{"id": "c295", "title": "Compatibility of reflection and K subdivision", "filename": "490d_C295_Fixed_Reflection_K_Compatibility_20260924.md", "role": "Research action", "step": 295, "sha256": "2d5d5b2fac0af80ebac9c643d0e777d3027fbc706e44a060cec1dde740eca9c5", "bytes": 2498, "origins": ["C01–C479/packets/C295/490d_C295_Fixed_Reflection_K_Compatibility_20260924.md"], "download": "/sources/2d5d5b2fac0af80ebac9c643d0e777d3027fbc706e44a060cec1dde740eca9c5.md", "format": "md", "derived": false, "tags": ["Mirror / 529"], "excerpt": "C295 — Compatibility of fixed reflection and K subdivision\n\n24 September2026. This distinguishes the two positive configurations found in C287 and C294.\n\nThe complete all-K configuration and the fixed13K/8K reflection have no simultaneous solution in the admitted domain. The fixed reflection selects one opening configu", "content": "# C295 — Compatibility of fixed reflection and K subdivision\n\n24 September2026. This distinguishes the two positive configurations found in C287 and C294.\n\n**The complete all-K configuration and the fixed13K/8K reflection have no simultaneous solution in the admitted domain.** The fixed reflection selects one opening configuration; the all-K criterion selects four different numerical configurations.\n\nLet j be the LXX ON Shem annual index and i the LXX OFF Flood index, each0–7. Write the restored MT Flood center as5K+r, r0–5, and SP Noah as7K+n, n2–7. The relevant source widths are:\n\n1060+i−j; 15K+r−i; 2K+n−r.\n\nThe fixed reflection of the13K-translated sources requires i+r=0 and j+n=2. Within the nonnegative source domains this gives i=r=j=0,n=2: C294's unique527/1587/2645/3705 arrangement.\n\nThe all-K requirement gives j=i+2 and r=n=i. Its four complete solutions have i2–5. Substituting these into the fixed-reflection condition would require2i=0, contrary to the admitted Noah domain. The exhaustive2304 configurations confirm one fixed-reflection solution, four all-K solutions and zero satisfying both. The two additional LXX labels at primary Noah coordinates do not change this numerical incompatibility.\n\nIf the13K bridge were replaced formally by13K+κ, the complete all-K rows would need κ=−2i, namely−4,−6,−8,−10 years. These are diagnostic corrections, not adopted bridges or fitted source dates. They show exactly which held condition would have to change.\n\nThe two-year excess in C294 is therefore meaningful. Its source opening pair is1060 apart, and the fixed-reflection requirement selects the SP companion at7K+2. Removing the excess to recover1058 would require a different source member and ultimately the missing7K Noah counterpart at3703.\n\nThis is a compatibility statement about explicitly held premises, not a claim that either observed pattern is invalid. The patterns express different qualified arrangements and must not be combined as independent properties of one row.\n\nNine mathematical/domain checks and seven authentication checks pass; the full2304-row ledger replays identically. Author review only. No formal bridge correction is executed.\n\n**Best next bounded step — C296:** locate exact K-multiple self-Mirror widths in the full source fields underlying the normal form. In particular, identify the precise source members supporting20K and24K, and check whether the nominal14K Noah counterpart exists. High is sufficient.\n"}