# 490d Mirror checkpoint after C314

24 September 2026. **C314 complete. C315 unexecuted.** 9 steps remain in the current C314–C323 authorization. Read this checkpoint and its report first; use the frozen predecessor checkpoint and certificate for inherited state. Do not repeat completed work or follow stale archived next-step paragraphs.

## Current finding

Five source-labelled500+600 biographies and ten components succeed under i=10−j, eN=−eS. The selected finite map is involutive; only j=i5 has full C287 support at both indices.

The explicitly reversed index and cumulative phase correspondence succeeds in all five selected source biographies and all ten components. For the fixed inherited formulas

`N(i,eN)=3703+i+eN`, `S(j,eS)=3213−j−eS`, `D(j,eS)=2613−j−eS`,

an exact500 requires **i+j=10 and eN=−eS**. The integer index term cannot absorb a nonzero half-year phase sum. A finite100-comparison check finds exactly one Noah component for each Shem component.

| Shem j | Noah i | SP state | Noah → Shem birth → Shem death, BC | C287 at i / at j |
|---:|---:|---|---|---|
|3|7|G3 primary|3710 →3210 →2610|No / Yes|
|4|6|G3 companion|3709 →3209 →2609|No / Yes|
|5|5|G2 primary|3708 →3208 →2608|Yes / Yes|
|6|4|G2 companion|3707 →3207 →2607|Yes / No|
|7|3|G1 primary|3706 →3206 →2606|Yes / No|

All states retain Cainan OFF/Terah0/full430 and the documented regular +155 normalization. Matched physical output phases preserve500,600 and1100; inherited cumulative phases are opposite. C313's zero same-ancestry result is unchanged.

The finite label map `J(j,e)=(10−j,−e)` is an involution on the selected five indices and two phases. It has five component two-cycles and no fixed exact component; j5 is fixed only as an annual center. In signed cumulative coordinates it is `R(q)=−10570−q`, with derived local center−5285. The original eight-index field is not closed under this map. This local algebra does not establish a new global Mirror axis.

Direct17K admission survives all five pairings. C287 full four-node support survives at the paired Noah index in three cases and at both indices only in the middle case. For paired i6/7 the required ON-Shem indices8/9 remain outside the frozen field. Source membership is checked against C286; exact Noah ancestry is independently checked against C271. File_18 §3.2.1 and File_09's component/coordinate distinctions supply the source and typing controls.

## Retained context

C277–C310 and C311–C313 remain completed. C311 found no prescribing annual selector in its three-source audit; C312 admitted four complete cumulative transports and five SP targets; C313 found a center500 match only at j5 and no same-ancestry exact component500 match. The +155 regular normalization is local. C287 complete four-node indices remain2…5; direct17K admission is weaker. The original AD1905–1911 proposal remains unexecuted. Supplemental Engine ReportIII explicitly derives the LXX OFF field; older182/777 and mixed Cainan headings yield to File_18. Corrected LXX crossover8464 observations remain awareness only:1564→1700 and2484→2700, difference920→1000; AD3746/2300 is superseded. C-series and original unprefixed/Engine report series remain distinct.

Mirror/529 remains the focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction x=1 January AD2; no civil year zero. Regular Gears remain Noah/Shem/Flood only. SP minus-one companion is local to SP Noah/Shem. No cumulative/upstream Gear, new endpoint or phase, fitted anchor, global axis, z-law, canonical or graph edit. Capture now; canonize later. Source state, event identity, generated coordinate and phase ancestry remain distinct. Exact arithmetic and source membership do not establish intention or independent historical witnesses.

## Verification

60 main assertions and 14 frozen-input/predecessor checks passed. A second main replay produced byte-identical DATA and RESULTS. Separate review scope and agreement are recorded in the evidence. All frozen originals and standing controls remain unchanged. These are verification counts, not independent-witness counts.

## Best next bounded question

C315: Can these five reversed pairings extend to the source-labelled Flood and Noah-death parts of each regular SP biography while retaining the existing8395 Flood path?

The500 binding now works conditionally. Testing the remaining admitted biography endpoints asks whether this success composes with the existing Flood interface, instead of repeating the same symmetry.

Continue within the authorized batch, reassessing after the next result.