490d C451 — Complete Directed E and Reflection Reachability
25 September 2026 UTC. Step 7 of 25, C445–C469.
The combined fixed E/reflection graph has245 operator-labelled arrows and522 reachable directed distinct pairs,140 beyond reflection-only reachability. None has a nonzero529-multiple gap. One merged strong component has eight coordinates; all other strong components retain the reflection partition.
The graph has271 strong components. The largest is2607,2609,2731,2733,2735,3765,3767,3769. Every vertex there is reachable from every other by a sourced directed word. The maximum shortest witness length anywhere in the graph is seven arrows.
The all-word529 exclusion follows from exhaustive directed reachability on the fixed373 vertices, not from a depth cutoff. Both reflection and admitted E arrows preserve parity; enumeration settles the remaining possible even multiples. The old2K E path remains an observation about its effective pivot gap, not a claim that its endpoints differ by2K.
The increase from382 reflection-directed pairs to522 mixed pairs is real, but does not itself create529 spans. Exact shortest witnesses are archived for every pair. No inverse E arrow was added. The unique strong-component merger is the most informative new local structure and warrants a source and affine analysis.
Verification and scope
245 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.
Reachability is numerical and direction-sensitive. A strong component is not a chronology, and coordinate closure does not erase the original source labels.
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
C452, proposed and unexecuted: Resolve the unique enlarged eight-coordinate strong component: enumerate its simple directed cycles containing E, retain their affine maps and source-label identities, and identify which arrows merge the old components.
Most added E arrows create one-way access only. The unique merger isolates the new feedback structure and makes a complete cycle/source analysis small and interpretable.