TFPT scientific source excerpt Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/J-DET16-REVIEW.txt Original file SHA-256: 09b5477d96b322f051fe841bf67a5d8bd7e5288cba63abf5ef1c5bd7873b5362 Inclusive original lines: 1-97 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. 000001 | J: INDEPENDENT REVIEW OF THE ACTUAL COUPLED DET16 SOURCE JOIN 000002 | joint_origin, 3 November2026. No new execution or canonical edit. 000003 | 000004 | [OMITTED: non-scientific conversation or execution metadata] 000005 | [OMITTED: non-scientific conversation or execution metadata] 000006 | [OMITTED: non-scientific conversation or execution metadata] 000007 | [OMITTED: non-scientific conversation or execution metadata] 000008 | [OMITTED: non-scientific conversation or execution metadata] 000009 | [OMITTED: non-scientific conversation or execution metadata] 000010 | [OMITTED: non-scientific conversation or execution metadata] 000011 | [OMITTED: non-scientific conversation or execution metadata] 000012 | [OMITTED: non-scientific conversation or execution metadata] 000013 | [OMITTED: non-scientific conversation or execution metadata] 000014 | [OMITTED: non-scientific conversation or execution metadata] 000015 | [OMITTED: non-scientific conversation or execution metadata] 000016 | [OMITTED: non-scientific conversation or execution metadata] 000017 | [OMITTED: non-scientific conversation or execution metadata] 000018 | [OMITTED: non-scientific conversation or execution metadata] 000019 | 000020 | VERDICT: THE WHOLE UNITARY SOURCE TRANSPORT IS CORRECT. 000021 | No change to the original flat coefficient2 parent is needed. The parent, 000022 | old versus dressed fields, physical projection and source normalization 000023 | are handled correctly. No hidden choice of an additive parent, physical 000024 | temperature or new state occurs in that coordinate transport. 000025 | 000026 | The only recommended change is one sentence in the root summary that 000027 | could be read as global physical ground selection: 000028 | 000029 | Current: "The dressed vacuum is canonical in these coordinates." 000030 | More precise: "The local DET line phi becomes the canonical c vacuum in 000031 | these coordinates. Every complete physical ground state is transported 000032 | as well; its mirror sector is not selected by this coordinate change." 000033 | 000034 | That qualification is already correctly present in the detailed DET16 000035 | report's section5, so it is a local summary repair, not a failed theorem. 000036 | 000037 | CHECKED IDENTITIES 000038 | 000039 | 1. With F=|full><0|, replace F by exp(i theta)F in the ORIGINAL 000040 | two-plane rotation. Then U|0>=phi, U*P_phi U=P_0. It is even for the 000041 | actual16-mode factor. Thus T=I_R tensor product_x U_x* gives 000042 | T H T*=H_R+2 SUM_x(I-P_0,x) 000043 | for the actual factorized v1013 table. The six other rows act on the 000044 | rest factor and commute with these onsite mirror rotations. This does 000045 | not apply unchanged to later mirror-hopping or mixed-parent contracts. 000046 | 000047 | 2. The original local CAR c_i transports to U*c_iU. The previously 000048 | dressed a_i=Uc_iU* transports to c_i. Calling both catalogs c_i would 000049 | change the original source. The reviewed documents keep them separate. 000050 | 000051 | 3. Exact cyclic trace conjugation carries H, all ordered insertions, 000052 | P_G, and each actual supplied reference operator/factor. It does not 000053 | require [U,G]=0. If one wants to retain the SAME untransformed charge 000054 | labels and gauge operators, the original determinant-singlet premise 000055 | must actually hold for that action. A Spin10 label alone is not a 000056 | printed embedding of the finite-link Gauss action; no such implication 000057 | is asserted in the review. 000058 | 000059 | 4. The old flat parent has energy2 on every orthogonal mirror vector. 000060 | For a two-dressed-particle state its persistence is exp(-2t). The 000061 | coefficient2 additive number parent gives exp(-4t). The later original 000062 | proof expressly says N_a differs from Q. The reviewed source retains 000063 | the exp(-2t) fingerprint and the same nonlinear multiparticle dynamics. 000064 | 000065 | 5. If the actual original P_phi,x are gauge invariant, P_G commutes 000066 | with each of them. The mutually orthogonal projectors 000067 | P_S=P_G PRODUCT_(x notin S)P_x PRODUCT_(x in S)Q_x 000068 | sum to P_G and commute with H_R. Hence the exact charge-resolved trace 000069 | and min-energy formulas in DET16-ORIGINAL-MAP section5 follow. Zero 000070 | subspaces must be omitted as written. The traces include the surviving 000071 | mirror charge multiplicities; they are not free rest traces by default. 000072 | Ground-state existence alone does not compare their energies. 000073 | 000074 | 6. Products of the actual even onsite rotations define a quasilocal 000075 | automorphism. Corresponding pulled-back states have a state-preserving 000076 | unitary between their GNS spaces. There need not be a unitary infinite 000077 | product inside one fixed old Fock representation. The detailed review 000078 | states precisely this distinction. Boundary and ground limits therefore 000079 | transport with their corresponding states, without a uniqueness claim. 000080 | 000081 | 7. Physical ground support is not inferred from ambient mirror ground 000082 | support. A physical Gauss projection may correlate rest charges and 000083 | mirror sectors. The strict S=empty energy condition in the detailed 000084 | report is sufficient for physical all-mirror-vacuum support; equalities 000085 | or lower other-sector energies give its stated alternatives. This does 000086 | not obstruct the exact whole-source coordinate transport. 000087 | 000088 | No actual mathematical error found in the finite trace, canonical CAR, 000089 | time transport or sector-decomposition claims. The new chart closes 000090 | the given R104 whole-source representation. It neither derives R104's 000091 | frozen interaction from P1 nor identifies its physical ground with every 000092 | other historical source. Those scopes are already retained by the texts. 000093 | 000094 | ROOT RESOLUTION: The recommended sentence was replaced by the precise 000095 | local DET-line/whole-physical-ground formulation before persistence. 000096 | The quasilocal-automorphism/GNS qualification is also explicit in the 000097 | root synthesis. No parent or physical ground sector was changed.