{"id": "c175", "title": "C175 — The one-residual model is a precise restricted grammar", "filename": "490d_C175_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 175, "sha256": "0a7b63303ea60ca0030214dbd7bde2869e986fe2ef774aa8167a213cd9adb62a", "bytes": 2435, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C175/490d_C175_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/0a7b63303ea60ca0030214dbd7bde2869e986fe2ef774aa8167a213cd9adb62a.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "C175 — The one-residual model is a precise restricted grammar\n\n23 September 2026 · Step 20 of 50, continuing C155.\n\nC166–C175 establish the conditions under which the compact δ model applies. They also provide admitted counterexamples outside that alignment.\n\n| Residual | Measurement | What zero fixes |\n|---|---|---|\n|", "content": "# C175 — The one-residual model is a precise restricted grammar\n\n23 September 2026 · Step 20 of 50, continuing C155.\n\n**C166–C175 establish the conditions under which the compact δ model applies.** They also provide admitted counterexamples outside that alignment.\n\n| Residual | Measurement | What zero fixes |\n|---|---|---|\n| α | D+X−17K | SP diagonal |\n| β | U+M−17K | MT diagonal |\n| η | D−b−868 | Cumulative/native member pairing |\n| γ | b+q−11K | Creation/Conquest pairing |\n| ρ | M−f−190 | MT profile and event-state pairing |\n| δ | X−M−2K | Regular side width |\n\nOn α=β=η=γ=ρ=0, the source-qualified family reduces to the earlier square and 13K−δ/10K partition formulas. Away from it, the general equations identify which assumption changed. Exact totals can coexist with altered internal subdivisions.\n\nThe gain is a smaller, explicit conditional grammar rather than a claim of unrestricted equivalence. The next ten steps carry these distinctions through the 8K complement so the post-Flood/Moses framework remains connected to the 529 analysis without generated coordinates acquiring unwarranted event identities.\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. **20 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"}]}