# 490d C326 — Four-endpoint overlap and bilateral field

24 September2026. Step3 of10 in the C324–C333 authorization.

Completing each C325 triple with the existing MT counterpart of its SP terminal gives **six source-admitted four-point configurations**. Their ordered gaps are460|40|460, with two500-year intervals overlapping by40 and outer width960.

| Family /Gear | A_SP →B_MT →C_SP →D_MT, BC |
|---|---|
|Noah/Shem birth G1|3706→3246→3206→2746|
|Noah/Shem birth G2|3708→3248→3208→2748|
|Noah/Shem birth G3|3710→3250→3210→2750|
|Flood/Shem death G1|3106→2646→2606→2146|
|Flood/Shem death G2|3108→2648→2608→2148|
|Flood/Shem death G3|3110→2650→2610→2150|

A andC retain SP OFF/Terah0/full430; B andD retain restoredMT ON/Terah60/full430. The fourth endpoint was already present in C322, not generated to close a pattern. A→C andB→D are500; A→B andC→D are460. The central B→C is40.

The complete metric comparison with File_09 is:

| Property | Regular source configuration | File_09 §3A.2.3 |
|---|---|---|
|Ordered gaps|460,40,460|40,460,40|
|Two equal intervals|500,500|500,500|
|Their overlap|40|460|
|Outer width|960|540|
|Endpoint status|Four admitted regular endpoints in two contexts|Declared cumulative core with generated completion shoulders|

The File_09 field is14511→14471→14011→13971. For two intervals of lengthL separated bydelta, overlap=L−delta and outer=L+delta. HereL=500, but the separations are460 and40 respectively. Displacement and overlap are complementary; the full configurations are not the same. A translation cannot change those lengths, and no uniform scaling can reconcile their ordered gap ratios while retaining the two500 intervals. Reversing order does not change this conclusion.

All96 independent quarter-phase quadruples were tested. Twelve preserve both source460 relations and both500 intervals, with equal physical offsets at all four vertices. The inherited ancestry distinctions remain as recorded in C325; no File_09 phase field is newly generated or assigned to the regular nodes.

The result preserves the source-qualified460+40=500 subpattern without importing the whole File_09 bilateral construction into it. The source-prescription gap remains, and neither the shared500 length nor the complementary geometry adds an independent historical witness.

## Verification and limits

40 main checks and 15 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.

Metric andsource-typecomparisononly. Complementaryoverlap is not a newlyauthorizedoperator; no endpoint,anchor orFile09scope transfer 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

**C327, proposed and unexecuted:** Remove the500-only target and classify every positive cross-context residual among the same five-role source biographies: after the held460 same-role leg, which existing SP endpoints remain later, and which full source durations do they partition?

The full configuration differs from the selectedbilateral template. A complete residual ledger will show whether40 is a lone selected feature or one member of a coherent source-biography structure, without adding endpoints or changing contexts.