Uniform split reliability v1.0.0 — unrefereed candidate

Uniformly most split reliable graphs — v1.0.0

Unrefereed mathematical candidate · Anonymous · 18 October 2026

This work classifies when a connected simple two-terminal graph can maximise
split reliability for every common edge-retention probability. For every n >= 7,
the written proof resolves existence outside two edge counts. Exact finite cone
certificates, small-order base cases and the written reduction complete the
classification through n = 51.

A further analytic theorem proves the sufficient cone comparison at every cone
order N >= 7 on [1/2,1], together with an explicit positive-length interval near
zero in the target family. The intervening probability range and the two uniform
boundary cases at unrestricted orders remain unresolved. No complete all-order
boundary solution or terminal-isomorphism classification is claimed.

Inspect and reproduce

The archive contains the self-contained manuscript, source code, historical data
and logs, exact checking scripts, claim-to-file AI index, source audit and explicit
assurance/licence records. Compile the C checker from source; no prebuilt binary
is included. verification/reproduce.sh distinguishes a bounded quick check
from the full N=7..50 finite cone replay, in both normal and optimized Python.

Graph-corpus completeness is inherited from the documented supplied enumeration,
not newly established by replaying arithmetic. Historical logs are not silently
represented as fresh runs. The universal written arguments and imported
literature theorems are distinct from finite computational checking.

There is no external peer review, unaffiliated reproduction, proof-assistant
verification or exhaustive novelty clearance. The model is not an empirical
reliability guarantee for physical networks.

Assets: uniform-split-reliability-v1.0.0.zip, split_reliability.pdf,
SHA256SUMS.txt. Original prose/data are CC0-1.0; original executable code is
MIT; external dependencies retain their terms.

Version DOI: https://doi.org/10.5281/zenodo.23450265 .
The published Zenodo record and all three public assets have been read back;
full downloads from both GitHub and Zenodo match the frozen local hashes.