ProofAtlas

Post-quantum cryptography · succinct arguments · extraction · STARKs

Loss-to-Time State-Preserving Quantum Extraction

Collaboration beta

The source rules out the unrestricted scalar-loss compiler, proves several conditional compiler routes, and classifies the current deterministic RPO endpoint as already additive. The leading open work is a real lossy-source theorem, a complete concrete parameter ledger, and stronger composition and public-output interfaces.

source certificate+coherent access⇒conditional loss-to-time compiler
Known results and sources
Problem-first open-research thumbnail for Loss-to-Time State-Preserving Quantum Extraction, showing an unresolved mathematical structure without a completion mark or navigation arrow.
Can extraction loss be moved into time without damaging state? The page presents source-reported partial structure without claiming a proof.

Research problem

Exact mathematical statement

Corrected target

Classify when a one-copy, state-preserving quantum knowledge extractor can relocate multiplicative extraction loss into polynomial coherent running time, and complete the strongest source-matched IBCS/RPO/STARK endpoint justified by those conditions. The unrestricted implication from scalar mean success is false, even with strictly positive spectrum. A positive compiler therefore needs an additional source certificate such as finite exact-verifiable branches on one retained history, a hard spectral floor or tail bound, positive defect, a negative moment, or same-trial hereditary security.

source certificate+coherent access⇒conditional loss-to-time compiler\text{source certificate}+\text{coherent access}\Longrightarrow\text{conditional loss-to-time compiler}

The current deterministic 2025/2166-to-RPO decoder is already projective and additive with L_term=1; the open work is to finish its concrete theorem and parameter ledger, identify or redesign a genuinely lossy source, and separately handle arbitrary active shared-QROM composition and public witness release. This is an open research program, not a complete proof or deployed extractor.

Problem infographic

Problem at a glance

Three-panel source-bound explainer for Loss-to-Time State-Preserving Quantum Extraction: exact target, strongest retained result, and the unresolved closing bridge.
The source separates the exact target, retained partial results, and the still-open bridge.

Current mathematical picture

Where work on Loss-to-Time State-Preserving Quantum Extraction stands

Open problem

The cumulative v57 source reports a corrected conditional loss-to-time boundary, an additive terminal-loss-one RPO endpoint, scoped hereditary and exact-OR compilers, exact private preservation, and bounded passive/batch results while leaving the genuine lossy-source, active composition, public-output, and complete parameter interfaces open.

Leading routeCurrent additive BCS/RPO baseline

Finish the existing terminal-loss-one BCS/RPO theorem and parameter ledger.

Route status · Active route
Useful failureTreating a marginal theorem as witness-aware composition

The payload register can remain correlated with retained extraction resources outside the marginal guarantee. Canonical payloads, released-channel formulations, and compressed-oracle routes remain viable under exact source interfaces.

Route status · Narrowed route
Main reductionCurrent reduction

Combine weighted loss-to-time algebra, a state-preserving terminalizer, payload-collapse control, and multi-round measure-and-reprogram bounds in a source-matched IBCS/STARK instantiation.

Evidence posture · Source-reported route statement · dependencies incomplete
Priority open bridgeProve the same-trial hereditary source interface or classify the loss as common-history branching

Select one genuine multiplicatively lossy purified trial and prove or refute the same-trial filtered witness-versus-bad interface; if the loss is instead finite branching, prove that every branch is an exact-verifiable function of one retained semantic history.

Task status · Prerequisites still open
Later mathematical updatev57 corrects the compiler boundary and adds scoped positive routes

The cumulative v57 source refutes the unrestricted scalar compiler, records the current additive endpoint, and adds conditional hereditary, exact-OR, private-preservation, passive-live, and bounded-batch results with explicit open interfaces.

v57 source revision order; not occurrence time or public priority

Work mapped so far

Loss-to-Time State-Preserving Quantum Extraction in numbers

17.9kretained lines of mathematical investigation1,142 in the current working snapshot
Argument development
14,209 · 79%
Explored or eliminated routes
551 · 3%
Computational analysis
870 · 5%
Open obligations
911 · 5%
Definitions and setup
1,384 · 8%
17selected mapped statements6routes investigated7open questions6contribution-ready tasks
How this is measured

This measures retained mathematical investigation, not proximity to a proof. Code, data, logs, repeated text, operational instructions, and generated presentation copy are excluded.

Status checkedAug 21, 2026
Source recordedAug 30, 2026

Argument map and routes

How the current approaches connect

Claims, reductions, open questions, active routes, and narrowed alternatives in one mathematical map.

Visible working map

Research route map

25 selected steps

Selected claims, active routes, useful failures, and open questions from the current research map. Arrows appear only for explicitly recorded relationships.

25 selected steps

Scroll horizontally to explore the route

Working route overview for Loss-to-Time State-Preserving Quantum ExtractionA selected map of recorded claims, active routes, useful failures, open questions, and their explicit relationships. Search, filter, zoom, or pan within this page.Adaptive bounded global-halt batch — Depends on missing premiseAdaptive bounded global-haltbatchConditional loss-to-time compiler boundary — Depends on missing premiseConditional loss-to-timecompiler boundaryCurrent RPO endpoint is additive — Depends on missing premiseCurrent RPO endpoint isadditiveHereditary loss-to-time compiler — Depends on missing premiseHereditary loss-to-timecompilerCurrent reduction — Depends on missing premiseCurrent reductionLoss-to-time compiler — Depends on missing premiseLoss-to-time compilerAll-cut projectivity — ActiveAll-cut projectivityBounded passive live deferral — Depends on missing premiseBounded passive livedeferralClosing target — Depends on missing premiseClosing targetCommon-label exact OR — Depends on missing premiseCommon-label exact ORPublic-witness boundary — ActivePublic-witness boundaryReject-preserving marginal — Depends on missing premiseReject-preserving marginalCurrent additive BCS/RPO baseline — activeCurrent additive BCS/RPObaselineSame-trial hereditary source route — activeSame-trial hereditary sourcerouteCommon-history exact-OR route — activeCommon-history exact-ORrouteConditional prefix-binding additive route — activeConditional prefix-bindingadditive routeTreating a marginal theorem as witness-aware composition — stoppedTreating a marginal theoremas witness-aware compositionDeriving an additive compiler from scalar mean success — stoppedDeriving an additivecompiler from scalar meansuccessProve payload collapse and retained-resource reversal. — OpenProve payload collapse andretained-resource reversal.Instantiate the full multi-round FRI/STARK reduction. — OpenInstantiate the fullmulti-round FRI/STARKreduction.Bad-sector reduction — OpenBad-sector reductionProve the same-trial hereditary source interface or classify the loss as common-history branching — OpenProve the same-trialhereditary source interfaceor…Complete the additive BCS/RPO theorem — OpenComplete the additiveBCS/RPO theoremAudit common-history branch losses — OpenAudit common-history branchlossesSeparate active composition and public output — OpenSeparate active compositionand public output
Working claimActive routeOpen, active, or blocked questionUseful failure

Working overview, not proof. The map shows selected recorded relationships; more nodes or edges do not establish correctness or completion.

Active routeCurrent additive BCS/RPO baseline

Finish the existing terminal-loss-one BCS/RPO theorem and parameter ledger.

Route status · Active route
Active routeSame-trial hereditary source route

Identify a real lossy trial, prove same-trial filter heredity, and invoke the conditional hereditary compiler.

Route status · Active route
Active routeCommon-history exact-OR route

Terminalize polynomial branch loss onto one recorded history and compile it by exact reversible OR.

Route status · Active route
Active routeConditional prefix-binding additive route

Complete the prefix-binding source theorem and substitute it into the current additive endpoint with its exact timing, masking, and parameter costs.

Route status · Active route
Active routeBounded passive live route

Type the complete private compiler by one stable database partition and apply the passive deferral bridge.

Route status · Active route

Explored alternatives

Other routes

1 recorded
Narrowed routeTreating a marginal theorem as witness-aware composition

The payload register can remain correlated with retained extraction resources outside the marginal guarantee. Canonical payloads, released-channel formulations, and compressed-oracle routes remain viable under exact source interfaces.

Route status · Narrowed route

Route statements and reductions

Statements the next route can inspect and build on

Route statementCommon-label exact OR

A polynomial exact-verifiable branch family that is reversible from one retained orthogonal semantic label can be combined by exact reversible OR into a strict polynomial-time loss-one decoder.

Source-reported route statement · dependencies incomplete
Route statementHereditary loss-to-time compiler

Combining the hereditary defect bound with the defect-matched fixed-point response yields a finite one-copy private loss-to-time compiler, conditional on the strong source-heredity interface.

Source-reported route statement · dependencies incomplete
Route statementCurrent RPO endpoint is additive

The current deterministic 2025/2166-to-RPO endpoint is source-reported as projective and additive with terminal loss one; it is a baseline and not a nontrivial lossy-source instantiation.

Source-reported route statement · dependencies incomplete
Route statementBounded passive live deferral

A compiler controlled by one stable database partition can be commuted through bounded passive future oracle use with the source-stated generalized-instability bridge, subject to exact register and passivity conditions.

Source-reported route statement · dependencies incomplete

More ways to contribute

Open questions

Additional prepared tasks for exploring this research frontier.

7 featured tasks
01
Separate active composition and public output

Develop protected namespaces or a global shared-memory source theorem and a separate public witness simulator or ideal functionality.

Suggested move: Specify the active shared-QROM and public-output interfaces independently of private passive deferral.
Ready to work on
02
Complete the additive BCS/RPO theorem

Write the complete current terminal-loss-one theorem through exact RPO witness transport with one consistent error and parameter ledger and the private global-halt state statement.

Suggested move: Freeze the full source-to-RPO theorem statement and parameter ledger.
Ready to work on
03
Audit common-history branch losses

Determine whether every polynomial QROM guessing or query-index factor is an exact-verifiable function of one recorded semantic history.

Suggested move: Classify each branch factor as common-history exact OR or record its precise obstruction.
Ready to work on
04
Prove payload collapse and retained-resource reversal.Suggested move: Prove the payload-collapse theorem across measurement, retained resources, reversal, and continuation.
Ready to work on
05
Bad-sector reduction

A complete implemented bad-sector reduction remains missing.

Suggested move: Resolve the exact source-reported obligation without treating it as an established negative result.
Ready to work on
06
Instantiate the full multi-round FRI/STARK reduction.Suggested move: Audit meaningful AIR/FRI parameters end to end.
Ready to work on
07
Prove the same-trial hereditary source interface or classify the loss as common-history branching

Select one genuine multiplicatively lossy purified trial and prove or refute the same-trial filtered witness-versus-bad interface; if the loss is instead finite branching, prove that every branch is an exact-verifiable function of one retained semantic history.

Suggested move: Audit one real lossy trial against same-trial heredity and the intended QROM branch losses against the common-history exact-OR interface.
Prerequisites still open

Sourced mathematical context

The known mathematical landscape

Context collected Aug 21, 2026
Current statusOpen problem

Current cryptographic literature supplies important post-quantum security and rewinding components, but the current work's full state-preserving, payload-aware multi-round compiler remains an open integration target.

[1][2]
External progress

What the literature has established

Selected external milestones in reverse chronological order, with their evidence posture.

  1. Peer reviewedHow to Prove Post-Quantum Security for Succinct Non-Interactive Reductions supplies a representative external result or boundary relevant to the problem; it is not treated here as a proof of the full packet…[1]
  2. PreprintQuantum Rewinding for IOP-Based Succinct Arguments supplies a representative external result or boundary relevant to the problem; it is not treated here as a proof of the full packet target.[2]
2 cited sources1 related results or reductionsReferences

Mathematical neighborhood

Related results and reusable starting points

Current focusLoss-to-Time State-Preserving Quantum Extraction
Related problemLoss-to-Time State-Preserving Quantum Extraction

Current cryptographic literature supplies important post-quantum security and rewinding components, but the packet's full state-preserving, payload-aware multi-round compiler remains an open integration target.

[1][2]

Formalization opportunities

Lean work can make these reusable foundations precise without being presented as a proof of the core problem.

  • Formalization targetA formal statement matching the exact public target and all quantifiers.
  • Formalization targetFormal libraries for the principal mathematical structures used by the strongest route.
  • Formalization targetA checked closing argument for the source-identified open bridge.

Later mathematical changes

What changed after the initial research map

Later recorded revisions that changed the mathematics, without inventing a date or an AI attribution.

v57 corrects the compiler boundary and adds scoped positive routesThe cumulative v57 source refutes the unrestricted scalar compiler, records the current additive endpoint, and adds conditional hereditary, exact-OR, private-preservation, passive-live, and bounded-batch results with explicit open interfaces.

Changed the research frontierLater mathematical revision

v57 source revision order; not occurrence time or public priority

The initial argument structure appears separately. Uploads, model runs, and presentation changes do not count as mathematical updates.

Research-record corrections

What changed in the research record

These notes describe corrections to cited passages, highlighted tasks, or connections between claims. The mathematical claims and their status did not change.

Research-record correctionWe corrected the cited passages. We updated the highlighted open task or route. The mathematical claims and their status did not change.

Corrected the research recordCorrection note

Correction details
Research-record correctionWe corrected the cited passages. We removed a duplicate or outdated task or route step. We updated the highlighted open task or route. The mathematical claims and their status did not change.

Corrected the research recordCorrection note

Correction details
Research-record correctionWe corrected the cited passages. We removed a duplicate or outdated task or route step. We updated the highlighted open task or route. The mathematical claims and their status did not change.

Corrected the research recordCorrection note

Correction details
Research-record correctionWe corrected the cited passages. We removed a duplicate or outdated task or route step. The mathematical claims and their status did not change.

Corrected the research recordCorrection note

Correction details
Research-record correctionWe corrected the cited passages. The mathematical claims and their status did not change.

Corrected the research recordCorrection note

Cited passages corrected
Research-record correctionWe corrected the cited passages. The mathematical claims and their status did not change.

Corrected the research recordCorrection note

Cited passages corrected

The initial argument structure appears separately. Uploads, model runs, and presentation changes do not count as mathematical updates.

Detailed research inventory

Claims, milestones, and routes in the current map

This view highlights the mathematical statements most useful for following the current route.

15 standing statements2 proposed statements7 open questions1 narrowed routes
Statements by mathematical role17 selected mapped statements
  • reduction1 of 171
  • lemma8 of 178
  • equivalence1 of 171
  • negative result3 of 173
  • theorem candidate4 of 174
Selected mathematical clusters1 mathematical clusters
Current research mapThe v57 source refutes the unrestricted scalar compiler premise, proves scoped spectral, exact-OR, projectivity, private-preservation, passive-live, and bounded-batch results, and leaves the genuine lossy-source, complete additive endpoint, active composition, and public-output interfaces open.40 displayed rows · 6 routes included
  • retained route statementAll-cut projectivityintermediate
  • retained route statementAdaptive bounded global-halt batchintermediate
  • retained route statementClosing targetintermediate
  • retained route statementCoherent-seed averagingintermediate
  • retained route statementCommon-label exact ORintermediate
  • retained route statementLoss-to-time compilerintermediate
  • retained route statementWitness-aware boundaryintermediate
  • retained route statementConditional loss-to-time compiler boundary
  • retained route statementCurrent RPO endpoint is additiveintermediate
  • retained route statementHereditary loss-to-time compilerintermediate
  • retained route statementSame-trial hereditary defect liftintermediate
  • retained route statementReject-preserving marginalintermediate
  • retained route statementBounded passive live deferralintermediate
  • retained route statementExact private terminal preservationintermediate
  • retained route statementPublic-witness boundaryintermediate
  • retained route statementCurrent reductionintermediate
  • retained route statementScalar mean success is insufficientintermediate
  • DerivationThe v57 source separates three ways to meet the conditional target: finish the current additive endpoint, prove same-trial heredity for a genuine lossy source, or reduce finite branch loss to exact common-history OR; the unrestricted scalar premise remains refuted.proposed
  • Recorded relationshipSection 16.2 applies the all-cut projectivity theorem to the complete deterministic endpoint and concludes that the current RPO terminal source is projective with terminal loss one.supports · reported by source
  • Recorded relationshipSection 17.5 applies the exact one-session current endpoint theorem to each delayed-output session wrapper before union-bounding the diagonal invalidity event effects.supports · reported by source
  • Recorded relationshipSection 12.5 explicitly combines the hereditary defect bound with the retained fixed-point response; the compiler therefore depends on the exact same-trial hereditary defect lift.supports · reported by source
  • Recorded relationshipThe v57 source reports the retained reduction as a route only under its corrected spectral/common-history source boundary; the current deterministic RPO endpoint is already additive and does not instantiate a nontrivial multiplicative loss.supports · reported by source
  • Recorded relationshipThis source-reported claim supports the retained route only within its stated, unaudited scope.supports · reported by source
  • Recorded relationshipThis source-reported claim supports the retained route only within its stated, unaudited scope.supports · reported by source
  • Recorded relationshipThis source-reported claim supports the retained route only within its stated, unaudited scope.supports · reported by source
  • Useful failureTreating a marginal theorem as witness-aware compositionreported failure
  • Useful failureDeriving an additive compiler from scalar mean successreported failure
  • Research targetSeparate active composition and public outputopen
  • Research targetComplete the additive BCS/RPO theoremopen
  • Research targetAudit common-history branch lossesopen
  • Research targetProve the same-trial hereditary source interface or classify the loss as common-history branchingopen
  • Research targetProve payload collapse and retained-resource reversal.open
  • Research targetBad-sector reductionopen
  • Research targetInstantiate the full multi-round FRI/STARK reduction.open
  • Active routeCommon-history exact-OR routeTerminalize polynomial branch loss onto one recorded history and compile it by exact reversible OR.
  • Narrowed routeTreating a marginal theorem as witness-aware compositionThe payload register can remain correlated with retained extraction resources outside the marginal guarantee. Canonical payloads, released-channel formulations, and compressed-oracle routes remain viable under exact source interfaces.
  • Active routeBounded passive live routeType the complete private compiler by one stable database partition and apply the passive deferral bridge.
  • Active routeConditional prefix-binding additive routeComplete the prefix-binding source theorem and substitute it into the current additive endpoint with its exact timing, masking, and parameter costs.
  • Active routeSame-trial hereditary source routeIdentify a real lossy trial, prove same-trial filter heredity, and invoke the conditional hereditary compiler.
  • Active routeCurrent additive BCS/RPO baselineFinish the existing terminal-loss-one BCS/RPO theorem and parameter ledger.
How to interpret these counts

A statement may be a lemma, conditional reduction, special case, documented limitation, or open target. These counts describe the work's structure; they do not estimate distance to a proof.

Research outlook

Conditions that would advance the current route

Priority open bridgeSelect one genuine multiplicatively lossy purified trial and prove or refute the same-trial filtered witness-versus-bad interface; if the loss is instead finite branching, prove that every branch is an exact-verifiable function of one retained semantic history.

1 approach has already been tested and narrowed. The task above is the current priority within the larger open route.

Evidence needed nextConcrete conditions for progress

A result can change the outlook by closing the bridge, narrowing its scope, or showing that the route cannot work.

  • Bind one fixed trial, bad-event typing, spectral-filter budget, and source-to-target bridge.
  • Do not infer the hereditary interface from the ordinary scalar multiplicative premise.

Continue the mathematics

Contribute

ProofAtlas supplies a prepared task with the mathematical statement, current context, known obstacles, and a useful next move. Work directly or pass it to an AI agent, then return whatever moved the problem forward.

Read-only beta · actions unavailable
Prepared starting pointSeparate active composition and public output

Loss-to-Time State-Preserving Quantum Extraction · ready to start

Mathematical updatesFollow this problem

Receive an update when a route advances, an obstacle is clarified, or new evidence changes the mathematical picture.

Research contextPrepared context for any AI agent

The source rules out the unrestricted scalar-loss compiler, proves several conditional compiler routes, and classifies the current deterministic RPO endpoint as already additive. The leading open work is a real lossy-source theorem, a complete concrete parameter ledger, and stronger composition and public-output interfaces.

  • Exact question and boundaries
  • Current routes and known obstacles
  • What a useful result should report
Return mathematical workReturn what you or your agent found

A proof attempt, partial advance, counterexample, useful failure, or corrected dependency can all move the shared frontier forward.

Proof attempt or partial resultSupporting notes or data
Hosted agentRun this task with a hosted agent

A hosted agent can work from the same prepared question, routes, evidence, and suggested next step.

Your own AI agentConnect an outside research agent

Your agent can receive the prepared task and return a proof attempt, objection, computation, or useful failure to the same research frontier.

Sources and references2 cited works · next context review by Nov 21, 2026

The mathematical context was checked on Aug 21, 2026. Status can be refreshed sooner after a material result or claim.

  1. 1
    How to Prove Post-Quantum Security for Succinct Non-Interactive Reductionspeer reviewed result · Alessandro Chiesa, Zijing Di, Zihan Hu, Yuxi Zheng · IACR ePrint; EUROCRYPT 2026 · 2025 · accessed Aug 21, 2026
  2. 2
    Quantum Rewinding for IOP-Based Succinct Argumentspreprint · Alessandro Chiesa, Marcel Dall'Agnol, Zijing Di, Ziyi Guan, Nicholas Spooner · IACR ePrint · 2025 · accessed Aug 21, 2026

Important qualifications

  • This was a bounded status and identity check, not an exhaustive bibliography, priority review, or legal review.
  • Private packet claims were not treated as external authority; submitted links and attachments were not executed or actively rendered.
  • No absence claim is inferred from the bounded search, and recent preprints remain subject to ordinary scholarly review.

Continue exploring

Compare another research frontier

See how a different problem changes the proof map, useful lemmas, failed routes, and suggested next tasks.

Explore all research workspaces

Expanded visual

Open original image