{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"catalytic_pathway_enablement__mathematics","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_id":"rotating_proof_interface_clinic","proposal_index":2,"version":0,"title":"Rotating Proof-Interface Clinic for Cross-Subfield Lemma Handoffs","problem":"In a collaborative mathematics project spanning two or more subfields, proof obligations can stall at disciplinary interfaces even when the required translation and handoff are feasible. For each stalled obligation, contributors separately reconstruct terminology correspondences, normalize hypotheses, locate compatible results, determine which side conditions survive translation, and identify an appropriate reviewer. The same interface work is paid again because no bounded, reusable service owns the transformation from an informal cross-field request to a precise, review-ready lemma packet.","actors":["Mathematicians submitting stalled cross-subfield proof obligations","Rotating specialists familiar with the participating subfields","The project proof architect or steering group","Mathematicians assigned to prove or review the resulting lemma","Contributors whose definitions, results, or attribution may be affected by a translation"],"observable_state":"The project's proof-dependency register contains obligations waiting at subfield boundaries. Their records show repeated requests for terminology clarification, incompatible definitions discovered after work begins, hypotheses added or lost during handoff, uncertain ownership, repeated specialist search, and tickets returned because the requested conclusion was not stated in a form the receiving mathematician could evaluate.","consequence":"Proof dependencies remain unresolved while specialist time is repeatedly spent reconstructing interfaces. Misstated hypotheses or definition mismatches can send contributors down irrelevant proof paths, and informal access to well-connected specialists can determine which obligations receive attention.","affected_objective":"Convert eligible cross-subfield proof obstructions into faithful, review-ready lemma handoff packets without changing the theorem, supplying the missing proof, or weakening mathematical scrutiny.","intervention":"Establish a governed, rotating proof-interface clinic. An intake contract requires the exact parent theorem, local definitions, desired conclusion, permitted assumptions, known dependencies, attempted routes, and the specific interface causing the stall. A rotating two-specialist team checks definitional compatibility, translates notation, separates established implications from open mathematical content, formulates the smallest faithful lemma contract, records side conditions and citations already supplied by the project, and identifies an appropriate destination or escalation route. The clinic releases the packet and returns to readiness after a capped session, documented handoff, conflict check, and rotation or rest. It does not prove the lemma or adjudicate the theorem. Routine translation and dependency-shaping cases enter the clinic; disputes over truth, foundational choices, credit, or genuinely new mathematics leave for full collaboration. Queue depth, specialist occupancy, reopen rate, translation defects, downstream review capacity, and recovery state govern intake and deactivation.","structural_mapping":[{"archetype_element":"Target transformation specification","domain_realization":"Transform an eligible, informally described cross-subfield proof obstruction into a versioned lemma packet containing an exact statement, translated definitions, preserved hypotheses, dependency links, unresolved mathematical content, intended recipient, and independent-review requirement."},{"archetype_element":"Activation barrier","domain_realization":"The recurring barrier is the search, interpretation, trust, notation translation, hypothesis normalization, and coordination required before a mathematician in another subfield can begin substantive proof work."},{"archetype_element":"Reusable facilitator","domain_realization":"A rotating, governed clinic reuses maintained interface knowledge, relationships, intake rules, and translation practice across distinct proof obligations while releasing each completed packet and returning for another case."},{"archetype_element":"Facilitator–substrate interface","domain_realization":"A published intake contract specifies the theorem context, definitions, proposed conclusion, admissible assumptions, attempted routes, requested interface, confidentiality level, and submitter availability required before clinic review."},{"archetype_element":"Selectivity rule","domain_realization":"The clinic admits obligations whose bottleneck is definitional translation or handoff construction. It reroutes cases requiring an original proof, a choice between incompatible foundations, adjudication of truth or priority, changes to the parent theorem, or resolution of authorship disputes."},{"archetype_element":"Permitted pathway boundary","domain_realization":"The clinic may clarify and translate a proof obligation but may not declare a lemma true, add assumptions without disclosure, waive independent review, alter the project's axioms, or substitute social agreement for proof."},{"archetype_element":"Turnover capacity","domain_realization":"Capacity is measured as faithful packets released per specialist session together with specialist minutes, queue time, contact time, reopen rate, downstream review load, and recovery time; raw packet count alone is not treated as success."},{"archetype_element":"Facilitator regeneration cycle","domain_realization":"After a capped case load, specialists document unresolved context, update the approved interface glossary when warranted, transfer custody, disclose conflicts, and rotate or rest. Defective templates or mappings are withdrawn and revalidated before reuse."},{"archetype_element":"Saturation and interference monitoring","domain_realization":"Queue growth and occupied clinic slots indicate saturation; increasing packet reopens, definition disputes, conflict-of-interest flags, fatigue signals, or downstream reviewer backlog indicate inhibition, drift, or overload requiring a different response."},{"archetype_element":"Byproduct and side-pathway guardrail","domain_realization":"Independent review checks for lost hypotheses, altered quantifiers, incompatible definitions, premature claims of equivalence, obscured uncertainty, inappropriate recipient selection, and uncredited intellectual contributions."},{"archetype_element":"Equilibrium neutrality","domain_realization":"The clinic accelerates preparation and routing of a proof obligation that collaborators could already perform. It does not make a false lemma true, resolve missing mathematical insight, or change what counts as a proof."},{"archetype_element":"Accountable catalyst steward","domain_realization":"A clinic coordinator owns transparent eligibility, workload limits, rotation, conflict handling, records, appeals, succession, and incident response but has no authority to accept mathematical claims."}],"mechanism_mapping":[{"mechanism_slug":"interface_contract_design","role":"Defines the required obstruction packet, the clinic's translation guarantees, protected mathematical invariants, versioning, and the boundary between clarification and substantive proof.","counterfactual_removal":"Without an explicit contract, specialists must renegotiate context for every case, and a completed handoff may silently change definitions, hypotheses, or scope."},{"mechanism_slug":"embedded_specialist_review_lane","role":"Places bounded cross-field judgment at the point where eligible proof obligations stall, with triage, case caps, escalation, conflict checks, coverage, and succession.","counterfactual_removal":"Without the review lane, contributors return to ad hoc specialist search; without its limits, the specialists become a bottleneck or an informal mathematical authority."},{"mechanism_slug":"reusable_broker_or_convener_service","role":"Maintains the relationships and translation knowledge needed to connect submitters with suitable lemma owners and reviewers across subfield boundaries.","counterfactual_removal":"Without the broker function, each contributor must rebuild trust and search for recipients independently, while access may depend on personal connections."},{"mechanism_slug":"prevalidated_transformation_template","role":"Provides a versioned lemma-packet structure that preserves statement, definitions, quantifiers, hypotheses, dependencies, uncertainties, attribution, and review status across handoffs.","counterfactual_removal":"Without the template, packets vary in what they preserve, and the receiving mathematician must reconstruct whether the translated obligation still matches the parent theorem."},{"mechanism_slug":"fast_track_with_eligibility_rules","role":"Routes routine notation and definition translations through a bounded clinic path while sending mathematically substantive, disputed, or incompatible cases to full collaboration.","counterfactual_removal":"Without eligibility and rerouting, the clinic may attempt to accelerate cases whose barrier is missing mathematics, creating rubber-stamped or misleading packets."},{"mechanism_slug":"catalyst_cofactor_system","role":"Makes explicit the complements required for clinic activity: current local definitions, access to supplied project references, submitter availability, specialist coverage from both sides of the interface, and downstream reviewer capacity.","counterfactual_removal":"Without mapping and checking these complements, the clinic may appear inactive or effective for reasons actually caused by missing context, unavailable contributors, or hidden unpaid specialist labor."},{"mechanism_slug":"active_site_capacity_dashboard","role":"Shows queue depth, specialist slots, session load, packet age, reopen signals, conflict holds, and downstream review backlog so intake follows usable human capacity.","counterfactual_removal":"Without joint capacity and quality visibility, high specialist utilization may be mistaken for health while waiting, fatigue, and defective handoffs increase."},{"mechanism_slug":"turnover_and_selectivity_assay","role":"Compares faithful, independently reviewable packets per bounded specialist session against ad hoc handoffs while counting reopens, misstatements, reroutes, labor, and downstream burden.","counterfactual_removal":"Without the assay, additional specialist attention or selection of easy obligations could be mislabeled as catalytic reuse, and translation defects would disappear behind packet counts."},{"mechanism_slug":"catalyst_regeneration_protocol","role":"Defines case release, documentation, rotation, rest, mapping refresh, template withdrawal, retraining, and retirement when a specialist or interface artifact cannot be restored to the required operating state.","counterfactual_removal":"Without regeneration and retirement, specialists may be treated as inexhaustible and stale interface mappings may repeatedly propagate mathematical errors."},{"mechanism_slug":"small_safe_to_fail_probe","role":"Tests the clinic on a bounded set of resolved obligations with concealed resolutions, a documented ad hoc baseline, independent review, and no effect on live theorem status.","counterfactual_removal":"Without a contained counterfactual test, the project cannot distinguish reusable barrier reduction from extra attention and could expose live proofs or contributors to an unvalidated gatekeeping process."}],"causal_chain":["A contributor submits a proof obstruction using the published intake contract.","An eligibility check distinguishes a translation-and-handoff barrier from unresolved mathematical invention, foundational disagreement, or attribution conflict.","An eligible case enters a capped queue matched to specialists covering both sides of the interface.","The specialists reuse maintained vocabulary mappings, relationships, and the lemma-packet template instead of reconstructing the interface from zero.","They translate the statement, preserve its logical structure, identify required side conditions, mark unresolved content, and select a destination or escalation path.","An independent reviewer compares the packet with the original obstruction and checks for altered definitions, hypotheses, quantifiers, attribution, or certainty.","A faithful packet is released to ordinary proof work; a defective, incompatible, or substantive case is returned or escalated without mathematical approval.","The specialists document the cycle, relinquish the case, rotate or rest, and return to a ready state.","Capacity, reopen, conflict, quality, and downstream-load signals meter subsequent intake and trigger pause or regeneration when necessary.","Comparison with ad hoc handoffs tests whether reusable interface capacity, rather than added authority or weaker review, removed the recurring barrier."],"baseline":"Contributors seek help through ordinary project meetings, correspondence, personal contacts, or direct requests to potential coauthors. Each recipient reconstructs the theorem context and terminology before deciding whether the request is meaningful. For each case, record waiting time, contributor and specialist minutes, number of handoffs, statement revisions, definition mismatches, reopen events, reviewer assessment, and time until substantive proof work can begin.","nearest_rivals":["Assigning a permanent senior proof architect to translate every interface obligation, which adds concentrated expert capacity but risks a single point of failure and does not test a rotating reusable service.","Maintaining a shared glossary or notation wiki, which may permanently reduce lookup friction but does not triage cases, construct lemma contracts, broker recipients, or complete a governed facilitator cycle.","Using a proof assistant to formalize all interfaces, which can expose definitional and logical mismatches but constitutes a broader formalization pathway with different setup costs and does not by itself supply cross-field interpretation or ownership.","Holding general seminars or office hours, which can generate insight and relationships but lack case eligibility, a specified output, turnover accounting, regeneration, and faithful-handoff review.","Redesigning the collaboration so one team owns each proof section end to end, which may remove interfaces structurally rather than catalyze repeated transformations at them."],"remaining_contrastive_claim":"The untested contrastive hypothesis is that a bounded, rotating clinic can reuse interface knowledge and trusted routing across multiple eligible proof obligations, reducing repeated translation and coordination work while preserving statement fidelity and ordinary proof review. Evidence must hold expert labor, eligibility, mathematical standards, and downstream review constant enough to distinguish this pathway from additional staffing, a glossary, informal consultation, or selection of easy cases.","authority_safety":{"decision_authority":"The project steering group may authorize a bounded shadow evaluation, publish eligibility rules, appoint the coordinator, and set workload limits. Existing theorem owners and reviewers retain sole authority over definitions, proof acceptance, attribution, and publication.","authorized_first_step":"Replay a bounded set of previously resolved cross-subfield obligations in shadow mode using rotating specialists who cannot see the archived resolutions, followed by independent fidelity review against the original records.","excluded_actions":["Declaring a lemma proved or a theorem dependency closed","Adding, removing, or weakening hypotheses without explicit return to the theorem owner","Changing axioms, definitions, or the parent theorem to make a handoff easier","Assigning authorship, priority, or mathematical credit through the clinic","Compelling a specialist to exceed the case cap or disclose confidential work","Using personal relationships or viewpoint agreement as eligibility criteria","Routing foundational disputes, genuinely new proof problems, or attribution conflicts through the fast lane","Expanding to live mandatory intake before review of the bounded evaluation"],"halt_rollback":"Stop new intake if a packet materially changes a statement, conceals an assumption, misattributes a contribution, breaches confidentiality, bypasses an unresolved conflict, exceeds the specialist workload cap, or produces a repeated fidelity defect. Mark all affected packets as unvalidated, restore their original obstruction records, notify their owners, and require independent review of the interface mappings and clinic process before restart."},"negative_tests":{"strongest_counterevidence":"The apparently recurring interface delays may actually arise from theorem-specific invention: each obligation could require unique mathematical insight, and the translation work may be inseparable from discovering the proof. In that case, a standardized clinic would add handoffs and consume scarce experts without providing reusable catalytic turnover.","problem_falsifier":"The proposed problem is falsified if an audit finds that stalled obligations are already precise and mutually intelligible, that cross-subfield translation is not repeated across cases, or that the dominant causes are false conjectures, missing proofs, foundational disagreement, unavailable reviewers, or project-priority decisions.","intervention_falsifier":"The intervention is falsified for the tested scope if clinic packets are no more faithful or review-ready than ad hoc handoffs; if total submitter, specialist, and reviewer labor or elapsed preparation does not improve under the fixed comparison; if reopens or lost assumptions increase; if most cases require substantive escalation; or if rotation and recovery cannot prevent gatekeeping, fatigue, or loss of continuity.","risks":["Translation may erase a restrictive hypothesis, alter a quantifier, or overstate an equivalence.","The clinic may confer unearned authority on its specialists or packets.","Eligibility rules may favor contributors already fluent in the project's preferred notation.","Personal or intellectual conflicts may distort routing and framing.","Maintained mappings may become stale as project definitions change.","Specialists may be exhausted, under-credited, or treated as interchangeable infrastructure.","A lemma packet may obscure the creative contribution involved in identifying the right formulation.","Faster packet production may overload proof authors and independent reviewers.","Confidential conjectures or correspondence may be exposed beyond their intended audience.","Contributors may optimize submissions for clinic acceptance instead of describing the actual mathematical obstruction."]},"next_evidence_step":"Choose eight archived, fully resolved proof obligations that originally crossed the same pair of subfields and include both successful translations and cases later found to require substantive mathematics. Conceal their resolutions and randomly order them. Have a rotating two-specialist clinic and a separate ad hoc-handoff team reconstruct packets under equal access to the original submitted context, with session caps and no live proof authority. Precommit fidelity, confidentiality, workload, and immediate-stop criteria. Blinded reviewers then compare each packet with the archived obstruction and resolution for statement fidelity, preserved hypotheses and definitions, explicit uncertainty, suitable routing, reviewer readiness, labor, elapsed preparation, reopens, and reroutes. Include one deliberately incompatible case to test rejection and rotate specialists after two cases to test release, recovery, and continuity. The result is bounded local evidence and does not authorize mandatory or live deployment.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Earlier proposal 1 addresses exact polynomial ideal-membership determinations using a verified Gröbner basis, deterministic normal-form reduction, and machine-checkable certificates. This proposal addresses cross-subfield interpretation, trust, and coordination barriers that arise before substantive proof work can begin. Its facilitator is a governed rotating human clinic supported by interface knowledge and relationships, not an algebraic basis or certificate-producing reducer. Its output is a faithful lemma handoff packet rather than a truth determination, and its causal path is intake, translation, brokerage, independent fidelity review, release, and human regeneration rather than computational reduction. It can be adopted by a collaborative proof project without adopting proposal 1, and proposal 1 can operate without this clinic.","revision_record":{"parent_version":null,"progress_targets_addressed":["Initial schema-complete proposal at index 2","Materially different mathematics problem and intervention from sealed proposal 1","Explicit reusable human-facilitator cycle with capacity, regeneration, safeguards, falsifiers, rivals, and bounded evidence"],"conceptual_changes":["Initial version; defined cross-subfield lemma-handoff preparation as the target transformation and separated it from proving or certifying mathematical claims."],"operational_changes":["Initial version; specified contract-based intake, dual-specialist triage, packet fidelity review, case caps, rotation, escalation, recovery, and deactivation."],"evidence_changes":["Initial version; defined an eight-case concealed archival replay with an ad hoc baseline, blinded reviewers, an incompatible input, and specialist rotation."],"claim_changes":["Initial version; limited the proposal to an untested hypothesis about reusable translation and coordination capacity, made no effect-size claim, and marked prior art unsearched."]}}