{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:53EN2IAOZTJV7LPNP2H6RPL66T","short_pith_number":"pith:53EN2IAO","canonical_record":{"source":{"id":"2102.07728","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2021-02-15T18:25:48Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"545badaab46bfbe3b346541e09e55a4f41412f8f532786fca38ce7a58cc2f422","abstract_canon_sha256":"be6cb1592bc4905ebbc0b2826931c0e5540be1a15d1006f18a60df06f870fa42"},"schema_version":"1.0"},"canonical_sha256":"eec8dd200eccd35faded7e8fe8bd7ef4c6796d9c62de7308c218da48127ff8ca","source":{"kind":"arxiv","id":"2102.07728","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.07728","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"arxiv_version","alias_value":"2102.07728v2","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.07728","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"pith_short_12","alias_value":"53EN2IAOZTJV","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"pith_short_16","alias_value":"53EN2IAOZTJV7LPN","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"pith_short_8","alias_value":"53EN2IAO","created_at":"2026-07-05T02:46:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:53EN2IAOZTJV7LPNP2H6RPL66T","target":"record","payload":{"canonical_record":{"source":{"id":"2102.07728","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2021-02-15T18:25:48Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"545badaab46bfbe3b346541e09e55a4f41412f8f532786fca38ce7a58cc2f422","abstract_canon_sha256":"be6cb1592bc4905ebbc0b2826931c0e5540be1a15d1006f18a60df06f870fa42"},"schema_version":"1.0"},"canonical_sha256":"eec8dd200eccd35faded7e8fe8bd7ef4c6796d9c62de7308c218da48127ff8ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:46:12.211713Z","signature_b64":"tyf3HupiSpEz4JCeY0ohpNXUcVqZ6Vx2KtUhbDP2LBimNvcVKuuPdjzPlOZIr3TsknbMtjyucVq0BFYU2o+tCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eec8dd200eccd35faded7e8fe8bd7ef4c6796d9c62de7308c218da48127ff8ca","last_reissued_at":"2026-07-05T02:46:12.211348Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:46:12.211348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.07728","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":"2026-07-05T02:46:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oK2+ok5Row/HKf8tL3Sr+BbyG1lL31Z2AuDDW+j5z5/h26hs4d2Mw6ElDXUGbqDTVvOzR9sV0wWcYS/FeiOXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:44:53.488574Z"},"content_sha256":"c3b896d7353b6dd998f39011c924fe2a9616aa43002b9457371b815fee17b913","schema_version":"1.0","event_id":"sha256:c3b896d7353b6dd998f39011c924fe2a9616aa43002b9457371b815fee17b913"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:53EN2IAOZTJV7LPNP2H6RPL66T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic Membership for Regular Languages","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.FL","authors_text":"Antoine Amarilli, Charles Paperman, Louis Jachiet","submitted_at":"2021-02-15T18:25:48Z","abstract_excerpt":"We study the dynamic membership problem for regular languages: fix a language L, read a word w, build in time O(|w|) a data structure indicating if w is in L, and maintain this structure efficiently under letter substitutions on w. We consider this problem on the unit cost RAM model with logarithmic word length, where the problem always has a solution in O(log |w| / log log |w|) per operation.\n  We show that the problem is in O(log log |w|) for languages in an algebraically-defined, decidable class QSG, and that it is in O(1) for another such class QLZG. We show that languages not in QSG admit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07728","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/2102.07728/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":"2026-07-05T02:46:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iMbxAidQ1cs5EL5EnAtolx9HD9ttdWxXNc+iDwMrNhOFSoCLwF7plypS2C00zWhsdP6MMpMb5Fy5Bd4CYhlhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:44:53.489076Z"},"content_sha256":"ae8ae644f60e40191ec2cc2cd8dc11a8d73f36fddf15126ac1895762a048bb51","schema_version":"1.0","event_id":"sha256:ae8ae644f60e40191ec2cc2cd8dc11a8d73f36fddf15126ac1895762a048bb51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53EN2IAOZTJV7LPNP2H6RPL66T/bundle.json","state_url":"https://pith.science/pith/53EN2IAOZTJV7LPNP2H6RPL66T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53EN2IAOZTJV7LPNP2H6RPL66T/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":"2026-08-12T22:44:53Z","links":{"resolver":"https://pith.science/pith/53EN2IAOZTJV7LPNP2H6RPL66T","bundle":"https://pith.science/pith/53EN2IAOZTJV7LPNP2H6RPL66T/bundle.json","state":"https://pith.science/pith/53EN2IAOZTJV7LPNP2H6RPL66T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53EN2IAOZTJV7LPNP2H6RPL66T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:53EN2IAOZTJV7LPNP2H6RPL66T","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":"be6cb1592bc4905ebbc0b2826931c0e5540be1a15d1006f18a60df06f870fa42","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2021-02-15T18:25:48Z","title_canon_sha256":"545badaab46bfbe3b346541e09e55a4f41412f8f532786fca38ce7a58cc2f422"},"schema_version":"1.0","source":{"id":"2102.07728","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.07728","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"arxiv_version","alias_value":"2102.07728v2","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.07728","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"pith_short_12","alias_value":"53EN2IAOZTJV","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"pith_short_16","alias_value":"53EN2IAOZTJV7LPN","created_at":"2026-07-05T02:46:12Z"},{"alias_kind":"pith_short_8","alias_value":"53EN2IAO","created_at":"2026-07-05T02:46:12Z"}],"graph_snapshots":[{"event_id":"sha256:ae8ae644f60e40191ec2cc2cd8dc11a8d73f36fddf15126ac1895762a048bb51","target":"graph","created_at":"2026-07-05T02:46:12Z","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/2102.07728/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the dynamic membership problem for regular languages: fix a language L, read a word w, build in time O(|w|) a data structure indicating if w is in L, and maintain this structure efficiently under letter substitutions on w. We consider this problem on the unit cost RAM model with logarithmic word length, where the problem always has a solution in O(log |w| / log log |w|) per operation.\n  We show that the problem is in O(log log |w|) for languages in an algebraically-defined, decidable class QSG, and that it is in O(1) for another such class QLZG. We show that languages not in QSG admit","authors_text":"Antoine Amarilli, Charles Paperman, Louis Jachiet","cross_cats":["cs.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2021-02-15T18:25:48Z","title":"Dynamic Membership for Regular Languages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07728","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:c3b896d7353b6dd998f39011c924fe2a9616aa43002b9457371b815fee17b913","target":"record","created_at":"2026-07-05T02:46:12Z","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":"be6cb1592bc4905ebbc0b2826931c0e5540be1a15d1006f18a60df06f870fa42","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2021-02-15T18:25:48Z","title_canon_sha256":"545badaab46bfbe3b346541e09e55a4f41412f8f532786fca38ce7a58cc2f422"},"schema_version":"1.0","source":{"id":"2102.07728","kind":"arxiv","version":2}},"canonical_sha256":"eec8dd200eccd35faded7e8fe8bd7ef4c6796d9c62de7308c218da48127ff8ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eec8dd200eccd35faded7e8fe8bd7ef4c6796d9c62de7308c218da48127ff8ca","first_computed_at":"2026-07-05T02:46:12.211348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:46:12.211348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tyf3HupiSpEz4JCeY0ohpNXUcVqZ6Vx2KtUhbDP2LBimNvcVKuuPdjzPlOZIr3TsknbMtjyucVq0BFYU2o+tCA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:46:12.211713Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.07728","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3b896d7353b6dd998f39011c924fe2a9616aa43002b9457371b815fee17b913","sha256:ae8ae644f60e40191ec2cc2cd8dc11a8d73f36fddf15126ac1895762a048bb51"],"state_sha256":"123a0b51dbe293c7618bfbb156720fa2a46c994260ad7546f9714119290d1af8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bIvs/Jn8C5+VF16J6UpBL3hR2XN4+rj1q2OJUNi7jiTOMCaHYKvuwW1NwxXjQEIb0JfFWw7dbd4AuXdy4eE8AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:44:53.493273Z","bundle_sha256":"44492bfc8d5c399c4f5b4f770a583574f74b60f3e28156b4b85b6590dda868e5"}}