{"id": "c432", "title": "Source and component audit of the 128 plus 64 factorization", "filename": "490d_C432_Source_Audit_of_the_128_Plus_64_Factorization_20260924.md", "role": "Research action", "step": 432, "sha256": "978c8bba96b25b5f57a783f9bcfb43689a64a22a0283c07e72e9980804b6c824", "bytes": 4541, "origins": ["C01–C479/packets/C432/490d_C432_Source_Audit_of_the_128_Plus_64_Factorization_20260924.md"], "download": "/sources/978c8bba96b25b5f57a783f9bcfb43689a64a22a0283c07e72e9980804b6c824.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Calendar Keys", "Mirror / 529"], "excerpt": "490d C432 — Source and component audit of the 128 plus 64 factorization\n\n24 September 2026. Step 9 of10, C424–C433.\n\nThe new factorization has two fully labelled source realizations, differing only in the second pivot's SP-primary/LXX-OFF identity. Nine current excerpt cards directly reconstruct all18 main and control ", "content": "# 490d C432 — Source and component audit of the 128 plus 64 factorization\n\n24 September 2026. Step 9 of10, C424–C433.\n\nThe new factorization has **two fully labelled source realizations**, differing only in the second pivot's SP-primary/LXX-OFF identity. Nine current excerpt cards directly reconstruct all18 main and control records.\n\n| Function | Coordinate | Actual source state |\n|---|---:|---|\n|Input|2148|MT Shem death G2/C1/T1/F1|\n|First pivot|3620|SP companion Noah birth G1/C1/T0/F0|\n|Intermediate|2020|MT Shem death G3/C0/T1/F1|\n|Second pivot|2756|SP primary or LXX-OFF Noah death G1/C0/T0/F1|\n|Output|1956|MT Shem death G1/C0/T0/F1|\n|Effective squared-E pivot|3206|SP primary or LXX-OFF Shem birth G1/C0/T0/F1|\n\nThe first actual gap expands1472=64×23 to1600=64×25, moving2148 to2020 by128. The second expands736=32×23 to800=32×25, moving2020 to1956 by64. The complete map is\n\n`F(t)=(625t−307776)/529`,\n\nexactly the squared-E map about3206. Its effective pivot is a description of the composed map; the two actual pivots remain3620 and2756. The missing fixed-pivot intermediate2056 has not been inserted or relabelled.\n\nThe two pivots do not form one864-year Noah biography. SP companion birth3620 belongs with companion death2670, preserving950. SP primary death2756 belongs with birth3706, also preserving the source's qualified950; LXX-OFF has the corresponding3706→2756 endpoints. The864 between3620 and2756 crosses Cainan, sojourn and person-rail contexts. The three path stations are different MT Shem-death states, with explicit G2→G3→G1 and Cainan/Terah changes.\n\nThe+2 factorization is exact arithmetically: pivots3622/2758 and endpoints2150/1958 are sourced, but its required intermediate2022 is absent. The analogous MT Shem-death state would require Gear4. C431's wider search also finds no other sourced factorization of the3208 target map; the failure is not repaired by another existing pivot pair.\n\nThe inherited quarter-component audit separates this integer source path from a fixed physical-time action. All eight input/intermediate/output component assignments fail with the two pivots fixed. Jointly shifting both pivots and every station by one common quarter offset preserves the corresponding comparisons, but changes the maps; these two comparisons do not establish one fixed-pivot seasonal action.\n\nThe source passages support endpoints, local rails, variants, qualified comparisons and the E gap ratio. The exact composition is derived here; no prescription for this combined sequence is established in those passages. This positive exception is therefore recorded as a **sourced affine factorization with explicit context changes**, with its+2 and component limits retained.\n\n## Verification and scope\n\n44 calculation checks and 15 source/predecessor authentication checks passed. A separate main replay is byte-identical. Root-agent analysis and replay; no new independent-agent review is claimed. Verification counts are not independent historical witnesses.\n\nTwo source labels at the second pivot are not two independent historical witnesses. The actual path changes context; it does not identify its pivots as one biography or infer a global calendar operation.\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## Decision after this result\n\n**C433, proposed and unexecuted:** Consolidate C424–C432, independently recompute the decisive finite/source-algebra results with a separate root implementation, audit the sealed packets, and publish C433 with reading index and recovery packages. Leave C434 unexecuted.\n\nThe four-template census, complete Mirror/harmonic tests and new source-qualified factorization now form a coherent bounded result. The final authorized step should verify and preserve that result before another branch is opened.\n", "evidenceLinks": [{"id": "d-24203a4c3b282f9b", "title": "File 02"}]}