{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X3UQX6TJMCIIMQIB4IE6SYFVIX","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":"623ceba9232ded081475d799d69bf58f827dca2a16707da30f9fad5f07b60032","cross_cats_sorted":["cs.DM","cs.DS","cs.LO","math.CO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.CC","submitted_at":"2025-06-07T08:53:38Z","title_canon_sha256":"eba371ce98d88baf8325033fcfb43fb458265236d13b6ef715562d06b32fb7a9"},"schema_version":"1.0","source":{"id":"2506.06716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.06716","created_at":"2026-07-05T11:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"2506.06716v1","created_at":"2026-07-05T11:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06716","created_at":"2026-07-05T11:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"X3UQX6TJMCII","created_at":"2026-07-05T11:17:54Z"},{"alias_kind":"pith_short_16","alias_value":"X3UQX6TJMCIIMQIB","created_at":"2026-07-05T11:17:54Z"},{"alias_kind":"pith_short_8","alias_value":"X3UQX6TJ","created_at":"2026-07-05T11:17:54Z"}],"graph_snapshots":[{"event_id":"sha256:4681e9b654536a9097d7cb7e8d0beb1062fe977033fc1ac479130861cbbedeaf","target":"graph","created_at":"2026-07-05T11:17:54Z","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/2506.06716/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The canonical class in the realm of counting complexity is #P. It is well known that the problem of counting the models of a propositional formula in disjunctive normal form (#DNF) is complete for #P under Turing reductions. On the other hand, #DNF $\\in$ spanL and spanL $\\not\\subseteq$ #P unless NL = NP. Hence, the class of functions logspace-reducible to #DNF is a strict subset of #P under plausible complexity-theoretic assumptions. By contrast, we show that two calls to a (restricted) #2DNF oracle suffice to capture gapP, namely, that the logspace many-one closure of the subtraction between ","authors_text":"Erik D. Demaine, Markus Hecher, Max Bannach, Timothy Gomez","cross_cats":["cs.DM","cs.DS","cs.LO","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.CC","submitted_at":"2025-06-07T08:53:38Z","title":"#P is Sandwiched by One and Two #2DNF Calls: Is Subtraction Stronger Than We Thought?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06716","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":"sha256:1293a601103e982542534d04ff5b783970c9cb20432a8905994cca20d59ea2e3","target":"record","created_at":"2026-07-05T11:17:54Z","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":"623ceba9232ded081475d799d69bf58f827dca2a16707da30f9fad5f07b60032","cross_cats_sorted":["cs.DM","cs.DS","cs.LO","math.CO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.CC","submitted_at":"2025-06-07T08:53:38Z","title_canon_sha256":"eba371ce98d88baf8325033fcfb43fb458265236d13b6ef715562d06b32fb7a9"},"schema_version":"1.0","source":{"id":"2506.06716","kind":"arxiv","version":1}},"canonical_sha256":"bee90bfa696090864101e209e960b545ebe25c276a642295b4363ced21ffbf04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bee90bfa696090864101e209e960b545ebe25c276a642295b4363ced21ffbf04","first_computed_at":"2026-07-05T11:17:54.592105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:54.592105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YMg23WyNXnkwXK2tM95bi/1iObcOi9ovxMw2zZ4jSVhzXte+Q6d0nFKij47up8LIdiWBrhxcpekPY1CPI0MfCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:54.592601Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.06716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1293a601103e982542534d04ff5b783970c9cb20432a8905994cca20d59ea2e3","sha256:4681e9b654536a9097d7cb7e8d0beb1062fe977033fc1ac479130861cbbedeaf"],"state_sha256":"28333133f7c5b08685c4ac190f6050189a3a3a17ba01fee2541ef9ca6975d6cb"}