{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3CHC5W4ZGBNVLTIUS3RAZVAITA","short_pith_number":"pith:3CHC5W4Z","canonical_record":{"source":{"id":"1207.1307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-05T17:43:50Z","cross_cats_sorted":[],"title_canon_sha256":"c51ea95e89f828eab94c545d618a8f9af355149a74dc97110c102f461cbbedc6","abstract_canon_sha256":"79ec519e82985c8387aa14f6fc0cb82bdc2b968f4aeb64cd2f1a7b517f536596"},"schema_version":"1.0"},"canonical_sha256":"d88e2edb99305b55cd1496e20cd4089822a5abbe0f0677a2436158282310c869","source":{"kind":"arxiv","id":"1207.1307","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1307","created_at":"2026-05-18T02:21:08Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1307v1","created_at":"2026-05-18T02:21:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1307","created_at":"2026-05-18T02:21:08Z"},{"alias_kind":"pith_short_12","alias_value":"3CHC5W4ZGBNV","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3CHC5W4ZGBNVLTIU","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3CHC5W4Z","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3CHC5W4ZGBNVLTIUS3RAZVAITA","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-05T17:43:50Z","cross_cats_sorted":[],"title_canon_sha256":"c51ea95e89f828eab94c545d618a8f9af355149a74dc97110c102f461cbbedc6","abstract_canon_sha256":"79ec519e82985c8387aa14f6fc0cb82bdc2b968f4aeb64cd2f1a7b517f536596"},"schema_version":"1.0"},"canonical_sha256":"d88e2edb99305b55cd1496e20cd4089822a5abbe0f0677a2436158282310c869","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:08.510065Z","signature_b64":"qFGez+ORNwSupZDaIbrTfGhZiw97PwQkNOW11K5ZPUPTWvCkloG6ZOo2CjXua14YmEOzFfD3XuDTqMtWTySjCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d88e2edb99305b55cd1496e20cd4089822a5abbe0f0677a2436158282310c869","last_reissued_at":"2026-05-18T02:21:08.509643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:08.509643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1307","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":"2026-05-18T02:21:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KczNXtmIBwBK4I/tytdr1hhxjjiZVuqnQEPn4/yuJ9DBaxWiHxpws37P8tMWxBLKddsU0viKuHnRA92hF/RIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:25:20.429860Z"},"content_sha256":"036597f5095847fbb3cb1d838824d93fe625ed91b5cc936052aeecdfccb61873","schema_version":"1.0","event_id":"sha256:036597f5095847fbb3cb1d838824d93fe625ed91b5cc936052aeecdfccb61873"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3CHC5W4ZGBNVLTIUS3RAZVAITA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Identifying all abelian periods of a string in quadratic time and relevant problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Costas S. Iliopoulos, Maxime Crochemore, Michalis Christou","submitted_at":"2012-07-05T17:43:50Z","abstract_excerpt":"Abelian periodicity of strings has been studied extensively over the last years. In 2006 Constantinescu and Ilie defined the abelian period of a string and several algorithms for the computation of all abelian periods of a string were given. In contrast to the classical period of a word, its abelian version is more flexible, factors of the word are considered the same under any internal permutation of their letters. We show two O(|y|^2) algorithms for the computation of all abelian periods of a string y. The first one maps each letter to a suitable number such that each factor of the string ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1307","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":"2026-05-18T02:21:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3gkC4wGQQm1Xl31rJQOaurfvSRjHA+8IqP8f9bA4KYEkOZne2Cdw48KXbbyCzKfjEVxhjZWUwoyOW2+Vr/JZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:25:20.430439Z"},"content_sha256":"a0a0cb809d952d50ae08a503d55e4e1c68de0724d2e75df2ecaeec23e9953f02","schema_version":"1.0","event_id":"sha256:a0a0cb809d952d50ae08a503d55e4e1c68de0724d2e75df2ecaeec23e9953f02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CHC5W4ZGBNVLTIUS3RAZVAITA/bundle.json","state_url":"https://pith.science/pith/3CHC5W4ZGBNVLTIUS3RAZVAITA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CHC5W4ZGBNVLTIUS3RAZVAITA/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":"2026-06-04T22:25:20Z","links":{"resolver":"https://pith.science/pith/3CHC5W4ZGBNVLTIUS3RAZVAITA","bundle":"https://pith.science/pith/3CHC5W4ZGBNVLTIUS3RAZVAITA/bundle.json","state":"https://pith.science/pith/3CHC5W4ZGBNVLTIUS3RAZVAITA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CHC5W4ZGBNVLTIUS3RAZVAITA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3CHC5W4ZGBNVLTIUS3RAZVAITA","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":"79ec519e82985c8387aa14f6fc0cb82bdc2b968f4aeb64cd2f1a7b517f536596","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-05T17:43:50Z","title_canon_sha256":"c51ea95e89f828eab94c545d618a8f9af355149a74dc97110c102f461cbbedc6"},"schema_version":"1.0","source":{"id":"1207.1307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1307","created_at":"2026-05-18T02:21:08Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1307v1","created_at":"2026-05-18T02:21:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1307","created_at":"2026-05-18T02:21:08Z"},{"alias_kind":"pith_short_12","alias_value":"3CHC5W4ZGBNV","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3CHC5W4ZGBNVLTIU","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3CHC5W4Z","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:a0a0cb809d952d50ae08a503d55e4e1c68de0724d2e75df2ecaeec23e9953f02","target":"graph","created_at":"2026-05-18T02:21:08Z","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":"Abelian periodicity of strings has been studied extensively over the last years. In 2006 Constantinescu and Ilie defined the abelian period of a string and several algorithms for the computation of all abelian periods of a string were given. In contrast to the classical period of a word, its abelian version is more flexible, factors of the word are considered the same under any internal permutation of their letters. We show two O(|y|^2) algorithms for the computation of all abelian periods of a string y. The first one maps each letter to a suitable number such that each factor of the string ca","authors_text":"Costas S. Iliopoulos, Maxime Crochemore, Michalis Christou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-05T17:43:50Z","title":"Identifying all abelian periods of a string in quadratic time and relevant problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1307","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":"sha256:036597f5095847fbb3cb1d838824d93fe625ed91b5cc936052aeecdfccb61873","target":"record","created_at":"2026-05-18T02:21:08Z","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":"79ec519e82985c8387aa14f6fc0cb82bdc2b968f4aeb64cd2f1a7b517f536596","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-05T17:43:50Z","title_canon_sha256":"c51ea95e89f828eab94c545d618a8f9af355149a74dc97110c102f461cbbedc6"},"schema_version":"1.0","source":{"id":"1207.1307","kind":"arxiv","version":1}},"canonical_sha256":"d88e2edb99305b55cd1496e20cd4089822a5abbe0f0677a2436158282310c869","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d88e2edb99305b55cd1496e20cd4089822a5abbe0f0677a2436158282310c869","first_computed_at":"2026-05-18T02:21:08.509643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:08.509643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qFGez+ORNwSupZDaIbrTfGhZiw97PwQkNOW11K5ZPUPTWvCkloG6ZOo2CjXua14YmEOzFfD3XuDTqMtWTySjCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:08.510065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:036597f5095847fbb3cb1d838824d93fe625ed91b5cc936052aeecdfccb61873","sha256:a0a0cb809d952d50ae08a503d55e4e1c68de0724d2e75df2ecaeec23e9953f02"],"state_sha256":"5cc6b38b654014252e32e873fc3da60049b1ca4cf6f7108009e7e6b53cb99d70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SbLeZqhd0gb7HBrNyy8lu2GerOFrQmZnrmIuSiNjjKlm+6TEX1Z2cp8pcQ41+twhZeikWA1V9t7JERG2QJTnAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:25:20.433500Z","bundle_sha256":"155ead2194aa776e00aca0fd5f0bbe01f4a9e096f0cdd9a9b64248b27e2b9a9c"}}