# 490d — Mirror/Rounded checkpoint after C481

27 September 2026. **C481 complete; C482 unexecuted.**

## Active direction

Continue the Strategy's search for a compact grammar relating chronological families. The controlling research draft is the latest **File_52c.Rounded_Whole_Span_Inverse_Detailed_Study_Draft (2)(1).md**, SHA256 a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530.

“Inverse of the inverse” is deferred. The former proposed C481 boundary-composition task was superseded by Dean's September 27 redirection. C480 remains a completed historical result.

## C481 kernel

1. Primary Rounded partitions give inverse-span gains +4×990, +4×990, −2×990 and 0. Thus regular Creation R and cumulative Creation C meet at A = 12026, with C = A+2×990 and R = A−8×990.
2. Therefore A = (4C+R)/5. Moving to the selected Actual completion pair changes (C,R) by (−2,+8), preserving 4C+R.
3. The Actual pair is C = A+2×989 and R = A−8×989, with 989 = 23×43.
4. Selected Actual 23-coordinates (A−X)/23 are cumulative Creation −86; regular Creation 344; Jared 364; Noah G1 390; Flood G2 416; Exodus 460.
5. Jared/Noah/Flood = 26×(14,15,16) in these units. Existing J and E turn their 598 steps into 600 and 650; E/P = 15/14 explains the Jared-E / Noah-P agreement at 2926.
6. Actual Creation−Noah = 4114−3056 = 460+598 = 1058 = 2×529. A−Exodus = 10580 = 10×1058. Hence A = 1446+10(4114−3056).
7. Width ladders 1058→1150→1250 and 10580→11500→12500 share E = 25/23. The latter's existing Rounded Mirror realization runs AD 1446→AD 526→476 BC with AD 12026 held.
8. The 14726 continuation remains 6+I(1400)+10620; its 14720 span expands to 16000.

These are linked consequences under the stated source inputs, not independent statistical successes. The current contribution is their combined explanation.

## Limits retained

- Actual 14004/4114 completion states are distinct from 14006/4116 Year-6 and 14006/4106 Rounded states.
- Noah 3056 is selected Gear 1; Flood 2458 is selected Gear 2; Jared's given coordinate does not open upstream Gear transport.
- Segmented reversal is not generally additive. Secondary cumulative paths give 13016; whole-span reversal gives other outputs.
- Duration grammar does not automatically identify endpoint maps. The first A-held Actual Creation/Noah expansion gives 3426/2276; repeating it yields rational coordinates with width 1250, not an added sourced pair.
- Prior graph, primers, LXX corrections, SKL appendix, Cainan states and local SP conventions are preserved.
- New anchored J calculations remain within File_52c's separate study.
- No target scan, probability estimate, category-theory equivalence or three-dimensional coordinate theorem was added.

## Evidence

The C481 report and portable evidence packet contain INPUT.json, RESULTS.json, check.py, source snapshots, source hashes and a certificate. Exact execution passes 23 structural checks plus 7 hash checks and 10 source bindings. This is same-agent verification.

The included C480 checkpoint UTF-8 snapshot hash is 0e2dcbb9dad9ed346ccfb6dcd6628e86f2573823bb9f0437888a56de25b897ad. Continuity is recorded through that checkpoint; the old evidence suite was not rerun.

## Best next bounded step

**C482, proposed only:** test the frozen primary source-path construction and weighted-anchor relation in one declared native-LXX state and one declared SP comparison state. Preserve source-controlled Cainan, Lamech and local-Gear distinctions. Assess explanatory transfer without selecting fresh anchors or partitions to repair failures.

The unresolved issue is cross-manuscript explanatory reach. **High is sufficient.**