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Original ledger classification: Identity/Lattice [I]/[L] (GL(2) covariance + family classification) + [P] physical readings

Recorded statement: MASTER-COVER THEOREM (answers next.txt P3; resolves P6 negatively; types P4) [I]/[L]: the anchor-block determinant is GL(2)-COVARIANT on the pencil plane span{K,Q} - det B((aK+bQ)+x(cK+dQ)) = (gamma x+alpha)^2 * p_KQ(moebius_G(x)) exactly…

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Paper context: Verification reference catalog

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FLAV.PENCIL.05

Original ledger classification: Identity/Lattice [I]/[L] (GL(2) covariance + family classification) + [P] physical readings

Original claim text

MASTER-COVER THEOREM (answers next.txt P3; resolves P6 negatively; types P4) [I]/[L]: the anchor-block determinant is GL(2)-COVARIANT on the pencil plane span{K,Q} - det B((aK+bQ)+x(cK+dQ)) = (gamma x+alpha)^2 * p_KQ(moebius_G(x)) exactly (symbolic identity), with disc = 81*det(G)^2 = N_fam^4 x square. CONSEQUENCE: there is exactly ONE anchor-block double cover up to Moebius reparametrisation of the line, the master cover y^2=(3x+2)(3x+5) of v81; the whole disc-81 family observed in next.txt P3 (branch {-8/3,-5/3} for L+xQ, {-5/8,-2/5} for K+xL, {-3/2,-3/5} for Q+xK) is its GL(2) orbit, and the conspicuous rung -8/3 = -rank(E8)/N_fam is the carrier branch point shifted by ONE transport period (rank E8 = g_car+N_fam: -(g_car+N_fam)/N_fam = -g_car/N_fam - 1), i.e. no new structure. NEGATIVE CONTROLS (anchor-first hardened): leaving the anchor plane in the R-direction gives non-square discriminants 153 (R+xQ) and 201 (K+xR) - non-split, no rational cover. P6 HONEST NEGATIVE: the natural 4-sheet candidate det B(K+xQ)*det B(L+xQ) factors through the forced square (3x+5)^2, so mu4=Z4 does NOT act as a genuine 4:1 cover of the pencil line; the transport tower generates a LADDER of double covers (rung n: branch {-2/3-n,-5/3-n}) with second level w^2=(3x+2)(3x+8) (disc 324=18^2) connecting Koide to rank E8 at branch separation 2=|Z2|. P4 TYPED: the branch-divisor trace -7/3=-scalaron/N_fam fixes only the SCALE exponent (M_scal=c3^{7/2}Mbar); n_s=1-2/N_star and r=12/N_star^2 are functions of the external N_star alone, so the cover cannot promote the tilt from [P]. Physical readings (Koide branch <-> physical Koide, sheet <-> half-spinor) stay [P] as in v81/v82

Original classification detail

Identity/Lattice [I]/[L]: one master cover; family = GL(2) orbit; mu4 not a 4:1 cover; tilt stays [P]

Dependencies as recorded

FLAV.PENCIL.04; v80; v81; v82

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Registered verification modules

  • v85_master_cover.pyRegistered verification module · registry
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    Master-Cover Theorem: GL(2) covariance ⇒ exactly ONE anchor-block double cover up to Möbius reparametrisation (disc = N_fam⁴·det G²); the −8/3 = −rank E₈/N_fam rung = carrier − one transport period; μ₄ is NOT a 4:1 cover (honest negative); branch trace fixes only the scalaron scale

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