# 490d C412 — Direct reconstruction and source warrant of the 500 comparison domain

24 September 2026. Step 9 of 10 in the C404–C413 authorization.

**All528 frozen regular records reconstruct exactly from the current source tables and scoped variant rules.** The52 labelled Shem-loop slots and ten labelled long-chain slots are all members of that reconstructed register.

Twelve excerpt cards preserve the exact reviewed passages with line locations and hashes. Person birth and death baselines were parsed separately: MT from File02's minimum table, LXX from its own native-Cainan rows, and both SP rails from File18's G1 field. Flood-start baselines were parsed independently from the universal start/close table. The reconstruction then applies only the stated Cainan, Terah, sojourn and scoped Gear adjustments.

|Claim|Source warrant|
|---|---|
|Noah/Shem births and deaths, Flood boundaries, variants and Gear offsets|Explicit current table data and rules;528 records reconstructed|
|Matched500 and alternative502 Noah-to-Shem bindings|Explicit qualified source relations; both modes retained|
|Flood-to-Shem-death500 relation and complete loop correspondence|Exact consequences of the source endpoints and600-year geometry|
|3395→2895 bridge and four-step500 chain|Derived cross-context comparison; no prescription for the combined sequence established in the reviewed passages|
|Affine path normal forms and commuting circuits|Derived mathematics of the selected comparisons|

File18 explicitly keeps SP primary Noah death's inclusive/harmonic qualification, matched950/600 lifespans, and the SP-only person companion. Flood close remains an independent event boundary. LXX native data already include Cainan; OFF is a theoretical removal and does not authorize a second insertion. The two100-year Shem modes remain qualified alternatives.

The present research applies ordinary regular Gears only to Noah/Shem/Flood, as currently instructed. Broader historical Gear paragraphs do not expand this batch's scope. J remains File02's gap conversion, explicitly distinguished from a date transformation and from the Residue Protocol.

This source audit supports the endpoints and arithmetic while keeping the status of the new combinations clear. No source node, canonical graph edge or new protocol prescription has been established by the census. C413 will consolidate the batch and its verification; it will not begin the next research question.

## Verification and limits

543 main checks and 20 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.

Source reconstruction and repeated arithmetic are verification, not independent historical witnesses. No general date operator, extra Gear, fitted phase, new axis or canonical edit is adopted.

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.

## Decision after this result

**C413, proposed and unexecuted:** Consolidate C404–C412, verify the main findings through a separately implemented root calculation, audit all sealed packets and publication receipts, and produce C413 synthesis and recovery files. Select a next bounded529/Mirror question without executing C414.

The source and interpretation boundaries are now settled for this batch. The final authorized step should bind the results and make the completed work recoverable, rather than open another research branch.