{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5ZGTPI6QMUEHJDB5DGHWRSXCB3","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":"63c988d6c97e88a1b0b1f2b2f56342279786a7ded28e8fe633ba2d14db6d259c","cross_cats_sorted":["cs.CG","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-10-09T10:53:07Z","title_canon_sha256":"e3872a909cfb5ffac24a081ab4a98339391c04bf115e35d7b97f365f217b9576"},"schema_version":"1.0","source":{"id":"1010.1834","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1834","created_at":"2026-05-18T04:39:30Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1834v1","created_at":"2026-05-18T04:39:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1834","created_at":"2026-05-18T04:39:30Z"},{"alias_kind":"pith_short_12","alias_value":"5ZGTPI6QMUEH","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5ZGTPI6QMUEHJDB5","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5ZGTPI6Q","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:17c848a44066dcb9f3b52ffd6052031007d392dbf2aaafb69ec9ba9955ef016a","target":"graph","created_at":"2026-05-18T04:39:30Z","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"},"paper":{"abstract_excerpt":"The Generalized Discretizable Molecular Distance Geometry Problem is a distance geometry problems that can be solved by a combinatorial algorithm called ``Branch-and-Prune''. It was observed empirically that the number of solutions of YES instances is always a power of two. We give a proof that this event happens with probability one.","authors_text":"Antonio Mucherino, Benoit Masson, Carlile Lavor, Jon Lee, Leo Liberti","cross_cats":["cs.CG","q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-10-09T10:53:07Z","title":"On the number of solutions of the discretizable molecular distance geometry problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1834","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":"sha256:67e9f3b3c0d992cfac7af5831b6f3131ca313da50548d9d604da733858e16441","target":"record","created_at":"2026-05-18T04:39:30Z","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":"63c988d6c97e88a1b0b1f2b2f56342279786a7ded28e8fe633ba2d14db6d259c","cross_cats_sorted":["cs.CG","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-10-09T10:53:07Z","title_canon_sha256":"e3872a909cfb5ffac24a081ab4a98339391c04bf115e35d7b97f365f217b9576"},"schema_version":"1.0","source":{"id":"1010.1834","kind":"arxiv","version":1}},"canonical_sha256":"ee4d37a3d06508748c3d198f68cae20ec407160a22bc0ea04ab9866a38aea7af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee4d37a3d06508748c3d198f68cae20ec407160a22bc0ea04ab9866a38aea7af","first_computed_at":"2026-05-18T04:39:30.246662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:30.246662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9OHURlci+XMG+Q7dHe2i+G2TKuwgiYqBXgbSQUp6HVtnojeVEvWohxWfLZAxSDChVt6bV7ZudBt+VFHimlunCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:30.247338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1834","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67e9f3b3c0d992cfac7af5831b6f3131ca313da50548d9d604da733858e16441","sha256:17c848a44066dcb9f3b52ffd6052031007d392dbf2aaafb69ec9ba9955ef016a"],"state_sha256":"4bf63b3a8656fa54eddfc8dc037f53438b2e5b01500133e0a8ad76ee22f4e24a"}