490d C474 — Equal Overall E-Square Maps With Different Source Admission
25 September 2026 UTC. Step 5 of 10, C470–C479.
The +500 translation preserves the complete affine map but does not preserve source admission at each factor. With :
| Comparison | Input interval | Intermediate interval | Final interval | Source support |
|---|---|---|---|---|
| Current Shem split word, pivots3620 then2756 | 2148 / 3206 | 2020 / 3170 | 1956 / 3206 | All points and pivots sourced; both pivots in the active menu |
| Its +500-translated word, pivots4120 then3256 | 2648 / 3706 | 2520 / 3670 | 2456 / 3706 | Pivots4120/3256 and intermediate3670 absent |
| Inherited C429 Noah-held word, pivot3706 twice | 2648 / 3706 | 2556 / 3706 | 2456 / 3706 | All points and pivot sourced; inherited fixed-upper diagnostic |
Each interval sequence is 1058→1150→1250. The Noah-held middle2556 is MT Shem birth, G1/C0/T0/F1; its final2456 is MT Flood start at that same context. The upper3706 is SP-primary Noah birth, also occupied by the LXX Cainan-OFF theoretical counterpart. The initial2648 is MT Flood start, G2/C1/T1/F1. The translated lower middle2520 is sourced, with both an MT Flood-start label and an SP-companion Shem-death alias; that does not supply the missing upper3670.
The initial2648/3706 interval is precisely the existing C287 annual i3 corner. Its cumulative coordinates−6345/−5287 give the inherited opposite cross-spans3706−(−5287)=2648−(−6345)=8993=17×529. This identifies an existing connection; it creates no new reflected anchor, annual phase, or Mirror exchange constant.
Whole-map equality is therefore weaker than equality of sourced factorizations. The held3706 operator remains the older C429 diagnostic and is not inserted into the current eight-pivot menu.
Verification and scope
8 calculation checks and 25 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.
C429 and C287 are inherited results. This step does not rediscover their ladders or expand the operator menu. Coordinate aliases, native/theoretical Cainan status, and annual phase ancestry remain separate.
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
C475, proposed and unexecuted: Compare all four authenticated C429 Noah-held ladders with their Shem-minus500 partners, the derived split-pivot factorizations, and the translated split words. Resolve every anchor and intermediate against the frozen register and keep the active eight-pivot menu separate.
The3706 case joins the current split word to an inherited17K corner. Comparing the finite set of four previously recorded held ladders can distinguish a general affine identity from the specific source/context conditions that admit the split word.