{"id": "c67", "title": "C67 — Two sourced 6877 placements share an endpoint through different affine maps", "filename": "490d_C67_Mirror_Report_20260922.md", "role": "Research action", "step": 67, "sha256": "cba0d366df228578f46597d5e77cedabe691212f39e019b8ff9c05e3e0bd9ca7", "bytes": 3611, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_10_step_phase_lift_20260922/C67/490d_C67_Mirror_Report_20260922.md"], "download": "/sources/cba0d366df228578f46597d5e77cedabe691212f39e019b8ff9c05e3e0bd9ca7.md", "format": "md", "derived": false, "tags": ["Regular", "Rounded", "Mirror / 529"], "excerpt": "C67 — Two sourced 6877 placements share an endpoint through different affine maps\n\n22 September 2026 · Step 5 of the authorized ten-step Mirror continuation (C63–C72).\n\nThe full N02 chain and C05's 12/13-family square reach the same 7475 interval from two different 6877 placements:\n\n| Construction | Initial interval ce", "content": "# C67 — Two sourced 6877 placements share an endpoint through different affine maps\n\n22 September 2026 · Step 5 of the authorized ten-step Mirror continuation (C63–C72).\n\nThe full N02 chain and C05's 12/13-family square reach the same 7475 interval from two different 6877 placements:\n\n| Construction | Initial interval centres | Affine anchor | Final interval centres |\n| --- | --- | --- | --- |\n| C01 / N02 | [-4419, 2458] | -4419 | [-4419, 3056] |\n| C05 square | [-4421, 2456] | -4444 | [-4419, 3056] |\n\nThe C05 initial interval is the N02 initial interval translated by −2. Its Creation endpoint is the ordinary week opening and its Flood endpoint is MT G1; N02 instead uses the Creation member two years later and MT G2 Flood. Both are already source-qualified placements. No Gear is applied to Creation.\n\nLet T_d(x)=x+d. The centre maps satisfy the exact identity\n\n\\[\nD_{-4419,25/23}=D_{-4444,25/23}\\circ T_{-2}.\n\\]\n\nIt holds on both seasonal components under C65's phase-preserving lift. The apparent anchor −4444 stands 25 before the N02 Creation centre; the affine coefficient makes this anchor difference compensate exactly for the two-year change in the initial interval.\n\nFor N04 the corresponding factorization is\n\n\\[\nD_{-4417,25/23}=T_2\\circ D_{-4444,25/23}\\circ T_{-4}.\n\\]\n\nThe intermediate C05 placements and the final N04 endpoints are retained comparisons. These translations express relations among selected records; they do not authorize transporting an entire chronology or its source labels.\n\nUsing the apparent-anchor map directly on the N02/N04 full-chain Flood pairs, while omitting the translations, overshoots the intended Noah pair by 50/23 or 54/23 year on both components. The scalar ratio and starting width alone therefore do not identify the endpoint transformation. The anchor and input placement are part of the operation.\n\nThe apparent field is used only through C05's already admitted fixed +30 comparison. This step derives a phase-compatible factorization connecting that result with the full 6877 chains; it does not reopen an apparent-age campaign.\n\n**Validation.** 10 exact arithmetic/structural checks passed. The 14 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 and exact phase); File_18 §§2.1.3, 2.4, 3.1 and 3.2 (regular source bindings and seasonal limits); frozen C15/C16/C22/C43/C50/C61/C62 certificates (retained graph and phase); C01/C04/C05 reports (completed expansions and their source limits). 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.** Lift both paths of the existing 6877/6900/7475/7500 comparison square to exact seasonal components.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}