TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/SOURCE-ERASURE-WARD-AND-CODE-CLOSURE.md
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000024 | ## 2. Fixed source action and erasure
000025 | 
000026 | For beta^2=2 and the original real vector v with beta.v=0,
000027 | 
000028 |     W_beta = (v.h(-1)) e^beta,  E_beta = e^beta,
000029 |     b_a = u_a.beta, c_a = u_a.v, a_a = bar(u_a)(1).
000030 | 
000031 | Here u_a=(e_(2a)-i e_(2a+1))/sqrt2, and the actual original erasure
000032 | acts as a_a f=partial_a f on the positive Fock polynomials. The derivative
000033 | columns partial_a f_i are the previously checked original20-column isometry.
000034 | We do not replace this neutral Sym3 carrier by a charged E8 current block.
000035 | 
000036 | With Y(A,z)=sum_n A_n z^(-n-1), o(W_beta)=W_beta,1 since wt(W_beta)=2.
000037 | The original Heisenberg action on the STATE W_beta gives
000038 | 
000039 |     a_a(0) W_beta = bar(b_a) W_beta,
000040 |     a_a(1) W_beta = bar(c_a) E_beta,
000041 |     a_a(j) W_beta = 0 for j>=2.
000042 | 
000043 | The VOA commutator identity at mode1 therefore gives, without a free coefficient,
000044 | 
000045 |     [a_a,Y(W_beta,z)] = bar(c_a)Y(E_beta,z)
000046 |                        +bar(b_a)zY(W_beta,z),
000047 |     [a_a,o(W_beta)] = bar(c_a)E_beta,1 + bar(b_a)W_beta,2.       (1)
000048 | 
000049 | These are algebraic Ward terms of the given lattice source. They are not
000050 | an additional physical contact/measurement prescription or a P1 time law.
000051 | The general commutator identity is Eq.(12) in Tuite and Zuevsky,
000052 | arXiv:1106.6149v2, p4 of the PDF (printed p4):
000053 | https://arxiv.org/pdf/1106.6149#page=4 . The identification of its states
000054 | with the actual native code and erasure is checked here, not asserted by
000055 | that external reference.
000056 | 
000057 | An explicit independent polynomial comparison checks (1) on every one of
000058 | the actual5 code inputs and4 erasures for the original witness below.
000059 | If F_k=(-1)^k D_b^k f/k!, G_k=(-1)^k D_b^k D_c f/k!,
000060 | B_m=beta(-m), V_m=v(-m), E2=(B1^2+B2)/2, then on quartic inputs:
000061 | 
000062 |     E_beta,1 f = F2 + B1 F3 + E2 F4,
000063 |     W_beta,2 f = V1(F3+B1 F4) + V2 F4 + G1+B1 G2+E2 G3.
000064 | 
000065 | Each term has total conformal grade3, charge beta and oscillator grade2.
000066 | The checker differentiates charged output mode1 variables without discarding
000067 | other modes. All20 Ward identities hold exactly, including7 nonzero terms.
000068 | The universal identity (1) follows analytically, not from finite sampling.