{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Y5V3HPWPWUNQWNX5CO22MK43SG","short_pith_number":"pith:Y5V3HPWP","canonical_record":{"source":{"id":"1410.4034","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-10-15T12:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"d741d991870556e103aaa3b974a3a34a6fbc8d656421524ad9a9964a2b43ea8a","abstract_canon_sha256":"ee87471970f2266ec8893472985a8b75af4a3f3bfe6e433ca2ac657451b70178"},"schema_version":"1.0"},"canonical_sha256":"c76bb3becfb51b0b36fd13b5a62b9b91b503af0a331ddf51c99be9908c687787","source":{"kind":"arxiv","id":"1410.4034","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4034","created_at":"2026-05-18T01:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4034v5","created_at":"2026-05-18T01:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4034","created_at":"2026-05-18T01:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"Y5V3HPWPWUNQ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y5V3HPWPWUNQWNX5","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y5V3HPWP","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Y5V3HPWPWUNQWNX5CO22MK43SG","target":"record","payload":{"canonical_record":{"source":{"id":"1410.4034","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-10-15T12:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"d741d991870556e103aaa3b974a3a34a6fbc8d656421524ad9a9964a2b43ea8a","abstract_canon_sha256":"ee87471970f2266ec8893472985a8b75af4a3f3bfe6e433ca2ac657451b70178"},"schema_version":"1.0"},"canonical_sha256":"c76bb3becfb51b0b36fd13b5a62b9b91b503af0a331ddf51c99be9908c687787","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:08.823018Z","signature_b64":"ZxBNnwpSU8j/o34Wt9SEPw+F4IuG5W4IbvpskDlwvg50XPDYf7NKhmJLZ3PUMQshyjFwslF3AYd9/sbgoQUrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c76bb3becfb51b0b36fd13b5a62b9b91b503af0a331ddf51c99be9908c687787","last_reissued_at":"2026-05-18T01:24:08.822306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:08.822306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.4034","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2TLsImnv/sRNSrWri5CXMZ83F8HAzyYiCmWuGeTrAfnH849uKdqcB1lYZi+0J6Kcq5tSVmUMxuw6locClghQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:09:21.983116Z"},"content_sha256":"c2fbdb9566407714eadbc96abf5e21d4495b9971de9cc9cee1c84900395e850d","schema_version":"1.0","event_id":"sha256:c2fbdb9566407714eadbc96abf5e21d4495b9971de9cc9cee1c84900395e850d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Y5V3HPWPWUNQWNX5CO22MK43SG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Synchronizing Probability Function and the Triple Rendezvous Time for Synchronizing Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Fran\\c{c}ois Gonze, Rapha\\\"el M. Jungers","submitted_at":"2014-10-15T12:18:05Z","abstract_excerpt":"Cerny's conjecture is a longstanding open problem in automata theory. We study two different concepts, which allow to approach it from a new angle. The first one is the triple rendezvous time, i.e., the length of the shortest word mapping three states onto a single one. The second one is the synchronizing probability function of an automaton, a recently introduced tool which reinterprets the synchronizing phenomenon as a two-player game, and allows to obtain optimal strategies through a Linear Program.\n  Our contribution is twofold. First, by coupling two different novel approaches based on th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4034","kind":"arxiv","version":5},"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":"2026-05-18T01:24:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5VIJgcFlsZevAcg4k8+VGE54HgVAVIl4+UoY/9BzmT46MvrqSqGH8LiCTzpT2hPnbEVSQpDwT1SXm+uGFNKHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:09:21.983804Z"},"content_sha256":"d365b690789221a1e5e98225c93a1806cf81a82dd9c241fc1ce3107d28073cf0","schema_version":"1.0","event_id":"sha256:d365b690789221a1e5e98225c93a1806cf81a82dd9c241fc1ce3107d28073cf0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5V3HPWPWUNQWNX5CO22MK43SG/bundle.json","state_url":"https://pith.science/pith/Y5V3HPWPWUNQWNX5CO22MK43SG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5V3HPWPWUNQWNX5CO22MK43SG/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":"2026-05-31T23:09:21Z","links":{"resolver":"https://pith.science/pith/Y5V3HPWPWUNQWNX5CO22MK43SG","bundle":"https://pith.science/pith/Y5V3HPWPWUNQWNX5CO22MK43SG/bundle.json","state":"https://pith.science/pith/Y5V3HPWPWUNQWNX5CO22MK43SG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5V3HPWPWUNQWNX5CO22MK43SG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Y5V3HPWPWUNQWNX5CO22MK43SG","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":"ee87471970f2266ec8893472985a8b75af4a3f3bfe6e433ca2ac657451b70178","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-10-15T12:18:05Z","title_canon_sha256":"d741d991870556e103aaa3b974a3a34a6fbc8d656421524ad9a9964a2b43ea8a"},"schema_version":"1.0","source":{"id":"1410.4034","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4034","created_at":"2026-05-18T01:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4034v5","created_at":"2026-05-18T01:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4034","created_at":"2026-05-18T01:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"Y5V3HPWPWUNQ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y5V3HPWPWUNQWNX5","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y5V3HPWP","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:d365b690789221a1e5e98225c93a1806cf81a82dd9c241fc1ce3107d28073cf0","target":"graph","created_at":"2026-05-18T01:24:08Z","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":"Cerny's conjecture is a longstanding open problem in automata theory. We study two different concepts, which allow to approach it from a new angle. The first one is the triple rendezvous time, i.e., the length of the shortest word mapping three states onto a single one. The second one is the synchronizing probability function of an automaton, a recently introduced tool which reinterprets the synchronizing phenomenon as a two-player game, and allows to obtain optimal strategies through a Linear Program.\n  Our contribution is twofold. First, by coupling two different novel approaches based on th","authors_text":"Fran\\c{c}ois Gonze, Rapha\\\"el M. Jungers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-10-15T12:18:05Z","title":"On the Synchronizing Probability Function and the Triple Rendezvous Time for Synchronizing Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4034","kind":"arxiv","version":5},"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:c2fbdb9566407714eadbc96abf5e21d4495b9971de9cc9cee1c84900395e850d","target":"record","created_at":"2026-05-18T01:24:08Z","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":"ee87471970f2266ec8893472985a8b75af4a3f3bfe6e433ca2ac657451b70178","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-10-15T12:18:05Z","title_canon_sha256":"d741d991870556e103aaa3b974a3a34a6fbc8d656421524ad9a9964a2b43ea8a"},"schema_version":"1.0","source":{"id":"1410.4034","kind":"arxiv","version":5}},"canonical_sha256":"c76bb3becfb51b0b36fd13b5a62b9b91b503af0a331ddf51c99be9908c687787","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c76bb3becfb51b0b36fd13b5a62b9b91b503af0a331ddf51c99be9908c687787","first_computed_at":"2026-05-18T01:24:08.822306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:08.822306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZxBNnwpSU8j/o34Wt9SEPw+F4IuG5W4IbvpskDlwvg50XPDYf7NKhmJLZ3PUMQshyjFwslF3AYd9/sbgoQUrBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:08.823018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4034","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2fbdb9566407714eadbc96abf5e21d4495b9971de9cc9cee1c84900395e850d","sha256:d365b690789221a1e5e98225c93a1806cf81a82dd9c241fc1ce3107d28073cf0"],"state_sha256":"e66e3399f9d5011cc20022aefec6909139cfa75c6a36a8ca6d0fbc95be6e8e91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l3mCFGZ/88v+VfQNPw2VA6UG+4AsG/gwcvzqVWxz0pr89OpeegRSDb+uDjnwDc6aEjC3CJ4mfh1NhFL2UcOPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:09:21.992684Z","bundle_sha256":"7282fa94443a09d6a71e63c05f2da9c21a89a15a515432babf7bcbaaabb40a98"}}