{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:N6QZZAW3I2SIZ7GYVE6DLXFODH","short_pith_number":"pith:N6QZZAW3","canonical_record":{"source":{"id":"2212.09060","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2022-12-18T10:54:03Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"4d3fffc6f53da88fc34700414adcba68368b8959eb628e8b39e20381056c62a7","abstract_canon_sha256":"7309b53a640531b074a35f93ba5b95c206602a94d2aa8277b95b12ffc52e7944"},"schema_version":"1.0"},"canonical_sha256":"6fa19c82db46a48cfcd8a93c35dcae19c83828d316d4f373569134af7baa6386","source":{"kind":"arxiv","id":"2212.09060","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.09060","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"arxiv_version","alias_value":"2212.09060v5","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.09060","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"pith_short_12","alias_value":"N6QZZAW3I2SI","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"pith_short_16","alias_value":"N6QZZAW3I2SIZ7GY","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"pith_short_8","alias_value":"N6QZZAW3","created_at":"2026-07-05T06:23:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:N6QZZAW3I2SIZ7GYVE6DLXFODH","target":"record","payload":{"canonical_record":{"source":{"id":"2212.09060","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2022-12-18T10:54:03Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"4d3fffc6f53da88fc34700414adcba68368b8959eb628e8b39e20381056c62a7","abstract_canon_sha256":"7309b53a640531b074a35f93ba5b95c206602a94d2aa8277b95b12ffc52e7944"},"schema_version":"1.0"},"canonical_sha256":"6fa19c82db46a48cfcd8a93c35dcae19c83828d316d4f373569134af7baa6386","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:23:00.951430Z","signature_b64":"sNr7ojDJIe3ta7kFz2/xrRoW2uNut4t3lQbN6Wrh5Rn97l7Th3vYkfLLRB5RF3B8UoCcA51j+CUlTZOSIWH9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fa19c82db46a48cfcd8a93c35dcae19c83828d316d4f373569134af7baa6386","last_reissued_at":"2026-07-05T06:23:00.951086Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:23:00.951086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.09060","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:23:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"53vjTFvV91sGNTv58D9xBO6P5Pl4Ca1XTwMWGJRCXSOTryQlmfTdsyjBVCyupGLlSbCWRoB/zCbxWkWbDgOWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:02:53.699222Z"},"content_sha256":"400e823f4cdbc6919b52727a409f38505eb40f754e6ba1d98a3ee15feb33240b","schema_version":"1.0","event_id":"sha256:400e823f4cdbc6919b52727a409f38505eb40f754e6ba1d98a3ee15feb33240b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:N6QZZAW3I2SIZ7GYVE6DLXFODH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parsing as a lifting problem and the Chomsky-Sch\\\"utzenberger representation theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CT","authors_text":"Noam Zeilberger, Paul-Andr\\'e Melli\\`es","submitted_at":"2022-12-18T10:54:03Z","abstract_excerpt":"We begin by explaining how any context-free grammar encodes a functor of operads from a freely generated operad into a certain \"operad of spliced words\". This motivates a more general notion of CFG over any category $C$, defined as a finite species $S$ equipped with a color denoting the start symbol and a functor of operads $p : Free[S] \\to W[C]$ into the operad of spliced arrows in $C$. We show that many standard properties of CFGs can be formulated within this framework, and that usual closure properties of CF languages generalize to CF languages of arrows. We also discuss a dual fibrational"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.09060","kind":"arxiv","version":5},"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/2212.09060/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":"2026-07-05T06:23:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syscTqmZOPW4rqRb00RxMgka6zvMxfORTpTZbOZKlHCFMUAkuDhuNenv04emX0mFtN8RSlwFgdsGhe6XMLfwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:02:53.706069Z"},"content_sha256":"44b9711c79057bde1936e2eb89ce9723f5b829151dd456039edc086fad673952","schema_version":"1.0","event_id":"sha256:44b9711c79057bde1936e2eb89ce9723f5b829151dd456039edc086fad673952"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6QZZAW3I2SIZ7GYVE6DLXFODH/bundle.json","state_url":"https://pith.science/pith/N6QZZAW3I2SIZ7GYVE6DLXFODH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6QZZAW3I2SIZ7GYVE6DLXFODH/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":"2026-08-13T01:02:53Z","links":{"resolver":"https://pith.science/pith/N6QZZAW3I2SIZ7GYVE6DLXFODH","bundle":"https://pith.science/pith/N6QZZAW3I2SIZ7GYVE6DLXFODH/bundle.json","state":"https://pith.science/pith/N6QZZAW3I2SIZ7GYVE6DLXFODH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6QZZAW3I2SIZ7GYVE6DLXFODH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:N6QZZAW3I2SIZ7GYVE6DLXFODH","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":"7309b53a640531b074a35f93ba5b95c206602a94d2aa8277b95b12ffc52e7944","cross_cats_sorted":["cs.FL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2022-12-18T10:54:03Z","title_canon_sha256":"4d3fffc6f53da88fc34700414adcba68368b8959eb628e8b39e20381056c62a7"},"schema_version":"1.0","source":{"id":"2212.09060","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.09060","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"arxiv_version","alias_value":"2212.09060v5","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.09060","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"pith_short_12","alias_value":"N6QZZAW3I2SI","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"pith_short_16","alias_value":"N6QZZAW3I2SIZ7GY","created_at":"2026-07-05T06:23:00Z"},{"alias_kind":"pith_short_8","alias_value":"N6QZZAW3","created_at":"2026-07-05T06:23:00Z"}],"graph_snapshots":[{"event_id":"sha256:44b9711c79057bde1936e2eb89ce9723f5b829151dd456039edc086fad673952","target":"graph","created_at":"2026-07-05T06:23:00Z","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/2212.09060/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We begin by explaining how any context-free grammar encodes a functor of operads from a freely generated operad into a certain \"operad of spliced words\". This motivates a more general notion of CFG over any category $C$, defined as a finite species $S$ equipped with a color denoting the start symbol and a functor of operads $p : Free[S] \\to W[C]$ into the operad of spliced arrows in $C$. We show that many standard properties of CFGs can be formulated within this framework, and that usual closure properties of CF languages generalize to CF languages of arrows. We also discuss a dual fibrational","authors_text":"Noam Zeilberger, Paul-Andr\\'e Melli\\`es","cross_cats":["cs.FL"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2022-12-18T10:54:03Z","title":"Parsing as a lifting problem and the Chomsky-Sch\\\"utzenberger representation theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.09060","kind":"arxiv","version":5},"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":"sha256:400e823f4cdbc6919b52727a409f38505eb40f754e6ba1d98a3ee15feb33240b","target":"record","created_at":"2026-07-05T06:23:00Z","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":"7309b53a640531b074a35f93ba5b95c206602a94d2aa8277b95b12ffc52e7944","cross_cats_sorted":["cs.FL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2022-12-18T10:54:03Z","title_canon_sha256":"4d3fffc6f53da88fc34700414adcba68368b8959eb628e8b39e20381056c62a7"},"schema_version":"1.0","source":{"id":"2212.09060","kind":"arxiv","version":5}},"canonical_sha256":"6fa19c82db46a48cfcd8a93c35dcae19c83828d316d4f373569134af7baa6386","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fa19c82db46a48cfcd8a93c35dcae19c83828d316d4f373569134af7baa6386","first_computed_at":"2026-07-05T06:23:00.951086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:23:00.951086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sNr7ojDJIe3ta7kFz2/xrRoW2uNut4t3lQbN6Wrh5Rn97l7Th3vYkfLLRB5RF3B8UoCcA51j+CUlTZOSIWH9BA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:23:00.951430Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.09060","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:400e823f4cdbc6919b52727a409f38505eb40f754e6ba1d98a3ee15feb33240b","sha256:44b9711c79057bde1936e2eb89ce9723f5b829151dd456039edc086fad673952"],"state_sha256":"9b690f69c5e3d9f64954a8bd52a1fbd19de28df026cae202471def93d501e7b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFdsxsupd92KM4sdwrSz6M2V/v/Tp9OTkm1uvqBM+NRIbIUb10obubes1E5SSmcIwt9u81X658TMsqR19d9rAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T01:02:53.722386Z","bundle_sha256":"7d3d29da43d61a32030655d06391a4bd1d08e75ae6c41f7a766d97763fd84494"}}