Verification-domain certificate profiles

This repository provides the validated computational implementation of a theory of positive scalarisation certificates over finite verification domains. For a selected feasible candidate, the central profile is

Gamma_V(B) = max  min_x [lambda^T d(x) + nu^T h(x)]
             s.t. lambda in the simplex, nu >= 0, 1^T nu <= B.

The profile records the best scalar margin achievable over a declared domain when normalised active-constraint multipliers receive budget B. It induces three exact domain classes:

• harmless: the minimum budget is zero
• repairable: a finite positive budget is necessary and sufficient
• irreparable: no finite multiplier budget can certify the candidate

The implementation contains exact rational profile masters, minimum-budget and fixed-budget row generation, structured assignment and layered shortest-path oracles, complete finite-domain baselines, exact augmented-Chebyshev intervals and a standard-library standalone checker.

Status

Version 2.0.1 is the citable post-deposit archival release for the verification-domain profile framework. It preserves the scientific case grid and retained exact evidence of version 2.0.0, while correcting release identifiers, repository metadata and post-deposit validation. The retained exact evidence and the source tree are validated by the included scripts; the GitHub Actions workflow repeats the checks after each push. For manuscript citation, use this release only after the public v2.0.1 GitHub Actions run is green and the Zenodo version DOI has been recorded consistently. Independent physical-machine replication is encouraged and should be recorded using docs/INDEPENDENT_REPLICATION.md.

No universal runtime superiority is claimed. On the retained small correctness cases the full-domain baseline is sometimes faster. On eight larger enumerated scaling cases the numerical full-domain LP was between 3.30 and 30.50 times slower than structured row generation, with a median factor of 7.10. The numerical LP is a timing baseline only; exact row-generation replay is the source of truth.

The profile is unit-invariant, not scale-free. Objective and active-constraint scales are part of the certificate semantics. They must be declared before comparing domains and must transform together with any change of measurement units.

Installation

python -m venv .venv
. .venv/bin/activate
python -m pip install --upgrade pip
python -m pip install -e ".[validation]"

On Windows PowerShell use .venv\Scripts\Activate.ps1.

Fast validation

make validate

The command validates metadata and JSON Schemas, runs the unit suite, replays all 84 minimum-budget certificates and all 196 profile records with the standalone checker, attacks representative objects with resealed semantic mutations and verifies the retained summary.

Full study

make study
make objects
make numeric-baseline
make figures
make validate

The normative case grid is frozen in protocol/COMPUTATIONAL_PROTOCOL.json. Candidate selection is independent of the certificate weight and finite grids are prohibited as ground truth.

Retained evidence

• 84/84 exact classification agreements
• 84/84 exact minimum-budget agreements
• 196/196 exact fixed-budget profile agreements
• 84/84 positive-rescaling invariance checks
• 28 harmless, 28 repairable and 28 irreparable cases
• 24 structured assignment and layered-path cases
• at most 15 structured oracle calls in the correctness corpus
• median 0.904% and maximum 5.79% of challenger outcomes retained
• 36 finite exact Chebyshev thresholds
• median exact/conservative threshold ratio 16.5 and maximum 193.08
• 73 of 84 declared finite budget grids missed the exact minimum budget
• scaling domains up to 177,147 alternatives

Repository structure

• src/mmor_certificates/ — exact masters, profile algorithms and oracles
• checker/ — standalone exact checker using only the Python standard library
• schemas/ — JSON Schemas for instances, certificates and profile records
• protocol/ — frozen computational protocol
• results/instances/ — finite instances bound to retained proof objects
• results/certificates/ — minimum-budget and irreparability certificates
• results/profiles/ — exact fixed-budget profile records
• results/raw/ — case-level numerical and exact evidence
• results/processed/ — aggregate study summary
• figures/ — deterministic publication figures
• validation/ — replay summaries and file manifest
• docs/ — mathematical, algorithmic and evidence contracts
• docs/MIGRATION_v1_TO_v2.md — conceptual, API and archival changes from version 1

Licences

Source code is licensed under BSD-3-Clause. Retained instances, proof objects, results, figures and prose documentation are licensed under CC BY 4.0. See LICENSE, LICENSE-DATA.md and NOTICE.

Archived DOI

Archived version DOI: https://doi.org/10.5281/zenodo.21011691