# 490d Mirror checkpoint after C310

24 September 2026. Latest completed: **C310 — Minimal context cover and final529 synthesis.**

## Research state at batch close

C277–C310 is complete:34 steps from C276. C311 is proposed only. Preserve the accepted C265 handoff and later corrections; do not restart historical report reading or revive old next-step paragraphs. The redirected C266–C276 work remains the predecessor chain.

### Core529 structure

K=529. The source-qualified mixed route is2K+15K=17K, obtained from598+460=1058 and8395−460=7935. C286’s fixed domain has528 regular Noah/Shem/Flood records and256 cumulative Shem/Flood state/index pairs:135168 comparisons,12 labeled all-K paths,10 coordinate paths.

C287 normal form: (S,F,R,N)=(−12K,−10K,5K,7K)+i. S=cumulativeLXXON Shem, F=cumulativeLXXOFF Flood, R=regularMTFloodON/+60/full430, N=regularSPNoahOFF/0/full430 with LXXOFF primary aliases. S/F/R existi0…5; N onlyi2…5. Missing3703/3704 are not supplied. Six pairwise durations have rank3; a common translation remains free at fixedK. Source placement remains a premise. Established16K interlacing yields(4,5,6,7)K+i, without historicalizing generated landings.

### Reflection, phases and operations

C294 fixed8K reflection with the held13K translation has the admitted ordered centers527,1587,2645,3705: gaps1060,1058,1060. C295 found1 fixed-reflection and4 all-K configurations in2304 combinations, with0 joint configurations. Do not conflate them or fit a new bridge.

C290:25/23 center matches do not preserve the physical half-year phase pair; its width becomes25/46. Cainan translation preserves pair width. Keep cumulativeCainan460, regularCainan130, Terah60, sojourn215 and MT/SP baseline650 separately typed. Mirror reverses seasonal ancestry; translation preserves it. Annual offsets are not newGears.

### Cross-bridge coverage

RegularW8464 to reflectedQ6 and cumulativeW12696 to reflectedQ1406 giveC−B2832. C301’s72×528 census yields28 labeled/18 coordinate points. C302 binds12 labeled/eight coordinate600 segments: MT4,SP5,LXX3. CumulativeLXXOFF supportedindices0,2,3,4,5,6,7; index1 needs3057/2457, upperabsent.

C310 proves the unique minimum context-family cover of those seven indices: MTNoah→Flood,OFF/Terah0/full430 atj0/2, plusSPShemlife,OFF/Terah+60/minimum215 atj3…7. LXXShemlife labels atj3/5/7 add no coordinates. WithGearalsofixed, fivegroups are needed, with two minimal covers differing only in the co-locatedGear1SP/LXX choice. The combined coverage changes tradition, Terah/sojourn settings and event roles. No existing rule selecting this transition has yet been established by this batch.

C308 changes only the cumulative supplied anchor toQ1446: offset2792,11 labeled/eight coordinate point matches, allSP_OFFShemi0…7, zero600segments. Requiredlower1924…1917 absent. Full point coverage is not full segment coverage; no statistical ranking ofanchors is claimed.

### Existing path overlap

C303 identifies joint8395/17K overlaps at cumulativeFlood5288/5287. C304 verifies both arestored C127N01/N02, direct17K and868+13K+1248. OnlyN02 carries299+299+650 viaSPNoahdeath2757/MTNoah3056. N01’s analogous ordinaryMTNoah3055 is absent. Fixed2832 MTpoints2456/2455 differ from stored13K interiorMTpoints2457/2458 by1/3.

C307 typed equations: n=q+8993,r=q+8395,b=−q−2832,p=b+650, q−5290+i. Hence n−r598, r−p2i−3, n−p595+2i. Jointadmittedi2/3give599/601. Exact600forceshalf-integerq−5287.5. C306 checks eightadmittedselector combinations and32actualphase comparisons; everycenter600 alternative changes one fixedinterface by±1. None repairs bothwhole-pairbindings.

### Reading and reproduction

Read C310 report and this checkpoint first; use the batch reading index to select dependencies. Key reports: C287(normalform), C294–C295(reflectionboundary), C301–C302(point/segment census), C304(provenance), C307(dependencyrank), C308(anchor specificity), C309(claim audit). Each evidence ZIP is self-contained for exact replay. The final aggregate contains all34 reports/checkpoints/evidence ZIPs and integrity records; the compact kit carries the immediate source documents and selected evidence only.

This is author-reviewed conditional research. Reproducibility and input authentication do not prove historical intentionality, a globalaxis/z-law or unique absoluteplacement. NoC311calculation orsource-ruleaudit hasbeen performed.

## Standing context

C276: the selected cross-index alignment fixes δ=h−f=598; source transport alone does not. Absolute placement remains a separate premise. Preserve source and map roles, annual indices and ±1/4 phase ancestry. Co-located images do not identify events.

K=529; E=25/23; P=70/69. Global Mirror January AD 1; established local junction x=1, January AD 2; no civil year zero. Regular Gears Noah/Shem/Flood only. No cumulative/upstream Gears, primer reopening, canonical/graph changes or new global axis/z-law. Capture now, canonize later.

Supplement: LXX Creation 5494 BC +8464→AD 2970 versus reflected Conquest AD 1406 gives1564→1700 by25/23; Jared4534→AD3930 versus reflected Exodus1446 gives2484→2700. LXX Creation→Jared960, MT460; offsets1380/880; difference920→1000. AD3746/2300 superseded. Awareness only.

C-series reports remain distinct from original unprefixed Reports01–10 and unestablished interrupted Reports11–25. The superseded AD1905–1911 lookup remains unexecuted.

## Verification

15 mathematical/domain checks and 13 source authentication checks passed; two generated readouts replay byte identically. Author review only. File_18, File_09, C265 certificate and C127 unchanged; graph208 nodes/382 duration edges.

## Best next bounded step

C311, not executed: audit File_18, File_09 and the existing axis-source statements for a pre-existing rule selecting the MT Noah/Flood→SP Shem-life context switch; preserve all endpoints, bridges, anchors and Gear limits.

Reason for selecting it after C310: C310 establishes the smallest composite cover; the unresolved question is the source basis for selecting its transition, rather than further numerical coverage.

High is sufficient unless a later dependency requires reassessment. The next step was not executed as part of C310. The authorized batch is complete at C310; C311 is not executed.