{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:F2UD6TRXVSU3SZNTAE23BZWHST","short_pith_number":"pith:F2UD6TRX","canonical_record":{"source":{"id":"1503.08326","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-03-28T16:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"e99802e73cd5ce95c3fc0c1cf79d5237dc52d9f291a4db3bdc253860bd543347","abstract_canon_sha256":"6954ea49c551dd0e4b7fb794e20eb74344e60f2d7901c2de85b5517af4701405"},"schema_version":"1.0"},"canonical_sha256":"2ea83f4e37aca9b965b30135b0e6c794e37dc74befa0fe751d3583f31928cefb","source":{"kind":"arxiv","id":"1503.08326","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08326","created_at":"2026-05-18T01:41:46Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08326v2","created_at":"2026-05-18T01:41:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08326","created_at":"2026-05-18T01:41:46Z"},{"alias_kind":"pith_short_12","alias_value":"F2UD6TRXVSU3","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F2UD6TRXVSU3SZNT","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F2UD6TRX","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:F2UD6TRXVSU3SZNTAE23BZWHST","target":"record","payload":{"canonical_record":{"source":{"id":"1503.08326","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-03-28T16:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"e99802e73cd5ce95c3fc0c1cf79d5237dc52d9f291a4db3bdc253860bd543347","abstract_canon_sha256":"6954ea49c551dd0e4b7fb794e20eb74344e60f2d7901c2de85b5517af4701405"},"schema_version":"1.0"},"canonical_sha256":"2ea83f4e37aca9b965b30135b0e6c794e37dc74befa0fe751d3583f31928cefb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:46.089655Z","signature_b64":"RXPIzQEEuwt2P51I0jW4nmX4MTfqZ2hV4jsDULZmnzygc9l73OIaKIaHigtFG7ggHd32lT7F+bi/C7GevyztCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ea83f4e37aca9b965b30135b0e6c794e37dc74befa0fe751d3583f31928cefb","last_reissued_at":"2026-05-18T01:41:46.089278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:46.089278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.08326","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":"2026-05-18T01:41:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t4LLCq36p8JOvQ4p1TIvFV3kN0mTE4RK+HST/vmx3K8zjhFE4DI71iel6L++ALYsX9ZBb5gYzAu6h/bhNWNdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:50:48.576283Z"},"content_sha256":"789eccf2b4a7295ab34bc380573714620b64db6a5c383cac1b0ae5cdb9a0e3d2","schema_version":"1.0","event_id":"sha256:789eccf2b4a7295ab34bc380573714620b64db6a5c383cac1b0ae5cdb9a0e3d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:F2UD6TRXVSU3SZNTAE23BZWHST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toward formalizing ologs: Linguistic structures, instantiations, and mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"David I. Spivak, Marco A. P\\'erez","submitted_at":"2015-03-28T16:48:48Z","abstract_excerpt":"We define the notion of linguistic structure on a small category, in order to provide a more formal description of ontology logs, also known as ologs, introduced by R. E. Kent and D. I. Spivak in their paper \"Ologs: A categorical framework for knowledge representation.\" In particular, we construct a bicategory $\\mathsf{Eng}$, of English noun phrases and verb phrases, endorsed as functional by varying sets of authors. An olog is then defined as a lax functor to $\\mathsf{Eng}$. We then present a new notion of linguistic functor, which extends Spivak's notion of meaningful functors. Finally, we d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08326","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":""},"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":"2026-05-18T01:41:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W996RjQlaIWrmtEPtbKUZhiaBN4pPcb4a46HqnWvj9jHWlsElSSH+bMWDNU1+qUNo/svzvwGXTYy6GBGNu2pBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:50:48.576674Z"},"content_sha256":"c7b92c6be5f7e006a2731ad23452ec01ba805761f73b5e8ba8256a7d576fce09","schema_version":"1.0","event_id":"sha256:c7b92c6be5f7e006a2731ad23452ec01ba805761f73b5e8ba8256a7d576fce09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2UD6TRXVSU3SZNTAE23BZWHST/bundle.json","state_url":"https://pith.science/pith/F2UD6TRXVSU3SZNTAE23BZWHST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2UD6TRXVSU3SZNTAE23BZWHST/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":"2026-06-08T21:50:48Z","links":{"resolver":"https://pith.science/pith/F2UD6TRXVSU3SZNTAE23BZWHST","bundle":"https://pith.science/pith/F2UD6TRXVSU3SZNTAE23BZWHST/bundle.json","state":"https://pith.science/pith/F2UD6TRXVSU3SZNTAE23BZWHST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2UD6TRXVSU3SZNTAE23BZWHST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F2UD6TRXVSU3SZNTAE23BZWHST","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":"6954ea49c551dd0e4b7fb794e20eb74344e60f2d7901c2de85b5517af4701405","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-03-28T16:48:48Z","title_canon_sha256":"e99802e73cd5ce95c3fc0c1cf79d5237dc52d9f291a4db3bdc253860bd543347"},"schema_version":"1.0","source":{"id":"1503.08326","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08326","created_at":"2026-05-18T01:41:46Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08326v2","created_at":"2026-05-18T01:41:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08326","created_at":"2026-05-18T01:41:46Z"},{"alias_kind":"pith_short_12","alias_value":"F2UD6TRXVSU3","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F2UD6TRXVSU3SZNT","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F2UD6TRX","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:c7b92c6be5f7e006a2731ad23452ec01ba805761f73b5e8ba8256a7d576fce09","target":"graph","created_at":"2026-05-18T01:41:46Z","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":"We define the notion of linguistic structure on a small category, in order to provide a more formal description of ontology logs, also known as ologs, introduced by R. E. Kent and D. I. Spivak in their paper \"Ologs: A categorical framework for knowledge representation.\" In particular, we construct a bicategory $\\mathsf{Eng}$, of English noun phrases and verb phrases, endorsed as functional by varying sets of authors. An olog is then defined as a lax functor to $\\mathsf{Eng}$. We then present a new notion of linguistic functor, which extends Spivak's notion of meaningful functors. Finally, we d","authors_text":"David I. Spivak, Marco A. P\\'erez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-03-28T16:48:48Z","title":"Toward formalizing ologs: Linguistic structures, instantiations, and mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08326","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":"sha256:789eccf2b4a7295ab34bc380573714620b64db6a5c383cac1b0ae5cdb9a0e3d2","target":"record","created_at":"2026-05-18T01:41:46Z","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":"6954ea49c551dd0e4b7fb794e20eb74344e60f2d7901c2de85b5517af4701405","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-03-28T16:48:48Z","title_canon_sha256":"e99802e73cd5ce95c3fc0c1cf79d5237dc52d9f291a4db3bdc253860bd543347"},"schema_version":"1.0","source":{"id":"1503.08326","kind":"arxiv","version":2}},"canonical_sha256":"2ea83f4e37aca9b965b30135b0e6c794e37dc74befa0fe751d3583f31928cefb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ea83f4e37aca9b965b30135b0e6c794e37dc74befa0fe751d3583f31928cefb","first_computed_at":"2026-05-18T01:41:46.089278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:46.089278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RXPIzQEEuwt2P51I0jW4nmX4MTfqZ2hV4jsDULZmnzygc9l73OIaKIaHigtFG7ggHd32lT7F+bi/C7GevyztCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:46.089655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08326","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:789eccf2b4a7295ab34bc380573714620b64db6a5c383cac1b0ae5cdb9a0e3d2","sha256:c7b92c6be5f7e006a2731ad23452ec01ba805761f73b5e8ba8256a7d576fce09"],"state_sha256":"55b10869534a3b2d2869d18b23f22407d0a70dd13f7d6af7477dc4019fe64549"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iWkfcTc1iAoYbmm38gw6UhxbEQnQzSpsEDj0orp4Gicj4ALEGgpKQr4dVLhaEc1DQGAXbAcqHERw+gj1UQmTCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:50:48.578526Z","bundle_sha256":"ca56d48e1598c4770e7066a35eb1d8f60622647a51b7008b4045c4c39aa3c7f3"}}