490d C460 — Modulo-23 Selection of the Unique Second Expansion
25 September 2026 UTC. Step 16 of 25, C445–C469.
Of16 possible second E applications to the two1150 intervals, exactly one has integer outputs and it is fully sourced:2020/3170→1956/3206 about2756. The rows have residues20 and19 modulo23; the eight fixed pivots include residue19 only at2756 and no residue20.
Since25x−2h is divisible by23 exactly when x≡h modulo23, and each row has span1150=50×23, one residue check decides integrality for both endpoints. The fixed pivot residues are19,21,10,12,9,11,0 and2. The275-year row separation is22 modulo23, explaining the one-residue difference.
The unsuccessful first row1745/2895 therefore fails integrality at every fixed second pivot. Its failure does not depend on a later source lookup or a choice of word length. The successful row uses the sole matching pivot2756, and both resulting endpoints1956/3206 are sourced.
For a separate covariance control only, translating the successful pivot by−275 would require2481 and would yield1681/2931. None of those three coordinates is in the register. They are explicitly excluded, not added to the operator menu.
The shared-word529 interval question is now closed for the declared local menu. The next bounded connection returns to the inherited Mirror comparison, using its two fixed exchanges and existing cumulative register, without changing either phase constant.
Verification and scope
17 calculation checks and 20 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.
Modulo23 is an admission criterion for this fixed E menu. It is not a new general chronology rule, and the hypothetical translated pivot remains unadmitted.
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
C461, proposed and unexecuted: Map all60 sourced529/1058 regular pairs through the two already fixed corner exchangesX_A(x)=A−x, A=−2639 and−2635, and require both reflected endpoints in the frozen48-record LXX cumulative register.
The local interval mechanism is fully classified. The actual60 direct529 pairs provide a finite, anchor-fixed way to test which of those intervals already connects to the cumulative Mirror records.