{"id": "c447", "title": "All-Word 529 Test and Established-Path Connectivity", "filename": "490d_C447_All_Word_529_Exclusion_and_E_Path_Boundary_20260925.md", "role": "Research action", "step": 447, "sha256": "ce10ab1bca64ad63f42dc3a5b590619f89b284dbdb94eb4362e3f26c981c7015", "bytes": 3070, "origins": ["C01–C479/packets/C447/490d_C447_All_Word_529_Exclusion_and_E_Path_Boundary_20260925.md"], "download": "/sources/ce10ab1bca64ad63f42dc3a5b590619f89b284dbdb94eb4362e3f26c981c7015.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Calendar Keys", "Mirror / 529"], "excerpt": "490d C447 — All-Word 529 Test and Established-Path Connectivity\n\n25 September 2026 UTC. Step 3 of 25, C445–C469.\n\nNo nonzero multiple of 529 occurs among all 191 reflection-reachable coordinate pairs. The nonzero E-path coordinates 2148, 2020 and 1956 are reflection-isolated. The source pivots 3620/2756 share a four-po", "content": "# 490d C447 — All-Word 529 Test and Established-Path Connectivity\n\n25 September 2026 UTC. Step 3 of 25, C445–C469.\n\nNo nonzero multiple of 529 occurs among all 191 reflection-reachable coordinate pairs. The nonzero E-path coordinates 2148, 2020 and 1956 are reflection-isolated. The source pivots 3620/2756 share a four-point component; 3206/3170 share a different four-point component; midpoint3188 is a loop-only singleton.\n\nThe exclusion is not limited to a selected maximum word length. C446 exhausted the finite connected components, and this step tested every distinct reachable pair. All gaps are even, since R_c(x)=2c−x preserves parity. Thus odd multiples of529 are already excluded algebraically; the finite census also excludes every possible even multiple within the register.\n\n| Coordinate | Complete reflection component |\n|---:|---|\n| 3620 | 2756, 2760, 3620, 3624 |\n| 3206 | 3166, 3170, 3206, 3210 |\n| 3188 | 3188 |\n| 3170 | 3166, 3170, 3206, 3210 |\n| 2756 | 2756, 2760, 3620, 3624 |\n| 2148 | 2148 |\n| 2020 | 2020 |\n| 1956 | 1956 |\n\nThe local reflection comparisons do connect the two E-loop stations, but cannot join that station component to its pivot component or to the nonzero2K E path. The exact E-loop and2K observations remain valid in their own source comparisons. This result limits what may be inferred from adding unrestricted word length to the four-reflection menu.\n\n## Verification and scope\n\n192 calculation checks and 19 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\nThis excludes 529 spans within the four fixed-reflection reachability relation only. It does not exclude direct 529 pairs elsewhere in the source register or paths using other declared operators.\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**C448, proposed and unexecuted:** Classify all simple cycles and fixed-point loops in the finite reflection graph, compute their full affine word, and separate formula identities from returns valid only at a particular point.\n\nThe 529 closure question is settled. The remaining unclassified feature of the graph is its cycle structure, which may explain repeated sourced returns without creating new 529 spans.\n", "evidenceLinks": [{"id": "d-24203a4c3b282f9b", "title": "File 02"}]}