{"id": "c186", "title": "C186 — One 25/23 expansion separates the exact grid from residual widths", "filename": "490d_C186_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 186, "sha256": "3054ab03e36daeea48e6dc30949d9db47dde69416005db271ca461194be62939", "bytes": 2199, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C186/490d_C186_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/3054ab03e36daeea48e6dc30949d9db47dde69416005db271ca461194be62939.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C186 — One 25/23 expansion separates the exact grid from residual widths\n\n23 September 2026 · Step 31 of 50, continuing C155.\n\nA25/23 expansion carries K to575 but carries δ to25δ/23. Hence the square becomes\n\n\\\n\\beginpmatrix17\\cdot575&19\\cdot575+25\\delta/23\\\\15\\cdot575-25\\delta/23&17\\cdot575\\endpmatrix.\n\\\n\nIn the fini", "content": "# C186 — One 25/23 expansion separates the exact grid from residual widths\n\n23 September 2026 · Step 31 of 50, continuing C155.\n\n**A25/23 expansion carries K to575 but carries δ to25δ/23.** Hence the square becomes\n\n\\[\n\\begin{pmatrix}17\\cdot575&19\\cdot575+25\\delta/23\\\\15\\cdot575-25\\delta/23&17\\cdot575\\end{pmatrix}.\n\\]\n\nIn the finite residual range−3…6, all four widths remain whole years only atδ=0. P6'sδ=1 produces opposite fractional-year residuals±25/23, while both diagonal widths are9775.\n\nThese are calculations on paired-center interval lengths. They do not yet specify a fixed dilation anchor or admit the resulting endpoints in a source field. The inherited convention lifts transformed centers back to the ordinary seasonal pair; it does not enlarge the half-year pair separation itself. Whole widths are therefore a necessary, but not sufficient, condition for an annual source-endpoint realization.\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"}]}