{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7NLXYCEF4C7M27LGYYQVURFQNC","short_pith_number":"pith:7NLXYCEF","canonical_record":{"source":{"id":"1204.1672","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-04-07T18:56:05Z","cross_cats_sorted":["cs.CG","cs.DM"],"title_canon_sha256":"49d3c51aab00525455804b9883938719641951fe140055cda7945dd60fc1faac","abstract_canon_sha256":"969f16bea6cbef7b3ca3dd932d547ecf0a49472c50029bcb6df73b46ab5cf276"},"schema_version":"1.0"},"canonical_sha256":"fb577c0885e0becd7d66c6215a44b06895827ec359f7fda1374bdcbeb2f046e7","source":{"kind":"arxiv","id":"1204.1672","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1672","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1672v4","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1672","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"pith_short_12","alias_value":"7NLXYCEF4C7M","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7NLXYCEF4C7M27LG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7NLXYCEF","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7NLXYCEF4C7M27LGYYQVURFQNC","target":"record","payload":{"canonical_record":{"source":{"id":"1204.1672","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-04-07T18:56:05Z","cross_cats_sorted":["cs.CG","cs.DM"],"title_canon_sha256":"49d3c51aab00525455804b9883938719641951fe140055cda7945dd60fc1faac","abstract_canon_sha256":"969f16bea6cbef7b3ca3dd932d547ecf0a49472c50029bcb6df73b46ab5cf276"},"schema_version":"1.0"},"canonical_sha256":"fb577c0885e0becd7d66c6215a44b06895827ec359f7fda1374bdcbeb2f046e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:16.467002Z","signature_b64":"5xxW6PA5MpW5JMWsE5ymjpV5VRwR3QF07RQjJ1bOewP0z21ZtQHQMMFsWhZ0IhQD3K9wkFwJE/L6yU+ylDD8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb577c0885e0becd7d66c6215a44b06895827ec359f7fda1374bdcbeb2f046e7","last_reissued_at":"2026-05-18T02:21:16.466380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:16.466380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.1672","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6DUCqUM69UVQ1WHUQaEYMsyWggq6Jaf51O9OCqixseFBRhC/AElvd/7zq823DPGKxiuZdKV3BLlymN0lYxJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:37:57.730044Z"},"content_sha256":"d15e4506ef60e092a8d3cf9381d1aca9da3c89add051ba4f21654d76b7b6d9db","schema_version":"1.0","event_id":"sha256:d15e4506ef60e092a8d3cf9381d1aca9da3c89add051ba4f21654d76b7b6d9db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7NLXYCEF4C7M27LGYYQVURFQNC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Characterization of Bispecial Sturmian Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"cs.FL","authors_text":"Gabriele Fici","submitted_at":"2012-04-07T18:56:05Z","abstract_excerpt":"A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1672","kind":"arxiv","version":4},"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":"2026-05-18T02:21:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qnZkZbYGk0xtAFtk4mKFZzF/6xYWmmyMyKiVY24UT4Xr1NS1nrnoZXBmbBmWsDjE95Lg7GWmp2GLwK1ZcvAvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:37:57.730426Z"},"content_sha256":"55cbe7eb948b95449b7c9b8b5c03e1975d0e1ff62ef2aa37350f5491606b826c","schema_version":"1.0","event_id":"sha256:55cbe7eb948b95449b7c9b8b5c03e1975d0e1ff62ef2aa37350f5491606b826c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7NLXYCEF4C7M27LGYYQVURFQNC/bundle.json","state_url":"https://pith.science/pith/7NLXYCEF4C7M27LGYYQVURFQNC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7NLXYCEF4C7M27LGYYQVURFQNC/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":"2026-05-26T11:37:57Z","links":{"resolver":"https://pith.science/pith/7NLXYCEF4C7M27LGYYQVURFQNC","bundle":"https://pith.science/pith/7NLXYCEF4C7M27LGYYQVURFQNC/bundle.json","state":"https://pith.science/pith/7NLXYCEF4C7M27LGYYQVURFQNC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7NLXYCEF4C7M27LGYYQVURFQNC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7NLXYCEF4C7M27LGYYQVURFQNC","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":"969f16bea6cbef7b3ca3dd932d547ecf0a49472c50029bcb6df73b46ab5cf276","cross_cats_sorted":["cs.CG","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-04-07T18:56:05Z","title_canon_sha256":"49d3c51aab00525455804b9883938719641951fe140055cda7945dd60fc1faac"},"schema_version":"1.0","source":{"id":"1204.1672","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1672","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1672v4","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1672","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"pith_short_12","alias_value":"7NLXYCEF4C7M","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7NLXYCEF4C7M27LG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7NLXYCEF","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:55cbe7eb948b95449b7c9b8b5c03e1975d0e1ff62ef2aa37350f5491606b826c","target":"graph","created_at":"2026-05-18T02:21:16Z","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":"A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for b","authors_text":"Gabriele Fici","cross_cats":["cs.CG","cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-04-07T18:56:05Z","title":"A Characterization of Bispecial Sturmian Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1672","kind":"arxiv","version":4},"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:d15e4506ef60e092a8d3cf9381d1aca9da3c89add051ba4f21654d76b7b6d9db","target":"record","created_at":"2026-05-18T02:21:16Z","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":"969f16bea6cbef7b3ca3dd932d547ecf0a49472c50029bcb6df73b46ab5cf276","cross_cats_sorted":["cs.CG","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-04-07T18:56:05Z","title_canon_sha256":"49d3c51aab00525455804b9883938719641951fe140055cda7945dd60fc1faac"},"schema_version":"1.0","source":{"id":"1204.1672","kind":"arxiv","version":4}},"canonical_sha256":"fb577c0885e0becd7d66c6215a44b06895827ec359f7fda1374bdcbeb2f046e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb577c0885e0becd7d66c6215a44b06895827ec359f7fda1374bdcbeb2f046e7","first_computed_at":"2026-05-18T02:21:16.466380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:16.466380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5xxW6PA5MpW5JMWsE5ymjpV5VRwR3QF07RQjJ1bOewP0z21ZtQHQMMFsWhZ0IhQD3K9wkFwJE/L6yU+ylDD8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:16.467002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1672","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d15e4506ef60e092a8d3cf9381d1aca9da3c89add051ba4f21654d76b7b6d9db","sha256:55cbe7eb948b95449b7c9b8b5c03e1975d0e1ff62ef2aa37350f5491606b826c"],"state_sha256":"2aa7dc12f5793b63b8d0566d8f733c216b9bfdf2acb8cd65991b47b29a0f72c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xdc1Xc2XE+7SOeEd+WS11CvVlOfIRu9qpj7rpXrKPPut4yifCYFIb9L2ShNys2bI/MXvwhqb3edmYUH9MnTLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:37:57.732853Z","bundle_sha256":"73600b87f3918c2b84da86fef7ad0bebd1321afca9aec4ac98876caa6a8d6c58"}}