C140 — P6 has a bounded residual family δ=1…6

23 September 2026 · Bounded step 5 of 20 (C136–C155).

P6's six squares obey one finite residual formula, with δ=1,…,6. The exact 529 grid is missed by at least one year at this boundary.

The diagonal sum and the off-diagonal sum are both 34K=17986. This conservation follows from recombining the same four endpoints; it is not an additional independent numerical witness. The residual shifts from one off-diagonal span to the other.

The P6 upper source boundary excludes δ=0: that would require M=2651 and U=6342. The observed minimum δ=1 uses the admitted G3 start. C136–C140 establish a wider finite family of equal-diagonal comparisons while preserving the original four exact C10 squares. The next five steps test whether the same residual controls the associated Creation-to-Flood and Noah partitions.

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; 31 passing assertions in RESULTS.json. The assertion list identifies the actual tests.