Established in scope
Three moments uniquely select exponential within positive Laplace cone
In the question: Automated construction of operator maps and sources
Complete analytic class/equality proof with shared27 controls. Original Bernstein and current action variables still require identification and independently derived moment values. v259 computes moments after inserting exp(-u), so its outputs are not independent selection premises. No new UV kernel or physical state is postulated.
Read the exact result, assumptions and evidence
Result
Across the entire positive Laplace cone, the moment determinant is nonnegative and vanishes exactly for one point measure, selecting the exponential for moments1,1,1. Variance supplies an automatic concentration bound. General smooth positivity alone is insufficient, as the exact same-moment polynomial counterprofile demonstrates; it is not completely monotone.
Required assumptions
- Positive finite Laplace measure and three finite positive moments. Identification of the original profile variables and independent physical moment values is explicitly not supplied by this mathematical comparison.
Positive finite Laplace measure and three finite positive moments. Identification of the original profile variables and independent physical moment values is explicitly not supplied by this mathematical comparison.
Original evidence
- B1-OPERATOR-INFORMATION.txt lines 1–155
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/B1-OPERATOR-INFORMATION.txt
f9ef51cfad6d16ce0b95b9a6793a4604f8d15a8bf08993aee197191b7af73e5c
- check_b1_operator_information.py lines 1–63
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_b1_operator_information.py
3fcbbc88f79fcaeaf0b6c53b3381efb97d2ac77f95e8a11200ff4b3f6314adcb
- B1-OPERATOR-INFORMATION.json lines 1–49
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/B1-OPERATOR-INFORMATION.json
7b2a14013e1e9af782691fa4e82d01f592dbb052632538b025b4cba8171c2f8b
- v259_modular_cutoff_kappa.py lines 51–106
Source checked at this snapshot
Original location and fingerprint
verification/v259_modular_cutoff_kappa.py
cc4ed41b68b91dba52e8e30552a41e671bba1d84a1c03837455c96c5121c18b8
- 001-section-primitive-core-and-carrier-interface-handoff.tex lines 345–350
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex
7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79
- 005-section-absolute-dimensionless-metrology-from-the-bounda.tex lines 65–128
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/005-section-absolute-dimensionless-metrology-from-the-bounda.tex
b19c58deb3ee905c16e659dd26b15ca8d1998bab6f703cd350e04e54129a9a4c
finding:three-moments-select-one-exponential-exactly-in-positive-laplace-class