TFPT scientific source excerpt Original repository path: experiments/theory-contracts/original-paper-source-reconciliation-20261102/shorttime_20261105J/shorttime20261105J_strategy/ALLORDER-SEARCH-AND-FINITE-FERMION-SD-STRATEGY.txt Original file SHA-256: 9fb1d46353836df4e4b793ea50ca8d2f8572364b342d400b792f41e50f64ccdf Inclusive original lines: 1-154 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 | TARGETED ALLORDER SEARCH AND AN ORIGINAL FINITE FERMION SOURCE STRATEGY 000002 | 5 November2026. Atlas entry487791896f84ba2c4cfeec86, plan143. 000003 | No canonical, Atlas or public edit. No fresh Python/Lean physics run. 000004 | 000005 | Result 000006 | The checked allorder, Ward and Lean candidates contain genuine closed mathematical results, but none of the specifically inspected candidates already evaluates the primitive I_orig[UY], K_U or full Higgs body. This is a statement about the named sources below, not a corpus-wide absence claim. The useful constructive consequence is instead an exact finite H-derivative fiber of the ORIGINAL unnormalized fermion source polynomial. It can be coupled to the actual whole field-translation equations without inverting a Pfaffian or deleting a zero fiber. Fermions-first finite algebra was already available; this is not a new primitive body producer or a claim that the remaining boson integration has been executed. 000007 | 000008 | 1. Candidate audit, including actual proof and code scope 000009 | 000010 | QFT4D.EG.ALLORDER.01 / v381 000011 | Owning SM007:141–155 explicitly restricts it to local perturbative EG/BRST construction under its stated hypotheses, and excludes a nonperturbative Higgs vacuum or controlled full S matrix. Actual v381 code computes dimensions, Jacobi residues and the given seam-gap number. T_n existence and allorder BRST appear as expressly imported True checks, not a numerical field/source evaluator or a Lean induction proving I_orig. The later ledger QFT4D.OS.RECON.01 repeats this binding scope. This is an established perturbative contract to preserve, not the requested nonperturbative source value. 000012 | 000013 | DERIVATION.txt / actual-folded-current-ward-and-state-determine-all-neutral-words 000014 | The whole29October original was read. It derives all ordered neutral current words from the actual eight-current CCR, actual H Ward action and the given vacuum/KMS conditions. It explicitly calls this a sufficient free current subtheory certificate, with a separate actual field/support/time join. It does not identify a dynamically integrated Higgs norm with that free cyclic sector. R103's already excluded all-word current replacement is not retried. This theorem remains useful if its actual source sector is already matched. 000015 | 000016 | R113 original gauge/BRST Ward 000017 | PROJECTED-JOINT-SOURCE-GENERATOR:165–199 gives the exact original ideal argument: gauge derivations and their regular combinations preserve the fermion-coordinate ideal; a Grassmann translation does not. Thus gauge Ward alone is not the full inhomogeneous field-translation equation. It cannot silently supply the source-force closure. All original same-caller maps and the actual Ward quotient remain closed and usable. 000018 | 000019 | Lean SourceReconstruction.lean 000020 | Current source SHA matches its stored successful kernel receipt6dcca979d2f2c89144f9fa241d7e78c69e271b13785c360d6eed53bbc31b8779. It proves exact algebraic compression/leakage identities and integer-character recurrences. Its hypotheses explicitly pass C,U,b and alpha; its header and receipt exclude constructing the physical source, state or field representation. Standard reported kernel axioms only, no sorryAx. No fresh kernel run was made. 000021 | 000022 | Lean T1Source.lean 000023 | Current SHA matches stored successful receipt8574dccc2112dba398c6c7b1cffbce32cae428f12df3a4a62bdf601217885750. It proves the actual ordered-cycle cocycle, supplied-time rational energy identity and conditional scalar-lift consequence. It neither supplies I_orig nor chooses a primitive source. Standard reported kernel axioms only. No fresh kernel run was made. 000024 | 000025 | Lean StateExpectation.lean 000026 | Current SHA matches stored successful receipt0db2061ab5ca739c6c4d129f6841f387256a024c42561518921ea4ee799d4824. The actual theorem dual_invariant_extension_unique explicitly passes the base omega0, and induced_time_invariant passes the grade-preserving time and base invariance. Positivity and the exact finite-word SOS identity are real results; a numerical base-state evaluator or primitive Higgs source is not their output. Its receipt explicitly excludes physical state selection and KMS/Gibbs construction. 000027 | 000028 | Lean BoundaryYukawaKernelInterface and HiggsIndexShadow 000029 | The actual sources were read, not inferred from theorem names. The former packages a trilinear form and contraction predicates, and explicitly distinguishes that typed target from a physical boundary-source derivation. The latter transfers rank2 through a supplied linear equivalence. Neither object is an expectation functional. This does not reopen the established geometric/index/Yukawa results or allege failed Lean proofs. No fresh build or global formalization claim was made. 000030 | 000031 | R026/DYNAMICAL-HIGGS-SOURCE-PROOF 000032 | This IS the positive original producer to reuse. Its actual shared affine coupling H_r j_r, original real four-component oneform map and finite Grassmann nilpotency already give Z_H[J-j|A], every finite fermionic source coefficient, and complementary minors/Pfaffians at singular matrices. It does not assume Gaussian H. Its original S_extra clause retains further H-dependent fermionic vertices. The actual bosonic fiber moments are input to that operation, not silently manufactured by it. 000033 | 000034 | No Ambient/QG integration conclusion is drawn here. Root independently audits the owning no-dependency/induced-gravity result. Whether that result removes an independent ambient integration is to be decided on its own physical Higgs inclusion and actual source scope. The present construction does not require adding such an integration. 000035 | 000036 | 2. Exact finite derivative fiber at the actual original affine Dirac caller 000037 | 000038 | Work at the actual compatible finite regulator, with its fixed Grassmann algebra and transported domain. Let x=(x_1,...,x_d) be the real coordinates of the ORIGINAL regulated Higgs field, using its actual test/mode map. All remaining original data A are conditional arguments, not newly selected physical parameters. No assertion d4 or m48 is made for every physical source: d and the2m Grassmann variables are those of the actual regulated pairing. 000039 | 000040 | For the genuinely bilinear original fermion branch write 000041 | 000042 | A_f(x)=A_0+sum_a x_a A_a, A_f^T=-A_f, 000043 | P_f(x,zeta)=integral dPsi exp[-Psi^T A_f(x)Psi/2+zeta^T Psi]. 000044 | 000045 | The original whole oneform/Higgs consumer supplies the affine matrices A_a after the original kinetic and skew-pairing maps. Their source orientation, chiral restriction, Majorana pairing and physical selector are not replaced by treating all96 labels as independent complex fermions. The source coefficients, with the original signs epsilon_I, are 000046 | 000047 | P_f=sum_I p_I(x) zeta_I, 000048 | p_I=epsilon_I Pf(-A_f(x)[I^c,I^c]) 000049 | 000050 | for even |I|, with odd coefficients0. The epsilon_I and the displayed minus are tied to the actually retained Berezin/source order; this formula is not a new orientation convention. 000051 | 000052 | Proof of degree: every term of the complementary Pfaffian is a product of exactly m-|I|/2 affine matrix entries. Therefore 000053 | 000054 | degree p_I <= m-|I|/2 <=m. 000055 | 000056 | Define the scalar coefficient fiber 000057 | 000058 | V_f = span_C{ partial_x^alpha p_I : all I,all alpha }. 000059 | 000060 | It is contained in Pol_{<=m}(R^d) and is closed under every original partial_a. Thus 000061 | 000062 | dim V_f <= binom(d+m,m). 000063 | 000064 | In the actual monomial presentation e_beta=x^beta, |beta|<=m, 000065 | 000066 | partial_a e_beta=beta_a e_(beta-e_a). 000067 | 000068 | These are exact commuting nilpotent derivative matrices, with each partial_a^(m+1)=0 and every derivative of total order>m zero. The actual minimal V_f may be smaller; no generic/full-rank assumption is needed. Keeping redundant monomials is a concrete finite implementation, not a conjectural moment closure. Coefficients depend on the remaining original A; the finite dimensional statement is at fixed A, or as a finite module over those untouched coefficients. 000069 | 000070 | For actual additional POLYNOMIAL fermionic vertices this conclusion survives. Remove the degree0 bosonic action first. The remaining Grassmann-positive action is nilpotent, so its exponential terminates. If every such coefficient has Higgs degree<=L and every action monomial has fermion degree>=2, the coarse bound D<=mL suffices. More sharply D is bounded by the maximum sum of the original vertex degrees in disjoint Grassmann-saturating products. Then V_f is contained in Pol_{<=D} and dim<=binom(d+D,D). This is the original finite nilpotency argument applied to derivatives; no new polynomial S_extra assumption is imposed on a caller that did not have it. 000071 | 000072 | Limits of this positive statement are essential. A fixed finite Grassmann algebra only bounds Grassmann degree. If an actual fermionic coefficient is genuinely nonpolynomial in x, it does NOT bound its Higgs derivative fiber. Already exp(-x²) has derivatives exp(-x²) times polynomials of every degree; these are linearly independent over constant scalars. Likewise a full Hamiltonian exponential as a function of x is not automatically in a finite derivative fiber merely because its matrices are finite. The cutoff dimensions may grow; no uniform finite closure after removing the regulator follows from the finite claim. 000073 | 000074 | 3. Whole original field translation, keeping every rest contact 000075 | 000076 | The finite fiber concerns only the unnormalized fermion source coefficients. It does not absorb the remaining action, the bound reference, eta, admissibility kernel or measure into a supposedly polynomial determinant. 000077 | 000078 | For an actual original conditional field chart write the same coefficient integral in the original order as 000079 | 000080 | I_p[f]=integral_C dmu_H(x) exp[-S_B(x)] R(x) p(x) f(x). 000081 | 000082 | R retains every actual remaining source factor and ordered contraction. In a nonmultiplicative projector/strip representation it is the genuine endpoint kernel, not a fabricated pointwise P_x. If H has a moving fermion basis or boundary domain, their original transport/contact terms also stay in R or its actual covariant derivative. A fixed outer Z_ref[0] can remain fixed; a bound H-dependent inner reference or C_ref(H) cannot be frozen by that notation. 000083 | 000084 | Let v be an ACTUAL allowed field variation with its original measure divergence div_mu(v), and let B_v,p[f] be the corresponding boundary flux. Entrywise Stokes on the same original kernel gives exactly 000085 | 000086 | I_p[vf] 000087 | = I_p[f(vS_B-div_mu(v))] 000088 | -I_(vp)[f] 000089 | -J_(vR),p[f] +B_v,p[f], 000090 | 000091 | J_(vR),p[f]=integral_C dmu_H exp[-S_B] (vR) p f. 000092 | 000093 | Every sign follows by expanding div_mu(v exp[-S_B]Rpf). No inverse of p,R or a determinant occurs. The p derivative closes in V_f on the polynomial branch. The R derivative includes the original H-dependent reference response, eta jumps/phases, source insertions, actual selector contacts and domain transport. Their ordering is unchanged. If a reference ratio is only valid on a nonsingular chart, its logarithmic derivative is not extended through its zeros; the original paired unnormalized source prescription is retained. 000094 | 000095 | For compactly supported field tests, or a variation tangent to an actually given domain, the appropriate flux is controlled without inventing a new contour. To extend to the requested polynomial/exponential source test one must use the ORIGINAL caller's tail/domain result. This is an application check, not a demand for a new global physical measure or Wick rule. On the finite R048 nonquadratic reweighting, Route3's actual bounded-tilt proof supplies such a concrete tail route; that evaluation is not duplicated here. The original full admissible fiber need not have a translation-invariant flat density merely because its notation is D H. If no local density exists, the correct object is its existing weak adjoint variation, not a freely supplied Jacobian. 000096 | 000097 | In the special actually supplied flat fixed chart, with no extra R variation and a polynomial S_B, the finite source vector Z_i[J]=I_(p_i)[exp(J.x)] obeys 000098 | 000099 | Z_(partial_a p_i)[J]+J_a Z_i[J] 000100 | -(partial_a S_B)(partial_J)Z_i[J] =B_a,i[J]. 000101 | 000102 | The first term is the finite derivative matrix acting on this vector. It is an exact finite COMPONENT system of source PDEs, not a finite moment truncation: the source dependence and higher bosonic derivatives are retained. For the actual nonpolynomial whole spectral profile one must retain its real untruncated force instead of inserting a finite polynomial differential operator by analogy. Dividing the first equation by a Pfaffian or dropping its complementary minor would change this system at precisely the singular fibers. 000103 | 000104 | 4. What this can calculate, and the first decisive application 000105 | 000106 | The original real contour/domain, tail behavior, normalization and full force select the original solution of these source equations. Generic SD equations by themselves have additional solutions. Garcia/Guralnik/Guralnik, hep-th/9612079, sectionII, constructs the different contour solutions explicitly; pages3–4 give the order(n-1) polynomial source equation and its contour boundary term. Bender/Karapoulitidis/Klevansky,2307.01008, pages1–2, show that setting higher Green functions to zero can converge to wrong answers even in their exactly soluble cases. These are methodological controls, not imported TFPT conditions or fresh physical counterexamples. 000107 | 000108 | The concrete new application is therefore to take the actual original p_I and their finite derivative matrices, pass their polynomial marks to the UNTRUNCATED same-source bosonic integration, and test the entire first field-translation identity including R/divergence/flux contacts. This produces a genuine coupled boson/fermion SD check, valid at Pfaffian zero, instead of another bare Gaussian or scalar UV seed. It gives Route3's controlled original integration all required fermionic marks without an extra fermion re-integration. At a source already identified as a physical IR sector, no independent ambient metric law is appended. 000109 | 000110 | This does not yet evaluate primitive UY or K_U. The remaining full force/rest/kernel might not be a finite polynomial and its actual primitive moment is not supplied by the finite derivative fiber alone. The algebraic reduction is useful because it isolates exactly which original nonperturbative value operation remains, and it protects the singular/phase/reference contributions while doing so. No field-current match is guessed; R098 truncation and R103 replacement are not revisited. No fresh proof status, physical completion or new measure/state choice is claimed. 000111 | 000112 | 5. New same-caller allorder radial reduction, without cumulant truncation 000113 | 000114 | This next consequence uses exactly the original R048 Gaussian subintegration and its literal V3/V4, not another caller. Keep the actual finite real Gaussian coordinates eta in R^N, actual symmetric positive quadratic precision K (including cell factors), source l, a=sqrt2 v and beta_i=lambda V_i>0. On this SUBINTEGRAL the untruncated action is 000115 | 000116 | S(eta)=eta^T K eta/2-l^T eta 000117 | +sum_i beta_i(a eta_i^3+eta_i^4/4). 000118 | 000119 | Its quartic tails dominate every fixed polynomial and every fixed complex linear source. Thus the original real-contour polynomial boundary flux vanishes for this literal integral. Write the UNNORMALIZED moments 000120 | 000121 | M_n=integral_(R^N) d eta eta^n exp[-S(eta)]. 000122 | 000123 | Any actual fixed original baseline factor multiplies every M_n together; it is not reset to1. This definition does not absorb or freeze an H-dependent reference, nonpolynomial Jacobian, physical kernel, angular factor or extra action. Such factors remain in the full original caller and in section3's explicit R/flux terms. 000124 | 000125 | Integration of partial_i(eta^n exp[-S]) gives the exact recurrence 000126 | 000127 | beta_i M_(n+3e_i) 000128 | =n_i M_(n-e_i)-sum_j K_ij M_(n+e_j) 000129 | -3a beta_i M_(n+2e_i)+l_i M_n, 000130 | 000131 | where the first term is0 when n_i=0. For any target m with m_i>=3 take n=m-3e_i. The RHS has total degrees |m|-4, |m|-2, |m|-1 and |m|-3 respectively. Therefore it is a terminating, exact reduction by total degree. Every polynomial moment is a linear combination of the actual original M_alpha with each alpha_i in{0,1,2}. There are AT MOST3^N such basis entries; their independence is not assumed. A fixed deterministic choice of reducible index suffices for an executable reduction. No higher moment or cumulant is set to0, and the cubic vertex is not dropped. 000132 | 000133 | The equivalent entire source Z(J)=integral exp[-S(eta)+J.eta] obeys 000134 | 000135 | E_i Z=0, 000136 | E_i=beta_i partial_(J_i)^3+3a beta_i partial_(J_i)^2 000137 | +sum_j K_ij partial_(J_j)-l_i-J_i. 000138 | 000139 | Independently checking the operator algebra gives 000140 | 000141 | [E_i,E_j]=K_ji-K_ij=0. 000142 | 000143 | Only the source multiplication term fails to commute with the first derivatives, with exactly these cancelling signs for the original symmetric K. Higher derivatives of J_i vanish. This is a compatible finite holonomic source strategy on this original polynomial branch. Differentiated source equations generate the same moment recurrence, including its n_i contact. The3^N collection of derivatives partial_J^alpha Z (alpha_i<=2) can therefore transport the whole source rather than a truncated Taylor expansion. No claim of generic rank exactly3^N, freely selectable physical initial data, or uniqueness from Ward/SD equations alone is needed. 000144 | 000145 | The base moments are not guessed. They are the SAME real-domain unnormalized integrals computed by the already constructed convergent quartic reweighting quadrature. To evaluate an original complementary Pfaffian/minor coefficient p_I, or an actual finite polynomial mark Q times it, first expand Q p_I in the original eta coordinates and reduce its moments by the recurrence. This maps every such original fermionic polynomial insertion to the SAME at-most3^N radial basis, with its complex coefficients and zeros unchanged. Error bounds propagate linearly by the absolute reduction coefficients times the corresponding basis integration errors; large cancellation can require tighter original integration tolerances. No Pfaffian inverse or normalization by a conditional zero is introduced. Exponential basis size is retained, with no fast large-N or uniform continuum claim. 000146 | 000147 | This closes ALL polynomial moments of the declared literal quartic radial subintegral, rather than merely the finite set of fermion derivatives. It does not close a whole nonpolynomial S_extra, H-dependent inner reference, discontinuous domain restriction or the full joint fields by declaration. If such a factor is actually a supplied polynomial mark on this same domain, it belongs in Q and is included exactly; otherwise section3's original force/rest/domain response remains. In particular the local gaugeorbit radial chart does not prove that R^N with this bare radial density is the global primitive Higgs pushforward. This is the decisive source-scope boundary, not a request for a new physical measure. 000148 | 000149 | Independent work in this lane: analytic recurrence, decreasing-degree proof and commutator/source matching. Root independently checks the symbolic and one-dimensional method controls. No fresh numerical physical values or extra run is claimed here. The positive new strategy is now precise: the existing untruncated quartic integration supplies actual base values, while exact field translation and the original unnormalized fermion polynomials generate all their polynomial source marks. Actual native regulator data and the full original rest are retained before any primitive UY/body evaluation is declared. 000150 | 000151 | Primary sources read for the SD strategy: 000152 | https://arxiv.org/pdf/hep-th/9612079 , pp1–4, sectionII. 000153 | https://arxiv.org/pdf/2307.01008 , pp1–2. 000154 | Original file paths, exact current hashes and receipt matches are in provenance.json.