{"id": "c451", "title": "Complete Directed E and Reflection Reachability", "filename": "490d_C451_Mixed_E_Reflection_All_Word_Closure_20260925.md", "role": "Research action", "step": 451, "sha256": "45af2c026cfa740d6d4ec97ea008ddf33019787afa776d4fde53c402f555f475", "bytes": 2974, "origins": ["C01–C479/packets/C451/490d_C451_Mixed_E_Reflection_All_Word_Closure_20260925.md"], "download": "/sources/45af2c026cfa740d6d4ec97ea008ddf33019787afa776d4fde53c402f555f475.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Inverse", "Calendar Keys", "Mirror / 529"], "excerpt": "490d C451 — Complete Directed E and Reflection Reachability\n\n25 September 2026 UTC. Step 7 of 25, C445–C469.\n\nThe 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 comp", "content": "# 490d C451 — Complete Directed E and Reflection Reachability\n\n25 September 2026 UTC. Step 7 of 25, C445–C469.\n\nThe 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.\n\nThe 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.\n\nThe 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.\n\nThe 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.\n\n## Verification and scope\n\n245 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.\n\nReachability is numerical and direction-sensitive. A strong component is not a chronology, and coordinate closure does not erase the original source labels.\n\nMirror/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.\n\n## Best next bounded step\n\n**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.\n\nMost 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.\n", "evidenceLinks": [{"id": "d-24203a4c3b282f9b", "title": "File 02"}]}