{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:53Y6IA6RBFW4VVGDMVBTZWH5RI","short_pith_number":"pith:53Y6IA6R","canonical_record":{"source":{"id":"1807.10483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-27T08:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"4f93b679e2e49137d001cb5fa71c0e09ade76759bcf25b31ba05fe2f7cd621ae","abstract_canon_sha256":"32c38218d4cd53f671c819b122c814078ddad931790526f940899aaeb95d85ac"},"schema_version":"1.0"},"canonical_sha256":"eef1e403d1096dcad4c365433cd8fd8a2c9201fb5adc623366c4d6d1442be515","source":{"kind":"arxiv","id":"1807.10483","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10483","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10483v1","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10483","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"53Y6IA6RBFW4","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"53Y6IA6RBFW4VVGD","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"53Y6IA6R","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:53Y6IA6RBFW4VVGDMVBTZWH5RI","target":"record","payload":{"canonical_record":{"source":{"id":"1807.10483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-27T08:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"4f93b679e2e49137d001cb5fa71c0e09ade76759bcf25b31ba05fe2f7cd621ae","abstract_canon_sha256":"32c38218d4cd53f671c819b122c814078ddad931790526f940899aaeb95d85ac"},"schema_version":"1.0"},"canonical_sha256":"eef1e403d1096dcad4c365433cd8fd8a2c9201fb5adc623366c4d6d1442be515","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:40.454831Z","signature_b64":"gNdS60NB6i1INnRA1StD05QmN/1O8nvj7BPtWbfZYnX5GNVXlfQDMEEqMppD+YZmp+98fGCOVGozL3PO25ZIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eef1e403d1096dcad4c365433cd8fd8a2c9201fb5adc623366c4d6d1442be515","last_reissued_at":"2026-05-18T00:09:40.454235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:40.454235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.10483","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":"2026-05-18T00:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/KwESfcpJ3cN4Gj28DkVUbMvCJbtCRaduvqV6IiWLVJwkXqc4zdNgWTLuqfNGH4uNm4fQPC9/wr6+5F09khCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:57:36.725800Z"},"content_sha256":"55806babfe1763854094833ee5ed759134bdcafa2250642578efdb54c559b366","schema_version":"1.0","event_id":"sha256:55806babfe1763854094833ee5ed759134bdcafa2250642578efdb54c559b366"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:53Y6IA6RBFW4VVGDMVBTZWH5RI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster Recovery of Approximate Periods over Edit Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jakub Radoszewski, Juliusz Straszy\\'nski, Tomasz Kociumaka, Tomasz Wale\\'n, Wiktor Zuba, Wojciech Rytter","submitted_at":"2018-07-27T08:16:29Z","abstract_excerpt":"The approximate period recovery problem asks to compute all $\\textit{approximate word-periods}$ of a given word $S$ of length $n$: all primitive words $P$ ($|P|=p$) which have a periodic extension at edit distance smaller than $\\tau_p$ from $S$, where $\\tau_p = \\lfloor \\frac{n}{(3.75+\\epsilon)\\cdot p} \\rfloor$ for some $\\epsilon>0$. Here, the set of periodic extensions of $P$ consists of all finite prefixes of $P^\\infty$.\n  We improve the time complexity of the fastest known algorithm for this problem of Amir et al. [Theor. Comput. Sci., 2018] from $O(n^{4/3})$ to $O(n \\log n)$. Our tool is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10483","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":"2026-05-18T00:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cit1M9coQo6LB5UP8tZwYSBidq9PuAFTWOH0j09Jep7uliXNJPxcmkfiHD2YCDELXXX/ixlFxdNGHyUlK0CaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:57:36.726142Z"},"content_sha256":"a3a154551250c442f567f06035640a68c9905f13c49e8862b047c5c16f87fba7","schema_version":"1.0","event_id":"sha256:a3a154551250c442f567f06035640a68c9905f13c49e8862b047c5c16f87fba7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53Y6IA6RBFW4VVGDMVBTZWH5RI/bundle.json","state_url":"https://pith.science/pith/53Y6IA6RBFW4VVGDMVBTZWH5RI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53Y6IA6RBFW4VVGDMVBTZWH5RI/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":"2026-06-04T21:57:36Z","links":{"resolver":"https://pith.science/pith/53Y6IA6RBFW4VVGDMVBTZWH5RI","bundle":"https://pith.science/pith/53Y6IA6RBFW4VVGDMVBTZWH5RI/bundle.json","state":"https://pith.science/pith/53Y6IA6RBFW4VVGDMVBTZWH5RI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53Y6IA6RBFW4VVGDMVBTZWH5RI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:53Y6IA6RBFW4VVGDMVBTZWH5RI","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":"32c38218d4cd53f671c819b122c814078ddad931790526f940899aaeb95d85ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-27T08:16:29Z","title_canon_sha256":"4f93b679e2e49137d001cb5fa71c0e09ade76759bcf25b31ba05fe2f7cd621ae"},"schema_version":"1.0","source":{"id":"1807.10483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10483","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10483v1","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10483","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"53Y6IA6RBFW4","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"53Y6IA6RBFW4VVGD","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"53Y6IA6R","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:a3a154551250c442f567f06035640a68c9905f13c49e8862b047c5c16f87fba7","target":"graph","created_at":"2026-05-18T00:09:40Z","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":"The approximate period recovery problem asks to compute all $\\textit{approximate word-periods}$ of a given word $S$ of length $n$: all primitive words $P$ ($|P|=p$) which have a periodic extension at edit distance smaller than $\\tau_p$ from $S$, where $\\tau_p = \\lfloor \\frac{n}{(3.75+\\epsilon)\\cdot p} \\rfloor$ for some $\\epsilon>0$. Here, the set of periodic extensions of $P$ consists of all finite prefixes of $P^\\infty$.\n  We improve the time complexity of the fastest known algorithm for this problem of Amir et al. [Theor. Comput. Sci., 2018] from $O(n^{4/3})$ to $O(n \\log n)$. Our tool is a ","authors_text":"Jakub Radoszewski, Juliusz Straszy\\'nski, Tomasz Kociumaka, Tomasz Wale\\'n, Wiktor Zuba, Wojciech Rytter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-27T08:16:29Z","title":"Faster Recovery of Approximate Periods over Edit Distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10483","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":"sha256:55806babfe1763854094833ee5ed759134bdcafa2250642578efdb54c559b366","target":"record","created_at":"2026-05-18T00:09:40Z","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":"32c38218d4cd53f671c819b122c814078ddad931790526f940899aaeb95d85ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-27T08:16:29Z","title_canon_sha256":"4f93b679e2e49137d001cb5fa71c0e09ade76759bcf25b31ba05fe2f7cd621ae"},"schema_version":"1.0","source":{"id":"1807.10483","kind":"arxiv","version":1}},"canonical_sha256":"eef1e403d1096dcad4c365433cd8fd8a2c9201fb5adc623366c4d6d1442be515","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eef1e403d1096dcad4c365433cd8fd8a2c9201fb5adc623366c4d6d1442be515","first_computed_at":"2026-05-18T00:09:40.454235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:40.454235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gNdS60NB6i1INnRA1StD05QmN/1O8nvj7BPtWbfZYnX5GNVXlfQDMEEqMppD+YZmp+98fGCOVGozL3PO25ZIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:40.454831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55806babfe1763854094833ee5ed759134bdcafa2250642578efdb54c559b366","sha256:a3a154551250c442f567f06035640a68c9905f13c49e8862b047c5c16f87fba7"],"state_sha256":"ff0758779270d7d6ef94dbf954e6c60e48074115627479e6ec2b6e013dae8b5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P29zcD4ynW0jbR0kQ2TYeXcDE9yvx6IS9o2lrhwkErSCUaSa0F8JZjvatCXLVkCdwOBJbzBMTL+HjCSDlwgACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:57:36.728144Z","bundle_sha256":"a28660998e38b0d1cd7acd8b62784a56200fb13da97289ee184cd10169692a86"}}