TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-paper-source-reconciliation-20261102/shorttime_20261105J/shorttime20261105J_gravity/INDEPENDENT-BOUNDED-METHOD-REVIEW.txt
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Inclusive original lines: 1-71
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 | [OMITTED: non-scientific conversation or execution metadata]
000002 | [OMITTED: non-scientific conversation or execution metadata]
000003 | 
000004 | Reviewed directly:
000005 | - work/shorttime20261105J_lean/BOUNDED-ORIGINAL-RADIAL-INTEGRATION.md
000006 | - work/shorttime20261105J_lean/integrate_original_radial_tilt.py
000007 | - work/shorttime20261105J_gravity/integrator-math-controls.json
000008 | - canonical COMMON-CURVATURE-RESPONSE-PROOF.txt:117-174 and DYNAMICAL-HIGGS-SOURCE-PROOF.txt:88-144.
000009 | No duplicate mathematical control run, no canonical/public writes.
000010 | 
000011 | Verdict
000012 | PASS for the stated mathematical subintegration, subject to the two small corrections sent to its owners below. This is constructive untruncated evaluation of the literal cubic and quartic R048 interaction on the supplied positive real finite Gaussian domain. It is not yet a numerical original physical source value or the whole global Higgs gauge integration.
000013 | 
000014 | Original match and mathematical scope
000015 | The original source really supplies lambda=8pi^2 B/(d A^2)>0, v>0, canonical radial chart Hc=(0,v+eta/sqrt2), K_R=-Delta+4lambda v^2+xi R, and the interaction sqrt2 lambda v eta^3+lambda eta^4/4. The implementation retains the supplied entire covariance, original mean and cell volumes. It does not choose physical K, lambda, v, N or proper time nu.
000016 | The shifted polynomial floor, global derivative polynomial bounds, Gaussian cell weights, truncation and Lipschitz bounds agree with the stated algebra. Polynomial insertions are evaluated with their original complex signs; absolute values occur in error envelopes only. The denominator disc rule does not divide through a zero Pfaffian. Zero determinant fibers are not removed by an inverse K formula.
000017 | The five Root controls are labeled mathematical controls, not native TFPT field data. Their recorded errors fall within the recorded analytic bounds. I did not rerun them. rounding_enclosed=false is consistently retained; analytic error formula plus float values does not supply outward rounded interval endpoints.
000018 | The document correctly preserves local radial chart versus global domain, angular/ghost/Jacobian factors, S_extra, remaining coupled field integrations, original Z0, UV and continuum scope. A discontinuous domain indicator does not inherit the smooth integrand Lipschitz bound. The finite positive radial integral is not the nonzero scalar claim for a complex weighted full fermionic caller.
000019 | 
000020 | Correction 1: prevent an omitted requested insertion from becoming adaptive success
000021 | In the reviewed code, normalize_insertions may contain a name absent from insertions/estimates. It is silently ignored in normalized_original_insertions, and integrate_until_original_tolerance then checks an empty dictionary and can return analytic_tolerance_met_before_rounding=true. Thus a caller asking for an absent UY coefficient could receive an apparent success without that coefficient.
000022 | Required local correction: validate every explicitly requested normalize_insertions name against actual supplied insertion names before any success path, and reject missing names. This follows directly from the code path; no repeated numerical run is necessary to diagnose it. Parent and route3 were informed.
000023 | 
000024 | Correction 2: state precisely which reference factors may stand outside
000025 | The sentence that every original reference factor remains bound with Z_quad needs its coordinate dependence made explicit. Only factors independent of the integrated eta coordinates may be factored out as a scalar baseline. COMMON-CURVATURE:165-168 expressly retains H dependent reference jets with their own integration/subtraction prescription. An actual eta dependent reference factor must remain inside as its supplied polynomial insertion, or as unchanged S_extra/domain data needing its own integration control. Merely naming it part of Z_quad does not evaluate it. This does not alter the pure radial V3/V4 identity.
000026 | 
000027 | No new physical identification is supplied by the quadrature method. It is useful because it turns an actually supplied finite original Gaussian caller plus its original higher vertices and polynomial legs into a convergent deterministic evaluation with explicit analytic remainder. Supplying the original coordinate/domain data is the next concrete native execution step, not permission to choose a replacement covariance.
000028 | 
000029 | [OMITTED: non-scientific conversation or execution metadata]
000030 | [OMITTED: non-scientific conversation or execution metadata]
000031 | 
000032 | Both requested corrections are now directly verified in the current files.
000033 | - original_insertions rejects a nonlist/malformed normalize_insertions argument, every requested absent polynomial name, and a missing original denominator before planning or integration. The previously empty adaptive success path for an absent requested UY insertion is closed.
000034 | - The current document allows only eta independent original reference factors outside with Z_quad. H dependent reference jets retain their own original interior integration/subtraction; nonpolynomial pieces remain in S_extra/domain data.
000035 | The updated integrator control record is6/6, including rejection of absent UY before integration. Its controls remain mathematical inputs and rounding_enclosed=false. Final verdict for the stated subcaller and its documented analytic error method: PASS. The old two corrections above are historical findings now resolved, not remaining objections.
000036 | 
000037 | The new exact <=3^N moment basis is an actual additional closure relation and differs from the old anchor and transfer closures reviewed by this agent. For the supplied real finite original R048 quartic weight define
000038 | M_n = integral_R^N eta^n exp[-eta^T K eta/2 + ell^T eta - sum_i beta_i(a eta_i^3+eta_i^4/4)] d eta,
000039 | with original beta_i=lambda V_i>0 and a=sqrt2 v. Scalar baseline factors may be restored afterward. Integration by parts gives exactly
000040 | beta_i M_(n+3e_i)=n_i M_(n-e_i)-sum_j K_ij M_(n+e_j)-3a beta_i M_(n+2e_i)+ell_i M_n.
000041 | The n_i term is absent at n_i=0. In a moment with exponent at least3 in slot i, choose n=m-3e_i. Every resulting moment has strictly smaller TOTAL degree than m. Repeating therefore terminates with exponents0,1,2 in every slot: no more than3^N actual basis integrals. This is an exact reduction of all polynomial insertions, with the untruncated cubic and quartic kept. It is not a claim of vanishing higher cumulants, an atomic law for eta, or a finite dimensional whole Higgs Hamiltonian. The finite trace obstruction for a finite Hilbert representation of the whole local Higgs dynamics does not apply to this finite basis of integral functionals on an infinite polynomial algebra.
000042 | 
000043 | Quartic dominance makes the real integration boundary terms vanish and supplies every polynomial moment. It also gives entire dependence on finite linear and quadratic source parameters through domination on compact complex parameter sets. Symmetry of K makes the original source differential operators E_i=beta_i d_i^3+3a beta_i d_i^2+sum_j K_ij d_j-ell_i-J_i mutually commute. The code checks this general two variable identity symbolically, compares several nontrivial reduction paths and verifies ten nonGaussian recurrences against direct45digit integration, recorded as14/14. Those checks support implementation; the degree descent and integration by parts are the general mathematical justification. The reduced basis values still have to be integrated using the original cycle/domain. SD equations alone do not select them or fix the original absolute normalization. The bounded Gaussian quadrature supplies an actual convergent procedure for them within its existing positive K_q branch; it does not numerically cover all complex sources or every indefinite K representation.
000044 | 
000045 | This is stronger and differently typed than v171's three spectral transfer recurrence or v1005's two atom anchor moment law: the relation follows from the actual given quartic radial interaction and retains full original cross covariance. The old finite CAR KMS/PBW producers do not already supply its3^N radial basis values. Conversely this new relation does not replace their state algebra conclusions.
000046 | 
000047 | Extra eta dependent action/reference factors, nonpolynomial S_extra or a restricted physical domain can modify the integration by parts equations or add boundary terms. They are not silently included in this3^N claim. Supplied polynomial numerator insertions are reducible; dividing by a vanishing conditional polynomial/Pfaffian remains forbidden. The exact missing native step stays the actual original finite coordinate/precision/domain input and any genuinely retained extra factors, followed by their controlled original integrations. No new physical source value, native UY result, UV limit or global physical kernel is asserted by the14/14 record.
000048 | 
000049 | Additional structural check: whole four component local Higgs integral
000050 | Requested by Root after the final fix review. No tests or model added.
000051 | For the actual supplied finite cell representation h in R^(4M) of the original local SH action,
000052 | S(h)=h^T K h/2-l^T h+sum_i beta_i |h_i|^4,
000053 | with real symmetric actual K and beta_i>0, set R=||h||, c=beta_min/M, alpha=max(0,tau-lambda_min(K))/2 and j=||l||, where tau>0 is only a compensated numerical Gaussian precision. Cauchy-Schwarz on the M cell radii gives sum_i beta_i|h_i|^4>=cR^4. The two Young inequalities
000054 | alpha R^2<=cR^4/4+alpha^2/c,
000055 | jR<=cR^4/4+(3/4)j^(4/3)c^(-1/3)
000056 | therefore imply
000057 | S-tau R^2/2>=cR^4/2-C,
000058 | C=alpha^2/c+(3/4)j^(4/3)c^(-1/3).
000059 | Thus f=exp(-S+tau R^2/2-C)<=exp(-cR^4/2)<=1. The absolute normalization is retained exactly:
000060 | Z=(2pi/tau)^(2M) exp(C) E_gamma_tau[f], gamma_tau=N(0,tau^-1 I).
000061 | This is an identity for an already supplied Lebesgue/domain caller, not a new physical Gaussian measure. A genuine restricted domain must still be integrated with its own indicator/error control.
000062 | 
000063 | A useful explicit global derivative bound is A0=1 and
000064 | A_k=sup_R R^k exp(-cR^4/2)=(k/(2ec))^(k/4), k>0.
000065 | Since ||grad S-tau h|| <= ||K-tau I||R+j+4 beta_max R^3,
000066 | Lip_h(f)<=||K-tau I||A1+j+4 beta_max A3.
000067 | For standard Gaussian z=sqrt(tau) h divide this by sqrt(tau). Original polynomial Pfaffian/Berezin insertions are controlled with the same A_degree monomial envelope and their actual derivative polynomials. Consequently the existing deterministic Gaussian cell/tail construction extends constructively to the entire four component local Higgs integral, retaining angular components. The local radial orbit chart is unnecessary for this particular actual local scalar caller.
000068 | 
000069 | This implication does not identify the untruncated spectral profile action with the local a4 SH polynomial, integrate original gauge/BRST/domain data, or remove nonpolynomial reference/eta/S_extra factors. If the supplied actual coordinates are not the positive cell representation, its real quartic norm/coercivity constant has to be transported rather than assumed.
000070 | 
000071 | The radial <=3^N moment basis does NOT automatically extend to the whole O(4) quartic. Its derivatives are 4 beta h_mu sum_nu h_nu^2, rather than separate cubic monomials beta_mu h_mu^3. The previous slotwise degree descent proof is not available. In particular the leading complex gradient system has nontrivial isotropic zeros sum_nu h_nu^2=0. No new 3^(4M) whole Higgs moment closure is claimed. The whole four component bounded quadrature is valid independently of that radial finite moment reduction.