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.