{"id": "c48", "title": "C48 — Source-only pairs extend farther than the joined construction", "filename": "490d_C48_Mirror_Report_20260922.md", "role": "Research action", "step": 48, "sha256": "2017c270f45fe8de35f5008caa4a4f1f564151e8259c9bbd12f0cd9ba12e3fad", "bytes": 3117, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_30_step_campaign_20260922/C48/490d_C48_Mirror_Report_20260922.md"], "download": "/sources/2017c270f45fe8de35f5008caa4a4f1f564151e8259c9bbd12f0cd9ba12e3fad.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Rounded", "Mirror / 529"], "excerpt": "C48 — Source-only pairs extend farther than the joined construction\n\n22 September 2026 · Step 26 of the authorized 30-step Mirror continuation (C23–C52).\n\nThe controlling tables give ON Shem 6343–6350 (native ON Flood 5743–5750 plus the retained 600), derived-OFF Flood 5283–5290, MT cumulative ON Flood 5289–5296, SP No", "content": "# C48 — Source-only pairs extend farther than the joined construction\n\n22 September 2026 · Step 26 of the authorized 30-step Mirror continuation (C23–C52).\n\nThe controlling tables give ON Shem 6343–6350 (native ON Flood 5743–5750 plus the retained 600), derived-OFF Flood 5283–5290, MT cumulative ON Flood 5289–5296, SP Noah 3705–3710 with its person tags, and alternate MT Flood 2645–2650 with its event-boundary tags. Inverting the linear endpoint formulas gives exact index bounds:\n\n| Endpointed path | Source-only j range | Joined j range |\n| --- | --- | --- |\n| 15: c to v | 0…5 | 2…5 |\n| 17: u to v | 0…5 | 2…5 |\n| 19: u to s | 2…5 | 2…5 |\n| 22: A to U | -1…5 | 2…5 |\n| 24: H to U | -2…2 | 2…2 |\n\nThis is a closed inequality calculation using named fields. It is not a search over arbitrary event pairs. The joined column additionally requires the previously established base domain 2≤j≤6.\n\nFor example, a source-only 22-fold pair exists at j=−1: MT cumulative ON Flood 5289 BC to reflected native ON Shem 6349 gives 11638. Its candidate OFF Flood member 5291 and SP Noah 3702 are outside their fields, so it is not a new joined branch. The j=0 and j=1 right-22 pairs likewise lack the joined Noah endpoint.\n\nThe source-only 19-fold domain already equals the joined 2…5 domain, because its two actual endpoint fields enforce that intersection themselves. The new 15/17 placements can occur at j=0 and j=1 as simpler pairs without acquiring the missing Noah join. Raw and joined counts must therefore remain separate.\n\nThe evidence reads only the controlling rows needed for these bounds; it does not execute the completed C16 campaign. The SP companion remains a Noah/Shem permission, while alternate MT Flood members retain start/close event tags.\n\n**Validation.** 8 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.** Locate 6877 inside the new 19-fold Mirror interval on the two full Creation branches.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}