{"id": "c40", "title": "C40 — One 24-fold path has five qualified two-part decompositions", "filename": "490d_C40_Mirror_Report_20260922.md", "role": "Research action", "step": 40, "sha256": "5691276d6aee88e6bb788afaf350fe21b223a27ed493608b5be8ef4686e356a3", "bytes": 2703, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_30_step_campaign_20260922/C40/490d_C40_Mirror_Report_20260922.md"], "download": "/sources/5691276d6aee88e6bb788afaf350fe21b223a27ed493608b5be8ef4686e356a3.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Rounded", "Mirror / 529"], "excerpt": "C40 — One 24-fold path has five qualified two-part decompositions\n\n22 September 2026 · Step 18 of the authorized 30-step Mirror continuation (C23–C52).\n\nThe N01 chain is fully endpointed:\n\n| Point | Signed coordinate | Role |\n| --- | --- | --- |\n| H | -6350 | native ON cumulative Shem head |\n| A | -5292 | MT cumulative", "content": "# C40 — One 24-fold path has five qualified two-part decompositions\n\n22 September 2026 · Step 18 of the authorized 30-step Mirror continuation (C23–C52).\n\nThe N01 chain is fully endpointed:\n\n| Point | Signed coordinate | Role |\n| --- | --- | --- |\n| H | -6350 | native ON cumulative Shem head |\n| A | -5292 | MT cumulative ON Flood |\n| X | -3705 | SP G1 companion Noah |\n| Y | -2647 | alternate MT G2 Flood close |\n| Z | -2 | comparison landing |\n| D | 5288 | reflected LXX cumulative OFF Flood |\n| U | 6346 | reflected native ON cumulative Shem |\n\nIts consecutive lengths are 2K, 3K, 2K, 5K, 10K and 2K. The retained cuts yield:\n\n| Cut | Decomposition |\n| --- | --- |\n| X | 5 + 19 = 24 |\n| Y | 7 + 17 = 24 |\n| Z | 12 + 12 = 24 |\n| D | 22 + 2 = 24 |\n| A | 2 + 22 = 24 |\n\nThe right-hand 19-fold interval X→U is the canonical reflection of u→s. The right-hand 17-fold interval Y→U reflects u→v. Thus 5+19 and 7+17 preserve explicit source roles rather than being arbitrary numerical partitions. The alternative 2+22, 12+12 and 22+2 cuts use the already qualified cumulative and landing endpoints.\n\nThese decompositions are incidence identities of one path. They provide a useful integrated display but do not constitute five extra confirmations of 529. Nor does the N01 chain acquire a valid MT Noah birth for the full Creation expansion merely because its longer outer interval closes.\n\n**Validation.** 7 exact arithmetic/structural checks passed. The ten 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 §3.1 (paired Mirror); File_18 §§2.1.3, 3.1–3.2, 6B and 6D (qualified regular and cumulative fields); frozen C15 typed graph, C16 domain certificate, and C22 reduced scale/constraint certificates.\n\n**Best next bounded step — High sufficient.** Solve the exact source-field bounds for raw and joined 24-fold intervals.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}