TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/INTRINSIC-EVENT-GEOMETRY-AND-COMPOSITION.txt
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Inclusive original lines: 261-309
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000261 | 6. Composition: compatible full products, necessary correlations
000262 | 
000263 | For INDEPENDENT tensor copies with product state and T12=T1 tensor T2,
000264 | 
000265 |   H12=H1 tensor H2, R12=R1 tensor R2, W12=W1 tensor W2
000266 | 
000267 | on the relevant supports. This is a theorem from positive functional
000268 | calculus, not an assumption that original local regions are independent.
000269 | 
000270 | Within the SAME source the actual local holomorphic products obey a
000271 | different exact relation. All u_a modes mutually commute, hence all
000272 | same-profile Delta_i(f) mutually commute on the common smooth domain.
000273 | Their two-step response kills every antisymmetric label tensor. It
000274 | therefore has rank at most15, whereas H_f tensor H_f would have rank25
000275 | for injective first response. This statement includes full smooth profiles,
000276 | not only one truncated coefficient. At the leading regular source
000277 | coefficient the ORDERED map M_tilde:L tensor L -> H8 has rank15 and
000278 | kernel wedge² L of dimension10. Its restriction M to Sym² L is injective.
000279 | This10 is a space of relations, not a10D physical source.
000280 | 
000281 | For a concrete ORIGINAL event field the complete polynomial calculation is
000282 | 
000283 |   ||Delta_0 Omega||²=2,
000284 |   ||leading_regular Delta_0 Delta_0 Omega||²=64,
000285 | 
000286 | where independent copies give4. No hidden outside states were discarded.
000287 | Associativity of the actual field products is maintained. The failure is
000288 | the identification of composition with independently tensoring reduced
000289 | responses. Other fields, conjugates, noncommuting roots and their ordered
000290 | products still use the full OPE; this is not an all-history classification.
000291 | 
000292 | Even on independent copies, correlated reference states matter. Compare
000293 | rho_corr=(|Omega,Omega><Omega,Omega|+|q,q><q,q|)/2 with rho_bar tensor rho_bar,
000294 | rho_bar=(|Omega><Omega|+|q><q|)/2. They have identical marginals. Their
000295 | actual product-field regular response tensors are
000296 | 
000297 |   B_corr=(I tensor I+B_q tensor B_q)/2,
000298 |   B_prod=((I+B_q)/2) tensor ((I+B_q)/2),
000299 |   B_corr-B_prod=(B_q-I) tensor (B_q-I)/4 !=0.
000300 | 
000301 | The checker computes all25 eigenvalues exactly. This is an explicit normal
000302 | finite-energy source-state correlation control, not an invented coupling
000303 | or proof that either state is the original physical preparation.
000304 | 
000305 | This sharpens the Universalraum connection: individual views/marginals
000306 | are insufficient for future composed answers. The complete product and
000307 | correlation data supply the missing information. No Universalraum-to-P1
000308 | existence/uniqueness theorem follows just from that consistency condition.
000309 |