TFPT scientific source excerpt Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/NATIVE-QUARTIC-MULTILOCAL-SUPPORT.txt Original file SHA-256: 7801643ed85df8be24659a66e9437db8f549aea1497900aeeb1bfbbafd0f17ea Inclusive original lines: 107-206 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. 000107 | FOLD-COVARIANCE-TO-NATIVE-FIELD-RESPONSE.txt55--75,95--107. 000108 | 000109 | CONDITIONAL LOCAL-NET LEMMA. Let H>=0 be the SAME full source Hamiltonian with 000110 | H Omega=0. Let bounded A lie in a proper-interval CAR von Neumann algebra F(I). 000111 | Assume covariance and that Omega is separating for F(J) whenever J is a proper 000112 | interval containing I and all its sufficiently small rotations. If 000113 | A Omega=psi, H psi=E psi, E>0, 000114 | then A=0 and psi=0. In particular no nonzero such exact target can be prepared. 000115 | 000116 | Proof: use alpha_t=Ad exp(+itH), the inverse sign to the existing Schrödinger 000117 | U(t). For all sufficiently small t, 000118 | (alpha_t(A)-exp(itE)A)Omega=0. 000119 | The difference is bounded and belongs to one proper F(J). Separation implies 000120 | alpha_t(A)=exp(itE)A. The group law extends this identity to every real t. 000121 | Taking adjoints gives exp(itH)A*Omega=exp(-itE)A*Omega. Positive H has no 000122 | negative-energy vector, so A*Omega=0. Separation again gives A*=0. No derivative 000123 | of an unbounded H and no invariance/closure of C5 was assumed. QED. 000124 | 000125 | INSTRUMENT COROLLARY. Let a normal outcome with finitely or countably many 000126 | BOUNDED LOCAL Kraus operators A_j in the same proper F(I) act on |Omega>=0 cost n+alpha>0; holes n<=-1 cost-(n+alpha)>0. On charge0 the source 000140 | energy used by the existing checker is sum_n n :a_n* a_n:=32; alpha Q=0. 000141 | The supplied K time is this full positive source generator divided by8, 000142 | not the scalar finite-code compression substituted for a full net dynamics. 000143 | 000144 | The standard free-fermion interval net has cyclic/separating vacuum. For the 000145 | quarter sea, transport its projection/current reference and local test-function 000146 | support jointly to the standard NS chart; a phase multiplication shifts alpha 000147 | to1/2 without moving support. This is a chart/bundle/reference correspondence, 000148 | NOT a globally periodic gauge equality or derivation of P1 physical locality. 000149 | If this CAR local-net realization of the original physical source is not 000150 | accepted, retain the above as a conditional lemma with explicit premises. 000151 | 000152 | Primary mathematical support: Bischoff--Tanimoto, arXiv:1111.1671, section2.1 000153 | properties(1)--(7), and section3.2 pp14--15, standard localized one-particle 000154 | subspaces and their fermionic Clifford von Neumann algebras; vacuum cyclic 000155 | and separating. https://arxiv.org/pdf/1111.1671 000156 | Witten, arXiv:1803.04993 sections2.3--2.4 explains cyclicity/separation and 000157 | bounded-energy analytic vectors, not exact controllability from a local region. 000158 | https://arxiv.org/html/1803.04993v3 000159 | 000160 | 5. Scope, controls, and next falsifiable test 000161 | 000162 | The bounded-local lemma excludes exact preparation from the stipulated sea 000163 | by ONE bounded proper-interval operation, including finite products whose 000164 | whole localization fits in a proper interval. It also applies to bounded 000165 | operators in a multi-interval algebra contained in a proper J. It does not 000166 | forbid the local fields F_i(z), their separated products, arbitrary unbounded 000167 | point fields, or their domain-controlled smooth smearings. Those are different 000168 | operator classes; a proof for arbitrary affiliated unbounded operators would 000169 | need its own domain argument. No such extension is claimed here. 000170 | 000171 | Formal VOA state-operator correspondence, contour mode extraction, an insertion 000172 | at a Euclidean radial origin and a bounded real-time interval operation are 000173 | different procedures. Smoothly localized fields generally carry a whole mode 000174 | family. Reeh--Schlieder gives norm-dense local approximations, not an exact 000175 | bounded preparator or an operational success probability. A changed initial 000176 | state/reference/time, a global mode operation, an approximate target, or an 000177 | unbounded-domain construction must be stated explicitly before comparing 000178 | physical preparation menus. None singles out q. 000179 | The primitive original admissible net itself is defined by supported field 000180 | insertions and A/A*-invariant restriction, not global compression: 000181 | documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/ 000182 | 001-section-primitive-core-and-carrier-interface-handoff.tex319--343. 000183 | Nothing here proves that its reconstructed physical representation equals 000184 | the conditional conformal/current CAR source used by the explicit fold. 000185 | 000186 | Countercheck1: a global rank-one |psi>