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: 71-210 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. 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. 000102 | 000103 | 4. Actual erasure across a higher geometric excursion 000104 | ---------------------------------------------------- 000105 | The ORIGINAL erasure is not a Virasoro intertwiner: it lowers conformal 000106 | weight by1, and its complete Ward rule follows from(1): 000107 | 000108 | [L_m,a_a]=-bar u_a(m+1). (5) 000109 | 000110 | For m=-1 the right side is a neutral zero mode and vanishes. The first 000111 | new term is at m=-2: 000112 | 000113 | a_a L_-2 f_i=L_-2 g_(i,a)+t_(i,a), 000114 | t_(i,a)=bar u_a(-1) f_i. (6) 000115 | 000116 | No coefficient, coupling or field identification is chosen in(5)-(6). 000117 | The t vectors are orthonormal20 of conformal weight5. The source gives 000118 | 000119 | L1 t=0, L2 t=g, L_m t=0 for m>=3. (7) 000120 | 000121 | Hence t is not yet primary. Isolate its component in the EXISTING 000122 | level2 descendants of the h3 erasure primary g. The original Virasoro 000123 | Gram and the overlap vector are 000124 | 000125 | Gram(L_-2g,L_-1^2g)=[[16,18],[18,84]], 000126 | (,)=(1,0). (8) 000127 | 000128 | The exact inverse Gram fixes coefficients (7/85,-3/170). Thus 000129 | 000130 | r_(i,a)=t_(i,a)-(7/85)L_-2g_(i,a) 000131 | +(3/170)L_-1^2g_(i,a), (9) 000132 | L0 r=5r, L_m r=0 for ALL m>0, 000133 | =(78/85) delta_ij delta_ab. (10) 000134 | 000135 | This is a forced20-dimensional nonzero primary carry at weight5, obtained 000136 | from the SAME original code, canonical stress and erasure. It is uniquely 000137 | the orthogonal primary remainder of(6) relative to the given erasure 000138 | descendant block; it is NOT a classification of every weight5 primary. 000139 | The orthogonal decomposition is mathematical, never a performed projection. 000140 | State-field correspondence supplies the associated original neutral source 000141 | fields; no physical Higgs/fermion assignment is inferred. 000142 | 000143 | The entire first Ward output has Gram 000144 | 000145 | Gram(a_a L_-2 f_i)=19 I20. (11) 000146 | 000147 | Indeed16+1+2=19 from(6),(8). The primary carry has Gram78/85 I20. 000148 | Tracing over the4 erased labels gives respectively76 I5 and312/85 I5. 000149 | Even retaining this required carry therefore does not by its unweighted 000150 | returned Gram distinguish a logical2-plane or3-plane. No fitted probe weights 000151 | or additional selection rule are introduced to make it do so. 000152 | 000153 | 5. Actual native sector action, not a matching dimension 000154 | -------------------------------------------------------- 000155 | For every original native G31 event, the already checked f and g transform 000156 | as rho5 and rho5 tensor bar rho4. The creation field bar u_a(-1) carries 000157 | bar rho4, so t carries exactly rho5 tensor bar rho4. The canonical stress 000158 | commutes with the original lattice isometries; equations(9) therefore 000159 | intertwine the SAME20 representation, with its original source normalization. 000160 | 000161 | The checker independently substitutes the actual native reflection lifts 000162 | at original ray IDs1,21,32 into the full Fock polynomials and verifies all60 000163 | carry intertwining identities. These are the SAME existing event lifts in 000164 | operator_checker.py; no fitting, relabeling or a new finite-group census. 000165 | The all-native covariance also follows algebraically from this construction. 000166 | 000167 | The two native20 copies have different conformal weights3 and5. They must 000168 | not be equated as states, and neither is the charged E8 F20 block. 000169 | The corresponding joint Virasoro/native source subspaces are copies of 000170 | M_(8,1) tensor V4, M_(8,4) tensor C5, M_(8,3) tensor V20 and 000171 | the newly forced M_(8,5) tensor V20. These are infinite graded source 000172 | cycles, not a new finite physical state space or a particle census. 000173 | 000174 | 6. A concrete clock test beyond the seed vectors 000175 | ----------------------------------------------- 000176 | Choose the coordinate-angle convention U_conf=exp(i*pi L0/2); no duration 000177 | or physical time is identified. On the original seed spaces it acts as 000178 | 000179 | native4: i I4, code5: I5, erasure20: -i I20. 000180 | 000181 | These agree with the corresponding restrictions of the original central 000182 | native J. This is only a restricted agreement. On the newly forced carry 000183 | at weight5, U_conf=i I20, whereas the SAME native20 representation still 000184 | has J=-i I20. Thus the source operators are different on actual vectors 000185 | already forced by the original geometric/erasure rule. 000186 | 000187 | A common Casimir/vacuum-energy phase cannot fix the relative minus sign 000188 | between the h3 and h5 copies of the SAME native20 representation. Merely 000189 | checking seed quarter phases is insufficient to identify the complete source 000190 | clock. This is not an exclusion of other originally derived clock laws. 000191 | 000192 | 7. Consequence and remaining source selection 000193 | --------------------------------------------- 000194 | The canonical geometrical history is fully specified once its coordinate 000195 | deformation is supplied; it is not an unknown field algebra. The theorem 000196 | shows that no choice of PURE canonical stress history can perform the 000197 | required nonscalar code operation. Altering the geometric schedule alone 000198 | cannot repair this restricted route. 000199 | 000200 | The actual erasure/conformal bridge now includes the source-forced r20 000201 | carry, with exact coefficients and native action and without a chosen 000202 | root or family omission. This extends the positive common-source structure. 000203 | It does not select a physical intervention, source state, event probability, 000204 | time scale, polar prescription or3+2 field coupling from P1. 000205 | 000206 | The next selection question must concern an ACTUAL originally allowed 000207 | nonstress field/intervention, with its ordered action on this enlarged graded 000208 | source and the existing4/5/20 readout. Reuse the exact Ward/carry bridge; 000209 | do not continue scanning pure conformal schedules, equate distinct clocks 000210 | from their seed phases, or optimize arbitrary new composite histories.