{"id": "c188", "title": "C188 — The 300/299 comparison singles out the 13-fold width", "filename": "490d_C188_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 188, "sha256": "cba0efdc41729e874468b7313a0d9eb00a54483f04746dead018bc5bc754e6e2", "bytes": 2097, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C188/490d_C188_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/cba0efdc41729e874468b7313a0d9eb00a54483f04746dead018bc5bc754e6e2.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C188 — The 300/299 comparison singles out the 13-fold width\n\n23 September 2026 · Step 33 of 50, continuing C155.\n\nThe inherited6877→6900 comparison requires an exact13K width. For the residual family,\n\n\\\n(13K-\\delta)\\frac300299=6900-\\frac300\\delta299.\n\\\n\nWhole-year widths require299|δ; onlyδ=0 qualifies in−3…6. At a ge", "content": "# C188 — The 300/299 comparison singles out the 13-fold width\n\n23 September 2026 · Step 33 of 50, continuing C155.\n\n**The inherited6877→6900 comparison requires an exact13K width.** For the residual family,\n\n\\[\n(13K-\\delta)\\frac{300}{299}=6900-\\frac{300\\delta}{299}.\n\\]\n\nWhole-year widths require299|δ; onlyδ=0 qualifies in−3…6. At a general nK width, integrality requires13|n because299=13×23 and K=23².\n\nThis explains why300/299 is not an integer-width operation on every529 multiple. The C05 source-qualified6900/7500 construction remains valid under its declared anchoring; this test does not extend its source realization to the whole square or repair P6's6876 interval.\n\nThe ratios25/23 and300/299 therefore have different divisibility conditions, even though their retained family connections are exact.\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. **30 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"}]}