{"id": "c438", "title": "Complete Regular Source Domains of Four Local Reflections", "filename": "490d_C438_Four_Local_Reflection_Source_Domains_20260925.md", "role": "Research action", "step": 438, "sha256": "42eec516ea0332d086e394d0704ef4cf8c623ebd9ab0a114886af4069cf12db7", "bytes": 3780, "origins": ["C01–C479/packets/C438/490d_C438_Four_Local_Reflection_Source_Domains_20260925.md"], "download": "/sources/42eec516ea0332d086e394d0704ef4cf8c623ebd9ab0a114886af4069cf12db7.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Calendar Keys", "Mirror / 529"], "excerpt": "490d C438 — Complete Regular Source Domains of Four Local Reflections\n\n25 September 2026 UTC. Step 4 of 10, C435–C444.\n\nThe four already sourced centers support a larger finite domain of local reflections, but none reflects the entire373-coordinate register into itself.\n\n| Center BC | Source coordinates retained | Coor", "content": "# 490d C438 — Complete Regular Source Domains of Four Local Reflections\n\n25 September 2026 UTC. Step 4 of 10, C435–C444.\n\nThe four already sourced centers support a larger **finite domain of local reflections**, but none reflects the entire373-coordinate register into itself.\n\n| Center BC | Source coordinates retained | Coordinate orbits, including center | Unoriented source-label pairs |\n|---|---:|---:|---:|\n|3188|61|31|86|\n|3190|67|34|91|\n|3248|19|10|18|\n|3250|61|31|63|\n\nAll1,492 input/center comparisons were tested. The four domains contain208 coordinate memberships,106 coordinate orbits (including four fixed centers),258 unoriented labelled pairings and512 directed labelled pairings. Overlap between centers and SP/LXX aliases remains explicit; these totals do not count independent observations.\n\nEach admitted pair satisfies x+y=2c and reverses exactly under the same local reflection. The source domain is maximal for that fixed center within the declared register, simply because every input was checked. This does not grant a reflection operation to coordinates outside that domain.\n\nAt3188, the original outer pivots2756↔3620 and inner stations3170↔3206 are retained. Further pairings include SP/LXX Noah births with Noah deaths or Shem deaths, Shem births with Flood boundaries, and Flood-start/close pairs. The MT center also reflects the adjacent Noah G1/G3 coordinates3186↔3190. These are cross-context source comparisons; roles and qualifications are recorded rather than collapsed.\n\nThe dominant subclass exchanges Noah birth and Noah death. Its repeated structure suggests a direct source rule using complementary Cainan/sojourn states and the local SP companion. That rule has not been assumed in the census and is the next bounded question.\n\nDATA.json preserves every failed and successful reflection trial, all source indices, all106 coordinate orbits, and every labelled pair. The global paired Mirror remains centered on January AD1. The four BC centers are local derived comparisons around existing MT Noah records.\n\n## Verification and scope\n\n1502 calculation checks and 18 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\nLocal reflection domains are partial and source-qualified. Coordinate or label counts are not historical witnesses; role aliases and SP-primary Noah-death qualification remain distinct.\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**C439, proposed and unexecuted:** Derive and verify the complete Noah-birth/Noah-death reflection subclass using the existing950 lifespan, complementary Cainan/sojourn states, SP companion choice and Gear/Terah sums; compare the rule with every C438 labelled hit.\n\nThe exhaustive reflection inventory is wider than the original five-point profile. Reducing its dominant role class to source rules is more informative than treating each coordinate hit as a separate pattern.\n", "evidenceLinks": [{"id": "d-24203a4c3b282f9b", "title": "File 02"}]}