structural interpretations. The female value register is not one fixed-anchor chronological walk because its comparison spans change endpoint roles.
The existing forward/reverse festival field is especially discriminating. Freeze the eight durations:
[30,29,28,27,26,25,24,10].
Their forward prefix values are0,30,59,87,114,140,165,189,199. Reverse prefixes are0,10,34,59,85,112,140,169,199. Their intersection is exactly0,59,140,199, so the scaled7 fields share0,413,980,1393. This explains why the same1859 anchor produces1446,879,466 after different numbers of steps. It is a complete finite intersection of two source-admitted sequences, not an alternative-order search. The common final199 is forced by permutation; the interior59 and140 reflect this particular row order and eighth-day component.
For the seven-day descending sequence, the forward prefix has closed form k(61−k)/2. The reverse eight-part field has the separately supplied10 first, then increasing24,…,30. These formulas should regenerate the full field before discussing selected historical landings.
D. Relate scaling and calendar selection without erasing types
Shemitah×7 is scalar multiplication of a declared animal-count measure, followed by a separate proposed year interpretation. It commutes with linear category summation and the fixed permutation. It does not establish that the animal counts historically encoded the selected chronology. An extra Sabbath changes the full source ledger by two lambs and its shemitah measure by14; the Leviticus16 overlay has its own explicit ritual/slaughtered predicate. These are source-defined input changes, not free endpoint adjustments.
Once these complete fields and their explicit new constraints are explained, transfer to the new inverse/NT objects. Avoid spending many actions on source-known individual sums.
C831 shared-path model: exact strengths and limits
- Constructive coverage is real. The same accumulation/difference pair, selected measurement, source-support masks and residual fields already reconstruct entire MT/LXX/SP and BJ objects. Reusing those operations for a new list domain is meaningful compression.
- Any ordered data can be encoded as a path. Encoding alone cannot explain why its input numbers, labels or chosen order occur. A stronger result reconstructs omitted/intermediate literal values from a smaller frozen packet, or shows an independently selected family obeys a previously fixed relation without added parameters.
- A recovered local vector is not independent evidence of that vector. Once all boundary values are supplied, taking adjacent differences is exact inversion. It proves representation fidelity and identifies support, not an ancient editorial sequence.
- Domain transfer differs from empirical holdout. File58 is new to the available four-cycle computations, but its canonical source already presents the numerical relationships. No new probability claim follows from implementing the source.
- Different predicates are not stochastic independence. The Genesis32 purity and sex classifications have distinct definitions; their matched totals reduce to one weighted constraint.
- Path, grid and index should remain distinct source objects. A sacrificial day×species table and a dual genealogy grid can be represented by ordered paths after a declared projection. The projection should remain visible; do not claim the one-dimensional path retains every original relation automatically.
- Formal inverses versus digit reversal. Adjacent differencing, residual subtraction and reversing the order of a festival list are legitimate here. None is the deferred second decimal inversion, and none grants new source variants.
Exact map of completed families available locally
The generated prep/completed_family_index_C482_C831.tsv contains350 completed actions, with step, cycle, title and finding on one line each. It is a convenience index, not a new research ledger. Its SHA256 is a8cfc6339e49f63e21a25523265e6b64641d81e2dca3d807ebff0b0fcc137514.
| Completed range | Family and exact scope |
|---|---|
| C482–494 | MT/LXX/SP endpoint transfers, local row projections, weighted12026 qualification, Cainan130/460, actual/rounded head offsets |
| C495–499 | Retained-component inversion, refinement defects, decimal gains and shared1400 continuation |
| C500–507 | Calendar calibration,897 integral domain,598 family,529 width and pivot integrality |
| C508–524 | SP rectangle, anchored maps, mirrored rounded529 endpoints, allnine14726 members, Cainantrio, Temple/Moses, actual field |
| C525–531 | Candidate grammar, three-axis reading and synthesis |
| C532–551 | File60 Covenant299+161, Joseph/Levi1566,137 biographies,147rails, full11-node network |
| C552–573 | Files61/62 full42-coordinate clutch family,12Joseph intervals,9fixed-Joseph states,C3 components,phase geometry,Isaacmacro,Actual/Round square |
| C574–586 | File63 common897n family, quartercarrier ladder, Creation/Flood transported cells, macro mixed-role path, phase/calibration laws |
| C587–607 | Files68/69 indexed Enoch/NT cells,48coords;49-row four-rail196cells;18-row attribution;weekly hierarchy;Lukan overlay;9000/9100 volumes |
| C608–631 | Covariance, retained-fraction endpoint laws, cumulative3430/989 relations and synthesis |
| C632–647 | File70 whole equal7+7rail field and conditional calendar-half congruence family |
| C648–651 | File70 five-node Creation/Terah refinement and coarse rail |
| C652–664 | File70 Jacob/Joseph fields,localNoah/Shemvariants,cumulative4900/13475 and637household families |
| C665–671 | SupplementA690core, retainedflank table, alternating720/30 ladder,1470 cell and calendarcomparison |
| C672–689 | Exact phase brackets,35/40/120 fields,25 |
| C690–702 | Retainedmacro12600/12740/13440,dual4346,full4304Ppath,directional690matrix,4900civilpath,Cainan460→500 |
| C704–710 | Fixed12-nodephase field5842reflection,8/12/8/4overlaps,anchoredquartet,Short/Long,conservation |
| C711–731 | Explanatory integration,partialratios,phasechartrelation,and checked12026/14726 continuation |
| C733–748 | Complete MT20/LXX21/SP20 modegap fields,shared12birthsuffix,cumulative support and suffixoperator |
| C749–770 | Fullroundingdefect/residualfields,mod5law,allMTboundaries,LXX/SPsupport,conditionalSP13406,dategridfailure |
| C772–788 | Finite8/4/2support,masks,Terahtriangle,modeprojection,Cainan,fullresidualequivariance,SP/LXX roundedtransfer |
| C792–810 | BJ22/23headindex,57contraction,role-sensitive2450/2400,reflectionobject,575paths,290refinement,timestamps,460bookend,NT2450 |
| C812–831 | Integrated source-path explanation and reviews/deliverables |
Useful exact shell searches:
rg -n 'Covenant|clutch|Joseph|Isaac' c832_c931/prep/completed_family_index_C482_C831.tsv
rg -n 'Enoch|Lukan|four-rail|carrier|generation' c832_c931/prep/completed_family_index_C482_C831.tsv
rg -n 'inverse|reversal|refinement|14726|12026' c832_c931/prep/completed_family_index_C482_C831.tsv
rg -n 'rounded|rounding|residual|Terah|Cainan' c832_c931/prep/completed_family_index_C482_C831.tsv
rg -n 'Numbers|Sukkot|Esau|purity|File58|File_58' c482_c531/journal.json c532_c631/journal.json c632_c731/journal.json c732_c831/journal.json
The last search returned no matches at preparation time. Earlier C01–C479 records were not exhaustively audited by this memo. The C831 checkpoint expressly says not to repeat prior endpoint totals as discoveries; its next-step criterion is one complete admitted source family, frozen before testing the proposed rule.
Bounded selection recommendation
Start with Numbers and Genesis32 complete objects, then the full paired inverse field, then the NT index/measure interface. Use File63's newly identified ordered carrier path if its source packet establishes that the new operation sequence is absent from prior work. Reassess after each complete-family result. Consolidate into an explanation that distinguishes row values, incidence/category data, order, measurement, and target-role assignment. These layers show how the chronological families fit together while making the still-unexplained inputs precise.