{"id": "c170", "title": "C170 — Sourced counterexamples show why the common alignment matters", "filename": "490d_C170_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 170, "sha256": "18e1d8e3a9ee574982ce8b8cf57b6f72f42e99209125b4306edaa611f18fc95b", "bytes": 2548, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C170/490d_C170_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/18e1d8e3a9ee574982ce8b8cf57b6f72f42e99209125b4306edaa611f18fc95b.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C170 — Sourced counterexamples show why the common alignment matters\n\n23 September 2026 · Step 15 of 50, continuing C155.\n\nExact squares and exact 13K Creation spans are not unconditionally equivalent across all admitted endpoint selections. Two adjacent native Creation/Conquest choices provide concrete counterexamples", "content": "# C170 — Sourced counterexamples show why the common alignment matters\n\n23 September 2026 · Step 15 of 50, continuing C155.\n\n**Exact squares and exact 13K Creation spans are not unconditionally equivalent across all admitted endpoint selections.** Two adjacent native Creation/Conquest choices provide concrete counterexamples while preserving 11K.\n\n| Choice | b | q | D | X | δ | η | b+f |\n|---|---|---|---|---|---|---|---|\n| Aligned N04 | 4417 | 1402 | 5285 | 3708 | 0 | 0 | 6877 |\n| Same square, next native pair | 4416 | 1403 | 5285 | 3708 | 0 | 1 | 6876 |\n| Aligned P6 | 4416 | 1403 | 5284 | 3709 | 1 | 0 | 6876 |\n| Same square, previous native pair | 4417 | 1402 | 5284 | 3709 | 1 | -1 | 6877 |\n\nAll four comparisons use source-admitted fields. In the second row, the square is exact but the Creation span is 6876. In the fourth, the Creation span is 6877 but the square retains its one-year residual. Both deviations arise from changing the native-member alignment η, not from inventing an event or changing the Mirror axis.\n\nThe original equivalence remains valid on its stated α=β=η=γ=ρ=0 family. These negative controls identify its boundary and prevent it from being generalized solely on the basis that all selected endpoints are individually sourced.\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. **25 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"}]}