TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/recursive-mirrored-source-20261103/SOURCE-INVERSE-APPLICATION-I.txt
Original file SHA-256: 0cae62189413db422df22abe26cfe5f0053f17c2cd2ee2cd5a68c26ccea05113
Inclusive original lines: 1-58
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 | SOURCEINV20261104. ACTUAL SOURCE-INVERSE APPLICATION AND FIRST FAILED IDENTIFICATION
000002 | 4 November 2026. Same original source; no replacement model or state.
000003 | 
000004 | VERDICT: ORIGINAL_PHYSICAL_INVERSE_NOT_EXECUTED.
000005 | The complete primitive S_adm, physical H_tr,pos and common interacting spectrum have not been derived. No physically distinct pair of full TFPT sources has been constructed. This continuation tests the feasibility of the previously proposed inverse; it does not promote a known inverse theorem to a physical calculation.
000006 | 
000007 | 1. REUSED ORIGINAL RESULT AND ACTUAL APPLICATION TARGET
000008 | 
000009 | BEREZIN-INVERSE.txt proves coefficient recovery on an actual regulated Grassmann chart. Its actual admissible test-space criterion (7) is retained without rederivation. The first open premise at lines150-172 is the original source/contact image and admissibility of a body-separating insertion, or an actual reduced physical chart. Gauge neutrality alone does not prove it. The target is the original physical source, including its given state/time, full field family, reference, eta, domains and contacts. Invisible ambient extensions are not different physical solutions.
000010 | 
000011 | Original physical local net: Boundary001:319-343 requires BOTH A and A* to preserve Ran(P_adm), with A originally local. For bounded A this means [A,P_adm]=0 in addition to the original local-algebra membership. Arbitrary global compression P_adm A P_adm is explicitly not the definition of that net.
000012 | 
000013 | Original selector: QFT002:12-104 fixes P=P_str P_gap, with P_gap=1_[epsilon_adm²/4,infinity)(P_str D_adm* D_adm P_str). This formula does not supply a new second-quantization lift or a field/contact image of a saturated Grassmann word. No Gamma(P_gap), CAR parity, or coordinate vacuum retention is inserted here.
000014 | 
000015 | 2. EXACT TEST AT THE ACTUAL GIVEN EXTERIOR FIBER
000016 | 
000017 | Use the existing original conditional exterior chart Q_F,b(t)=s_b(t) Gamma(R_b(t)), with all original Y and M_R retained in R_b and with the actual reference/sea factor s_b. This is reused from REFERENCE-FIBER-EVALUATION.txt and the R112/R113 source results, not newly claimed primitive physics.
000018 | 
000019 | Its raw open coherent kernel is K_b(bar eta,xi)=s_b exp(bar eta R_b xi). Therefore:
000020 |   body(K_b)=s_b,
000021 |   coefficient_(full ordered bar eta,xi)(K_b)=sign_orientation s_b det R_b,
000022 |   ordinary exterior trace(Q_F,b)=s_b det(I+R_b).
000023 | 
000024 | These follow directly by expanding the exponential into exterior minors and summing the diagonal minors. They retain every exterior degree. The raw top coefficient is not the ordinary trace: at the original identity R_0=I_m the two factors are1 and2^m. The original coherent overlap and trace closure cannot be deleted. On a matching finite exterior fiber an actual selector changes the trace to Tr(P Gamma(R)), not the unselected determinant formula. The whole original P must not be assumed fiberwise; it remains outside the actual common integration.
000025 | 
000026 | On a genuinely matching finite coherent OPERATOR chart, body(K_Q)=<0|Q|0>. That identity only constructs the body probe for this specified boundary symbol. It does not show that the full original bulk density, with all odd/ghost variables, normalization, contact ordering and domains, equals that boundary symbol. The latter identification is precisely required before claiming the physical bulk top probe equals a Fock vacuum projector. The coordinate vacuum is not declared the physical OS vacuum.
000027 | 
000028 | 3. PROJECTOR ORDER AND THE ACTUAL BOSON OPERATOR
000029 | 
000030 | In the same original compatible boson/Fock coordinate chart let J_0 u=u tensor|0>. A body of the projected operator kernel is exactly
000031 |   B_t^phys=J_0* P Q_t P J_0=V* Q_t V,  V=P J_0.
000032 | No fiberwise P, independent boson measure, or new vacuum is assumed by this algebraic expression. R113 already identifies the unprojected empty fermion matrix leg as a WHOLE BOSON OPERATOR. A matrix element is not by itself a configuration density or an evaluated bare action.
000033 | 
000034 | For any actual multiplier M_s and remaining factor F, exact multiplication gives
000035 |   P M_s F P=M_s P F P+[P,M_s]F P.
000036 | The proposed factorization body(P M_s F P)=s body(P F P) drops the last term and requires its actual vanishing. No commutator with a boson multiplier is implied by the definition of P_str P_gap. If P is nonlocal on the boson coordinates, the safe expression is the whole original kernel convolution; s cannot be pulled through P merely by calling it a scalar background weight.
000037 | 
000038 | Although P J_0 f J_0* P commutes with P, its locality and membership in the original source algebra do not follow. This is exactly why the original local-net definition disallows replacing restriction by arbitrary compression.
000039 | 
000040 | 4. WHAT THE PHYSICAL INFORMATION DOES AND DOES NOT DETERMINE
000041 | 
000042 | For unrestricted finite operator densities and complete matrix data on Ran(P), an ambient linear probe Tr(D Q) can be inferred for every Q iff D=PDP. Proof: data see P Q P, so every deltaQ with P deltaQ P=0 must pair to zero with D; the trace pairing is nondegenerate. This is the finite dual form of the already known criterion(7), not a theorem that every local physical net is the full matrix algebra. For a restricted original density class use its annihilator and actual allowed source words instead.
000043 | 
000044 | The physically projected target Tr(D P Q P)=Tr(PDP Q) differs from the ambient target. Altering unseen complementary blocks is not physical TFPT nonuniqueness. Furthermore a full specified physical source already includes the weights of its integrated fields (FULL-SOURCE-CORRECTION.txt:38-56). Failure to calculate those values is not proof that another free state, measure or axiom is necessary.
000045 | 
000046 | 5. BOSON-RESPONSE ALTERNATIVE TESTED
000047 | 
000048 | On an ACTUAL multiplicative conditional density class w=w0(b) exp(-theta^T M_b theta/2), the boson marginal is orientation_sign w0 Pf(M_b). Where Pf(M_b) is nonzero and the actual physical boson tests separate the relevant quotient, this gives a conditional inverse for the body measure. It does not select a new base measure. At corank2k, appropriate2k-leg complementary minors may be needed; a bilinear is not a universal cure at arbitrary corank. No higher-corank zero is divided away.
000049 | 
000050 | For the original whole nonmultiplicative selector the previous scalar formula cannot simply be reused. The complete selected kernel must be retained. Likewise a boson marginal is not by itself the entire mixed multi-time source. Neither the physical boson marginal values nor a full original body-separating physical probe were evaluated in this continuation. Thus the promised physical inverse has not been executed.
000051 | 
000052 | 6. INDEPENDENT REVIEW AND SCOPE
000053 | 
000054 | [OMITTED: non-scientific conversation or execution metadata]
000055 | 
000056 | [OMITTED: non-scientific conversation or execution metadata]
000057 | 
000058 | This is an inconclusive physical application with explicit rejection of two invalid shortcuts. No numerical TFPT spectrum, new physical model, full source ambiguity, or ledger promotion. No verification-suite, Lean or Wolfram execution. Existing42 findings,52 completed scoped F1 subtasks and active ownership are retained. The original given state and time are retained. Before reusing this inverse as a solution, provide its actual physical source/contact image AND computed same-source coefficients; the inverse algebra itself is already available.