{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7QNK75W3Q3SPPSQ2TQV5GVM3EH","short_pith_number":"pith:7QNK75W3","canonical_record":{"source":{"id":"1501.07464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-01-29T14:48:38Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"9c3b59a1213b0d1052d2e45c977347e9a3b567cc64310333583348dcbdaa17cb","abstract_canon_sha256":"a0d1404f5a426d808b01ad814b49dc1b10be19ab25456bbd78a07b87be8c2725"},"schema_version":"1.0"},"canonical_sha256":"fc1aaff6db86e4f7ca1a9c2bd3559b21fc2766ad255e61b505cae158a55ff028","source":{"kind":"arxiv","id":"1501.07464","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07464","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07464v1","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07464","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"7QNK75W3Q3SP","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7QNK75W3Q3SPPSQ2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7QNK75W3","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7QNK75W3Q3SPPSQ2TQV5GVM3EH","target":"record","payload":{"canonical_record":{"source":{"id":"1501.07464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-01-29T14:48:38Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"9c3b59a1213b0d1052d2e45c977347e9a3b567cc64310333583348dcbdaa17cb","abstract_canon_sha256":"a0d1404f5a426d808b01ad814b49dc1b10be19ab25456bbd78a07b87be8c2725"},"schema_version":"1.0"},"canonical_sha256":"fc1aaff6db86e4f7ca1a9c2bd3559b21fc2766ad255e61b505cae158a55ff028","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:21.861448Z","signature_b64":"90j8Y30+yy68QeN22u1oPD/z6NQcRgzBpOUxiDIRFwfinf9Saw8UnUJC2SrAithex2BBagRnwbb7gtVtfhLJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc1aaff6db86e4f7ca1a9c2bd3559b21fc2766ad255e61b505cae158a55ff028","last_reissued_at":"2026-05-18T02:28:21.860809Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:21.860809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.07464","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":"2026-05-18T02:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h62uDfe2+Pnf+rOrV1/2AOeDF87+1VeUiGzmeyF3plyzqN28YrzqA7GwHAk5vWd8DRUyOvv013S3A6y0WnAFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:03:08.419256Z"},"content_sha256":"3a3bf4c2a9a12bbf991eb2b5c216dd7778a5de652513bc91ae17b5d79cfeaac3","schema_version":"1.0","event_id":"sha256:3a3bf4c2a9a12bbf991eb2b5c216dd7778a5de652513bc91ae17b5d79cfeaac3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7QNK75W3Q3SPPSQ2TQV5GVM3EH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abelian bordered factors and periodicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.FL","authors_text":"Emilie Charlier, Luca Zamboni, Svetlana Puzynina, Tero Harju","submitted_at":"2015-01-29T14:48:38Z","abstract_excerpt":"A finite word u is said to be bordered if u has a proper prefix which is also a suffix of u, and unbordered otherwise. Ehrenfeucht and Silberger proved that an infinite word is purely periodic if and only if it contains only finitely many unbordered factors. We are interested in abelian and weak abelian analogues of this result; namely, we investigate the following question(s): Let w be an infinite word such that all sufficiently long factors are (weakly) abelian bordered; is w (weakly) abelian periodic? In the process we answer a question of Avgustinovich et al. concerning the abelian critica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07464","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":"2026-05-18T02:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xTdfcWic2w7rcCa7jgQlQNqwwWIPje3xJxLGXzPldcL+1f3OBfPxqwxGX5SPpm1ePxl+TGsS11wq7OkG2HJjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:03:08.419626Z"},"content_sha256":"b083e9f764b853e31daa76c5ef5ed2aedaf740d59fd970669d2a3117807ee125","schema_version":"1.0","event_id":"sha256:b083e9f764b853e31daa76c5ef5ed2aedaf740d59fd970669d2a3117807ee125"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QNK75W3Q3SPPSQ2TQV5GVM3EH/bundle.json","state_url":"https://pith.science/pith/7QNK75W3Q3SPPSQ2TQV5GVM3EH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QNK75W3Q3SPPSQ2TQV5GVM3EH/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":"2026-06-04T23:03:08Z","links":{"resolver":"https://pith.science/pith/7QNK75W3Q3SPPSQ2TQV5GVM3EH","bundle":"https://pith.science/pith/7QNK75W3Q3SPPSQ2TQV5GVM3EH/bundle.json","state":"https://pith.science/pith/7QNK75W3Q3SPPSQ2TQV5GVM3EH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QNK75W3Q3SPPSQ2TQV5GVM3EH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7QNK75W3Q3SPPSQ2TQV5GVM3EH","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":"a0d1404f5a426d808b01ad814b49dc1b10be19ab25456bbd78a07b87be8c2725","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-01-29T14:48:38Z","title_canon_sha256":"9c3b59a1213b0d1052d2e45c977347e9a3b567cc64310333583348dcbdaa17cb"},"schema_version":"1.0","source":{"id":"1501.07464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07464","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07464v1","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07464","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"7QNK75W3Q3SP","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7QNK75W3Q3SPPSQ2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7QNK75W3","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:b083e9f764b853e31daa76c5ef5ed2aedaf740d59fd970669d2a3117807ee125","target":"graph","created_at":"2026-05-18T02:28:21Z","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 word u is said to be bordered if u has a proper prefix which is also a suffix of u, and unbordered otherwise. Ehrenfeucht and Silberger proved that an infinite word is purely periodic if and only if it contains only finitely many unbordered factors. We are interested in abelian and weak abelian analogues of this result; namely, we investigate the following question(s): Let w be an infinite word such that all sufficiently long factors are (weakly) abelian bordered; is w (weakly) abelian periodic? In the process we answer a question of Avgustinovich et al. concerning the abelian critica","authors_text":"Emilie Charlier, Luca Zamboni, Svetlana Puzynina, Tero Harju","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-01-29T14:48:38Z","title":"Abelian bordered factors and periodicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07464","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":"sha256:3a3bf4c2a9a12bbf991eb2b5c216dd7778a5de652513bc91ae17b5d79cfeaac3","target":"record","created_at":"2026-05-18T02:28:21Z","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":"a0d1404f5a426d808b01ad814b49dc1b10be19ab25456bbd78a07b87be8c2725","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-01-29T14:48:38Z","title_canon_sha256":"9c3b59a1213b0d1052d2e45c977347e9a3b567cc64310333583348dcbdaa17cb"},"schema_version":"1.0","source":{"id":"1501.07464","kind":"arxiv","version":1}},"canonical_sha256":"fc1aaff6db86e4f7ca1a9c2bd3559b21fc2766ad255e61b505cae158a55ff028","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc1aaff6db86e4f7ca1a9c2bd3559b21fc2766ad255e61b505cae158a55ff028","first_computed_at":"2026-05-18T02:28:21.860809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:21.860809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"90j8Y30+yy68QeN22u1oPD/z6NQcRgzBpOUxiDIRFwfinf9Saw8UnUJC2SrAithex2BBagRnwbb7gtVtfhLJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:21.861448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a3bf4c2a9a12bbf991eb2b5c216dd7778a5de652513bc91ae17b5d79cfeaac3","sha256:b083e9f764b853e31daa76c5ef5ed2aedaf740d59fd970669d2a3117807ee125"],"state_sha256":"6a330fe634ce6688e1e0dddabbd390bb40e17c10c231d210696a011471b589f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"36z6FQzN/47ixSa3lEfwf4bdgrOu6ENjG/p5Ip9AVZ4TXfQbdYzIUgB+Rc0Nw4KwAUccPYMlXv3HRWC++NIKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:03:08.421580Z","bundle_sha256":"5f72fe2636e86f9909c03264168c26b72bbb05251f13a2ce44f269906efc2849"}}