Certified Commitment Horizons in Dynamic Lot Sizing: Exact Prefix Stability, Optimal-Face Witnesses and One-Step Forecast Calibration

Summary

Forecasts change after purchasing, production and supplier decisions have begun. This release asks how far demand forecasts may move before an optimal revised lot-sizing plan can stop sharing a protected prefix of setup decisions with the nominal plan.

Version 3.0.0 makes the modelling boundary explicit. Its basic mathematical object is a forced-source path graph, where every complete path begins at period 1. That object has an ordinary uncapacitated Wagner–Whitin interpretation only under the stated classical active-horizon conditions: the first-period demand floor is strictly positive, every later setup cost is strictly positive, reduced slopes are ordered, initial inventory is zero and backlogging is absent.

A retained negative control shows why the distinction matters. With setup costs $(100,1)$, reduced slopes $(1,0)$ and demand $(0,1)$, the forced-source graph costs 101 while the physical model can wait until period 2 and costs 1. Classical mode rejects that instance.

Within the declared domain, the candidate supplies exact fixed-path tie distances, an exact-rational frozen-comparator lower certificate, certified brackets, a prefix-to-arc decomposition and a single-detour optimal-face theorem. The software reports exact values, certified intervals, guarded refusals and solver-only outcomes separately.

Status: Anonymous · unrefereed theoretical-computational candidate. Producer replay, CI, finite audits and internal editorial review pass. Independent reproduction, proof-assistant verification, external specialist review, journal peer review, exhaustive priority and field validation have not occurred.

The central result

Let a protected nominal setup prefix contain $k$ arcs. The strong commitment radius is the nearest admissible demand revision at which some optimal path can leave that prefix. Version 3.0.0 proves that this radius decomposes as the minimum of at most $k$ one-protected-arc suffix radii.

At every finite nearest loss, the optimal face contains a retaining path and a leaving path that are adjacent and differ on one divergence–remergence interval. This single-detour witness turns a global-looking loss of prefix optimality into a local exact boundary object. The family of possible detours can still be exponential, so the theorem does not settle computational complexity.

For the familiar positive-demand three-period example,

The polynomial frozen certificate is therefore safe but can be conservative for a partial prefix.

What “certified” means here

For a fixed competing path, the candidate derives the exact weighted-$L_\infty$ distance to a cost tie while respecting coordinate demand floors. For a protected prefix, a prefix-deviation directed acyclic graph represents the paths that leave it. The frozen-comparator calculation supplies an exact lower bound; a feasible outside path supplies an upper witness. Coincident bounds close the exact radius.

The interface deliberately preserves unresolved states:

• exact_certified means the lower and upper evidence close to one exact rational value;
• certified_interval means the exact radius lies inside a valid interval but is not closed;
• enumeration_completed_with_certified_interval means all candidates were processed but at least one disjunct remained unresolved;
• refused_by_candidate_guard means a declared finite cap stopped enumeration and no safety conclusion follows;
• solver_level_only means a numerical optimization result lacks the exact evidence needed for certification;
• proven infinity requires either no outside path or a closing exact residual-gap argument.

Evidence and replay

Use the immutable v3.0.0 GitHub candidate release or Zenodo version DOI. The sealed archive SHA-256 is 4d09e03fc3146018e6c11d3dce8ac9e3cb74bcc07bf4564583207a7c01784744.

From a fresh extraction, the quick deterministic replay is:

bash run_all.sh --quick

The release verifier and independent record check are:

PYTHONPATH=src python scripts/verify_release.py --run-tests
python scripts/check_certificate.py \
  examples/sample_decision.json \
  examples/strict_gap_instance.json

The public evidence ledger records:

Python 3.11 and 3.13 GitHub Actions passed. GitHub and Zenodo expose byte-identical copies of the archive, paper, verification receipt and checksum ledger. Finite replay can refute implementation defects; it does not machine-prove the universal theorems.

Statistical and operational boundary

The statistical layer provides one-step marginal split-conformal coverage under exchangeability. It does not provide conditional, adaptive, rolling or time-uniform coverage. A Bonferroni construction gives a finite-family marginal statement under the paper’s assumptions.

The deterministic rolling bound concerns structural loss when quantities may adjust inside retained replenishment cycles. A certified radius protects setup epochs and cycle boundaries, not fixed order quantities. Capacity, service constraints, backlogging, multi-item coupling and behavioural implementation effects are outside the release.

The UCI exercise uses real observed demand but reconstructed forecast vintages and stylised costs. It demonstrates an interface; it does not estimate savings, service improvements, causal effects or field validity.

What the result does not establish

• It does not prove the sufficient classical active-horizon bridge conditions are necessary.
• It does not give an exact polynomial-time algorithm, an NP-hardness result or another complexity classification for the one-protected-arc core.
• It does not turn exact arithmetic, a separate producer checker, finite audit agreement, CI or internal review into independent reproduction or formal verification.
• It does not establish exhaustive novelty or priority. The Richter–Vörös conclusion is a source-specific, hash-bound producer reading inside a targeted literature audit.
• It does not validate the rule in an operating supply chain or establish economic benefit.
• It does not extend to capacitated, multi-item, backlogging, fixed-quantity or service-constrained planning without new analysis.

Who should care, and why

The most valuable next projects

1. Obtain an unaffiliated clean-environment rerun tied to the exact archive hash.
2. Commission an operations-research specialist review of the semantic bridge and setup-cycle interpretation.
3. Reimplement the fixed-path radius, deviation graph, frozen certificate and single-detour audit in a separate codebase.
4. Classify the exact complexity of the demand-induced one-protected-arc problem.
5. Formalize the bridge, graph reduction, tie theorem, decomposition and certificate logic in a proof assistant.
6. Broaden the literature and priority audit with independent attestation.
7. Run a preregistered prospective study with genuine forecast vintages, actual constraints and a predeclared operational comparator.

Version and correction history

Version 3.0.0 supersedes the v2.1.2 research package and active Evidence Press briefing. It repairs the leading-zero-demand semantic counterexample, introduces explicit graph-only and classical modes, corrects an invalid test of monotonicity across independently found unresolved upper witnesses, replaces ambiguous completion labels, adds the prefix decomposition and single-detour theorem, stratifies the compact-model corpus, strengthens the literature boundary, and rebuilds the package under Anonymous scholarly attribution with an explicit CC0/MIT/third-party rights map.

Earlier immutable DOI and Git tags remain part of the concept history; this page points to version DOI 10.5281/zenodo.22086554.

What is in the public package

The sealed archive contains the 40-page manuscript and LaTeX source; exact-rational Python package and version-matched wheel; accessible documentation; examples and decision records; 94 tests; semantic, certificate, equivalence, calibration, rolling and benchmark audit programs and results; source-data provenance; exact claim, operating-model, literature, rights and assurance records; a separately implemented producer-side record checker; fresh-extraction and PDF-quality evidence; internal editorial role reports and confirmation; and the final SHA-256 manifest and verification receipt.

Original research prose, metadata and result tables are dedicated under CC0 1.0. Original code is MIT. The included UCI data retain CC BY 4.0. Third-party literature PDFs used during review are not redistributed. The page art, Open Graph card, transcript, audio and thumbnail are communication aids, not additional research evidence.

@misc{certifiedcommitmenthorizons2026,
  title        = {Certified Commitment Horizons in Dynamic Lot Sizing: Exact Prefix Stability, Optimal-Face Witnesses and One-Step Forecast Calibration},
  author       = {Anonymous},
  year         = {2026},
  doi          = {10.5281/zenodo.22086554},
  url          = {https://doi.org/10.5281/zenodo.22086554},
  version      = {3.0.0-candidate},
  howpublished = {Zenodo},
  note         = {Unrefereed; internally replayed evidence package. Press page: https://evidencepress.org/releases/certified-commitment-horizons/}
}