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Construction-Reuse Trade-offs for Exact Certificates in Fixed-Rank Threshold Screening

Zisu Li, Jingyang Du

arXiv:2609.34424v1cs.CE

TL;DR

Engineering screening returns the first k records meeting changing requirements under a fixed preference order, while remaining distinct from broader qualification work. The paper defines SLA certificates and compares them with other certificates and uncached backends; cheaper construction does not yield a primary full-API improvement, and results remain conditional on workload and scope.

  • Problem

    Engineering selection screens existing records against changing requirements while retaining a fixed preference order, and this screening is only one part of a broader workflow.

    Source: Introduction · p. 1

  • Method

    The paper defines selected-lower, atomic-upper (SLA) certificates for fixed-rank screening and compares them with other certificates and uncached bitmap and NumPy implementations.

    Source: Introduction · p. 2

  • Results

    SLA's construction savings against Cover do not yield a primary full-API improvement, and repeats and configuration exploration show conditional trade-offs rather than a universally superior method.

    Source: Discussion and limitations · p. 17, Conclusions · p. 18

  • Takeaways & Limitations

    The paper concludes that services should measure the complete response contract and compare a strong uncached backend before optimizing certificate geometry alone.

    Source: Discussion and limitations · p. 17

    The results do not establish physical connection qualification, unrestricted novelty, or universal selection speedup.

    Source: S4. Reproduction, provenance and… · p. 25

Abstract

from arXiv · show

Repeated threshold queries may reuse selected identities without reusing stale reports, but cheaper certificates need not shorten the complete response. We study selected-lower, atomic-upper (SLA) certificates for fixed-rank conjunctive screening with explicit missing-information semantics. An endpoint characterization and a counterexample separate same-source containment from policy-dependent online behavior. The original 320-session experiment reduces summed construction medians by 31.18% against an exclusion-cover certificate, yet its Cover/SLA full-API geometric time ratio is 0.9682 (95% conditional blocked interval 0.9593-0.9769), and SLA takes 12.94% more summed time than uncached Bitmap. Three separately launched complete repeats preserve this adverse ordering, with Cover/SLA ratios of 0.9665-0.9718. An additional 720-configuration exploration varies catalogue size, construction period, requested count and query locality on empirically resampled tables. SLA is faster in 295 configurations against Cover and 271 against Bitmap, descriptive counts that do not establish universal superiority. Separately instrumented additive costs distinguish construction savings from retrieval and report costs. A plane-stress component case adds an independent analytical displacement check and 4,608 boundary-challenging queries: five implementations agree exactly, while medium- and fine-mesh selections differ at 459 positions. A state-stratified public bolt-record exercise preserves 185 incomplete positions among 1,479 requests. Raw timings, complete configuration results and a tested clean-environment package support reproducibility. The SLA construction was explored and refined through the self-evolving AI system ZiYor; the named authors specified, implemented and evaluated it. This is a bounded mechanics-to-query study, not physical joint qualification or universal speedup.

Introduction

The paper studies whether certificate construction can be made cheaper for repeated fixed-order screening without sacrificing the complete response. It distinguishes identity reuse from current-report generation and places screening within, but not in place of, broader engineering qualification.

Introduction

  • The screening task returns the first k records satisfying changing requirements under a fixed preference order, but does not replace compatibility, capacity, assembly, or compliance analyses.Its outputs are useful only when those distinctions are preserved.Source: Introduction · p. 1
  • The central question is whether cheaper certificate construction improves complete screening when retrieval already uses an efficient bitmap backend.The paper frames this as a narrower question than whether caching works in principle.Source: Introduction · p. 1
  • Timing only certificate membership can overstate reuse benefits because selected identities may persist while their margins to current thresholds change.A downstream tool still needs a current report, not merely a cached identifier list.Source: Introduction · pp. 1–2
  • The paper compares SLA with atomic-cell and exclusion-cover certificates plus uncached bitmap and NumPy implementations under a shared full-response interface.The candidate SLA construction was explored and refined through ZiYor; the named authors specified, implemented, and evaluated it.Source: Introduction · p. 2
  • The study separates construction cost, fixed-stream geometric coverage, online hits, and complete-response time to explain when local savings do not become end-to-end gains.It adds complete fresh-process repeats, a size/period/count/locality matrix, additive diagnostics, and boundary-focused engineering checks.Source: Introduction · p. 2

Related work and positioning

The paper positions fixed-rank threshold screening within established range top-k and caching work, while distinguishing its certificate and response contract from prior reuse objects. It does not claim a new general caching principle or improved range-search bound.

Related work and positioning

  • Fixed-rank threshold screening and atomic threshold cells are not new; Rahul et al. study weighted orthogonal-range top-k queries and recognize answer invariance between neighboring coordinates.The certificate layer follows an exact retrieval backend and makes no stronger range-search data-structure-bound claim.Source: Related work and positioning · p. 2
  • Prior reuse approaches address distinct objects and query changes, including spatial safe regions, top-k views [5], and cached bitmap segments [3].These are not inferior implementations of the present interface.Source: Related work and positioning · p. 2
  • Other work treats conservative descriptions, reusable empty answers, and cache maintenance [7, 8], while the paper claims no improved dynamic bound or priority for semantic caching.Its distinction is a bounded fixed-rank/report-contract study, not a comparison of complete prior systems.Source: Related work and positioning · p. 2
  • The full text of Ehlers’s thesis was inaccessible for method-level inspection, so overlap with its certificate rules cannot be excluded.The authors therefore state that exhaustive novelty clearance remains unresolved.Source: Related work and positioning · p. 3

Screening contract and exact certificates

The paper defines exact fixed-rank screening with explicit treatment of missing information, then constructs and compares certificates for reusing selected identities. Correctness and online behavior depend on completeness, endpoint conventions, and the construction-permission policy.

Fixed ranking, completeness and current reports

  • A fixed strict ranking and conjunctive upper-bound query determine the first k known-feasible records; unresolved missing records can block completeness even when selected records are feasible.Incomplete results return known feasible records and unresolved identifiers but cannot create a certificate; successful calls produce current reports rather than reusing stale margins.Source: Fixed ranking, completeness and… · p. 3

SLA construction and correctness

  • For a complete source result, every query in the SLA box preserves ordered selected identities and completeness, and its lower endpoint is the selected-coordinate maximum.With fixed atomic upper endpoints, that lower bound is necessary and sufficient; this is not a globally maximal safe region.Source: SLA construction and correctness · pp. 4–5

Exclusion cover, complexity and the digital domain

  • For the same source query, the exclusion-cover certificate contains SLA, while SLA avoids scanning the competing prefix; neither construction bound includes retrieval or current-report costs.A certificate hit still checks bounds and materializes selected fields and margins, and the implementation uses an admissible finite digital domain.Source: Exclusion cover, complexity and the… · pp. 5–6

Equal construction permissions and a counterexample

  • Under the nonaccumulating permission policy, SLA records 61 hits and three misses versus Cover’s 32 hits and 32 misses, despite two builds each.This counterexample rejects an implication from same-source containment to online hit dominance, but does not compare elapsed time.Source: Equal construction permissions and a… · p. 6

Experimental design

The experiments combine observed engineering tables, controlled timing comparisons, exploratory configurations, public bolt records, and a plane-stress plate case. Each workload and timing boundary is specified separately, with explicit limits on what the engineering cases represent.

Data and original matrix

  • The original matrix uses 320 sessions across two engineering tables, with frozen threshold streams and ten technical repeats per method.Airfoil and concrete rankings use measured responses, not predictions or estimates of physical design optimality; the generated thresholds are not measurement noise or physically realizable experiments.Source: Data and original matrix · pp. 6–7

Timing boundaries, repeats and estimands

  • The timing design separates same-source construction measurements from fresh-state online runs, whose full API clock includes retrieval, permitted construction, and report materialization.The original matrix uses ten technical repeats; timing differences are conditioned on the measured host, tables, and generators, with no dedicated idle-host condition.Source: Timing boundaries, repeats and estimands · p. 7

Full supplementary sensitivity and direct diagnostics

  • The exploratory matrix spans 720 configurations and retains all outcomes, while separately instrumented passes measure six additive stages and a residual.Configurations resample the original empirical tables, so increasing catalogue size does not add new physical diversity; descriptive pooled comparisons carry no confidence or multiplicity claims.Source: Full supplementary sensitivity and… · p. 8

State-stratified public bolt records

  • The bolt-record exercise retains all 92 archive specimens, quarantines two conflicting conditions as unknown on derived responses, and defines capacity from finite recorded force-displacement windows.The four analyst-defined windows are not code deflection limits, and satisfying their predicates does not certify one simultaneous loading path.Source: State-stratified public bolt records · p. 8
  • Bolt queries rank by an administrative proxy, enforce exact temperature and fixture, and test answered, empty, and incomplete reports across five methods.The 1,479 retained positions include duplicates; the workload preserves the two quarantined conditions and does not support temperature interpolation or cross-fixture extrapolation.Source: State-stratified public bolt records · p. 9

Verified elastic attributes and decision boundaries

  • The plate verification prescribes exact analytical Kirsch tractions on the quarter-domain and checks plane-stress Q8 solutions against an independent analytical displacement field.The reference case uses three meshes, with finest-grid displacement errors required to be at most 1%; the exact-boundary problem is distinct from the finite-boundary catalogue case.Source: Verified elastic attributes and… · p. 9
  • The finite catalogue contains nine uniformly end-loaded analyst-defined plates, and 4,608 boundary-challenging queries compare five complete reports with scalar enumeration.The probes include neighboring binary64 thresholds, mesh-interpolated attributes, geometry constraints, and no-result cases; medium/fine selection disagreement and envelope ambiguity are distinct, and neither is a certified error bound.Source: Verified elastic attributes and… · pp. 9–10, Figure 2 · p. 10

Results

SLA lowers construction cost relative to Cover, but the original full-API comparison and three complete repeats retain an adverse ordering. Results also span exploratory configurations, mechanics checks, state-stratified bolt queries, and clean-environment recomputation.

Original outcome and three complete repeats

  • 0.9682 [0.9593,0.9769] is the original Cover/SLA geometric ratio; SLA uses 3.10% more summed session-median time than Cover and 12.94% more than Bitmap.Three additional runs retain the adverse ordering, with Cover/SLA ratios of 0.9665–0.9718.Source: Table 4 · p. 11, Original outcome and three complete… · p. 11

Scale, permissions, locality and measured costs

  • 295 of 720 configurations have Cover/SLA ratios above one and 271 have Bitmap/SLA ratios above one; these descriptive counts are not significance-tested wins.The exploration varies catalogue size, construction period, requested count, and query locality; no single certificate is best across all query families.Source: Scale, permissions, locality and… · pp. 11, 14, Table 5 · p. 11
  • 36.80 ms of SLA construction versus 54.99 ms for Cover accompanies 303.69 ms of SLA retrieval versus 230.19 ms for Cover across 40,960 positions.All three repeats have 5,294 SLA hits versus 13,917 Cover hits; the full instrumented totals are 1,584.63 and 1,523.56 ms, respectively.Source: Scale, permissions, locality and… · p. 14, Figure 5 · p. 14

Mechanics and state-stratified functional results

  • The unchanged exact-traction reference reaches 0.00182% finest-grid hole-stress error and 0.01396% profile NRMSE, while displacement errors decrease across the three meshes.Finest-mesh displacement relative L2 errors are 0.0001414% globally and 0.0003947% near the hole, below the 1% criterion.Source: Mechanics and state-stratified… · p. 14
  • Medium- and fine-mesh selected IDs differ at 459 of 4,608 positions; the 1,323 coordinate-envelope ambiguities are a separate, more conservative count.All 23,040 new full-report comparisons agree with the reference, but that agreement does not eliminate mesh sensitivity.Source: Mechanics and state-stratified… · pp. 15–16, Figure 7 · p. 16
  • The additional bolt workload has 994 answered, 300 empty, and 185 incomplete positions among 1,479 requests; all 7,395 comparisons agree, including 925 incomplete-state comparisons.The exercise measures declared finite-record predicates, not design resistance.Source: Mechanics and state-stratified… · p. 16, Table 7 · p. 16

Reproducibility checks

  • A fresh isolated Python 3.12 environment reproduced the original and new statistical summaries and rebuilt correctness tests and figures, but did not verify cross-platform performance.The clean-environment checks also did not fully re-solve all 23 finite-element cases.Source: Reproducibility checks · p. 17

Discussion and limitations

The discussion distinguishes construction economy from same-source containment and online speed: cheaper SLA construction does not improve the primary full-API result. Its empirical and engineering evidence remains bounded by exploratory workloads, fixed-rank assumptions, and an unqualified elastic-component model.

Discussion and limitations

  • Construction savings do not establish online speed: instrumentation shows lower SLA construction cost alongside greater retrieval work and unavoidable current-report costs.The deterministic counterexample also shows that same-source containment cannot order every retained online state under a nonaccumulating permission policy.Source: Discussion and limitations · p. 17
  • The sensitivity matrix is exploratory: its resampled support, shared seed prefixes, catalogue-derived anchors, and synthetic threshold motion do not model unseen projects or measurement noise.A new held-out workload would be needed to test a policy selected from the matrix; no adaptive selector is implemented or validated.Source: Discussion and limitations · p. 17
  • Engineering checks cover a narrow model family and do not validate uncertain material properties, experimental noise, or an actual joint.The NIST window minima are finite-archive observations, not statistically justified design resistances.Source: Discussion and limitations · p. 17
  • The screening model assumes fixed rank and monotone per-coordinate inequalities; query-dependent rankings, coupled nonlinear predicates, and incremental index maintenance require new algorithms or justified reductions.All timed-table fields are known, and the bolt-record exercise does not model realistic missingness or measurement-error probabilities.Source: Discussion and limitations · p. 17
  • The literature comparison is not exhaustive novelty clearance: the full method of Ehlers’s thesis remains inaccessible for comparison.The paper also does not benchmark complete cited caching systems or modern external database implementations.Source: Discussion and limitations · p. 17
  • The elastic component omits bearing contact, friction, pretension, plasticity, fatigue, and failure; performance transport is also limited by background load, library changes, and one CPU architecture.The authors do not claim physical-joint qualification, comprehensive code compliance, or human structural-engineer blind review.Source: Discussion and limitations · p. 17

Conclusions

The conclusions present SLA as exact identity reuse under a stated contract, but its construction savings do not produce primary full-API acceleration. Expanded repeats, exploratory configurations, and engineering checks support bounded trade-offs rather than universal speedup or physical qualification.

Conclusions

  • Cover/SLA = 0.9682 [0.9593,0.9769], so SLA does not accelerate the primary full-API comparison despite exact fixed-rank identity reuse under its stated contract.The characterization is restricted to fixed upper endpoints.Source: Conclusions · p. 17
  • Three complete repeats preserve the adverse ordering, while the 720-configuration exploration and additive diagnostics show conditional trade-offs rather than a universally superior method.ZiYor explored and refined candidate construction; the named authors specified, implemented, and evaluated the method.Source: Conclusions · p. 18
  • The engineering chain includes an independent plane-stress reference, and medium- versus fine-mesh selections differ at 459 positions; physical connection qualification remains outside the demonstrated result.The bolt exercise reports 994 answered and 185 explicitly incomplete positions; a tested raw-data package supports audit and reuse.Source: Conclusions · p. 18

Declarations

The declarations report no external funding or competing interests. They describe source-data availability and a reviewer archive while leaving author contribution roles pending confirmation.

Declarations

  • The research received no external funding.Source: Declarations · p. 18
  • The authors declare no competing interests; UCI datasets and original NIST bolt workbooks are identified as available sources.Derived predicates are not endorsed NIST design values, and the source manifest records hashes and treatment of conflicted records.Source: Declarations · p. 18
  • The reviewer archive includes raw timings, references, solver materials, locked dependencies, and reproducible entry points, with fresh-environment recomputation and two representative FE re-solves passed.No public repository, archive DOI, cross-platform result, or approved open-source licence is asserted.Source: Declarations · p. 18
  • Individual CRediT roles remain pending genuine author confirmation; the preparation draft does not assign unverified roles.Source: Declarations · p. 18

S1. Six-axis closest-method comparison

The closest-method comparison is explicitly bounded: its tables form one six-axis comparison, while inspected formulations and unavailable thesis material limit novelty claims. No external system is implemented and timed.

S1. Six-axis closest-method comparison

S2. Workload, measurement and complete outputs

The supplemental workload records reproducible randomization, repeated original sessions, and a broad configuration matrix. It retains raw outputs and separates instrumented stage costs from primary timing measurements.

S2. Workload, measurement and complete outputs

  • Deterministic PCG64 streams derive seeds from labeled SHA-256 digests, while paired query orders preserve shared source and anchor dependence.The original aggregate bootstrap jointly resamples the four orders within dataset/k/stratum blocks.Source: S2. Workload, measurement and complete… · p. 22
  • The retained same-source construction and coverage table reports medians of source medians, not session speed; construction covers 1,280 locations, three constructors, and ten timings per constructor.Table S3 records original native units and ranges with source rows and precision retained.Source: Table S4 · p. 22, S2. Workload, measurement and complete… · p. 22, Table S3 · p. 22
  • Three fresh processes repeat the sealed 320-session queries, each retaining 2,048,000 main calls and 204,800 diagnostic positions.Each measured repetition creates a new instance; all processes share fixed CPU affinity and one-thread settings.Source: S2. Workload, measurement and complete… · p. 23
  • The 720-configuration exploration crosses two datasets, five sizes, four periods, three k values, two strata, and three localities; its counts are descriptive, not a held-out policy-selection test.Each configuration contains three sessions, and each displayed size/period/locality cell pools 18.Source: S2. Workload, measurement and complete… · p. 23
  • The complete configuration CSV retains paired ratios and measured counters, while JSON records preserve sessions and raw-file bindings.Original and supplemental raw per-query latency arrays remain separate; reported percentiles are not raw maxima.Source: S2. Workload, measurement and complete… · p. 23
  • Instrumented diagnostics partition parse, domain, contains, retrieve, build, materialize, and residual costs, which sum to instrumented_full for each method and query.Instrumentation perturbs measurements, so the analysis does not subtract these stage values from separately aggregated primary times.Source: S2. Workload, measurement and complete… · p. 23

S3. Finite-element and bolt-record verification details

The engineering checks pair finite-element verification with boundary-challenging component queries and state-stratified public bolt-record requests. The reported results remain bounded to numerical verification and preserved record states.

Finite-element verification

  • Three systematic meshes use 192, 768, and 3,072 elements, with predeclared finest-grid and medium-to-fine acceptance thresholds below 1%.The hole-stress profile uses the same nonsingular location and 21 points across y/a=1 to 3.Source: S3. Finite-element and bolt-record… · p. 23
  • The constitutive differentiation check uses four step sizes to compare plane-stress stresses with the analytical field, checking sign, angular orientation, and κ independently of FE agreement.Finite-plate checks also require medium-to-fine changes below 2% for hole stress and below 1% for displacement and strain energy.Source: S3. Finite-element and bolt-record… · p. 23
  • The finest mesh’s maximum absolute nodal-component error is 2.7890×10-11 mm at σ∞=0.001 MPa, a numerical verification result rather than physical measurement accuracy.The independent plane-stress displacement reference is read only after loading the stored numerical field; it does not prescribe the outer boundary.Source: S3. Finite-element and bolt-record… · pp. 23–24

Component queries

  • The component catalogue ranks full net volume, and its stress/displacement threshold grid is not asserted to represent material allowables or code limits.The finite catalogue uses a different load from the exact-reference case; k=1 and the four-coordinate upper-threshold interface are specified.Source: S3. Finite-element and bolt-record… · p. 24
  • The boundary-focused test retains 4,608 query occurrences across 108 nextafter positions and 4,500 crossed positions, representing 4,572 unique vectors.The medium/fine confusion matrix includes empty ID 0.Source: S3. Finite-element and bolt-record… · p. 24

Bolt-record queries

  • The NIST exercise preserves 5,460 original requests with 66 answered, 4,306 empty, and 1,088 incomplete outcomes; supplemental requests include 185 incomplete positions among 1,479.Supplemental answered, empty, and incomplete requests are compared against the literal original-row reference without imputation or cross-fixture extrapolation.Source: S3. Finite-element and bolt-record… · p. 24

S4. Reproduction, provenance and remaining limits

The reviewer package binds inputs and raw arrays and includes separate archive and computational checks. Fresh-environment runs reproduce scientific summary fields, while the stated limits exclude physical qualification and universal speedup claims.

Reproduction and provenance

  • The archive includes the original raw run, finite-element and NIST case materials, and a manifest covering 14,221 checked files.The package is a local reviewer deliverable; the exact manifest is authoritative.Source: S4. Reproduction, provenance and… · p. 25
  • The computational verifier recomputes original statistics and supplemental summaries, checks scientific fields, and runs representative correctness and engineering checks, but does not remeasure all performance calls.Complete archive-manifest validation is a separate check; a new timing campaign requires the documented experiment script.Source: S4. Reproduction, provenance and… · p. 25
  • An independently initiated run from the extracted archive completed all ten verification stages in 102.70 s and reproduced scientific summary fields.These durations include I/O and checks, not API latency; the medium exact-traction and fine central-plate solves also reproduced retained numeric fields.Source: S4. Reproduction, provenance and… · p. 25

Remaining limits

  • The evidence does not establish nonlinear connection behavior, physical experimental replication, assembly collision freedom, comprehensive design-code compliance, or universal retrieval speedup.The archive is not an approved public open-source release, and public distribution requires rights-holder approval.Source: S4. Reproduction, provenance and… · p. 25
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