TFPT scientific source excerpt
Original repository path: verification/v189_riemann_roch_carrier.py
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000001 | """v189 -- The Riemann-Roch carrier reading (external-review proposal, point 1):
000002 | the five-slot carrier and the three families are the two canonical invariants of
000003 | ONE object, the four-point seam divisor D = mu4 on P^1. The arithmetic is exact
000004 | [E]; the *identification* 'carrier = the meromorphic mode space H^0(P^1, O(mu4))'
000005 | is a [C] geometric reading (it does NOT replace the over-determined g_car=5 of the
000006 | Pascal/bootstrap/Lean route -- it adds a fourth, geometric reading, and it is
000007 | matched by rank(D5)=5).
000008 | 
000009 |   [E] 1. THE DIVISOR HAS TWO CANONICAL INVARIANTS.  For D = mu4 (degree
000010 |         |mu4| = 4) on P^1, Riemann-Roch gives the function side
000011 |         h^0(P^1, O(D)) = deg D + 1 = 5, and the cycle side is
000012 |         rank H_1(P^1 \\ D) = deg D - 1 = 3.  So from ONE four-point object:
000013 |         g_car = |mu4| + 1 = 5  and  N_fam = |mu4| - 1 = 3.
000014 |   [E] 2. BOTH MATCH THE COMPILER PRIMITIVES.  g_car = 5 = rank(D5) (the carrier
000015 |         is the so(10) half-spinor, rank D5 + rank A3 = 5 + 3 = 8 = rank E8, v1),
000016 |         and N_fam = 3 is the homology side already closed as QGEO.COHOM.01
000017 |         (n(P^1\\mu4) = C.w1 + C.w2 + C.w3, the eigenforms z^{k-1}dz/(z^4-1), v177).
000018 |   [C] 3. THE CARRIER READING (geometric, conjectural identification).  Under
000019 |         QGEO.SYM.01 the carrier is read as the space of meromorphic seam-boundary
000020 |         modes with at most simple poles on the mu4 divisor: C_car ~= H^0(P^1,
000021 |         O(mu4)), dim = 5.  This is more natural than 'five slots' (less number,
000022 |         more geometry), BUT the identification 'carrier = this mode space' is a
000023 |         physical [C] step, not derived.  It does NOT weaken P2: g_car=5 stays
000024 |         OVER-determined (Pascal 2*5=C(5,2)=10 v2; bootstrap forced three ways v6;
000025 |         Lean FORM.LADDER.01).  Honest scope: h^0 and rank H_1 are BOTH fixed by
000026 |         deg=4, so this is ONE object read two ways (a unification), not two
000027 |         independent confirmations.
000028 | 
000029 |   Exact (integer Riemann-Roch / homology); Wolfram-mirrored.