{"id": "c172", "title": "C172 — The sourced route supplies an exact residual conservation law", "filename": "490d_C172_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 172, "sha256": "c0bedb33341bf64e5c50fe7b2247671e5294d41082f800759845ed1d747ceace", "bytes": 2326, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C172/490d_C172_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/c0bedb33341bf64e5c50fe7b2247671e5294d41082f800759845ed1d747ceace.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C172 — The sourced route supplies an exact residual conservation law\n\n23 September 2026 · Step 17 of 50, continuing C155.\n\nThe residuals around the ordered D→b→q→f→M→X route satisfy one exact conservation equation. Put φ=f−q−2K. Then\n\n\\\n\\boxed\\gamma+\\phi+\\delta+\\rho+\\eta-\\alpha=0.\n\\\n\nThis follows by adding the actual c", "content": "# C172 — The sourced route supplies an exact residual conservation law\n\n23 September 2026 · Step 17 of 50, continuing C155.\n\n**The residuals around the ordered D→b→q→f→M→X route satisfy one exact conservation equation.** Put φ=f−q−2K. Then\n\n\\[\n\\boxed{\\gamma+\\phi+\\delta+\\rho+\\eta-\\alpha=0.}\n\\]\n\nThis follows by adding the actual consecutive segment lengths and using 868+190=2K. It applies to the generalized endpoint comparisons, including the source-admitted counterexamples, because the intermediate boundaries cancel algebraically.\n\nβ does not appear: the other 17K diagonal U→M is not part of this route. Its source support must be supplied separately to obtain the whole square. This cleanly separates route conservation from equal-diagonal geometry.\n\nConservation is a dependency certificate rather than another independent calibration. It can diagnose a bookkeeping or profile inconsistency when the measured residuals fail to close, but it cannot choose which source endpoints or theological interpretation should control.\n\n## Evidence and scope\n\nK=529. Positive BC base B denotes (B+1)t/Bn BC; reflected AD base A denotes AD At/(A+1)n. Their same-season civil span is B+A, after the no-year-zero correction. AD source projections are not historical AD occurrences. Generated coordinates and interval midpoints do not acquire event identity from numerical coincidence.\n\nRegular Gears remain confined to Noah/Shem/Flood. Creation and Conquest use fixed source-field members; no fourth Gear is admitted. File_18/File_09 and the C127 graph are unchanged. C133–C155 source corrections remain controlling, with the C10 ancestry of the next-Flood-Gear rule now explicit. No historical campaign is rerun, no quarantined primer is reopened, and no N01/N03 expansion or missing Shem join is repaired. Original Reports 01–10 remain previously verified; interrupted original Reports 11–25 remain unestablished.\n\nSources: controlling File_18 §§2–3, 6A–6D; File_09 paired Mirror rules; selectively retained C05, C08, C10, C123, C128 and C133–C155 evidence. Specific dependencies are named in the body/certificate. **60 assertions passed**; see `RESULTS.json` and `CERTIFICATE.json`. Assertions, selected field combinations and inherited identities are not independent historical witness counts.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}