Aug 2026· Zenodo (CERN European Organization for Nuclear Research)
Abstract
This record contains the corrected deterministic implementation freeze for HLV-R-MECH-001. The controlling scientific protocol is: Krūger, M. (2026). HLV-R-MECH-001: Prospective Triangle-Matched Mechanism Test of the Surviving Degree-Preserving Rewire Spectral Residual — Pre-Execution Protocol Freeze v0.1.0. Zenodo. DOI: 10.5281/zenodo.22166283 The public predecessor implementation is: Krūger, M. (2026). HLV-R-MECH-001: Deterministic One-Click Engine for Triangle-Matched Rewire Mechanism Testing — Implementation Freeze v0.1.0 [Computer software]. Zenodo. DOI: 10.5281/zenodo.22166434 Version v0.1.1 corrects only the numerical-runtime bootstrap of the One-Click Colab launcher. The first locked execution under v0.1.0 terminated before any scientific evaluation because the assigned Google Colab runtime exposed: NumPy 2.1.3 SciPy 1.16.3 while the frozen scientific implementation requires: NumPy 2.3.5 SciPy 1.17.0. The resulting machine state was: RMECH001_INCONCLUSIVE_NUMERICAL with spectral_computation_started = false. Therefore the stopped execution did not evaluate the confirmatory R_DEG or R_TRI spectra, did not compute target QSPEC or RRESP scores, and did not produce a scientific HLV-R-MECH-001 mechanism verdict. The scientific engine itself has not been changed. The v0.1.1 launcher contains the exact byte-identical scientific engine used in public implementation freeze v0.1.0. Frozen scientific engine SHA-256: 317df650991120f686768ffc07d12f044f58e38ce8f2c47c083901bf1d7a8a14 The corrected launcher now performs the following runtime bootstrap before starting the unchanged scientific engine: 1. inspect the assigned host numerical environment; 2. if the host already provides exactly NumPy 2.3.5 and SciPy 1.17.0, use that environment directly; 3. otherwise create an isolated Python virtual environment; 4. install exact binary versions: NumPy 2.3.5 SciPy 1.17.0; 5. verify the installed versions explicitly; 6. verify the embedded scientific-engine SHA-256; 7. only after these checks execute the unchanged frozen HLV-R-MECH-001 scientific engine. The correction occurs entirely outside the scientific engine. No scientific rule has been modified. In particular, v0.1.1 does not change: - the DG-001 target; - the target graph identity; - the R_DEG control family; - the R_TRI control family; - confirmatory seed streams; - candidate ordering; - accepted-swap counts; - proposal caps; - structural admission rules; - the 40–45% edge-replacement-depth requirement; - the 31-control family size; - exact degree-sequence preservation; - exact global triangle preservation T = 6960 in R_TRI; - the between-family rewiring-depth gate; - QSPEC; - RRESP; - spectral bands; - leave-one-out scoring; - the robust-margin threshold; - numerical scientific hard gates; - or scientific machine-verdict logic. The frozen mechanism design therefore remains identical to the controlling protocol DOI 10.5281/zenodo.22166283. The two confirmatory control families remain: R_DEG: fresh degree-preserving structural rewires of the fixed DG-001 target graph. R_TRI: fresh rewires preserving both the exact labelled target degree sequence and the exact global triangle count T = 6960. Each family requires 31 accepted controls. The structural firewall remains unchanged: the complete R_DEG and R_TRI control banks must be generated, structurally validated, written to disk, and hash-fixed before any confirmatory spectral calculation is permitted. No control may be admitted or rejected using eigenvalues, QSPEC, RRESP, spectral-band distances, target-control scores, or scientific verdict information. The corrected implementation was validated only with burned development seeds and synthetic numerical checks. Correction validation confirmed: - exact protocol verification: PASS; - NumPy 2.3.5 / SciPy 1.17.0 environment validation: PASS; - burned R_DEG generation: PASS; - exact labelled degree-sequence preservation: PASS; - burned R_TRI generation with 10,000 accepted swaps: PASS; - exact triangle preservation T = 6960: PASS; - connectivity: PASS; - approximately 40–45% edge replacement: PASS; - deterministic replay: PASS; - synthetic QSPEC/RRESP implementation checks: PASS. No confirmatory HLV-R-MECH-001 seed stream was used during correction validation. No confirmatory target spectrum was computed. No confirmatory target QSPEC or RRESP score was computed. No scientific HLV-R-MECH-001 verdict was generated. The corrected One-Click notebook SHA-256 is: e8d1f516bc7a600039b44a7f2de8bdf5ecdc51a739d39aaf1e839d97d7e4bc95 The corrected implementation-freeze PDF SHA-256 is: e75aee3a4c790fefafda41aee93c6c267c814b66739bd1070355b519eb98452c The corrected implementation package SHA-256 is: d6e2d6ef3bf0b315bcbf7270c3be591bca28b7c13ef5730af30cb9bbead70b0f The unchanged scientific engine SHA-256 is: 317df650991120f686768ffc07d12f044f58e38ce8f2c47c083901bf1d7a8a14 This record supersedes implementation freeze v0.1.0 only with respect to numerical-environment bootstrapping. It does not supersede or alter the scientific protocol. HLV-R-MECH-001 remains a finite graph-mechanism test. Neither this corrected implementation nor any later HLV-R-MECH-001 result can by itself establish unique HLV geometry, physical selection of the golden ratio, extra dimensions, spacetime, particle physics, an absolute energy scale, gravity, dark matter, dark energy, cosmology, or experimental validation. The purpose of this corrected implementation freeze is solely to ensure that the prospectively frozen scientific engine can execute in a numerically reproducible environment despite changes in the externally assigned Colab runtime.
This paper investigates a dynamic heterogeneous mobile edge computing network (HMECN), where mobile devices (MDs) could offload their full tasks to a small base station (SBS) directly or the macro base station (MBS) in direct or relay mode. As age of information (AoI) is a comprehensive and accurate metric to capture the freshness of computation results, we formulate a long-term weighted sum AoI (LWSA) minimization problem in the HMECN by jointly optimizing the offloading decisions of MDs as well as the bandwidth and computation resource allocation of all base stations, subject to energy, delay and peak AoI constraints. To address the formulated non-convex mixed integer nonlinear programming problem, we decompose it into the offloading decision optimization (ODO) top-problem and the resource allocation optimization (RAO) sub-problem. Based on the decomposition, we propose a federated learning (FL)-assisted hybrid DRL and convex approach that is comprised of a safe multi-agent DRL algorithm, convex optimization and FL. The ODO top-problem is solved by the safe multi-agent DRL algorithm, which strictly ensures that the actions of each agent do not exceed its energy constraint and then paves the way for using convex optimization to solve the RAO sub-problem. FL is used to alleviate the training instability problem aggravated by multi-agent settings via breaking the limitation of partial knowledge for each individual agent. Simulation results demonstrate the superiority of the proposed approach in terms of the LWSA, convergence, scalability and robustness in dynamic environments.
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The deflated-Welch statistic: a closed-form, guaranteed-level test for heteroscedastic one-way ANOVA William J. Dwyer, MD, MPH, FAAP — Department of Mathematics and Statistics, University of Massachusetts Lowell. ORCID 0009-0004-0855-7222. Concept DOI (always resolves to the latest version): 10.5281/zenodo.21908169. What this is The reproducibility deposit for the deflated-Welch statistic T_BB, a closed-form, guaranteed-level test for heteroscedastic one-way ANOVA (the Behrens–Fisher problem for k ≥ 3 groups). Welch's test becomes liberal under skew and unstable variance weights at small samples; T_BB = Q(s²)·exp(−R) keeps the ordinary group means and buys a guaranteed level by deflating the Welch quadratic by a Berger–Boos scale-inflation radius R. Three operating points are provided: a fixedcalibrated radius (κ_s), a design-adaptive near-guarantee radius (closed-form polygamma Cornish–Fisher with a finite-nkurtosis guard), and a fully proved smallest-eigenvalue radius R_eig (Gaussian, extended under bounded kurtosis). What the deposit contains Manuscript (author + anonymized) and a derivations supplement (DA1–DA13) plus a long-form derivations companion, covering: why Welch fails under skew in closed form; the Berger–Boos deflation and its exact worst-case radius; the polygamma-cumulant Cornish–Fisher radius with saddlepoint-exact normal backbone; the excess-kurtosis tail term with its finite-n upper-confidence guard; the imbalance correction; the fully proved smallest-eigenvalue radius (with the k-group multiplicity fix, free-β optimization, and the proved-under-bounded-kurtosis widening); and the k-sample Behrens–Fisher null distribution. Interactive demonstrator rerun_cochran/honest_anova.html — computes raw-mean Welch, the fixed / adaptive / proved T_BB radii, the estimand-changing transform routes, and the full routing receipt in the browser, reproducing the deposited Python. Its engine is extracted as a standalone Node module (m01A_anova_engine.js) and checked cell-by-cell against Python across an 84-design taxonomy (verify_anova_engine_taxonomy.py/.js, max |Δp| = 0.00000). Reproducibility scripts (rerun_cochran/, rerun/) — every reported number traces to a named, deterministically-seeded script (size/power/surface, the calibration and information-limit decompositions, the proved-radius verification, the imbalance calibration, the skew-router branch, and the figures). Real-data evidence — anova_flip_scan.py scans 2,783 public one-way layouts (254 datasets): guaranteed T_BBwithholds ~41% of Welch-significant calls, concentrated where the weight-instability screen fires, and never manufactures significance (Table 7 / Figure 15). Figures and the deterministic deposit builder (fixed timestamps → stable md5). All evaluation is simulation-based; the one empirical component is the public-dataset scan, which uses only openly distributed data. Code is released under the MIT License; text and figures under CC BY 4.0. Version history (consolidated changelog) Published version DOIs are marked ✅; the concept DOI above always resolves to the latest. Staged versions were rolled into the next published one unless noted. v1.0.77 ✅ 10.5281/zenodo.22167690 (2026-08-30): CSDA guide-for-authors conformance — abstract trimmed to 247 words (from 284), keywords cut to 7 (from 11), the withholding highlight shortened to ≤85 characters, and the arXiv PDF/source regenerated. No change to methods, results, figures, or code. v1.0.76 ✅ 10.5281/zenodo.22167536 (2026-08-30) — AI-disclosure heading aligned to Elsevier. The manuscript's declaration heading is now "Declaration of generative AI and AI-assisted technologies in the manuscript preparation process" (was "Use of generative AI"); the disclosure body is unchanged. Prepared alongside an Elsevier-compliant cover-letter variant and an EM suggested-reviewer sheet (both kept outside the deposit). docx/pdf rebuilt; deterministic md5 refreshed. v1.0.75 ✅ 10.5281/zenodo.22167304 (2026-08-30) — Submission-sharpening pass. Graphical abstract + Elsevier Highlights; figures and tables renumbered into reading order with per-table Source clauses; the validity–power frontier (Figure 8) now carries the proved R_eig operating point (100% validity, size-adjusted power 0.613, merge_tbb_proved_frontier.py); new Section 7 "Recovering power by design" + Table 8 (rc_anova_power_by_design.py); and a live required-n calculator in honest_anova.html (per-group and total n for 80% power, "power now @ total n"), with a numeric-heading CSS fix and the engine re-verified against Python at 0.00000. v1.0.74 ✅ 10.5281/zenodo.22165892 (2026-08-29) — Proved-under-bounded-kurtosis radius (DA12.6). The proved non-normal widening now keys on excess kurtosis, √(1 + κ̂·(n−1)/(2n)), from the exact Var(s²/σ²) = 2/(n−1) + κ/n, so symmetric heavy tails (Student-t) are covered where the old skew form √(1 + 0.75·skew²) under-covered; tbbProvedswitched to the kurtosis form across the demonstrator, engine, and Python truth (re-verified JS-vs-Python at 0.00000); new rc_anova_kurtosis_proof.py + deep-dive. v1.0.73 ✅ 10.5281/zenodo.22165709 (2026-08-29) — Reconstructed & verified demonstrator engine (standalone Node module + taxonomy verifier, max |Δp| = 0.00000 across 84 designs; Yuen zero-variance fix; T_BB-routed presets both directions); series-impact deep-dive (the corrected R_eig k-group multiplicity gap also reaches m03 and m01t). v1.0.72 (2026-08-29) — Title set to "The deflated-Welch statistic…"; corrected + optimized proved radius R_eig (β/k multiplicity fix + β-optimization, DA12); real-data Welch-vs-T_BB flip scan (2,783 layouts; Table 7 / Figure 15) + demonstrator imbalance-factor fix; long-form derivations companion. v1.0.71 / v1.0.70 (2026-08-21) — Zhang normal-reference comparator benchmarked on the efficiency frontier (valid on only 24% of designs, in the calibrated-liberal cluster); k = 2 adaptive-radius case-study fold (design-scaling vs shape-keying distinction). v1.0.69 ✅ 10.5281/zenodo.22035826 (2026-08-20) — HTML R1/R2 presentation pass + Figure 9 adaptive per-cluster label merge. v1.0.68 ✅ 10.5281/zenodo.22033737 (2026-08-20) — Companion consolidation into a single six-column Table 6; Figures 11–14 harmonized into one story. v1.0.67 / v1.0.65 / v1.0.60 (2026-08-19/20) — Guarded-reference naming-collision fix; the 40,000-replication expanded-frontier pin (Table 3 + Figure 8) with the symmetric-heteroscedastic skew-router branch; the mean-preserving lightened-R_eig do-not-use fallback. v1.0.59 ✅ 10.5281/zenodo.21995320 (2026-08-18) — Reporting standard + honest_anova.html demonstrator re-aligned to the current T_BB methods paper. v1.0.57 ✅ 10.5281/zenodo.21986847 (2026-08-17) — Reviewer-comprehension pass (multi-paragraph abstract, contributions list, trimmed captions); proved radius R_eig added as a Table 3 scorecard row; corner tail-index correction (N−k)/2 (low-order moments exist in every deployed design). v1.0.56–v1.0.49 (2026-08-16) — The k-sample Behrens–Fisher corner-distribution program: two-moment scaled-χ² corner reference, derived corner cumulants, the secular-eigenvalue law + closed CGF + power-law tail, consolidated into derivations DA13 with a prior-art/novelty audit. v1.0.48 ✅ 10.5281/zenodo.21963458 (2026-08-16) — The unifying λ(z) correction (a smooth instability-keyed deflation strength). v1.0.45 ✅ 10.5281/zenodo.21962965 (2026-08-16) — Atomic sparsity index + bootstrap-t edge hardening + shape-aware pooled standardized-residual bootstrap (SA-PSRB); multivariate transfer to m03. v1.0.44–v1.0.41 (2026-08-16) — Shape-moment re-injection order (skew is the sweet spot), validated and hardened pooled standardized-residual bootstrap, atomic weight-noise probes. v1.0.40 ✅ 10.5281/zenodo.21961667 (2026-08-16) — Log-domain weight-stabilization probe (negative for stabilization; clarifies the size-adjusted oracle ceiling); includes the oracle-power gap decomposition (≈92% conservatism, ≈8% estimation). v1.0.37 ✅ 10.5281/zenodo.21961327 (2026-08-16) — Residual-bootstrap qualification of the shoot-out + the first proved Gaussian smallest-eigenvalue radius R_eig (DA12, the p = 1 specialization of the m03 theorem). v1.0.36 (2026-08-15) — Figure 11 T_BB-region colour fix (amber, matching the routing figures). v1.0.27 ✅ 10.5281/zenodo.21908170 — Earlier published baseline of the deposit. Provenance: every number traces to a named, deterministically-seeded script listed in the manuscript Declarations; the demonstrator engine reproduces the deposited Python to max |Δp| = 0.00000 across the taxonomy verification. License. Code and scripts in the deposit are released under the MIT License; text and figures under CC BY 4.0. Reuse is permitted with attribution to the author and citation of the concept DOI above. How to cite. Dwyer, W. J. The deflated-Welch statistic: a closed-form, guaranteed-level test for heteroscedastic one-way ANOVA. Reproducibility deposit, Zenodo. https://doi.org/10.5281/zenodo.21908169
William Dwyer· Zenodo (CERN European Organi...· 2 citations
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