{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ADWFYVG55HN3IST63FUYQIVEB3","short_pith_number":"pith:ADWFYVG5","schema_version":"1.0","canonical_sha256":"00ec5c54dde9dbb44a7ed9698822a40ed84c12dbb75b96c99697027eaa1c18b0","source":{"kind":"arxiv","id":"2504.20262","version":5},"attestation_state":"computed","paper":{"title":"Closure Properties and Characterizations of TotP","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Yaroslav Ivanashev","submitted_at":"2025-04-28T21:07:13Z","abstract_excerpt":"The class TotP consists of functions that count the number of all paths of a nondeterministic polynomial-time Turing machine. In this paper, we give a predicate based definition of TotP, analogous to a standard definition of #P. From a new characterization of TotP it follows that many well known #P problems belong to TotP, and TotP = #P if and only if P = NP. We show that TotP has several closure properties of #P and GapP, and also properties that are not known to hold for #P and GapP. We also prove that the closure of TotP under left composition with FP+ is equivalent to TotP = FP+ and P = PP"},"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":"2504.20262","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2025-04-28T21:07:13Z","cross_cats_sorted":[],"title_canon_sha256":"c903db53a230471c01ad911d40ed43d15369c2199f4c1a646736f0c41c0477b6","abstract_canon_sha256":"add17cf59dacad1ccde61b327bbcbdb1b9a06c31aa6e537f46b3f06addf10cf3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:29.059792Z","signature_b64":"WqIYKPy1M/1zrlbxg8bAGhvNi2D44I+pJdbYcQvmTteR0957/OZDSfdEzZ6tbO0eU97Tq0+f2T39t/H+6IMYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00ec5c54dde9dbb44a7ed9698822a40ed84c12dbb75b96c99697027eaa1c18b0","last_reissued_at":"2026-07-05T11:38:29.059231Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:29.059231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closure Properties and Characterizations of TotP","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Yaroslav Ivanashev","submitted_at":"2025-04-28T21:07:13Z","abstract_excerpt":"The class TotP consists of functions that count the number of all paths of a nondeterministic polynomial-time Turing machine. In this paper, we give a predicate based definition of TotP, analogous to a standard definition of #P. From a new characterization of TotP it follows that many well known #P problems belong to TotP, and TotP = #P if and only if P = NP. We show that TotP has several closure properties of #P and GapP, and also properties that are not known to hold for #P and GapP. We also prove that the closure of TotP under left composition with FP+ is equivalent to TotP = FP+ and P = PP"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.20262","kind":"arxiv","version":5},"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/2504.20262/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":"2504.20262","created_at":"2026-07-05T11:38:29.059292+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.20262v5","created_at":"2026-07-05T11:38:29.059292+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.20262","created_at":"2026-07-05T11:38:29.059292+00:00"},{"alias_kind":"pith_short_12","alias_value":"ADWFYVG55HN3","created_at":"2026-07-05T11:38:29.059292+00:00"},{"alias_kind":"pith_short_16","alias_value":"ADWFYVG55HN3IST6","created_at":"2026-07-05T11:38:29.059292+00:00"},{"alias_kind":"pith_short_8","alias_value":"ADWFYVG5","created_at":"2026-07-05T11:38:29.059292+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.04110","citing_title":"Low Sets and Closure Properties of Counting Function Classes","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ADWFYVG55HN3IST63FUYQIVEB3","json":"https://pith.science/pith/ADWFYVG55HN3IST63FUYQIVEB3.json","graph_json":"https://pith.science/api/pith-number/ADWFYVG55HN3IST63FUYQIVEB3/graph.json","events_json":"https://pith.science/api/pith-number/ADWFYVG55HN3IST63FUYQIVEB3/events.json","paper":"https://pith.science/paper/ADWFYVG5"},"agent_actions":{"view_html":"https://pith.science/pith/ADWFYVG55HN3IST63FUYQIVEB3","download_json":"https://pith.science/pith/ADWFYVG55HN3IST63FUYQIVEB3.json","view_paper":"https://pith.science/paper/ADWFYVG5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.20262&json=true","fetch_graph":"https://pith.science/api/pith-number/ADWFYVG55HN3IST63FUYQIVEB3/graph.json","fetch_events":"https://pith.science/api/pith-number/ADWFYVG55HN3IST63FUYQIVEB3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ADWFYVG55HN3IST63FUYQIVEB3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ADWFYVG55HN3IST63FUYQIVEB3/action/storage_attestation","attest_author":"https://pith.science/pith/ADWFYVG55HN3IST63FUYQIVEB3/action/author_attestation","sign_citation":"https://pith.science/pith/ADWFYVG55HN3IST63FUYQIVEB3/action/citation_signature","submit_replication":"https://pith.science/pith/ADWFYVG55HN3IST63FUYQIVEB3/action/replication_record"}},"created_at":"2026-07-05T11:38:29.059292+00:00","updated_at":"2026-07-05T11:38:29.059292+00:00"}