{"id": "c127", "title": "C127 — Finite integration of the Conquest and Peleg paths", "filename": "490d_C127_Finite_Conquest_Peleg_Graph_Integration_20260922.md", "role": "Research action", "step": 127, "sha256": "72c52efbe8e9cabe407b6e9a84f1a7547c600deb71dc6768f43a46aca60830aa", "bytes": 2484, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C119_C128_529_Conquest_Batch_20260922/C127/490d_C127_Finite_Conquest_Peleg_Graph_Integration_20260922.md"], "download": "/sources/72c52efbe8e9cabe407b6e9a84f1a7547c600deb71dc6768f43a46aca60830aa.md", "format": "md", "derived": false, "tags": ["Mirror / 529"], "excerpt": "C127 — Finite integration of the Conquest and Peleg paths\n\nThe verified records now form a208-node working graph of rank208. C120’s178-node placed graph remains an unchanged prefix. Thirty new coordinate variables are defined from existing records; they introduce no additional source-placement freedom.\n\nThe additions c", "content": "# C127 — Finite integration of the Conquest and Peleg paths\n\n**The verified records now form a208-node working graph of rank208.** C120’s178-node placed graph remains an unchanged prefix. Thirty new coordinate variables are defined from existing records; they introduce no additional source-placement freedom.\n\nThe additions comprise a distinct Conquest1406 annual-boundary pair, missing ordinary reflections of retained Creation/Conquest records, eight generated8K Conquest-preimage pairs, and the generated image pair for the alternative1874 boundary. The closing Conquest preimage2826 coincides numerically with the existing translated Moses-death record but remains separately identified by provenance.\n\n| Graph collection | Final count |\n|---|---:|\n| Paired-boundary nodes |208 |\n| Duration edges |382 |\n| Global reflection relations |92 |\n| Coordinate equalities preserving roles |12 |\n| Explicit component expressions |20 |\n| Component equations |27 |\n| Equation rank |208 |\n\nThe added durations encode the seven native3K+8K paths, their reversed global reflections, the native closing3K+1residual, the Conquest annual field, the fixed Moses windows, Peleg’s palindrome/refinement, and the two famine images. C126’s detailed phase table remains in its certificate; no extra free phase variables are introduced.\n\nSixty-three exact dependency certificates show how added consequences follow from the existing graph and new endpoint definitions. Thirty rank increments define the thirty added variables. No old diagnostic source pin is used to obtain full rank.\n\nThe conditional4413Creation boundary is **not admitted** to this graph. Native closing4414 still carries its one-year residual. Likewise, the generated2358 alternative image remains one year after reflected Peleg birth2357; the two are not merged. Moses death and Conquest beginning share an annual pair through explicit equality while retaining separate event roles and no claim of identical event timing.\n\nThe four3+8+2paths retain their original Flood records and full/partial statuses. There are no new Gear applications and no source-domain extension. Full rank means these encoded coordinates are determined; it does not prove every narrative or compression hypothesis.\n\n729 checks passed, including independent final-rank reconstruction and all final equations. **Next:** consolidate the ten-step results and separate source inputs, derived529identities and remaining interpretations. High sufficient.\n"}