490d C325 — Existing460+40=500 endpoint chains

24 September2026. Step2 of10 in the C324–C333 authorization.

The fixed endpoint census finds six admitted460+40=500 triples, in two event-role families repeated across the three primary Gears. No new date or expansion anchor is generated.

All coordinates are BC numerical values, equivalently their reflected-coordinate centers. SP is OFF/Terah0/full430; MT is restoredON/Terah60/full430. Each first leg is the already verified same-role context difference460. Each second leg is an existing cross-role/cross-context40-year interval. Each outer leg is a source500 interval. The second family is Flood start→Shem death, not a secondNoah→Shem birth witness.

The census covers all75 same-Gear choices of fiveSP anchor roles, their MT counterparts, and fiveSP terminal roles. Exactly six meet the three stated lengths. Independent choice of the two quarter-year components at all three vertices gives600 trials, of which twelve pass. Every success uses the same physical output offset at its three endpoints; seasonal mixing supplies no extra match.

The inherited ancestry labels are retained. The SPNoah anchor comes from cumulativeOFFFlood_i, the SPFlood anchor from cumulativeOFFShem_i, while the Shem birth/death target uses C314's j=10−i and opposite cumulative phase. Thus equal physical phases do not mean one shared cumulative ancestor. C271 and C314 exact components verify these bindings.

The40-year interval is forced once A−B=460 and A−C=500: B−C=40. Endpoint admission is genuine source validation; the extra subtraction is not an independent numerical witness. C324's source-prescription gap remains. The result supplies concrete existing endpoints for the proposed comparison, but does not identify a source-authorizedE path or replace the translation by a dilation.

The source states remain Noah-bound/Flood-bound500/100. The distinct textual502 binding and SP primaryNoah-death qualification are untouched. No companion, Gear, annual index or event-role extension was used.

Verification and limits

70 main checks and 16 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.

The40leg is a consequence ofheld460and500relations. Source membership does not prescribeE, ananchor or a preferred modalstate.

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

C326, proposed and unexecuted: Complete each triple with the already admitted MT counterpart of its SP terminal. Compare the resulting four-endpoint overlap and outer width with File_09’s declared bilateral460→500 field, retaining source labels and phases.

Three-point equality does not establish equality of whole configurations. The fourth admitted endpoint can distinguish a full bilateral completion from a narrower arithmetic resemblance without adding an endpoint.