{"schema_version":1,"research_id":"eoa_inverse_innovation_exp06_external_evaluation_20260803","source_assessment_id":"predictive_residual_processing__mathematics:P2:v0","cell_id":"predictive_residual_processing__mathematics","search_queries":["site:lmfdb.org large scale computations mathematical objects invariants database project","site:mersenne.org GIMPS results residues proof files verification distributed computing","BOINC validation redundant computing workunit results official documentation","predictive coding residual standard lossless data compression CCSDS","LMFDB paper database mathematical objects millions invariants computational challenges","site:lmfdb.org/about LMFDB computation database mathematical objects","site:mersenne.org \"proof\" \"residue\" GIMPS","large finite mathematical search computation counterexamples data storage results paper","site:lmfdb.org reliability completeness provenance computation data LMFDB","LMFDB data quality provenance completeness 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123.0-B-2 PDF prediction residual official","site:ccsds.org/Pubs 123x0b2 PDF"],"sources":[{"source_id":"S1","title":"Data and Data Quality in Mathematics","publisher":"IntechOpen","url":"https://www.intechopen.com/chapters/1232506","source_class":"AUTHORITATIVE_SECONDARY","publication_date":"2026-01-20","accessed_at":"2026-08-03","claims_supported":["Bounded enumerations are used to test hypotheses and locate counterexamples; generated collections can contain billions of objects.","Storage, computation, and researcher effort constrain whether complete generated collections are retained; recreating the LMFDB is estimated at roughly 3,000 CPU-years.","Mathematical-database quality practices already include independent recomputation, random-subset checks, certificates, and formal verification.","Exact mathematical data may have low redundancy, so useful residual compression cannot be presumed.","Pure-mathematics datasets are generally public and nonsensitive, but correctness, completeness, consistency, provenance, and licensing remain important."]},{"source_id":"S2","title":"LMFDB Auxiliary Datasets","publisher":"L-Functions and Modular Forms Database","url":"https://www.lmfdb.org/datasets/","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"n.d.","accessed_at":"2026-08-03","claims_supported":["The LMFDB hosts mathematical datasets ranging from hundreds of megabytes to 2.24 TB, including 10^11 zeta zeros.","Prospective datasets are reviewed through the LMFDB Editorial Board and must document their computation and use a specified license.","The project identifies NSF, EPSRC, and the Simons Foundation as funders, establishing identifiable authorizers and funders for mathematical-data infrastructure."]},{"source_id":"S3","title":"The L-Functions and Modular Forms Database Project","publisher":"Foundations of Computational Mathematics / Springer Nature","url":"https://link.springer.com/article/10.1007/s10208-016-9306-z","source_class":"PRIMARY_RESEARCH","publication_date":"2016","accessed_at":"2026-08-03","claims_supported":["LMFDB is an international collaboration of mathematicians operating a large searchable database of mathematical objects.","It stores and indexes expensive-to-compute or searchable invariants while omitting some values that are inexpensive to regenerate.","Its workflow already uses reviewed code, automated tests, backups, reproducible text data, and open-source infrastructure."]},{"source_id":"S4","title":"House of Graphs 2.0: A Database of Interesting Graphs and More","publisher":"Discrete Applied Mathematics authors / arXiv","url":"https://arxiv.org/abs/2210.17253","source_class":"PRIMARY_RESEARCH","publication_date":"2022-10-31","accessed_at":"2026-08-03","claims_supported":["House of Graphs keeps complete lists for some finite graph classes but intentionally maintains a smaller searchable collection of interesting graphs.","Precomputed invariant vectors, extremal cases, and counterexamples are used to give researchers manageable result sets for inspection.","The maintainers explicitly identify graph theorists and conjecture investigators as users, making them plausible adopters of attention-routing tools."]},{"source_id":"S5","title":"BOINC: A Platform for Volunteer Computing","publisher":"University of California, Berkeley / Journal of Grid Computing","url":"https://boinc.berkeley.edu/boinc_a_platform_for_volunteer_computing.pdf","source_class":"PRIMARY_RESEARCH","publication_date":"2020","accessed_at":"2026-08-03","claims_supported":["Distributed work-unit systems must distinguish missing, erroneous, and valid results rather than treating silence as confirmation.","BOINC supports replication, application-specific comparison, quorum validation, adaptive replication, deadlines, and intermediate-result-dependent outputs.","These established mechanisms cover much of the proposal's heartbeat, verification, retry, and coverage-control layer."]},{"source_id":"S6","title":"GIMPS: The Math","publisher":"Great Internet Mersenne Prime Search / PrimeNet","url":"https://www.mersenne.org/various/math.php","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"n.d.","accessed_at":"2026-08-03","claims_supported":["GIMPS transmits and records a compact 64-bit final residue from large primality computations.","It validates computations through repeat runs, matching residues, deliberately varied computation paths, and error checks.","This is an operating mathematical-search analogue for compact result summaries plus independent verification, although it does not predict full invariant vectors."]},{"source_id":"S7","title":"CCSDS 123.0-B-2: Low-Complexity Lossless and Near-Lossless Multispectral and Hyperspectral Image Compression","publisher":"Consultative Committee for Space Data Systems","url":"https://ccsds.org/publications/bluebooks/","source_class":"STANDARD","publication_date":"2019-02","accessed_at":"2026-08-03","claims_supported":["CCSDS maintains an implementable recommended standard for low-complexity lossless and near-lossless compression of structured data.","The standard establishes predictive compression and reconstructive residual coding as mature engineering prior art outside mathematics.","The standard does not supply mathematical completeness, witness, or theorem-authority semantics."]},{"source_id":"S8","title":"Counterexample-Guided Abstraction Refinement","publisher":"Springer, Computer Aided Verification 2000; Stanford-hosted author copy","url":"https://web.stanford.edu/class/cs357/cegar.pdf","source_class":"PRIMARY_RESEARCH","publication_date":"2000","accessed_at":"2026-08-03","claims_supported":["CEGAR starts from an abstract model, checks candidate counterexamples, and iteratively refines the abstraction when counterexamples expose inadequacy.","This substantially overlaps the proposal's idea of splitting or revising atlas regions from verified residuals.","CEGAR concerns verification abstractions rather than reconstructive transmission of mathematical invariant vectors."]}],"problem_evidence":{"support":"MODERATE","rationale":"Large finite mathematical collections, expensive invariant computations, terabyte-scale storage, and the need to find counterexamples or interesting objects are directly visible. House of Graphs also documents an inspection-manageability objective. However, no source establishes that full invariant vectors within a candidate family are sufficiently predictable, that transfer is the binding constraint, or that researchers currently spend measurable time scanning conforming rows. S1 cautions that exact mathematical data can have low redundancy, directly limiting the generality of the proposed problem.","source_ids":["S1","S2","S3","S4"]},"stakeholder_evidence":{"support":"WEAK","rationale":"The LMFDB Editorial Board, LMFDB contributors and funders, and House of Graphs maintainers are identifiable authorizers, adopters, or funders with expressed needs for scalable storage, search, reliability, and manageable inspection. None expresses demand for a synchronized predictive atlas or residual-only routing, and existing projects may prefer complete indexed data, curated interesting subsets, or on-demand generation.","source_ids":["S2","S3","S4"]},"prior_art":{"proximity":"SUBSTANTIAL_COLLISION","closest_analogues":[{"name":"House of Graphs searchable database of interesting graphs","similarity":"Precomputes invariant vectors and deliberately concentrates researchers on extremal graphs, counterexamples, and other informative cases while retaining complete lists separately for some classes.","remaining_difference":"Selection is curated or rule-based after computation; it does not predict every object's full vector, transmit reconstructive typed residuals, or automatically decompress a region after model failure.","source_ids":["S4"]},{"name":"LMFDB storage, indexing, and sampled integrity checking","similarity":"Stores expensive mathematical invariants, makes them searchable, and already uses reproducible data, internal checks, random-object audits, and independent recomputation.","remaining_difference":"It generally treats object records as authoritative stored data rather than a synchronized predictor-plus-residual stream.","source_ids":["S1","S2","S3"]},{"name":"GIMPS compact residues and verification","similarity":"A large distributed mathematical search returns compact residues rather than complete computation traces and checks them through independent computations and error controls.","remaining_difference":"The compact residue is a verification fingerprint for a fixed computation, not a learned multi-invariant prediction, consequence-weighted residual gate, or adaptive atlas.","source_ids":["S6"]},{"name":"BOINC work-unit validation and adaptive replication","similarity":"Provides work-unit status, deadlines, quorums, replicated validation, retries, and adaptive checking needed to keep missing or corrupt distributed results from appearing valid.","remaining_difference":"It validates returned results but does not prioritize semantic deviations from a mathematical family model or reconstruct suppressed invariant vectors.","source_ids":["S5"]},{"name":"Predictive residual compression and CEGAR","similarity":"CCSDS establishes reconstructive predictive compression, while CEGAR establishes counterexample-driven refinement of an initially coarse model; together they cover the proposal's principal algorithmic ideas.","remaining_difference":"No searched source combined these mechanisms with typed mathematical invariants, protected conjecture failures, full coverage manifests, and investigator-attention measurement in one finite-family workflow.","source_ids":["S7","S8"]}],"distinctive_claim_remaining":"For one preregistered finite family, a frozen and synchronized atlas can encode object-level invariant vectors as typed reconstructive residuals and reduce both transmitted bytes and blinded investigator triage time versus (i) full indexed results, (ii) a fixed exception filter, and (iii) ordinary lossless compression, while preserving 100% exact reconstruction and 100% recall of protected events and while costing less in total after prediction, audit, fallback, and maintenance overhead. Any failure of those conditions falsifies the incremental claim.","confidence":"MODERATE"},"implementation_evidence":{"support":"MODERATE","rationale":"Predictive lossless compression, distributed work-unit validation, compact mathematical result summaries, independent checks, random audits, and counterexample-guided model refinement are all technically established. Public mathematical collections and open-source database infrastructure make a read-only replay feasible. The unverified parts are semantic canonicalization of heterogeneous invariants, useful atlas predictability, stable thresholds, exact reconstruction across software versions, protected-event coverage, and net workflow benefit. Dataset licenses and attribution must be respected, but a replay on authorized or self-generated data has no apparent legal or sensitive-data stop.","source_ids":["S1","S3","S5","S6","S7","S8"]},"scores":{"meaningful_impact":{"score":3,"rationale":"Potentially material for exceptionally large enumerations with costly inspection, but the binding constraint and prevalence of compressible repetition are unmeasured and may be narrow.","source_ids":["S1","S2","S4"]},"stakeholder_pull":{"score":2,"rationale":"Credible organizations and funders visibly need mathematical-data infrastructure, but no maintainer requested residual routing or reported the specific workflow pain.","source_ids":["S2","S3","S4"]},"incremental_advantage":{"score":2,"rationale":"Complete indexed tables, curated interesting-object databases, on-demand generation, generic compression, compact residues, and sampled verification already address much of the objective more simply.","source_ids":["S1","S3","S4","S6"]},"distinctiveness_plausibility":{"score":3,"rationale":"The mathematics-specific combination of reconstructive typed residuals, protected-event bypasses, coverage manifests, and model-refining audits was not found as one system, although its central mechanisms substantially collide with established practices.","source_ids":["S4","S5","S6","S7","S8"]},"technical_implementability":{"score":4,"rationale":"A full-retention replay can be built from mature database, distributed-validation, residual-coding, and audit techniques; semantic versioning and canonicalization remain nontrivial.","source_ids":["S3","S5","S6","S7"]},"adoption_authority_feasibility":{"score":4,"rationale":"A responsible mathematician or database editorial board can authorize a read-only replay without delegating theorem or counterexample authority to the system.","source_ids":["S2","S3","S4"]},"evidence_readiness":{"score":4,"rationale":"Complete finite-family datasets, invariant vectors, and established baselines exist, enabling a bounded retrospective experiment before any destructive suppression.","source_ids":["S1","S2","S4"]},"safety_net_benefit":{"score":4,"rationale":"Full-result retention, protected bypasses, independent verification, random audits, manifests, and fallback directly address known correctness and missing-result hazards, though their effectiveness needs injected-fault testing.","source_ids":["S1","S5","S6"]},"scalability":{"score":3,"rationale":"Residual routing could scale across workers, but atlas synchronization, audits, exact metadata, and low intrinsic redundancy may erase the savings as families or schemas diversify.","source_ids":["S1","S3","S5"]}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"10K_TO_50K","scope":"Read-only replay on one existing complete family: canonical schema, frozen atlas, three comparators, injected protected events, automated metrics, and a small blinded investigator task.","confidence":"MODERATE","assumptions":["Existing complete results and computation-status records are available without new enumeration.","Approximately 4-8 engineer-weeks, 1-3 mathematician-weeks, and under $5,000 of compute/storage are required.","The experiment does not alter production routing or discard data."],"source_ids":["S1","S3","S4"]},"initial_deployment_startup":{"band_2026_usd":"50K_TO_250K","scope":"Research-grade prototype integrated with one enumerator: typed schemas, version handshakes, manifests, replay buffer, audit sampler, dashboards, and region fallback.","confidence":"LOW","assumptions":["One software engineer for roughly 6-12 months plus part-time mathematical and verification owners.","Existing worker and database infrastructure can be extended rather than replaced.","No formal certification of every invariant computer is included."],"source_ids":["S1","S3","S5"]},"operational_launch":{"band_2026_usd":"250K_TO_1M","scope":"Production launch for one substantial collaboration: hardened distributed integration, migration tooling, monitoring, independent verification capacity, incident procedures, documentation, and user training.","confidence":"LOW","assumptions":["Two to four engineering-equivalent staff-years plus mathematical governance and compute capacity.","Launch retains or archives full results until acceptance criteria are met.","Scope is one project and invariant vocabulary, not a cross-domain platform."],"source_ids":["S1","S3","S5"]},"annual_recurring":{"band_2026_usd":"50K_TO_250K","scope":"Model and schema maintenance, audit compute, storage, incident review, threshold governance, contributor support, and periodic full-baseline evaluations for one deployed project.","confidence":"LOW","assumptions":["Approximately 0.5-1.5 continuing staff-equivalents plus moderate compute and storage.","No major re-enumeration or new mathematical domain is included.","Independent audit and full-fallback capacity are not reduced to preserve savings."],"source_ids":["S1","S3","S5"]}},"verified_pipeline_gates":{"externally_supported_problem":{"status":"YES","reason":"External sources show billion-object enumerations, terabyte datasets, thousands of CPU-years of recomputation, and an explicit desire to keep inspection result sets manageable; family-level predictability remains the principal uncertainty.","source_ids":["S1","S2","S4"]},"externally_credible_adopter_or_authorizer":{"status":"YES","reason":"The LMFDB Editorial Board and House of Graphs maintainers are identifiable mathematical-data authorizers, and LMFDB names institutional funders; no evidence of their specific willingness to adopt this proposal was found.","source_ids":["S2","S3","S4"]},"distinct_testable_incremental_claim":{"status":"YES","reason":"The remaining claim compares typed reconstructive residual routing against full indexed output, a fixed exception filter, and ordinary compression under exact reconstruction, protected recall, human-time, and total-cost criteria.","source_ids":["S4","S6","S7","S8"]},"bounded_next_evidence_step":{"status":"YES","reason":"A full-retention replay on one public or partner-authorized finite family can freeze training and evaluation partitions, inject faults, and measure all claimed outcomes without production suppression.","source_ids":["S1","S4","S5"]},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"The first step is read-only; complete results remain authoritative, witnesses require independent reproduction, and mathematical datasets are generally nonsensitive. Dataset licensing, attribution, and provenance must still be documented.","source_ids":["S1","S2","S5","S6"]},"credible_cost_scope_and_range":{"status":"YES","reason":"Broad resource-equivalent bands are credible for the explicitly bounded replay and single-project deployments, although no vendor quote or project-specific staffing estimate was available and deployment bands therefore have low confidence.","source_ids":["S1","S3","S5"]}},"next_evidence_step":"With one LMFDB, House of Graphs, or comparable maintainer, preregister a full-retention replay over exactly one complete finite family. Freeze a feature vocabulary and atlas on 30% of objects and evaluate the untouched 70%. Compare: (A) complete indexed vectors, (B) a fixed predicate/threshold exception filter, (C) complete vectors compressed with an ordinary lossless columnar codec, and (D) the proposed typed atlas residual. Blindly inject predicate flips, missing-worker reports, unknown classes, boundary cases, invalid witnesses, and version mismatches. Require 100% exact vector reconstruction, 100% protected-event recall, zero missing-as-conforming errors, and automatic fallback on every version or manifest fault. Measure bytes, storage, compute, investigator completion time and error rate, residual structure, audit disagreement, fallback rate, and all maintenance/audit labor. Falsify the proposal if any protected event is missed, any vector fails exact semantic reconstruction, residuals remain feature-structured without fallback, investigator accuracy falls, or total resource cost is not lower than both the full-result and simpler-filter baselines. Predefine a meaningful-efficiency threshold before seeing results, such as at least 25% lower median triage time and 30% lower transferred bytes after all overhead.","blocking_evidence":["No external measurement shows what fraction of invariant vectors in a proposed family are predictable or exactly reconstructible from a stable feature partition.","No maintainer or funder was found expressing demand for predictive atlas residual routing specifically.","No comparison exists against complete indexed tables, fixed exception filters, on-demand generation, or ordinary lossless compression at equal correctness.","Protected-event recall, missing-worker behavior, fallback reliability, and semantic reconstruction require injected-fault or live replay testing.","Researcher-attention savings and total maintenance cost require observed workflow data rather than further bounded web research.","Production licensing, attribution, schema ownership, and long-term model-governance responsibilities have not been agreed with an adopter."],"research_disposition":"PARTNERED_RESEARCH_PROGRAM","world_novelty_boundary":"World novelty, patentability, freedom to operate, market size, and realized impact were not measured. The search only establishes substantial collision with accessible products, standards, practices, and research; absence of an exact combined system in these eight sources is not evidence of world novelty.","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_version":0,"controller_recommendation":{"action":"STOP_EMPIRICAL_RESEARCH_NEEDED","repairable":false,"material_progress_observed":true,"progress_targets":["Secure one mathematical-database maintainer or enumeration operator as authorizer and obtain a complete, versioned result family plus baseline workflow records.","Preregister the atlas, protected classes, audit sample, comparators, meaningful-efficiency threshold, and immutable falsifiers before evaluating the holdout.","Demonstrate 100% exact reconstruction, 100% protected-event recall, zero missing-as-conforming errors, and reliable fallback under blinded injected faults.","Measure investigator accuracy and time with blinded users, and measure total bytes, compute, storage, audit, and maintenance resources against all three comparators.","Document dataset license, attribution, provenance, model/schema ownership, incident authority, and rollback responsibility."],"reason":"Web evidence supports a real high-scale mathematical-data problem and identifies credible authorizers, but it also reveals close established practices and no direct stakeholder pull for the proposed package. The decisive incremental questions—family predictability, exact semantic reconstruction, protected-event recall, investigator-time savings, and net cost—require partner data, injected-fault replay, and live user measurement, so they cannot be resolved by additional bounded web search."},"proposal_index":2}