{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QDQQCGDE63V2FCOCQCTVLFX75R","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"45ac6f77298b21ccd9f6864d22de79db79452055beee815ff867f244a0bb8b06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-12-28T10:50:53Z","title_canon_sha256":"a99a3e2c52ab5560f36bfe240d0a6c30ec6ed22785fd05c8ea36cbc5e289d2b1"},"schema_version":"1.0","source":{"id":"2412.20114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.20114","created_at":"2026-07-05T09:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"2412.20114v1","created_at":"2026-07-05T09:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20114","created_at":"2026-07-05T09:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"QDQQCGDE63V2","created_at":"2026-07-05T09:54:54Z"},{"alias_kind":"pith_short_16","alias_value":"QDQQCGDE63V2FCOC","created_at":"2026-07-05T09:54:54Z"},{"alias_kind":"pith_short_8","alias_value":"QDQQCGDE","created_at":"2026-07-05T09:54:54Z"}],"graph_snapshots":[{"event_id":"sha256:38ade16100b1ee601763201451a6dccbc83435c4ca7d5190dca0e201e3f04fad","target":"graph","created_at":"2026-07-05T09:54:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.20114/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Strong algebraic proof systems such as IPS (Ideal Proof System; Grochow-Pitassi [GP18]) offer a general model for deriving polynomials in an ideal and refuting unsatisfiable propositional formulas, subsuming most standard propositional proof systems. A major approach for lower bounding the size of IPS refutations is the Functional Lower Bound Method (Forbes, Shpilka, Tzameret and Wigderson [FSTW21]), which reduces the hardness of refuting a polynomial equation f(x) = 0 with no Boolean solutions to the hardness of computing the function 1/f(x) over the Boolean cube with an algebraic circuit. Us","authors_text":"Iddo Tzameret, Nutan Limaye, Tuomas Hakoniemi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-12-28T10:50:53Z","title":"Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20114","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fdf68dc1bd6ca437aede12631d7e2823fe5f34758345b34211c9afcd2eb197de","target":"record","created_at":"2026-07-05T09:54:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"45ac6f77298b21ccd9f6864d22de79db79452055beee815ff867f244a0bb8b06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-12-28T10:50:53Z","title_canon_sha256":"a99a3e2c52ab5560f36bfe240d0a6c30ec6ed22785fd05c8ea36cbc5e289d2b1"},"schema_version":"1.0","source":{"id":"2412.20114","kind":"arxiv","version":1}},"canonical_sha256":"80e1011864f6eba289c280a75596ffec4a34d9192abf4fc0371d125fbc2b0be5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80e1011864f6eba289c280a75596ffec4a34d9192abf4fc0371d125fbc2b0be5","first_computed_at":"2026-07-05T09:54:54.815391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:54.815391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YJHDjfHn8Y7JD6W2l2NNjE0BKYuKBxAZxkd1z6DZnSJDn2Phbc1YRowVvGACTs6Rw66foMrFG528MBqJrlc0CA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:54.815870Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.20114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdf68dc1bd6ca437aede12631d7e2823fe5f34758345b34211c9afcd2eb197de","sha256:38ade16100b1ee601763201451a6dccbc83435c4ca7d5190dca0e201e3f04fad"],"state_sha256":"fc8dbd6e95e5422407c4ca2e99632e6ee08f509b10ffb804b3eb10e57a14e851"}