{"id": "c197", "title": "C197 — The named 5+5 midpoint also needs the Noah first-leg condition", "filename": "490d_C197_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 197, "sha256": "97b4864e268eab9fd1965ee9c9c2b284a9ee354d5d6a1bfaff40ba4d1b6244e9", "bytes": 2155, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C197/490d_C197_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/97b4864e268eab9fd1965ee9c9c2b284a9ee354d5d6a1bfaff40ba4d1b6244e9.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C197 — The named 5+5 midpoint also needs the Noah first-leg condition\n\n23 September 2026 · Step 42 of 50, continuing C155.\n\nAn exact named Flood midpoint does not, by itself, force an exact3+2+5 Noah subdivision. With ν=A−X−3K and ζ=A−Z−10K,\n\n\\\nA\\to X\\to M\\to Z:\n\\quad(3K+\\nu)+(2K+\\delta)+(5K+\\zeta-\\nu-\\delta).\n\\\n\nThe m", "content": "# C197 — The named 5+5 midpoint also needs the Noah first-leg condition\n\n23 September 2026 · Step 42 of 50, continuing C155.\n\n**An exact named Flood midpoint does not, by itself, force an exact3+2+5 Noah subdivision.** With ν=A−X−3K and ζ=A−Z−10K,\n\n\\[\nA\\to X\\to M\\to Z:\n\\quad(3K+\\nu)+(2K+\\delta)+(5K+\\zeta-\\nu-\\delta).\n\\]\n\nThe midpoint condition is ν+δ=ζ/2. On an exact10K total it becomes ν+δ=0, reducing toδ=0 only when the Noah first leg also hasν=0.\n\nFor sourced A5294,X3708,M2649 and retained comparison landing Z4, the halves remain2645+2645, but the finer partition is1586+1059+2645. Thus the first two one-year deviations cancel inside the exact half.\n\nZ remains a comparison landing without an independent historical birth claim. This diagnostic qualifies the equivalence among the10K,13K and17K constructions by all of their held alignment conditions.\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. **61 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"}]}