TFPT scientific source excerpt Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/CONFORMAL-HISTORY-AND-ERASURE-CARRY.txt Original file SHA-256: 8a50ef4c3621005d39ecaa93f38fa1d06f6c32f46c57e138fadcebb49c0ab184 Inclusive original lines: 28-101 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000028 | 2. The existing source and all-mode representation 000029 | ------------------------------------------------- 000030 | Original source normalization: 000031 | 000032 | T_E8=(1/2) sum_(A=0)^7 :h_A h_A:, 000033 | [h_A(m),h_B(n)]=m delta_AB delta_(m,-n), c=8. 000034 | 000035 | The same T is returned as states['T'] by neutral_source_response. 000036 | Its vacuum-state squared norm is4; B64=16 T in the existing neutral source. 000037 | No improved/background-charge stress tensor is substituted. 000038 | 000039 | For the ORIGINAL J-positive directions 000040 | 000041 | u_a=(e_(2a)-i e_(2a+1))/sqrt2, 000042 | u_a.u_b=0, bar u_a.u_b=delta_ab, 000043 | 000044 | put x_a=u_a(-1)Omega. The actual code consists of the five previously 000045 | normalized degree4 polynomials f_i(x). Actual erasure is a_a=bar u_a(1), 000046 | and g_(i,a)=a_a f_i=partial_a f_i. All20 g columns are orthonormal in the 000047 | original Fock norm and span the actual neutral Sym3(H+) carrier. 000048 | This is not the differently charged E8 F20 current block. 000049 | 000050 | The canonical source commutator is 000051 | 000052 | [L_m,h_A(n)]=-n h_A(m+n). (1) 000053 | 000054 | Move positive L_m through a degree-d polynomial in u(-1). For m=1, 000055 | the resulting u(0) vanishes on the neutral sector. For m=2, all possible 000056 | contractions vanish because u_a.u_b=0. For larger m the remaining 000057 | positive Heisenberg mode cannot contract a mode-1 creation operator. 000058 | Consequently EVERY such degree-d polynomial is Virasoro primary: 000059 | 000060 | L_0 f=d f, L_m f=0 for m>0. (2) 000061 | 000062 | Thus the actual existing three carriers are primary spaces of 000063 | dimensions/weights (4,1), (5,4), (20,3), respectively. These are actual 000064 | source actions on the specified vectors, not dimension identifications. 000065 | 000066 | Primary reference: Tuite and Zuevsky, arXiv:1106.6149v2, Sec.3/Eq.(36)-(37), 000067 | original rank-l Heisenberg Fock construction and stress tensor, c=l: 000068 | https://arxiv.org/pdf/1106.6149#page=8 . The original Fock vectors and 000069 | their native code/erasure identification are checked here. 000070 | 000071 | 3. Exact all-word theorem, including excursions and returns 000072 | ---------------------------------------------------------- 000073 | For orthonormal primaries e_i of fixed h and any lowering words lambda,mu, 000074 | normal-order the Virasoro algebra with central charge8. Positive modes 000075 | annihilate e_i, L0 gives h, and the center gives8. Therefore 000076 | 000077 | =G_(8,h)(lambda,mu) delta_ij. (3) 000078 | 000079 | Unequal total lowering grades are orthogonal. Quotient by any common 000080 | null vectors; no additional irreducibility assertion is needed. The 000081 | algebraic cyclic space, and its Hilbert completion, therefore factor as 000082 | 000083 | common unitary highest-weight cycle M_(8,h) tensor C^r, 000084 | L_m acts as ell_m tensor I_r. (4) 000085 | 000086 | For the actual code r=5,h=4. Any finite canonical stress-word history 000087 | has code compression a scalar I5. The same holds for well-defined 000088 | stress-generated flows/limits preserving this representation. Excursions 000089 | and returns do not supply a component-dependent phase or mixing. An endpoint 000090 | unitary preserving the code restricts to a common phase, not the given 000091 | nonscalar marked R5 (spectrum1,1,-1,i,-i). 000092 | 000093 | The matching original primary factorization applies to native4 at h1 000094 | and native20 at h3. Native G31 acts on their multiplicity factors and 000095 | commutes with the canonical stress. This is not a new physical U(r) gauge 000096 | postulate. Pure geometric stress histories contain no operator selecting 000097 | a proper logical P2, so they cannot select the original3+2 marking. 000098 | 000099 | This analytic result covers all words; the finite checker verifies actual 000100 | descendant Grams through level3 for all original4/5/20 vectors, rather 000101 | than treating these checks as an all-level proof.