# 490d C478 — Alternate Arithmetic Verification and Sealed Batch Audit

25 September 2026 UTC. Step 9 of 10, C470–C479.

A separately written calculation agrees with the decisive results. It uses the same authenticated sources and was performed by the same agent; it is not an independent historical witness or independent-agent review.

The second implementation:

- Regenerates all528 normalized regular labels at373 coordinates from the MT bases, tradition650 offset, bounded Gear/Cainan/Terah/full430 shifts and qualified SP person rails.
- Recovers the three admitted E expansions by searching input/output intervals and solving for the pivot, reversing the main forward sweep. It independently confirms the single complete2K ancestry.
- Classifies all130 labelled1250 pairs by disjoint role/rail signatures and checks every recorded context displacement; it confirms the24 matched triplets and all six failed translated E comparisons.
- Evaluates all16 factorization profiles directly with integer polynomial coefficients, reproducing five fully sourced profiles.
- Verifies all48 primary/companion held cases, including the fifth companion input at2841 and the absence of every companion middle.
- Regenerates the48 cumulative records from their six fixed annual bands and reproduces all18 Mirror trials: five initial images, no sourced middle, and two isolated final hits belonging to the3899 case.

**All98 calculation checks passed**, with38 source/predecessor authentication checks. Both result files replay byte for byte.

The sealed audit through C477 verifies eight packets,243 payloads,96 certificate bindings,139 frozen source entries, eight predecessor links, eight evidence ZIPs and24 successful publications. The canonical graph and standing source controls are unchanged. No discrepancy remains to resolve before synthesis.

## Verification and scope

98 calculation checks and 38 source/predecessor authentication checks passed. Main result files replay byte for byte. These are root-agent checks, not an independent-agent review or independent historical witnesses.

The98 alternate-method checks are part of this step’s main check count. Repeated implementations and source aliases are not independent historical evidence. C479 will provide the final all-ten-packet audit after its own publication.

Mirror/529 focus: K=529, E=25/23, P=70/69; J=300/299 remains File02 gap conversion, not a calendar date operator or Residue Protocol. Regular Gears are Noah/Shem/Flood only. SP person companions are local to Noah/Shem; Flood close is an independent event boundary. Both500/100 and502/98 bindings remain valid; SP primary Noah death retains its inclusive/harmonic qualification. LXX native Cainan is ON; OFF is theoretical removal. Global paired Mirror January AD1; local junction January AD2; no civil year zero. No new source point, phase, fitted axis, upstream/cumulative Gear, primer reopening or canonical/graph edit. Capture now; canonize later. Coordinates, source labels, context aliases and derived comparisons remain distinct. Counts are not independent historical witnesses.

## Best next bounded step

**C479, proposed and unexecuted:** Synthesize C470–C478, preserve the inherited-versus-current result distinction and finite domain limits, seal the ten-step checkpoint, and publish a reading index plus compact and complete recovery packages. Select but do not execute C480.

The finite arithmetic, source identity, predecessor chain and completed publications agree. The final authorized step should consolidate the conclusions, their limits and the next bounded question into a recoverable handoff.