{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AGX4LDTIEOFYYF37R5NGBRTDT7","short_pith_number":"pith:AGX4LDTI","canonical_record":{"source":{"id":"1812.05765","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-14T03:07:29Z","cross_cats_sorted":["cs.LO","math.LO"],"title_canon_sha256":"1df536cc9e19c5153e05b323e104eb9e295c3f3ebe7764f595875b30e06f040e","abstract_canon_sha256":"f303afa38147e3a36f43deee233d7fea4eea981de34660b7df3d133cf7b2884a"},"schema_version":"1.0"},"canonical_sha256":"01afc58e68238b8c177f8f5a60c6639fc9af470b0b45f507e5f18d0e24105730","source":{"kind":"arxiv","id":"1812.05765","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05765","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05765v3","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05765","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"AGX4LDTIEOFY","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AGX4LDTIEOFYYF37","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AGX4LDTI","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AGX4LDTIEOFYYF37R5NGBRTDT7","target":"record","payload":{"canonical_record":{"source":{"id":"1812.05765","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-14T03:07:29Z","cross_cats_sorted":["cs.LO","math.LO"],"title_canon_sha256":"1df536cc9e19c5153e05b323e104eb9e295c3f3ebe7764f595875b30e06f040e","abstract_canon_sha256":"f303afa38147e3a36f43deee233d7fea4eea981de34660b7df3d133cf7b2884a"},"schema_version":"1.0"},"canonical_sha256":"01afc58e68238b8c177f8f5a60c6639fc9af470b0b45f507e5f18d0e24105730","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:49.833860Z","signature_b64":"sGpNMKOylIiZ/dLua3UkuYCj3hM2iGptoDnXN9idp4vTgCFYO7TQuOQQnN9PzhNxW6PGn0XVETWlnl6cs08KAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01afc58e68238b8c177f8f5a60c6639fc9af470b0b45f507e5f18d0e24105730","last_reissued_at":"2026-05-17T23:42:49.833346Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:49.833346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.05765","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3k7qHLuguGsJygN19kPQI1aaDRX/m2hfSyOQAeVVD872PeS9l+lvAngO4SPHh4DptPXJVeEaFxmOpJJAnAoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:57:51.912360Z"},"content_sha256":"77e8855ae352d0bb57ee3193d5f1a34693ba8e4586292fd3d415dc4bfa28bfb6","schema_version":"1.0","event_id":"sha256:77e8855ae352d0bb57ee3193d5f1a34693ba8e4586292fd3d415dc4bfa28bfb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AGX4LDTIEOFYYF37R5NGBRTDT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphical Regular Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.LO"],"primary_cat":"math.CT","authors_text":"Brendan Fong, David I Spivak","submitted_at":"2018-12-14T03:07:29Z","abstract_excerpt":"Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free regular category $\\mathsf{FRg}(\\mathrm{T})$ on a set $\\mathrm{T}$. From this point of view, regular theories are certain monoidal 2-functors from a suitable 2-category of contexts---the 2-category of relations in $\\mathsf{FRg}(\\mathrm{T})$---to the 2-category of posets. Such functors assign to each context the set of formulas in that context, ordered by ent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05765","kind":"arxiv","version":3},"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":"2026-05-17T23:42:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rw1hjuwf1kA2HaQJc6Q12g0gjKkobDfJddVjp4EkGrPx4o0sMNync0LpE7c7ZN7QcKooHMS3BOWqL4cFmGBHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:57:51.913289Z"},"content_sha256":"ba20074339fa0543c2a7cd9418a5cc28519dc626ce438bab0b19cc21049de435","schema_version":"1.0","event_id":"sha256:ba20074339fa0543c2a7cd9418a5cc28519dc626ce438bab0b19cc21049de435"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AGX4LDTIEOFYYF37R5NGBRTDT7/bundle.json","state_url":"https://pith.science/pith/AGX4LDTIEOFYYF37R5NGBRTDT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AGX4LDTIEOFYYF37R5NGBRTDT7/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":"2026-08-09T13:57:51Z","links":{"resolver":"https://pith.science/pith/AGX4LDTIEOFYYF37R5NGBRTDT7","bundle":"https://pith.science/pith/AGX4LDTIEOFYYF37R5NGBRTDT7/bundle.json","state":"https://pith.science/pith/AGX4LDTIEOFYYF37R5NGBRTDT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AGX4LDTIEOFYYF37R5NGBRTDT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AGX4LDTIEOFYYF37R5NGBRTDT7","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":"f303afa38147e3a36f43deee233d7fea4eea981de34660b7df3d133cf7b2884a","cross_cats_sorted":["cs.LO","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-14T03:07:29Z","title_canon_sha256":"1df536cc9e19c5153e05b323e104eb9e295c3f3ebe7764f595875b30e06f040e"},"schema_version":"1.0","source":{"id":"1812.05765","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05765","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05765v3","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05765","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"AGX4LDTIEOFY","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AGX4LDTIEOFYYF37","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AGX4LDTI","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:ba20074339fa0543c2a7cd9418a5cc28519dc626ce438bab0b19cc21049de435","target":"graph","created_at":"2026-05-17T23:42:49Z","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":"Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free regular category $\\mathsf{FRg}(\\mathrm{T})$ on a set $\\mathrm{T}$. From this point of view, regular theories are certain monoidal 2-functors from a suitable 2-category of contexts---the 2-category of relations in $\\mathsf{FRg}(\\mathrm{T})$---to the 2-category of posets. Such functors assign to each context the set of formulas in that context, ordered by ent","authors_text":"Brendan Fong, David I Spivak","cross_cats":["cs.LO","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-14T03:07:29Z","title":"Graphical Regular Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05765","kind":"arxiv","version":3},"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":"sha256:77e8855ae352d0bb57ee3193d5f1a34693ba8e4586292fd3d415dc4bfa28bfb6","target":"record","created_at":"2026-05-17T23:42:49Z","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":"f303afa38147e3a36f43deee233d7fea4eea981de34660b7df3d133cf7b2884a","cross_cats_sorted":["cs.LO","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-14T03:07:29Z","title_canon_sha256":"1df536cc9e19c5153e05b323e104eb9e295c3f3ebe7764f595875b30e06f040e"},"schema_version":"1.0","source":{"id":"1812.05765","kind":"arxiv","version":3}},"canonical_sha256":"01afc58e68238b8c177f8f5a60c6639fc9af470b0b45f507e5f18d0e24105730","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01afc58e68238b8c177f8f5a60c6639fc9af470b0b45f507e5f18d0e24105730","first_computed_at":"2026-05-17T23:42:49.833346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:49.833346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sGpNMKOylIiZ/dLua3UkuYCj3hM2iGptoDnXN9idp4vTgCFYO7TQuOQQnN9PzhNxW6PGn0XVETWlnl6cs08KAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:49.833860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.05765","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77e8855ae352d0bb57ee3193d5f1a34693ba8e4586292fd3d415dc4bfa28bfb6","sha256:ba20074339fa0543c2a7cd9418a5cc28519dc626ce438bab0b19cc21049de435"],"state_sha256":"8a9813927964bedf84da2781216edfcab6f078486ea6a5ba55419a6af4d7e6a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fBHPa7aaDbvKERBtSa+87vgUsln8lUAo/NfW8RY1Kv3gxek9ele2laYH77Z07f7EHGEH8GoOa6v/qoCd1t1yAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T13:57:51.918427Z","bundle_sha256":"c021b0c6c24c284638d4d1876f50980bf76ce6cb7b0ded644bc81028530d87d2"}}