{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:QEMIWW3F5XK6FIGRCFS2LPQ3ZE","short_pith_number":"pith:QEMIWW3F","canonical_record":{"source":{"id":"2001.02296","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2020-01-02T22:37:12Z","cross_cats_sorted":["cs.AI","cs.LO"],"title_canon_sha256":"1ee7304aa3e92e71ab6841e8b15faa21e4619cf0e577a50389e104ea1f24f34d","abstract_canon_sha256":"a63c3235d97f507da2a91754a2597b3d1948a28f01b98071cacc57a1c76af842"},"schema_version":"1.0"},"canonical_sha256":"81188b5b65edd5e2a0d11165a5be1bc91b84db9e6588e3ff1523b6c8b8052573","source":{"kind":"arxiv","id":"2001.02296","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.02296","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"2001.02296v2","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.02296","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"QEMIWW3F5XK6","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"pith_short_16","alias_value":"QEMIWW3F5XK6FIGR","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"pith_short_8","alias_value":"QEMIWW3F","created_at":"2026-07-05T00:32:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:QEMIWW3F5XK6FIGRCFS2LPQ3ZE","target":"record","payload":{"canonical_record":{"source":{"id":"2001.02296","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2020-01-02T22:37:12Z","cross_cats_sorted":["cs.AI","cs.LO"],"title_canon_sha256":"1ee7304aa3e92e71ab6841e8b15faa21e4619cf0e577a50389e104ea1f24f34d","abstract_canon_sha256":"a63c3235d97f507da2a91754a2597b3d1948a28f01b98071cacc57a1c76af842"},"schema_version":"1.0"},"canonical_sha256":"81188b5b65edd5e2a0d11165a5be1bc91b84db9e6588e3ff1523b6c8b8052573","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:32:41.103487Z","signature_b64":"NO1DPDnufufi5z+X0JSckoNPNw0tNEvE2jc6Gwc0limVGWmSNjvVnRm6thfQcdvzzEwDRbH0XGF4J+Rtm/ZCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81188b5b65edd5e2a0d11165a5be1bc91b84db9e6588e3ff1523b6c8b8052573","last_reissued_at":"2026-07-05T00:32:41.103105Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:32:41.103105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2001.02296","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":"2026-07-05T00:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xr9vQwCFDhIRoDiHEuJwvdKVXgjQCrbCbz/XrlGJNezEYh4A2W4dlOp3G1LwLWInKEoRqO1iT/bNbZFjaV3VDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T11:59:33.767251Z"},"content_sha256":"8e6a94050017be6ba9ea2dbb5d4b3b6c3688f6cf5be5d726efb2792b70dc8e08","schema_version":"1.0","event_id":"sha256:8e6a94050017be6ba9ea2dbb5d4b3b6c3688f6cf5be5d726efb2792b70dc8e08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:QEMIWW3F5XK6FIGRCFS2LPQ3ZE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incremental Monoidal Grammars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LO"],"primary_cat":"cs.FL","authors_text":"Alexis Toumi, Dan Shiebler, Mehrnoosh Sadrzadeh","submitted_at":"2020-01-02T22:37:12Z","abstract_excerpt":"In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our construction to weighted formal grammars and weighted automata. This allows us to link the categorical viewpoint on natural language to the standard machine learning notion of probabilistic language model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.02296","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/2001.02296/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":"2026-07-05T00:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"64mmgDWljTL69gzeBX4IWcEXJoa72Q8XJJLhm4J6elDPZHYxYkxL2znRCAPjagaNai2EifIMIbpgO7NU0Tb6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T11:59:33.767661Z"},"content_sha256":"13f9c86eb4ebfcce475b3fad59f185f06db59f12e465e3625b4c5eba4b87f0ed","schema_version":"1.0","event_id":"sha256:13f9c86eb4ebfcce475b3fad59f185f06db59f12e465e3625b4c5eba4b87f0ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QEMIWW3F5XK6FIGRCFS2LPQ3ZE/bundle.json","state_url":"https://pith.science/pith/QEMIWW3F5XK6FIGRCFS2LPQ3ZE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QEMIWW3F5XK6FIGRCFS2LPQ3ZE/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":"2026-07-09T11:59:33Z","links":{"resolver":"https://pith.science/pith/QEMIWW3F5XK6FIGRCFS2LPQ3ZE","bundle":"https://pith.science/pith/QEMIWW3F5XK6FIGRCFS2LPQ3ZE/bundle.json","state":"https://pith.science/pith/QEMIWW3F5XK6FIGRCFS2LPQ3ZE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QEMIWW3F5XK6FIGRCFS2LPQ3ZE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:QEMIWW3F5XK6FIGRCFS2LPQ3ZE","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":"a63c3235d97f507da2a91754a2597b3d1948a28f01b98071cacc57a1c76af842","cross_cats_sorted":["cs.AI","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2020-01-02T22:37:12Z","title_canon_sha256":"1ee7304aa3e92e71ab6841e8b15faa21e4619cf0e577a50389e104ea1f24f34d"},"schema_version":"1.0","source":{"id":"2001.02296","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.02296","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"2001.02296v2","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.02296","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"QEMIWW3F5XK6","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"pith_short_16","alias_value":"QEMIWW3F5XK6FIGR","created_at":"2026-07-05T00:32:41Z"},{"alias_kind":"pith_short_8","alias_value":"QEMIWW3F","created_at":"2026-07-05T00:32:41Z"}],"graph_snapshots":[{"event_id":"sha256:13f9c86eb4ebfcce475b3fad59f185f06db59f12e465e3625b4c5eba4b87f0ed","target":"graph","created_at":"2026-07-05T00:32:41Z","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/2001.02296/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our construction to weighted formal grammars and weighted automata. This allows us to link the categorical viewpoint on natural language to the standard machine learning notion of probabilistic language model.","authors_text":"Alexis Toumi, Dan Shiebler, Mehrnoosh Sadrzadeh","cross_cats":["cs.AI","cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2020-01-02T22:37:12Z","title":"Incremental Monoidal Grammars"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.02296","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":"sha256:8e6a94050017be6ba9ea2dbb5d4b3b6c3688f6cf5be5d726efb2792b70dc8e08","target":"record","created_at":"2026-07-05T00:32:41Z","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":"a63c3235d97f507da2a91754a2597b3d1948a28f01b98071cacc57a1c76af842","cross_cats_sorted":["cs.AI","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2020-01-02T22:37:12Z","title_canon_sha256":"1ee7304aa3e92e71ab6841e8b15faa21e4619cf0e577a50389e104ea1f24f34d"},"schema_version":"1.0","source":{"id":"2001.02296","kind":"arxiv","version":2}},"canonical_sha256":"81188b5b65edd5e2a0d11165a5be1bc91b84db9e6588e3ff1523b6c8b8052573","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81188b5b65edd5e2a0d11165a5be1bc91b84db9e6588e3ff1523b6c8b8052573","first_computed_at":"2026-07-05T00:32:41.103105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:32:41.103105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NO1DPDnufufi5z+X0JSckoNPNw0tNEvE2jc6Gwc0limVGWmSNjvVnRm6thfQcdvzzEwDRbH0XGF4J+Rtm/ZCAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:32:41.103487Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.02296","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e6a94050017be6ba9ea2dbb5d4b3b6c3688f6cf5be5d726efb2792b70dc8e08","sha256:13f9c86eb4ebfcce475b3fad59f185f06db59f12e465e3625b4c5eba4b87f0ed"],"state_sha256":"8dca92aab77cc72149edf9939b542b7aedaddf2810f50f7a5a6eef8f236dec6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JTOwbr3NbqAsjW0Iv5m8apmYz79G1t0QgTVGgwwSFQm8cBj1QZr00sxG8+NKv+Qp8F1OpIg0DbtoDBvqc1htCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T11:59:33.769778Z","bundle_sha256":"0eba13d875bf1f9bf510ccb9d4b3aabefd7aa1a8235e7e91f76af82d26eee329"}}