{"id": "c187", "title": "C187 — The second expansion retains the square-of-23 obstruction", "filename": "490d_C187_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 187, "sha256": "0848f1480ef40b36b3793b188e2b3b2ff5dc8d75a776d73dd497d90ff339d2d9", "bytes": 2032, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C187/490d_C187_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/0848f1480ef40b36b3793b188e2b3b2ff5dc8d75a776d73dd497d90ff339d2d9.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C187 — The second expansion retains the square-of-23 obstruction\n\n23 September 2026 · Step 32 of 50, continuing C155.\n\nTwo successive25/23 expansions carry K=23² to625=25², while the residual becomes625δ/529. Whole expanded widths require529 to divideδ, since625 and529 are coprime.\n\nOnlyδ=0 satisfies that condition in ", "content": "# C187 — The second expansion retains the square-of-23 obstruction\n\n23 September 2026 · Step 32 of 50, continuing C155.\n\n**Two successive25/23 expansions carry K=23² to625=25², while the residual becomes625δ/529.** Whole expanded widths require529 to divideδ, since625 and529 are coprime.\n\nOnlyδ=0 satisfies that condition in the retained finite domain. The exact square scales to625×[[17,19],[15,17]]; P6 retains a fractional residual and does not become an exact source square by repeating the expansion.\n\nThis is the arithmetic reason the original529 unit matters across two expansion stages. It does not establish a source map for all four vertices, even where the widths are integers. No expanded endpoint is inserted into the historical graph.\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. **79 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"}]}