{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:TXC4C6Y66XUTVM7YPIUML754UW","short_pith_number":"pith:TXC4C6Y6","schema_version":"1.0","canonical_sha256":"9dc5c17b1ef5e93ab3f87a28c5ffbca5be29d3bb6bab3f0402f31de5c99c8731","source":{"kind":"arxiv","id":"2506.23404","version":1},"attestation_state":"computed","paper":{"title":"Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Arnaud Durand, Juha Kontinen, Melissa Antonelli","submitted_at":"2025-06-29T21:31:12Z","abstract_excerpt":"In this paper, we provide a uniform framework for investigating small circuit classes and bounds through the lens of ordinary differential equations (ODEs). Following an approach recently introduced to capture the class of polynomial-time computable functions via ODE-based recursion schemas and later applied to the context of functions computed by unbounded fan-in circuits of constant depth (FAC^0), we study multiple relevant small circuit classes. In particular, we show that natural restrictions on linearity and derivation along functions with specific growth rate correspond to kinds of funct"},"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":"2506.23404","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2025-06-29T21:31:12Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"83325b4fd8dea104742657af92fb50b4dab657e1fbfa242372be38a2fb03ce0a","abstract_canon_sha256":"bf32d54334374424f9b146748d5c3d27cc6263406d3b940ba92615dfb3157768"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:21.099778Z","signature_b64":"xFCcFff2Rv2Y4ax5EV5vZmP2Zg+RmCSBBshRJfVNXPV8siGt9MhEMEROB2BPGzuUOca5irg037dLSpc8xE59Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dc5c17b1ef5e93ab3f87a28c5ffbca5be29d3bb6bab3f0402f31de5c99c8731","last_reissued_at":"2026-07-05T11:29:21.099252Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:21.099252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Arnaud Durand, Juha Kontinen, Melissa Antonelli","submitted_at":"2025-06-29T21:31:12Z","abstract_excerpt":"In this paper, we provide a uniform framework for investigating small circuit classes and bounds through the lens of ordinary differential equations (ODEs). Following an approach recently introduced to capture the class of polynomial-time computable functions via ODE-based recursion schemas and later applied to the context of functions computed by unbounded fan-in circuits of constant depth (FAC^0), we study multiple relevant small circuit classes. In particular, we show that natural restrictions on linearity and derivation along functions with specific growth rate correspond to kinds of funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23404","kind":"arxiv","version":1},"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/2506.23404/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":"2506.23404","created_at":"2026-07-05T11:29:21.099321+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.23404v1","created_at":"2026-07-05T11:29:21.099321+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23404","created_at":"2026-07-05T11:29:21.099321+00:00"},{"alias_kind":"pith_short_12","alias_value":"TXC4C6Y66XUT","created_at":"2026-07-05T11:29:21.099321+00:00"},{"alias_kind":"pith_short_16","alias_value":"TXC4C6Y66XUTVM7Y","created_at":"2026-07-05T11:29:21.099321+00:00"},{"alias_kind":"pith_short_8","alias_value":"TXC4C6Y6","created_at":"2026-07-05T11:29:21.099321+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TXC4C6Y66XUTVM7YPIUML754UW","json":"https://pith.science/pith/TXC4C6Y66XUTVM7YPIUML754UW.json","graph_json":"https://pith.science/api/pith-number/TXC4C6Y66XUTVM7YPIUML754UW/graph.json","events_json":"https://pith.science/api/pith-number/TXC4C6Y66XUTVM7YPIUML754UW/events.json","paper":"https://pith.science/paper/TXC4C6Y6"},"agent_actions":{"view_html":"https://pith.science/pith/TXC4C6Y66XUTVM7YPIUML754UW","download_json":"https://pith.science/pith/TXC4C6Y66XUTVM7YPIUML754UW.json","view_paper":"https://pith.science/paper/TXC4C6Y6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.23404&json=true","fetch_graph":"https://pith.science/api/pith-number/TXC4C6Y66XUTVM7YPIUML754UW/graph.json","fetch_events":"https://pith.science/api/pith-number/TXC4C6Y66XUTVM7YPIUML754UW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TXC4C6Y66XUTVM7YPIUML754UW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TXC4C6Y66XUTVM7YPIUML754UW/action/storage_attestation","attest_author":"https://pith.science/pith/TXC4C6Y66XUTVM7YPIUML754UW/action/author_attestation","sign_citation":"https://pith.science/pith/TXC4C6Y66XUTVM7YPIUML754UW/action/citation_signature","submit_replication":"https://pith.science/pith/TXC4C6Y66XUTVM7YPIUML754UW/action/replication_record"}},"created_at":"2026-07-05T11:29:21.099321+00:00","updated_at":"2026-07-05T11:29:21.099321+00:00"}