TFPT scientific source excerpt Original repository path: experiments/theory-contracts/source-sector-reconstruction-20260920/PROOF.txt Original file SHA-256: a5796f90f4fa079badc5a07c451f1ea1028fcff3f258ac3f6992c6ae8d65d7d6 Inclusive original lines: 176-205 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. 000176 | 4. ODD FIELDS REQUIRE INTERTWINERS, NOT ONLY PARTITION FUNCTIONS 000177 | 000178 | The existence of four traces alone would not fix odd-field correlation 000179 | functions. We retain the original Gamma vertex intertwiners, their 000180 | oscillator action, adjunction and cocycle. For an odd integral x they 000181 | shift cosets by f: 000182 | M_0 <-> M_f, M_h <-> M_c. (5) 000183 | They act within the reconstructed NS space M_0+M_f and within its R 000184 | space M_h+M_c. Relative to the bosonic L theory they connect untwisted 000185 | and twisted spaces; they are defect endpoints, not ordinary local L 000186 | fields. The last terminology describes this conditional field-theory 000187 | construction; a microscopic source for these endpoints remains missing. 000188 | 000189 | On Gamma one explicit cocycle is 000190 | epsilon(x,y)=(-1)^(sum_{i>j} x_i y_j). 000191 | Its commutator obeys 000192 | epsilon(x,y)/epsilon(y,x)=(-1)^(B(x,y)+p(x)p(y)), 000193 | p(x)=B(x,x) mod2. 000194 | Together with the vertex exchange phase this gives the inherited graded 000195 | locality. The Ramond module and the defect junctions must use compatible 000196 | intertwiners. They are retained from the original lattice quantization; 000197 | we do not purport to derive their normalization from the four numbers 000198 | A,B0,C,D or from an abstract finite discriminant group. 000199 | 000200 | For example, with 0