C144 — Opposite residuals cancel throughout the finite 17K routes

23 September 2026 · Bounded step 9 of 20 (C136–C155).

Every one of the thirty endpoint combinations preserves the sourced 17K comparison route found at P6 in C135. What changes is its internal division around the two Flood profiles.

The ordered route is cumulative OFF D (BC) → native Creation b (BC) → reflected Conquest q → ordinary MT Flood f → alternate MT Flood M → SP Noah X. Its successive spans are

\boxed{868+11K+(2K-\delta)+190+(2K+\delta)=17K.}

The δ terms cancel. The non-K terms satisfy 868+190=1058=2K. In particular, q→X is always 2306=4K+190. All thirty routes have positive segments and admitted endpoint fields under the retained profiles.

This is a dependent decomposition of the retained diagonals. Choosing another permitted Flood start or close redistributes time between q→f and M→X; it does not create a new outer 17K span. The 868 comparison remains between cumulative OFF and native Creation, while 190 remains a separation between ordinary and alternate MT Flood profiles. Grouping them algebraically does not relocate them into one contiguous historical interval.

The formula explains why P6 can retain 17K after losing its exact 13K prefix. It also shows why conservation of 17K by itself cannot establish the missing exact 2K segment.

Source and scope control

All numerical bases in this packet stand for paired coordinates: BC base B is (B+1)t/Bn BC; reflected AD base A is AD At/(A+1)n. Thus a cross-Mirror same-season span is B+A, after the civil no-year-zero subtraction. AD stations are reflected source events, not historical AD occurrences. K=529 throughout.

Regular Gears remain restricted to Noah/Shem/Flood. Creation and Conquest are fixed source-field selections. C133–C135 corrections remain controlling. The C127 graph and canonical controls are frozen; source-field admission is distinguished from an existing graph node and from a generated comparison coordinate. No wider N01/N03 expansion or missing N03 Shem join is repaired. Original Reports 01–10 remain previously verified references; interrupted original Reports 11–25 remain unestablished. Check counts are computational assertions, not independent historical witnesses.

Evidence: CERTIFICATE.json; 108 passing assertions in RESULTS.json. The assertion list identifies the actual tests.