{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:P35GCDEP4A6QRS3SZYDK6R2IQB","short_pith_number":"pith:P35GCDEP","canonical_record":{"source":{"id":"1906.01346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-06-04T11:07:29Z","cross_cats_sorted":["cs.FL","math.CO"],"title_canon_sha256":"3d03698c0d688852636335bede3d1a691fd71d05f4471aacda39858428a8d3d4","abstract_canon_sha256":"5446b322b1ea2a8c28238e528ac7825bc4c8409c2e08b4eaf66d79ec96265a26"},"schema_version":"1.0"},"canonical_sha256":"7efa610c8fe03d08cb72ce06af4748806a0ceaad9283d0859d43f8ab2f824068","source":{"kind":"arxiv","id":"1906.01346","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01346","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01346v1","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01346","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"pith_short_12","alias_value":"P35GCDEP4A6Q","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"P35GCDEP4A6QRS3S","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"P35GCDEP","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:P35GCDEP4A6QRS3SZYDK6R2IQB","target":"record","payload":{"canonical_record":{"source":{"id":"1906.01346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-06-04T11:07:29Z","cross_cats_sorted":["cs.FL","math.CO"],"title_canon_sha256":"3d03698c0d688852636335bede3d1a691fd71d05f4471aacda39858428a8d3d4","abstract_canon_sha256":"5446b322b1ea2a8c28238e528ac7825bc4c8409c2e08b4eaf66d79ec96265a26"},"schema_version":"1.0"},"canonical_sha256":"7efa610c8fe03d08cb72ce06af4748806a0ceaad9283d0859d43f8ab2f824068","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:16.962109Z","signature_b64":"UThagmOBPtbJ21YSdhk3T5li11FfA5HFsyI6iXsWw5uJ+o352Oi4M9HVKY3jFedWY9tEKMO9P15ue6Pxnyh5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7efa610c8fe03d08cb72ce06af4748806a0ceaad9283d0859d43f8ab2f824068","last_reissued_at":"2026-05-17T23:44:16.961474Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:16.961474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.01346","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":"2026-05-17T23:44:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gmEVpBMJoL+qzpGEfttxmvOs//BQenrobOpVl2Uu8CGYjJG0lS0BHJAbF1p0KMwxFCQR1OPOjNvvMQPTrFuZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:17:12.431229Z"},"content_sha256":"f87f60a18508676a41cde75aaa31054e604b9d1d175ef6e326285e9308e9deb8","schema_version":"1.0","event_id":"sha256:f87f60a18508676a41cde75aaa31054e604b9d1d175ef6e326285e9308e9deb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:P35GCDEP4A6QRS3SZYDK6R2IQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characteristic Parameters and Special Trapezoidal Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.CO"],"primary_cat":"cs.DM","authors_text":"Alessandro De Luca, Alma D'Aniello","submitted_at":"2019-06-04T11:07:29Z","abstract_excerpt":"Following earlier work by Aldo de Luca and others, we study trapezoidal words and their prefixes, with respect to their characteristic parameters $K$ and $R$ (length of shortest unrepeated suffix, and shortest length without right special factors, respectively), as well as their symmetric versions $H$ and $L$. We consider the distinction between closed (i.e., periodic-like) and open prefixes, and between Sturmian and non-Sturmian ones. Our main results characterize right special and strictly bispecial trapezoidal words, as done by de Luca and Mignosi for Sturmian words."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01346","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":"2026-05-17T23:44:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/4bdRL2CnUMNxEEPuvLocphRq5G2SyHMwhHIbNoEgudvH61YmUaevDHc9qoG3lAsyGjRI7c9wU61hm5GuOEEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:17:12.431595Z"},"content_sha256":"e4c66ec573efb83e2a8dce250184d0b1964e833f4a3136e4c244461f9872b125","schema_version":"1.0","event_id":"sha256:e4c66ec573efb83e2a8dce250184d0b1964e833f4a3136e4c244461f9872b125"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P35GCDEP4A6QRS3SZYDK6R2IQB/bundle.json","state_url":"https://pith.science/pith/P35GCDEP4A6QRS3SZYDK6R2IQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P35GCDEP4A6QRS3SZYDK6R2IQB/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":"2026-07-04T22:17:12Z","links":{"resolver":"https://pith.science/pith/P35GCDEP4A6QRS3SZYDK6R2IQB","bundle":"https://pith.science/pith/P35GCDEP4A6QRS3SZYDK6R2IQB/bundle.json","state":"https://pith.science/pith/P35GCDEP4A6QRS3SZYDK6R2IQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P35GCDEP4A6QRS3SZYDK6R2IQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:P35GCDEP4A6QRS3SZYDK6R2IQB","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":"5446b322b1ea2a8c28238e528ac7825bc4c8409c2e08b4eaf66d79ec96265a26","cross_cats_sorted":["cs.FL","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-06-04T11:07:29Z","title_canon_sha256":"3d03698c0d688852636335bede3d1a691fd71d05f4471aacda39858428a8d3d4"},"schema_version":"1.0","source":{"id":"1906.01346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01346","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01346v1","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01346","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"pith_short_12","alias_value":"P35GCDEP4A6Q","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"P35GCDEP4A6QRS3S","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"P35GCDEP","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:e4c66ec573efb83e2a8dce250184d0b1964e833f4a3136e4c244461f9872b125","target":"graph","created_at":"2026-05-17T23:44:16Z","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":"Following earlier work by Aldo de Luca and others, we study trapezoidal words and their prefixes, with respect to their characteristic parameters $K$ and $R$ (length of shortest unrepeated suffix, and shortest length without right special factors, respectively), as well as their symmetric versions $H$ and $L$. We consider the distinction between closed (i.e., periodic-like) and open prefixes, and between Sturmian and non-Sturmian ones. Our main results characterize right special and strictly bispecial trapezoidal words, as done by de Luca and Mignosi for Sturmian words.","authors_text":"Alessandro De Luca, Alma D'Aniello","cross_cats":["cs.FL","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-06-04T11:07:29Z","title":"Characteristic Parameters and Special Trapezoidal Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01346","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:f87f60a18508676a41cde75aaa31054e604b9d1d175ef6e326285e9308e9deb8","target":"record","created_at":"2026-05-17T23:44:16Z","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":"5446b322b1ea2a8c28238e528ac7825bc4c8409c2e08b4eaf66d79ec96265a26","cross_cats_sorted":["cs.FL","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-06-04T11:07:29Z","title_canon_sha256":"3d03698c0d688852636335bede3d1a691fd71d05f4471aacda39858428a8d3d4"},"schema_version":"1.0","source":{"id":"1906.01346","kind":"arxiv","version":1}},"canonical_sha256":"7efa610c8fe03d08cb72ce06af4748806a0ceaad9283d0859d43f8ab2f824068","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7efa610c8fe03d08cb72ce06af4748806a0ceaad9283d0859d43f8ab2f824068","first_computed_at":"2026-05-17T23:44:16.961474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:16.961474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UThagmOBPtbJ21YSdhk3T5li11FfA5HFsyI6iXsWw5uJ+o352Oi4M9HVKY3jFedWY9tEKMO9P15ue6Pxnyh5Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:16.962109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f87f60a18508676a41cde75aaa31054e604b9d1d175ef6e326285e9308e9deb8","sha256:e4c66ec573efb83e2a8dce250184d0b1964e833f4a3136e4c244461f9872b125"],"state_sha256":"0743249924811a6b66de8706af8818c57567221ba209bfd96b739d8deef4ff4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EpsDJsZO0Nw/5KwlnmgOQlvDqlGlXJHPXb3pLyAKEV6sOdhDzJfAlJqaELbqYWT7yN0f11hxAMalTz28hMJoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T22:17:12.433655Z","bundle_sha256":"e4a57f25dbd301c5a613cb5fcaadadf0fb275cb9b64510d451dbed39038a4d3a"}}