TFPT scientific source excerpt Original repository path: experiments/theory-contracts/seam-positive-kernel-search-20261015/RESPONSE-SEARCH-20261102.txt Original file SHA-256: 0c00ffee481cfab9cf299a116a6c9c7ab91ab9bffaf7c2f1a7db6b2118f7affd Inclusive original lines: 1-104 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 | R098: Automated withheld responses and whole process segments 000002 | 2 November 2026. Experiment scope only. No ledger, Lean or physical promotion. 000003 | 000004 | Requested outcome 000005 | The fundamental goal remains one originally justified common source producing 000006 | state, time, reflection, memory and coupled field responses together. Software 000007 | must expose a missing selection rule rather than manufacture one from a fit. 000008 | 000009 | Implemented in the existing search 000010 | run_search.py now accepts --withheld-response FILE. The JSON contains a 000011 | Hermitian word polynomial, with rational real/imaginary coefficients and NO 000012 | target value. The query is not imposed in the supplied source equations. 000013 | response_search.py minimizes and maximizes its expectation with the existing 000014 | MomentSearch constraints. Numerical endpoints are explicitly estimates, not 000015 | certified outer bounds or full realizations. A nonzero numerical interval is 000016 | not by itself a proof of ambiguity of full processes. 000017 | 000018 | Independently of the numerical optimizations, rational sparse elimination 000019 | tries to express the response as a linear combination of the original affine 000020 | equalities: CAR reduction, adjoint, declared INTERNAL quarter, reference-vector 000021 | relations, supplied fixed moments and supplied linear source relations. 000022 | A successful combination certifies the conditional response for every full 000023 | realization satisfying those equalities. It does not prove nonemptiness. 000024 | The saved combination can be replayed with --verify without calling a solver. 000025 | Replay shares the equation generator and is independent of elimination, not 000026 | an independently written semantics for the original equations. 000027 | 000028 | Exact and numerical coefficients 000029 | The certificate treats the rational input contract exactly. MomentSearch 000030 | converts coefficients to binary floats. A contradiction of size 2^-53 may 000031 | therefore disappear in numerical input; it is retained by the exact checker. 000032 | No numerical equality or infeasibility is promoted to an exact result. 000033 | An affine identity in a positivity-empty class remains conditional; both 000034 | endpoints report infeasible in the active negative control. 000035 | 000036 | Executed controls 000037 | check_response_search.py ran with -B -OO. A full 2D CAR representation with 000038 | Omega=(1,0), gamma0=sigmaX, gamma1=sigmaY, T=diag(1,t), quarter=diag(1,i) 000039 | proves the entire response interval [0,1] for 0<=t<=1. Supplying the DIFFERENT 000040 | response omega(gamma0 T gamma0)=1/3 forces the withheld gamma1 response to 000041 | 1/3, with a full exact witness at t=1/3. These are software controls, NOT 000042 | new physical source inputs. Altered certificates, non-Hermitian queries, 000043 | fit targets, conflicting affine constraints and positivity-empty controls 000044 | are explicitly checked. 66 existing tests passed in 21.664 seconds. 000045 | The real run_search CLI with the new option completed and emitted the exact 000046 | conditional identity 1/3. Its finite recovery honestly remained inconclusive: 000047 | a numerically chosen higher moment had no rational recovery within its 000048 | existing denominator/tolerance contract. The independent exact 2D witness 000049 | establishes existence for this control; no recovery success was fabricated. 000050 | 000051 | Application to the existing five-mode source-clustering run 000052 | certify_response_segment.py first replays both stored full exact certificates 000053 | with the existing proof_check. Their Omega, ten gammas and internal quarter 000054 | are identical. Let T(s)=(1-s)Tmin+sTmax, 0<=s<=1. 000055 | Every one of the 2245 supplied moment polynomials is exactly CONSTANT in s. 000056 | The exact difference also annihilates Omega and each gamma_i Omega. Thus 000057 | all simple field responses are unchanged; at degree<=4 a possible insertion 000058 | of the difference has a side of field length<=1, or reduces to gamma_i T^2 000059 | gamma_j with both factors acting identically on the one-field space. 000060 | The common inequalities I/4<=T and T<=(3/4)I+(1/4)|Omega>