490d research checkpoint after C531

27 September 2026. C482–C531 complete:50 sequential bounded research actions. C532 proposed, unexecuted.

Current explanation

The families share a construction grammar: source-row changes, regular/cumulative projections, rounding with retained residuals, source-specified reversed paths, anchored calendar dilations, scoped state changes, and declared reflections. The new readable draft is 490d_How_Chronological_Families_Fit_Together_Draft_20260927.md.

Key advances:

1. Current local rows reconstruct LXX regular/cumulative movements+1380/+890 and SP+300/−608 relative to MT. These explain weighted-anchor shifts;12026 is not universal.
2. Rounded paths are evaluated with their segmentation retained. Their gains explain MT12026 convergence, secondary13016, the LXX refinement difference990, and the14726 continuation by a shared1400 leg.
3. MT regular Actual-minus-Rounded+8 is+6 row residual plus2 from the declared comparison convention. Cumulative rounding preserves12600 and14006;−2 is completion selection. Together4ΔC+ΔR=0 preserves12026.
4. The three Keys share calibration8400/23. Their common integral input domain is897Z, explaining why Noah alone in the14/15/16 field admits all three integral outputs.
5. Two E applications send k529→k575→k625. Endpoint completion additionally requires matching pivot residues. C480 matches19; the fixed12026 Actual trial mismatches22 against20 and yields common4/23 fractions, while retaining width1250.
6. The diagram’s forwarded magnitudes4232/8464/12696 become4600/9200/13800, then5000/10000/15000. The middle duration ladder connects to the SP and Shem9200→10000 examples; endpoint roles are not identified.
7. All nine nonzero14726-member outputs follow from X=6+115k and result125k−1274. The tenth member is the backbone; its nonzero14720 Nativity span expands to16000. Changing the held anchor to6 shifts each member output by1280.
8. Cainan’s330 remainder connects his cross-mode insertion difference with the trio’s23×330→25×330 width. Its mixed1950+1950 midpoint adds a separate companion placement constraint.
9. SP rectangle4206/13406 relates to the completion pair4414/13396 through−215+7 on the regular side and+10 on the cumulative side. The gap increase218 explains9200 versus8982.
10. Temple/Moses/526/476 dependencies reduce to the first526 convergence, the matching920 widths, and the supplied80-year Moses placement. Their derivative displays are not independent trials.

Frozen limits and source decisions

• Latest File52c SHA256: a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530.
• Second-order inversion remains deferred. No new target scan or significance estimate was performed.
• Main LXX Lamech182/753;777 appendix only;188 non-operative. LXX native Cainan ON refers here to the full430 comparison frame. Regular130 and cumulative460 remain distinct projections of one row.
• SP primary completed-year and653-inclusive conventions retained; local−1 companions not silently applied.
• Gear scope remains Noah/Shem/Flood only. Actual completion, Year6, rounded and generated node classes remain distinct.
• Civil and rounded crossings retain their respective BC+AD−1 andBC+AD−2 rules. The schematic origin is not a historical year zero.
• The LXX rounded Noah/Flood path is a derived transfer test. Complete rounded cumulative LXX/SP paired paths remain uninstantiated from the supplied source tables.
• No canonical source, prior graph, protected LXX8464 execution, SKL appendix or quarantined primer was altered. The forwarded calculation is duration algebra, not permission for new endpoint transports.
• No universal scalar mode conversion, global minimality proof, historical redaction sequence or natural equivalence of chronology families is claimed.

Verification and artifacts

The packet contains50 step scripts, a sequential hash-linked journal, source snapshots, five ten-step reports, the combined report, this checkpoint, the synthesis and four independent review notes. Three agents independently reviewed48 analytical steps. C530–C531 are review/synthesis actions. Reviewers requested wording and dependency clarifications, incorporated in the synthesis; no numerical correction was needed.

Run python3 evidence/verify.py after extracting the packet for a read-only replay of all50 records using an independently implemented reversal function. Exact replay results and source-hash checks are in VERIFY.json. Assertion counts include scope checks and are not independent evidence. The historical C480 suite was not rerun.

Best next bounded test

C532 proposed only: freeze this operation inventory and reconstruct the source-defined161/299/460 family from its controlling files. Declare the input rows, anchors, endpoint classes and admitted operations before calculation. Record what is generated unchanged, what needs a source-justified extension, and what fails. Do not add fitted anchors or treat the familiar family as an untouched statistical holdout.