Aug 2026· Zenodo (CERN European Organization for Nuclear Research)
Abstract
This record contains the prospectively frozen scientific protocol for HLV-R-MECH-001, a mechanism-focused successor test motivated by the surviving degree-preserving rewire residual observed in earlier HLV specificity studies. HLV-R-MECH-001 is not a retry of full HLV carrier specificity. The previously published DS-SPEC-001R overall verdict remains permanently: DSSPEC001R_FAIL_PARTIAL_SIGNATURE_OR_FAMILY_ONLY The purpose of the present protocol is narrower: to test whether the previously observed R-family graph-spectral separation reproduces under fresh degree-preserving controls at matched structural perturbation depth, and whether that separation collapses when the exact target triangle count is additionally preserved. The protocol is motivated by an explicitly exposed exploratory result from HLV-R-MECH-DISC-001. For the DG-001 target: N0 = 1110 N1 = 5345 N2 = 6960 graph triangle count = 6960 The exploratory analysis verified that the complete set of 6960 graph triangles is exactly identical to the set of 6960 DG-001 two-cell face vertex-triples. By contrast, the earlier degree-preserving DS-SPEC R controls contained on average only approximately 285.74 triangles, corresponding to a mean retention of about 4.1% of the target triangle count. This exposed observation is not treated as confirmatory evidence. It is used only to define the new prospectively frozen mechanism question. The protocol defines two fresh control families. R_DEG: fresh degree-preserving rewires that preserve - the exact labelled target degree sequence; - N0 = 1110; - N1 = 5345; - graph simplicity; - connectivity; - and a frozen edge-replacement fraction between 0.40 and 0.45. The global triangle count is not constrained in R_DEG. R_TRI: fresh degree-preserving rewires that preserve all R_DEG constraints and additionally preserve the exact global triangle count T = 6960. Both families require 31 accepted controls. The two families are also required to have matched perturbation depth: the absolute difference between their median edge-replacement fractions may not exceed 0.02. If that condition fails, no spectral mechanism inference is permitted. The mathematical motivation is especially strong because for a simple graph with graph Laplacian L = D - A, the following exact identities hold: Tr(L) = sum_i d_i Tr(L^2) = sum_i d_i^2 + sum_i d_i Tr(L^3) = sum_i d_i^3 + 3 sum_i d_i^2 - 6T. Therefore degree preservation fixes the first two raw Laplacian moments, while simultaneous degree and exact triangle preservation also fixes the third raw Laplacian moment. Accordingly, every accepted R_TRI control matches the target in Tr(L), Tr(L^2), and Tr(L^3) exactly. This does not imply matching of the full spectrum, lambda_max, scale-quotiented eigenvalue distribution, QSPEC, or RRESP. The primary spectral observables are inherited unchanged from the published DS-SPEC-001R recovery protocol: Krūger, M. (2026). HLV-DS-SPEC-001R: Prospective Recovery of the Native 6D-to-3D Carrier Spectral-Specificity Gate After Q-Control Capacity Stop — Pre-Execution Protocol Freeze v0.1.0. Zenodo. DOI 10.5281/zenodo.22162097. The two frozen primary signatures are: QSPEC and RRESP. No new spectral feature is selected from the exposed R-MECH discovery result. For each family and signature, the target must satisfy all of the following to obtain a signature PASS: 1. target distance must exceed the maximum leave-one-out control distance; 2. the robust target-to-control margin must be at least 1.50; 3. at least two of the three prospectively frozen spectral bands must exceed the corresponding maximum leave-one-out band distance. A family PASS requires both QSPEC and RRESP to pass. The primary mechanism verdicts are frozen as follows. RMECH001_PASS_TRIANGLE_MATCH_COLLAPSE_PATTERN requires: R_DEG family PASS and R_TRI QSPEC FAIL and R_TRI RRESP FAIL. This result would support the conclusion that exact global triangle matching removes the previously observed robust R-family spectral separation under the frozen generator and perturbation-depth contract. It would not prove that triangle count alone is the unique causal invariant, because triangle preservation may simultaneously preserve correlated local structure. RMECH001_FAIL_TRIANGLE_SUFFICIENCY_RESIDUAL_SURVIVES requires: R_DEG family PASS and R_TRI family PASS. This result would show that degree sequence plus exact global triangle count are insufficient to eliminate the surviving R-family spectral residual. It would motivate stronger successor controls involving local triangle profiles, short cycles, graph motifs, or higher-order incidence structure. RMECH001_PARTIAL_SIGNATURE_DEPENDENCE_AFTER_TRIANGLE_MATCH is returned if R_DEG passes but exactly one of the two R_TRI signatures passes. If the fresh R_DEG family does not reproduce the previous degree-preserving separation, the result is: RMECH001_INCONCLUSIVE_FRESH_RDEG_BASELINE_NOT_REPRODUCED. Additional frozen inconclusive states cover insufficient control capacity, rewiring-depth mismatch, numerical audit failure, source mismatch, or protocol invalidation. The control-generation process is fully prospectively specified. R_DEG seeds are generated from: seed = 730100000 + offset for offsets 0 through 127. R_TRI seeds are generated from: seed = 730200000 + offset for offsets 0 through 127. Candidates are evaluated in increasing offset order, and the first 31 structurally admissible controls are accepted. If fewer than 31 controls are accepted in either family by offset 127, the run becomes inconclusive for control capacity. Previously exposed pilot and development seeds are permanently excluded from confirmatory use. A hard feature firewall is part of the protocol. No eigenvalue, lambda_max, QSPEC, RRESP, spectral band, target-control distance, leave-one-out score, or scientific mechanism verdict may be computed until both complete 31-member structural control banks have been: - generated; - structurally validated; - written to disk; - and hash-fixed. Control admission therefore cannot depend on spectral information. The protocol also freezes numerical identity and eigensolver checks, including trace identities, Frobenius consistency, connected-graph zero-mode checks, nonnegative-spectrum tolerance, and cross-solver eigenvalue audits on the target and selected controls. Secondary diagnostics are declared in advance but are non-load-bearing. These include: - triangle count and transitivity; - average clustering; - per-vertex triangle-count distribution; - four-cycle count; - degree assortativity; - k-core summaries; - Tr(L^4)/N; - lambda_2; - lambda_max. They may be inspected only after the structural control banks are frozen and may not alter the primary verdict. Controlling provenance: DG-001 locked results: DOI 10.5281/zenodo.22107618 DS-SPEC-001R recovery protocol: DOI 10.5281/zenodo.22162097 DS-SPEC-001R corrected implementation freeze: DOI 10.5281/zenodo.22164304 DS-SPEC-001R locked results: DOI 10.5281/zenodo.22165100 HLV Mathematical Core v2.1.4: DOI 10.5281/zenodo.22165745 The pre-freeze technical triangle-preserving pilot produced 12/12 structurally valid controls, each preserving the exact target degree sequence and exact triangle count T = 6960 while replacing approximately 41.3%–42.5% of target edges. No QSPEC, RRESP, spectral-specificity score, or scientific mechanism verdict was calculated during that pilot. The pilot is therefore treated strictly as technical feasibility evidence. HLV-R-MECH-001 does not test or establish: - unique HLV geometry; - physical selection of the golden ratio; - a unique 6D-to-3D microscopic substrate; - spacetime; - extra dimensions; - particle masses; - an absolute HLV energy scale; - gauge interactions; - gravity; - dark matter; - dark energy; - cosmology; - or experimental validation. The allowed scientific claim is narrower: HLV-R-MECH-001 prospectively tests whether the previously observed degree-preserving graph-spectral residual can be explained, removed, or further localized by exact matching of the target's global triangle/face count while controlling perturbation depth. Any stronger interpretation requires a separately frozen successor experiment.
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.
Xiaoying Liu, Junhao Zheng, Kechen Zheng et al.· IEEE Transactions on Mobile...· 8 citations
High-altitude airships (HAS) and uncrewed aerial vehicles (UAVs) equipped with Multiaccess Edge Computing (MEC) servers have emerged as promising aerial MEC nodes for providing task offloading (TO) services to intelligent mobile devices (IMDs) in post-disaster scenarios. HAS offers robust computing and energy resources, while UAVs provide flexible, low-altitude coverage for rapid deployment. However, direct task offloading from IMDs to HAS often leads to task failures due to high transmission delays. UAVs with limited onboard resources require to minimize resource waste. Additionally, IMDs in sparse areas face insufficient TO services due to unfair UAV coverage. This paper defines these challenges as a joint optimization problem involving TO, RA, and UAV coverage fairness. It proposes a cooperative aerial Multiaccess Edge Computing (AMEC) framework integrating HAS and UAVs to address the issue. Within this framework, a hybrid TO scheme is first developed to mitigate the high transmission delay between IMDs and HAS. Second, a Distance, Resource, Urgency-based Decision Mechanism (DRUDM) is designed to enhance the accuracy of UAVs in selecting target IMDs for TO services. Third, a Coverage Fairness Guarantee (CFG) strategy is proposed to optimize UAV flight trajectories, ensuring IMDs in sparse areas receive fair TO services. Finally, the joint optimization problem is modeled as a Multi-Agent Partially Observable Markov Decision Process (MA-POMDP), and a DRUDM–CFG algorithm is presented to efficiently solve this complex non-convex optimization problem. Experimental results demonstrate that the proposed algorithm outperforms other compared algorithms in task completion rate and average delay, benefiting from the DRUDM mechanism. Meanwhile, the CFG strategy effectively improves TO service fairness for IMDs in sparse areas.
Xiting Peng, Chuanqi Qin, Xiaoyu Zhang et al.· IEEE Transactions on Mobile...· 4 citations
Hyperbolic surfaces are a fundamental object in mathematics and play an increasingly important role in computational geometry and topology. A key ingredient in the design of efficient algorithms on such surfaces is the availability of a geometric discretization of controlled complexity. In this paper, we present the first algorithm for constructing e-nets on hyperbolic surfaces starting from a fundamental polygon representation. Our approach is based on Delaunay refinement and relies on maintaining Delaunay triangulations through edge flips. The size of an e-net cannot be bounded solely as a function of the genus because of the presence of arbitrarily long collars around short geodesics. To overcome this difficulty, we introduce the notion of a pseudo e-net, which decomposes the surface into e-thin cylinders together with a Delaunay triangulation over an e-net of the remaining thick part. As applications, we obtain algorithms for computing the length spectrum of an e-thick hyperbolic surface and for computing the systole from a pseudo log(sqrt(2))-net. These results demonstrate that Delaunay-based discretizations provide a practical and versatile framework for algorithmic computations on hyperbolic surfaces.
V. Delecroix, Vincent Despré, Camille Lanuel et al.· 3 citations
Future 6G networks are envisaged to tightly integrate communication, sensing, and computing, demanding real-time, intent-driven intelligence at the edge. While large language models (LLMs) excel in intent recognition and semantic reasoning, their application to real-time network lifecycle management at the edge is limited by heterogeneous application intents (APPIs), dynamic network conditions, and severe resource constraints. This paper proposes a novel lightweight LLM architecture, KGLlama-KD, that synergizes knowledge graphs (KGs) with knowledge distillation (KD) to enable intent-driven networking and enhance 6G edge intelligence. Specifically, a KG is constructed to formally describe the relationships among application scenarios, functional primitives, performance requirements within APPIs, and the correspondences between APPIs and network service requests (NSRs), thereby producing a structured intent training dataset. Building upon the Llama 3 foundation model, a two-phase optimization framework is designed to support lightweight edge deployment while preserving translation fidelity. The LLM is first fine-tuned with KG guidance and compressed via KD in the cloud, and then deployed on resource-constrained edge nodes to perform real-time, accurate, and efficient APPIs interpretation. Experiments validate that KGLlama-KD achieves 95% accuracy for APPI understanding, surpassing DeepSeek and Qwen by an average of 8%. The distilled model reduces inference latency by 60% compared to full-scale LLMs, fulfilling the sub-100 ms requirement for 6G latency-sensitive services.
Bing Wu, Sai Zou, Minghui Liwang et al.· IEEE Transactions on Mobile...· 3 citations
Dispersed computing has emerged as a promising paradigm that leverages underutilized resources from massive Internet of Things devices (IoTDs) to enhance the computing capacity at the network edge. However, existing works about the dispersed computing overlook the heterogeneous computing environment with parallel and serial computations and task reliability requirements for the hardware-constrained IoTDs, and they lack multi-objective optimization approaches to optimize the task offloading. To address the challenges, we propose a comprehensive scheme to achieve a delay-aware and economic-aware dispersed computing paradigm by using a multi-objective optimization approach. Particularly, we consider parallel processing at an edge server and serial processing at the lightweight IoTDs, and leverage the task redundancy to satisfy the task reliability requirements on the IoTD side. We further formulate a constrained multi-objective optimization problem (CMOP) aiming at jointly optimizing the task assignment, bandwidth allocation, and CPU frequency allocation to simultaneously minimize the total delay cost and the total charge cost of the tasks. To address the CMOP, we propose an improved constrained multi-objective evolutionary algorithm that employs a dual-population cooperative mechanism between two populations and a repairing constraint-handling technique. The dual-population cooperative mechanism can balance convergence toward Pareto optimality and solution diversity maintenance. The repairing constraint-handling technique is designed to guide solutions toward feasible regions, achieving efficient exploration of complex constrained search spaces. Simulation results demonstrate the superiority of our algorithm in seeking the better-converged and better-distributed Pareto optimal solutions to well address the tradeoffs between the two objectives.
Xumin Huang, Zexiong Wu, Chaoda Peng et al.· IEEE Transactions on Mobile...· 2 citations
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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