{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7GVEKFFFMOOMOIKZ6QTHMFRXDN","short_pith_number":"pith:7GVEKFFF","schema_version":"1.0","canonical_sha256":"f9aa4514a5639cc72159f4267616371b4144f3ede5a0bdac43b50fde04cfda3f","source":{"kind":"arxiv","id":"2602.23809","version":3},"attestation_state":"computed","paper":{"title":"Black-Box PWPP Is Not Turing-Closed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Pavel Hub\\'a\\v{c}ek","submitted_at":"2026-02-27T08:47:33Z","abstract_excerpt":"We establish that adaptive collision-finding queries are strictly more powerful than non-adaptive ones by proving that the complexity class PWPP (Polynomial Weak Pigeonhole Principle) is not closed under adaptive Turing reductions in the black-box setting. Previously, PWPP was known to be closed under non-adaptive Turing reductions (Je\\v{r}\\'abek 2016). We demonstrate this black-box separation by introducing the NESTED-COLLISION problem, a natural collision-finding problem defined on a pair of shrinking functions. We show that while this problem is solvable via two adaptive calls to a PWPP ora"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2602.23809","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-02-27T08:47:33Z","cross_cats_sorted":[],"title_canon_sha256":"d93261b31928a36e6ebe90042bc1dc045f8eae5bff5abf206b07b4c77ddb1c37","abstract_canon_sha256":"446fa2df18a72696c118669c7f2ff0ce4191817c41d655f60e1c96b0fa2d453d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:24.164452Z","signature_b64":"VjH7oT8jjFXD3jznu/cKmY4Dz5FTHcZ5LrlCngYzeFrizaoYlox+S0tyubb1IU/lW6bpSghE7OWXzPeGlp6nAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9aa4514a5639cc72159f4267616371b4144f3ede5a0bdac43b50fde04cfda3f","last_reissued_at":"2026-06-12T01:09:24.163739Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:24.163739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Black-Box PWPP Is Not Turing-Closed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Pavel Hub\\'a\\v{c}ek","submitted_at":"2026-02-27T08:47:33Z","abstract_excerpt":"We establish that adaptive collision-finding queries are strictly more powerful than non-adaptive ones by proving that the complexity class PWPP (Polynomial Weak Pigeonhole Principle) is not closed under adaptive Turing reductions in the black-box setting. Previously, PWPP was known to be closed under non-adaptive Turing reductions (Je\\v{r}\\'abek 2016). We demonstrate this black-box separation by introducing the NESTED-COLLISION problem, a natural collision-finding problem defined on a pair of shrinking functions. We show that while this problem is solvable via two adaptive calls to a PWPP ora"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.23809","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.23809/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2602.23809","created_at":"2026-06-12T01:09:24.163801+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.23809v3","created_at":"2026-06-12T01:09:24.163801+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.23809","created_at":"2026-06-12T01:09:24.163801+00:00"},{"alias_kind":"pith_short_12","alias_value":"7GVEKFFFMOOM","created_at":"2026-06-12T01:09:24.163801+00:00"},{"alias_kind":"pith_short_16","alias_value":"7GVEKFFFMOOMOIKZ","created_at":"2026-06-12T01:09:24.163801+00:00"},{"alias_kind":"pith_short_8","alias_value":"7GVEKFFF","created_at":"2026-06-12T01:09:24.163801+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.16989","citing_title":"Bolzano: Case Studies in LLM-Assisted Mathematical Research","ref_index":41,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7GVEKFFFMOOMOIKZ6QTHMFRXDN","json":"https://pith.science/pith/7GVEKFFFMOOMOIKZ6QTHMFRXDN.json","graph_json":"https://pith.science/api/pith-number/7GVEKFFFMOOMOIKZ6QTHMFRXDN/graph.json","events_json":"https://pith.science/api/pith-number/7GVEKFFFMOOMOIKZ6QTHMFRXDN/events.json","paper":"https://pith.science/paper/7GVEKFFF"},"agent_actions":{"view_html":"https://pith.science/pith/7GVEKFFFMOOMOIKZ6QTHMFRXDN","download_json":"https://pith.science/pith/7GVEKFFFMOOMOIKZ6QTHMFRXDN.json","view_paper":"https://pith.science/paper/7GVEKFFF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.23809&json=true","fetch_graph":"https://pith.science/api/pith-number/7GVEKFFFMOOMOIKZ6QTHMFRXDN/graph.json","fetch_events":"https://pith.science/api/pith-number/7GVEKFFFMOOMOIKZ6QTHMFRXDN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7GVEKFFFMOOMOIKZ6QTHMFRXDN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7GVEKFFFMOOMOIKZ6QTHMFRXDN/action/storage_attestation","attest_author":"https://pith.science/pith/7GVEKFFFMOOMOIKZ6QTHMFRXDN/action/author_attestation","sign_citation":"https://pith.science/pith/7GVEKFFFMOOMOIKZ6QTHMFRXDN/action/citation_signature","submit_replication":"https://pith.science/pith/7GVEKFFFMOOMOIKZ6QTHMFRXDN/action/replication_record"}},"created_at":"2026-06-12T01:09:24.163801+00:00","updated_at":"2026-06-12T01:09:24.163801+00:00"}