{"id": "c152", "title": "C152 — Residual-preserving shifts are partial source correspondences", "filename": "490d_C152_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 152, "sha256": "f530db7fa4f2f7591f6c30c7cd48ec11122d116bd53d9ffb7f2b753d62e2a717", "bytes": 2536, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C136_C155_529_Square_Batch_20260923/C152/490d_C152_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/f530db7fa4f2f7591f6c30c7cd48ec11122d116bd53d9ffb7f2b753d62e2a717.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C152 — Residual-preserving shifts are partial source correspondences\n\n23 September 2026 · Bounded step 17 of 20 (C136–C155).\n\nMoving both finite selector indices together preserves δ and the square matrix, but only while both endpoints remain in their admitted domains. This is a partial correspondence, not a global chr", "content": "# C152 — Residual-preserving shifts are partial source correspondences\n\n23 September 2026 · Bounded step 17 of 20 (C136–C155).\n\n**Moving both finite selector indices together preserves δ and the square matrix, but only while both endpoints remain in their admitted domains.** This is a partial correspondence, not a global chronology operator.\n\nFor T(d,j)=(d+1,j+1), δ=d+1−j is invariant. The finite runs have these lengths:\n\n| δ | Number of admitted pairs |\n|---|---|\n| -3 | 1 |\n| -2 | 2 |\n| -1 | 3 |\n| 0 | 4 |\n| 1 | 5 |\n| 2 | 5 |\n| 3 | 4 |\n| 4 | 3 |\n| 5 | 2 |\n| 6 | 1 |\n\nThe two-index-step move (d,j)→(d+2,j+2) preserves Noah's primary/companion bit and Flood's start/close bit while increasing both regular Gears by one. That is consistent with their regular two-year Gear spacing where available. In contrast, a one-index-step move can switch event-state bits; it is not uniformly a Gear change.\n\nOther coordinates also change along the comparison: A and X increase, D and native b decrease, and reflected q increases. The b/q changes select different fixed source-field members; they are not Creation or Conquest Gears. The regular Gear interpretation is restricted to the Noah/Flood selectors.\n\nThe exact δ=0 run terminates at d=4,j=5. Its next formal index pair d=5,j=6 is outside the allowed MT field. No wraparound, fourth Gear or missing event is admitted. Invariance of a matrix along a finite run cannot establish a source-preserving transformation beyond that run.\n\n## Source and scope control\n\nAll 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.\n\nRegular 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.\n\nEvidence: `CERTIFICATE.json`; **64 passing assertions** in `RESULTS.json`. The assertion list identifies the actual tests.\n"}