C172 — The sourced route supplies an exact residual conservation law
23 September 2026 · Step 17 of 50, continuing C155.
The residuals around the ordered D→b→q→f→M→X route satisfy one exact conservation equation. Put φ=f−q−2K. Then
This 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.
β 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.
Conservation 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.
Evidence and scope
K=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.
Regular 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.
Sources: 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.