{"id": "c34", "title": "C34 — Two 17-fold paths share a 15-fold intersection", "filename": "490d_C34_Mirror_Report_20260922.md", "role": "Research action", "step": 34, "sha256": "fb5c71a1979b531fb29933dc295362b6970dfb70662648a78db4cba02585365d", "bytes": 2785, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_30_step_campaign_20260922/C34/490d_C34_Mirror_Report_20260922.md"], "download": "/sources/fb5c71a1979b531fb29933dc295362b6970dfb70662648a78db4cba02585365d.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Rounded", "Mirror / 529"], "excerpt": "C34 — Two 17-fold paths share a 15-fold intersection\n\n22 September 2026 · Step 12 of the authorized 30-step Mirror continuation (C23–C52).\n\nThe new 19-fold interval has an exact 2+15+2 decomposition:\n\n\\\nu\\;\\xrightarrow2K\\;c\\;\\xrightarrow15K\\;v\\;\\xrightarrow2K\\;s.\n\\\n\nThe two overlapping intervals u,v and c,s both have l", "content": "# C34 — Two 17-fold paths share a 15-fold intersection\n\n22 September 2026 · Step 12 of the authorized 30-step Mirror continuation (C23–C52).\n\nThe new 19-fold interval has an exact **2+15+2** decomposition:\n\n\\[\nu\\;\\xrightarrow{2K}\\;c\\;\\xrightarrow{15K}\\;v\\;\\xrightarrow{2K}\\;s.\n\\]\n\nThe two overlapping intervals [u,v] and [c,s] both have length 17K=8993. Their intersection [c,v] is 15K=7935, and their union [u,s] is 19K=10051.\n\n| Branch | u: ON Shem | c: OFF Flood | v: alternate MT Flood | s: SP Noah |\n| --- | --- | --- | --- | --- |\n| N01 | -6346 | -5288 | 2647 | 3705 |\n| N02 | -6345 | -5287 | 2648 | 3706 |\n| N03 | -6344 | -5286 | 2649 | 3707 |\n| N04 | -6343 | -5285 | 2650 | 3708 |\n\nThe 15-fold width was already present arithmetically as B−E in the earlier work. Here its specific cumulative-OFF-Flood to reflected alternate-MT-Flood endpoints are made explicit. Likewise u→v supplies another placement of the known 17-fold value. Neither is claimed as a new independent numerical discovery.\n\nThe profile qualification on v is essential: it is the separately retained MT full430/CainanON/+60 Flood. Replacing v with ordinary MT Flood f would shorten this intersection by p=190, yielding 7745 instead of 7935. The construction does not apply the alternate profile to all regular rows.\n\nBoth full Creation rows and the two partial companion rows support this overlap. The next extension reflects the actual u endpoint, preserving its native-ON cumulative role.\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.** Admit the paired reflection of the existing native-ON cumulative Shem member.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}