{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:TU5JD5KADXBS73E53GVHPGKSC6","short_pith_number":"pith:TU5JD5KA","canonical_record":{"source":{"id":"2209.00271","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-09-01T07:18:12Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"2344f2243a6658110b4a310c17433bc324e05335e173ee5a101aaceef4eca1c7","abstract_canon_sha256":"f28594c87b9e5c8909a477c2ea5a8900db84232a45702dfc46bc5c80fc551b05"},"schema_version":"1.0"},"canonical_sha256":"9d3a91f5401dc32fec9dd9aa779952178cc0558e257fb5e2ece1d17ed908a599","source":{"kind":"arxiv","id":"2209.00271","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.00271","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"arxiv_version","alias_value":"2209.00271v2","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.00271","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"pith_short_12","alias_value":"TU5JD5KADXBS","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"pith_short_16","alias_value":"TU5JD5KADXBS73E5","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"pith_short_8","alias_value":"TU5JD5KA","created_at":"2026-07-05T08:18:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:TU5JD5KADXBS73E53GVHPGKSC6","target":"record","payload":{"canonical_record":{"source":{"id":"2209.00271","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-09-01T07:18:12Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"2344f2243a6658110b4a310c17433bc324e05335e173ee5a101aaceef4eca1c7","abstract_canon_sha256":"f28594c87b9e5c8909a477c2ea5a8900db84232a45702dfc46bc5c80fc551b05"},"schema_version":"1.0"},"canonical_sha256":"9d3a91f5401dc32fec9dd9aa779952178cc0558e257fb5e2ece1d17ed908a599","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:18:39.614151Z","signature_b64":"YyeKME6FG9Emxce4dCEVmhoZeKnSOxzjN0BIvzQp/Imu5/CKUM3VM1xdnC4hLikFbJ9r2mQOOs+LqYkuxag0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d3a91f5401dc32fec9dd9aa779952178cc0558e257fb5e2ece1d17ed908a599","last_reissued_at":"2026-07-05T08:18:39.613639Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:18:39.613639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.00271","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:18:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DBGT4KxEEaKQ8vvNY8OhijsCR0CvWAvH44ucb2aMPaDxXnvNb9tj8eADXGz7jbloNavFTFOfOAEm/pPaxAImBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:04:47.537395Z"},"content_sha256":"6a5d8f55782050a5152be387e8259c96f5ad5f176ec0868f38b8ea7ee164bf1c","schema_version":"1.0","event_id":"sha256:6a5d8f55782050a5152be387e8259c96f5ad5f176ec0868f38b8ea7ee164bf1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:TU5JD5KADXBS73E53GVHPGKSC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal Closed Substrings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"cs.DS","authors_text":"Alessandro De Luca, Gabriele Fici, Golnaz Badkobeh, Simon Puglisi","submitted_at":"2022-09-01T07:18:12Z","abstract_excerpt":"A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a \\emph{maximal closed substring} (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least $2$ are commonly called \\emph{runs}; those with exponent smaller than $2$, instead, are particular cases of \\emph{maximal gapped repeats}. We provide an algorithm that, given a string of length $n$ locates all MCSs the string contains in $\\mathcal O(n\\log n)$ tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00271","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.00271/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:18:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"14cdLRID9tM1DAg+NP2kZIxKai5UUVzzbXS1/KvN4Gkfoa/1p/2YtUDHKJ4PxC6fBdr8xpqM74aF0f7ghbWzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:04:47.537769Z"},"content_sha256":"aa014b59f2ca30fd13198793312e87871d781d68d820e61ceef75c42a5790b6d","schema_version":"1.0","event_id":"sha256:aa014b59f2ca30fd13198793312e87871d781d68d820e61ceef75c42a5790b6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TU5JD5KADXBS73E53GVHPGKSC6/bundle.json","state_url":"https://pith.science/pith/TU5JD5KADXBS73E53GVHPGKSC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TU5JD5KADXBS73E53GVHPGKSC6/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":"2026-07-07T08:04:47Z","links":{"resolver":"https://pith.science/pith/TU5JD5KADXBS73E53GVHPGKSC6","bundle":"https://pith.science/pith/TU5JD5KADXBS73E53GVHPGKSC6/bundle.json","state":"https://pith.science/pith/TU5JD5KADXBS73E53GVHPGKSC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TU5JD5KADXBS73E53GVHPGKSC6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:TU5JD5KADXBS73E53GVHPGKSC6","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":"f28594c87b9e5c8909a477c2ea5a8900db84232a45702dfc46bc5c80fc551b05","cross_cats_sorted":["cs.FL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-09-01T07:18:12Z","title_canon_sha256":"2344f2243a6658110b4a310c17433bc324e05335e173ee5a101aaceef4eca1c7"},"schema_version":"1.0","source":{"id":"2209.00271","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.00271","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"arxiv_version","alias_value":"2209.00271v2","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.00271","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"pith_short_12","alias_value":"TU5JD5KADXBS","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"pith_short_16","alias_value":"TU5JD5KADXBS73E5","created_at":"2026-07-05T08:18:39Z"},{"alias_kind":"pith_short_8","alias_value":"TU5JD5KA","created_at":"2026-07-05T08:18:39Z"}],"graph_snapshots":[{"event_id":"sha256:aa014b59f2ca30fd13198793312e87871d781d68d820e61ceef75c42a5790b6d","target":"graph","created_at":"2026-07-05T08:18:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.00271/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a \\emph{maximal closed substring} (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least $2$ are commonly called \\emph{runs}; those with exponent smaller than $2$, instead, are particular cases of \\emph{maximal gapped repeats}. We provide an algorithm that, given a string of length $n$ locates all MCSs the string contains in $\\mathcal O(n\\log n)$ tim","authors_text":"Alessandro De Luca, Gabriele Fici, Golnaz Badkobeh, Simon Puglisi","cross_cats":["cs.FL"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-09-01T07:18:12Z","title":"Maximal Closed Substrings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00271","kind":"arxiv","version":2},"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":"sha256:6a5d8f55782050a5152be387e8259c96f5ad5f176ec0868f38b8ea7ee164bf1c","target":"record","created_at":"2026-07-05T08:18:39Z","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":"f28594c87b9e5c8909a477c2ea5a8900db84232a45702dfc46bc5c80fc551b05","cross_cats_sorted":["cs.FL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-09-01T07:18:12Z","title_canon_sha256":"2344f2243a6658110b4a310c17433bc324e05335e173ee5a101aaceef4eca1c7"},"schema_version":"1.0","source":{"id":"2209.00271","kind":"arxiv","version":2}},"canonical_sha256":"9d3a91f5401dc32fec9dd9aa779952178cc0558e257fb5e2ece1d17ed908a599","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d3a91f5401dc32fec9dd9aa779952178cc0558e257fb5e2ece1d17ed908a599","first_computed_at":"2026-07-05T08:18:39.613639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:18:39.613639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YyeKME6FG9Emxce4dCEVmhoZeKnSOxzjN0BIvzQp/Imu5/CKUM3VM1xdnC4hLikFbJ9r2mQOOs+LqYkuxag0Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:18:39.614151Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.00271","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a5d8f55782050a5152be387e8259c96f5ad5f176ec0868f38b8ea7ee164bf1c","sha256:aa014b59f2ca30fd13198793312e87871d781d68d820e61ceef75c42a5790b6d"],"state_sha256":"2f50de5c5a448908ff0dc94e526d77e4de7e7d7373d00a206f75a4f7bf62ee5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uNYpBQGYK0lURtICC3XHc48WIr7wGDZuFYXcC5y/919g7qiYAFYDMYkMdLB6Ja3g0D2Nmxt3Ei0WYr1Q3fSoCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:04:47.539854Z","bundle_sha256":"2cc601d13a8ac85bf3ff9b9a93315a37906bce3654b92311f064d10c9eb34d38"}}