# 490d Mirror checkpoint after C324

24 September2026. **C324 complete; C325 unexecuted.** 9 steps remain in the current authorization. Read this checkpoint and report first; frozen predecessor records retain earlier findings. Current decisions override stale archive instructions. Do not repeat completed research.

## Current result

Explicitlocal460→500rules exist, but the specificregularSP→MT/E/Noah500dependency is notestablished in the boundedfour-source audit. A commonE dilation cannot equal the source-preserving wholebiographytranslation.

The supplied sources **do prescribe local460→500 endpoint completions**, but the audited passages do not prescribe a connecting rule from the newly verified regularSP→MT context correspondence to the Noah-bound500 relation. This is a bounded dependency gap, not an absence of all endpoint rules.

| Evidence | Location | Supported result | Remaining distinction |
|---|---|---|---|
|Bilateral460→500|File_09 §3A.2.3, lines1045–1074|Named cumulative field with40-year shoulders, two overlapping500 intervals, outer540|CumulativeCainan construction, not the regularSP→MT biography|
|Flood/Arphaxad andCainan/Shelah completions|File_09 §3A.3.3–4, lines1133–1193|Explicit460 and500 component-wise endpoint comparisons|Generated completed coordinates retain their roles and provenance|
|Noah-bound500|File_18 §1.3.5 and §3.2.1|Source-qualified500/100 relation; separate textual binding retained|No E derivation or context-selection rule is supplied|
|RegularCainan comparison|AXIS_REPORT §8.1, lines474–487|DeclaredQ1405 comparison yields raw4508/4968 and expanded4900/5400; difference460→500|Different events and declared comparison from the presentSP/MT map|
|Double expansion|File_46 §6A.3 and AppendixA.3|23² permits two integral expansions;4232→4600→5000|TheNoah500 resonance is explicitly a display motif; appendix777 provenance remains|

The independent source ledger records26 exact excerpts, source hashes and keyword-search coverage across File_18, File_09, File_46 and the axis report. None of the reviewed passages identifies the specific cross-context460 leg as input toE and its output as the regularNoah-bound500 leg with endpoint, direction, context and phase specified. The conclusion is limited to those reviewed passages; no repository-wide absence is asserted.

The arithmetic is exact:460E=500, the gain is40, and529E²=625. But the C322 map is a translation with slope1, preserving all biography spans. A single affine dilation D_a(x)=a+E(x−a) has slope25/23 regardless of anchor. It would turn the500 birth gap into12500/23, a discrepancy of1000/23. Therefore no common anchoredE map equals the entire460-year biography translation. This is an anchor-independent obstruction to that particular interpretation, not a rejection of source-qualified local interval completion.

The operator types must remain separate. CumulativeCainan460 is not regularCainan130. The regular context composition−650+130+60 has net−460 without changing that distinction. File_46's static460+30 motif guard is explicitly local to its Matthew–Luke lattice; its non-collapse guard preserves legitimate deep-time460 uses. No global prohibition is inferred.

Notation: this batch uses K=529 andE=25/23. The axis report usesK for the ratio25/23; its quoted notation is translated explicitly here. No new anchor, completed event coordinate or expansion path has been adopted.

## Retained context

C323 remains the completed predecessor synthesis. Retain the six-coordinate OFF600 rectangle family and three nativeON/restored-MT primary counterparts; the full same-Gear Noah-bound SP→MT biography translates by460, with source textual502 a distinct binding. C314 reversal requires i+j=10 and opposite cumulative phases. C313/C315 same-ancestry500/600 failures remain. C287 full domain is i2…5. The paired+2 choices produce its all-K form, but the00 control also retains two17K paths. The optional combined support criteria alone isolate i=j5. No source-prescribed selector has been established. Corrected LXX8464 supplement remains awareness only (1564→1700;2484→2700;920→1000); AD3746/2300 is superseded. Earlier reports, original unprefixed reports and Engine series remain distinct.

Mirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.

## Verification

22 main checks and 17 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. Independent review and its scope are recorded in the evidence. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.

## Best next bounded step

C325: Census the existing fifteen primary SP/MT role correspondences for admitted460+40=500 endpoint triples. Hold Gear, role, context and exact phase; create no new endpoint, expansion anchor or E-generated date.

An existing40-year leg could supply a concrete endpoint relation worth studying. It would remain a qualified arithmetic construction until a source rule selects it. The finite census is more informative than repeating the scalaridentity or extending a source absence claim.

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