{"id": "c111", "title": "C111 — Ratio, scale and origin require distinct bindings", "filename": "490d_C111_Mirror_Report_20260922.md", "role": "Research action", "step": 111, "sha256": "090d6bc96e017c24f0c3138683277f5e890fcde55eb91e32696ff03c944cb3f6", "bytes": 3674, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_10_step_graph_confluence_20260922/C111/490d_C111_Mirror_Report_20260922.md"], "download": "/sources/090d6bc96e017c24f0c3138683277f5e890fcde55eb91e32696ff03c944cb3f6.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Rounded", "Mirror / 529"], "excerpt": "C111 — Ratio, scale and origin require distinct bindings\n\n22 September 2026 · Step 9 of the authorized ten-step Mirror continuation (C103–C112).\n\nThe reduced junction model has four continuous parameters: apparent origin α, anchor difference d, base unit k and common ratio r. Its assumptions have separate jobs:\n\n| Bind", "content": "# C111 — Ratio, scale and origin require distinct bindings\n\n22 September 2026 · Step 9 of the authorized ten-step Mirror continuation (C103–C112).\n\nThe reduced junction model has four continuous parameters: apparent origin α, anchor difference d, base unit k and common ratio r. Its assumptions have separate jobs:\n\n| Bindings admitted | Parameters still free | Exact local rank |\n| --- | --- | --- |\n| Both junction equations | k and α | 2 |\n| Then the source interval 600 | α | 3 |\n| Then the source Flood coordinate 2456 | none | 4 |\n\nThe rank calculation is the exact Jacobian rank at the reconstructed solution. The explicit factorization in C108 and calibration in C109 also give uniqueness throughout the declared positive expansion domain; local rank alone would not establish that global statement.\n\nEither junction alone is insufficient. In a formal unit model, the Flood junction admits r=13/12 with a positive anchor difference while missing the Noah junction; the Noah junction admits r=12/11 while missing the Flood junction. These are diagnostic parameter examples, not alternate sourced chronologies. Other source constraints are intentionally not imported into this reduced-model deletion test.\n\nEven after all four numeric parameters are fixed, geometry supplies a coordinate rather than a person's identity. Calling the first apparent target Joseph still requires the original Kohath +110 source rule and its admitted member. That requirement cannot be replaced by matrix rank.\n\nThe full fixed-width graph has a different count: 104 variables and rank 101. Its three remaining freedoms occur only in the isolated C5/C6/C7 Creation–Conquest pairs. One already recorded source coordinate per pair raises a diagnostic pinned system to rank 104 without inconsistency. The stored relation graph remains unchanged at rank 101; these explicit source pins are reported separately. The selected junction construction is not left underdetermined by those unrelated graph components.\n\n**Validation.** 9 exact arithmetic/structural checks passed. The 20 frozen dependencies passed hash verification; all three generated outputs replayed byte for byte in isolation, and the original dependencies remained unchanged. This step reads completed certificates and does not execute their campaigns.\n\n**Scope and provenance.** Controlling File_18 and File_09 remain unchanged. Regular Gears apply only to Noah/Shem/Flood; SP person companions only to Noah/Shem. Creation and Conquest fields remain fixed. Native LXX ON, explicitly derived OFF, independent Flood start/close, and paired suffix inversion at January AD 1 remain in force. No civil year zero, upstream Gear transport, primers, Rounded campaign, or localized −33 is introduced. These are new continuation reports, not recovered historical Reports 11–25. Evidence is conditional on the supplied project model, not a proof of literary intention or independent historical dating.\n\n**Source locators.** File_09 §3 and Appendix A (paired Mirror); File_18 §§2.1.3, 3.1 and 6A (regular fields and cumulative source members); File_61 §11.2 (original backward Joseph +110); File_62 collateral-scope guards; C05 admitted apparent field; C43 frozen graph; C95 and C100–C102 named carrier rows; preceding current certificates. The forthcoming 529 × 4 × 2 cycle has not been explored. The declared phase model does not infer an unstated birthday or event month from an annual source row.\n\n**Best next bounded step — High sufficient.** Synthesize the graph extension and the conditional ratio/scale reconstruction, publish the completed ten-step checkpoint, then await the user’s 529 × 4 × 2 cycle.\n", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}, {"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-d580afd48d6e12d6", "title": "File 61"}, {"id": "d-45851004c5864229", "title": "File 09"}]}