{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UVIOXBPRVSJXYW5UQJDDJOFPCK","short_pith_number":"pith:UVIOXBPR","canonical_record":{"source":{"id":"1802.04708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2018-02-13T16:23:07Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"a147001af86f4860f52ee98c94d050a2c49b892672129513444786eb983ba335","abstract_canon_sha256":"59a56b0a61fdb19d99f24a4c74348b9b2fa2ce8cabbffd59dc3bf8c763df9cf7"},"schema_version":"1.0"},"canonical_sha256":"a550eb85f1ac937c5bb4824634b8af1297f8ba1e822752650a972f0b9592215b","source":{"kind":"arxiv","id":"1802.04708","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04708","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04708v1","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04708","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"pith_short_12","alias_value":"UVIOXBPRVSJX","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UVIOXBPRVSJXYW5U","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UVIOXBPR","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UVIOXBPRVSJXYW5UQJDDJOFPCK","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2018-02-13T16:23:07Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"a147001af86f4860f52ee98c94d050a2c49b892672129513444786eb983ba335","abstract_canon_sha256":"59a56b0a61fdb19d99f24a4c74348b9b2fa2ce8cabbffd59dc3bf8c763df9cf7"},"schema_version":"1.0"},"canonical_sha256":"a550eb85f1ac937c5bb4824634b8af1297f8ba1e822752650a972f0b9592215b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:41.608146Z","signature_b64":"281P+8Jg5jTXxRV5xmjYEPFyDn9LjhQ+DOH9LjSsPn5JDKgLv3Aaa02kEb4gj3P/h7fmZBk5KeRGFkx24nXbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a550eb85f1ac937c5bb4824634b8af1297f8ba1e822752650a972f0b9592215b","last_reissued_at":"2026-05-18T00:23:41.607648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:41.607648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04708","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9OLQYiqyfkdssgly4PaCQScJMx6SNILWogN2F0WwArtyNQkCbtuu/rWHoguEiL+BLuVGcnGNOOxLMWiQHtVFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:36:32.053137Z"},"content_sha256":"29ceb48f7b127aa897d8d908e40b132a979f8b9a4181e0fe65cb3549024e13db","schema_version":"1.0","event_id":"sha256:29ceb48f7b127aa897d8d908e40b132a979f8b9a4181e0fe65cb3549024e13db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UVIOXBPRVSJXYW5UQJDDJOFPCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lengths of Words Accepted by Nondeterministic Finite Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.FL","authors_text":"Aaron Potechin, Jeffrey Shallit","submitted_at":"2018-02-13T16:23:07Z","abstract_excerpt":"We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition reduces to this problem, and give an O(n^{\\omega} (log n)^{1+{\\epsilon}} log l)-time algorithm to solve it, where {\\omega} is the optimal exponent for matrix multiplication. Second, provided L(M) is finite, we consider the problem of listing the lengths of all words accepted by M. Although this problem seems like it might be significantly harder, we show that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04708","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yeWAklIAkwLmvXG08KIpR5dYiKKSYh9f/fIWxBIttf5mKD8j6vUt50z777tZxNIKCcXmVrP0+yo6cJXNjfLDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:36:32.053812Z"},"content_sha256":"6cffeda44c89d6c6d37cba1c17e55d2e119f4409e4a4d083f920775a6dd17c58","schema_version":"1.0","event_id":"sha256:6cffeda44c89d6c6d37cba1c17e55d2e119f4409e4a4d083f920775a6dd17c58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UVIOXBPRVSJXYW5UQJDDJOFPCK/bundle.json","state_url":"https://pith.science/pith/UVIOXBPRVSJXYW5UQJDDJOFPCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UVIOXBPRVSJXYW5UQJDDJOFPCK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T05:36:32Z","links":{"resolver":"https://pith.science/pith/UVIOXBPRVSJXYW5UQJDDJOFPCK","bundle":"https://pith.science/pith/UVIOXBPRVSJXYW5UQJDDJOFPCK/bundle.json","state":"https://pith.science/pith/UVIOXBPRVSJXYW5UQJDDJOFPCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UVIOXBPRVSJXYW5UQJDDJOFPCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UVIOXBPRVSJXYW5UQJDDJOFPCK","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":"59a56b0a61fdb19d99f24a4c74348b9b2fa2ce8cabbffd59dc3bf8c763df9cf7","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2018-02-13T16:23:07Z","title_canon_sha256":"a147001af86f4860f52ee98c94d050a2c49b892672129513444786eb983ba335"},"schema_version":"1.0","source":{"id":"1802.04708","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04708","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04708v1","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04708","created_at":"2026-05-18T00:23:41Z"},{"alias_kind":"pith_short_12","alias_value":"UVIOXBPRVSJX","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UVIOXBPRVSJXYW5U","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UVIOXBPR","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:6cffeda44c89d6c6d37cba1c17e55d2e119f4409e4a4d083f920775a6dd17c58","target":"graph","created_at":"2026-05-18T00:23:41Z","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":"We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition reduces to this problem, and give an O(n^{\\omega} (log n)^{1+{\\epsilon}} log l)-time algorithm to solve it, where {\\omega} is the optimal exponent for matrix multiplication. Second, provided L(M) is finite, we consider the problem of listing the lengths of all words accepted by M. Although this problem seems like it might be significantly harder, we show that t","authors_text":"Aaron Potechin, Jeffrey Shallit","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2018-02-13T16:23:07Z","title":"Lengths of Words Accepted by Nondeterministic Finite Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04708","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":"sha256:29ceb48f7b127aa897d8d908e40b132a979f8b9a4181e0fe65cb3549024e13db","target":"record","created_at":"2026-05-18T00:23:41Z","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":"59a56b0a61fdb19d99f24a4c74348b9b2fa2ce8cabbffd59dc3bf8c763df9cf7","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2018-02-13T16:23:07Z","title_canon_sha256":"a147001af86f4860f52ee98c94d050a2c49b892672129513444786eb983ba335"},"schema_version":"1.0","source":{"id":"1802.04708","kind":"arxiv","version":1}},"canonical_sha256":"a550eb85f1ac937c5bb4824634b8af1297f8ba1e822752650a972f0b9592215b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a550eb85f1ac937c5bb4824634b8af1297f8ba1e822752650a972f0b9592215b","first_computed_at":"2026-05-18T00:23:41.607648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:41.607648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"281P+8Jg5jTXxRV5xmjYEPFyDn9LjhQ+DOH9LjSsPn5JDKgLv3Aaa02kEb4gj3P/h7fmZBk5KeRGFkx24nXbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:41.608146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04708","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29ceb48f7b127aa897d8d908e40b132a979f8b9a4181e0fe65cb3549024e13db","sha256:6cffeda44c89d6c6d37cba1c17e55d2e119f4409e4a4d083f920775a6dd17c58"],"state_sha256":"89c2fbf0407b4c5aa25fdeeb31e0484ef1c7ac18fde887517d00ebad3f787161"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PRJGOTR0tYhItor0eN7nSVX93vNWZBvB7LuCkrICmeHNzZLsvQYFORjNxCBN6xWpa7usFDw+sLqRFgnKvfBcCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T05:36:32.057365Z","bundle_sha256":"3d059303122248d452c2756f524eb258fa774dad65ee6522c5304ff4df8b1517"}}