A registered result in its source context
Original ledger classification: Physical/structural [C] (exact affine relabeling, not a theorem)
Recorded statement: THE UNIVERSAL BRANCH LINE (external-review proposal 2026-06-14; HONESTLY typed [C], an exact affine RELABELING, NOT a theorem): the map q=7/2+(N_fam^2/2)m carries the SdS branch points m=+-1/N_fam onto the flavor branch points…
Statement, assumptions and sources
Paper context: Horizon readouts
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HOR.BRANCHLINE.01
Original ledger classification: Physical/structural [C] (exact affine relabeling, not a theorem)
Original claim text
THE UNIVERSAL BRANCH LINE (external-review proposal 2026-06-14; HONESTLY typed [C], an exact affine RELABELING, NOT a theorem): the map q=7/2+(N_fam^2/2)m carries the SdS branch points m=+-1/N_fam onto the flavor branch points {2,5}={|Z2|,g_car} (m=0 -> 7/2, the branch-divisor sum 7 over 2 / scalaron half-exponent). [E] arithmetic, but the map exists for ANY two pairs of points (two intervals are always affinely equivalent), so the slope N_fam^2/2 and midpoint 7/2 are DETERMINED by {-1/3,1/3}->{2,5}, NOT forced independent predictions; a decoy pair {3,4} admits an equally exact map (negative control). The genuine shared content -- the 2/3=|Z2|/N_fam ramification of the mass<->transport double cover -- is already established (FLAV.PENCIL.*, HOR.NARIAI.01). Recorded as a [C] structural alignment, never promoted to [E]
Original classification detail
Structural [C]: an affine relabeling exhibiting the known 2/3 ramification; NOT an independent theorem (decoy pairs admit equally exact maps)
Dependencies as recorded
HOR.NARIAI.01; HOR.NARIAI.02; FLAV.PENCIL.01; v101_horizon_anchor.py
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- 2026-06-14 (geometry round: Riemann-Roch carrier, Nariai bound, branch line, energy clock — v189–v192)Research changelog; TFPT — Introduction and reading guide
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- The maximal black hole is the anchor: SdS in seam unitsHorizon readouts
Registered verification modules
- v191_universal_branch_line.pyRegistered verification module · registry
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the universal branch line, HONESTLY typed [C] — an exact affine RELABELING, not a theorem. The map q=7/2+(N_fam²/2)m carries the SdS branch points m=±1/N_fam onto the flavor branch points {2,5}={|Z₂|,g_car} (m=0→7/2). [E] arithmetic, but the map exists for ANY two pairs of points (two intervals are always affinely equivalent), so the slope N_fam²/2 and midpoint 7/2 are DETERMINED by the data, not forced independent predictions; a decoy pair {3,4} admits an equally exact map (negative control). The genuine shared content — the 2/3=|Z₂|/N_fam ramification of the mass↔transport double cover — is already established. Recorded as a [C] alignment, never promoted to [E].
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