# Verification report: four-point stress-sign stratification

Author: Alper Ferudun, Mercury Software GmbH. Version 1.0, 6 October 2026.

## Precisely accepted claim

The seven-page manuscript proves a complete classification of all connected
stress-sign strata of B_3(K_4), including coincident and collinear points,
their dimensions and their entire closure order. There are 65 strata,
800 strict closure incidences and 207 Hasse edges. For d>=4 the same
description has one connected top stratum and hence 64 strata.

This completes only the four-point component of Karpenkov's Problem 1.
Neither B_2(K_6) nor B_3(K_5) is resolved here. The original multi-part
AMR-068-0001 source record is not claimed fully closed.

## Proof and self-audit

The analytic proof derives the stress-space dimension from symmetric
stress matrices, recovers the dependence signs at affine rank two and
ordered coincidence partitions at rank one, and proves connectedness
and dimensions by explicit parameterizations. Necessity of the boundary
rules follows from normalized affine dependences and weak orders. An
explicit rank-two matrix perturbation proves sufficiency, including
degenerations to collinear and coincident configurations. Thus the
closure claims do not rest solely on finite enumeration.

The originating researcher's detailed self-audit found no unresolved
mathematical gap within that scope. This is not peer review or formal
verification. AI tools assisted literature navigation, algebraic checks,
drafting and self-audit; responsibility for the manuscript remains with
the author. The paper itself discloses this assistance in ordinary prose.

## Reproducible finite checks

The standard-library Python checker uses rational Fraction arithmetic,
not floating point. Two runs produced byte-identical report and poset
files. They enumerate all 65 combinatorial representatives, test the
800 strict incidences and 207 Hasse edges, and check 1,587 exact planar
boundary samples, 1,200 integer-grid configurations and 37 positive
diagonal isomorphisms for collinear fibers. These finite checks
supplement, but do not prove, the continuum classification. Repeating
the same checker is not independent computational verification.

Reproduce with:

    python3 reproducibility/check_four_points.py --output /path/to/fresh-output

The machine-readable reports and full poset are under
`reproducibility/computations/`. File hashes are recorded in the package
manifest and source-archive manifest.

## Sources, limitations and presentation checks

The definitions and earlier planar classifications are credited to
Doray, Karpenkov, Schepers and Servatius. The 2018 primary problem
statement, rather than conflicting frozen dataset metadata, fixes the
scope. A bounded primary-source search found no matching full spatial
classification, but absolute novelty and priority remain uncertified.
Third-party source PDFs are not redistributed.

The native editor compiled the saved source successfully. The exported
PDF has seven pages and zero TeX warnings. Every final page was visually
inspected: no clipping, overlap, missing mathematical symbols or
unresolved references were found. Only the author's name appears in
the title block; affiliation and contact are in the footnote.