Year: 2008
Type: preprint
Abstract: A propagator-based fermionic construction must satisfy positivity before its kernel can define canonical anticommutation relations (CAR). We examine a specified massless Dirac kernel on fixed-cardinality sprinklings into a two-dimensional Minkowski diamond. Its nonzero Hermitian finite matrix has zero diagonal and is therefore necessarily indefinite. We test smooth smeared forms against a positive continuum reference and assess sign-symmetric small-magnitude spectral cuts. An exploratory ensemble and an independent-seed replication each use six realisations at N = 1000, 2000, 4000, with three paired bump widths. Every tested uncut range bank is positive, whereas every nonempty product-bank cut retains resolved negativity. In the replication, the thirteen fixed range-part functions have mean negative-to-positive spectral weight ratios of 1.263–1.297% at N = 4000. No endpoint decrease in their negative-weight median or 90th-percentile spectral location is detected under the prespecified rule. One function does flag a decrease in the weight ratio, so only three of four replication criteria pass. The failed criterion is retained; no plateau or positive asymptotic admixture is established. Original-batch exploratory diagnostics show cuts removing compensating positive null-sector weight and damaging the full signal through null and cross terms; these mechanism diagnostics were not replication criteria. The results motivate controlled range restriction as a separate project, while leaving growing-bank positivity, state selection and continuum admissibility open. Contents of this record- The manuscript (PDF) and its LaTeX source, figures and tables.- Full raw result files for both batches: the original seed-20260927 run and the independent-seed 20260929 replication. Each file is identified by SHA-256 in the manifests and in Appendix D of the paper.- The unchanged experimental script fsj_spectral_cut_v3_4.py (fsj-spectral-cut-3.4.0; SHA-256 28fb915d681b3b6d74e8bab38f7ffb43a4bc694c5ec48b593853730eeb8b5e08).- The frozen replication protocol, the original and amended evaluators, the evaluator failure log and amendment record, and the replication evaluation.- Extraction scripts (build_evidence.py, build_replication_evidence.py, build_occupancy.py, extract_raw_spectrum.py, build_bank_illustration.py), their evidence JSON files, and SHA-256 manifests.The README describes how to regenerate every table and figure from the raw files. LicensingThe paper, data, figures and documentation are released under Creative Commons Attribution 4.0 International (CC BY 4.0). The Python code is released under the MIT License. Both licence texts are included in the archive
Source: arXiv (Cornell University)
Author: Sverdlov, Roman
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1522054559