{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YGSCXXQMWOOW4RXRSICHZDA4ZQ","short_pith_number":"pith:YGSCXXQM","canonical_record":{"source":{"id":"1806.08304","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-06-21T16:03:04Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"283f2f2c0087599e0754947e7c30d568770cc495260dedfb93eecede69aee0ea","abstract_canon_sha256":"93b087481e6c681b75c0e02eb6741e8861b5a3d7eb79912677fa9a0bbbccbdb2"},"schema_version":"1.0"},"canonical_sha256":"c1a42bde0cb39d6e46f192047c8c1ccc221a3cc1038495071a4a6ba9ed34678b","source":{"kind":"arxiv","id":"1806.08304","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08304","created_at":"2026-05-17T23:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08304v3","created_at":"2026-05-17T23:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08304","created_at":"2026-05-17T23:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"YGSCXXQMWOOW","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YGSCXXQMWOOW4RXR","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YGSCXXQM","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YGSCXXQMWOOW4RXRSICHZDA4ZQ","target":"record","payload":{"canonical_record":{"source":{"id":"1806.08304","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-06-21T16:03:04Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"283f2f2c0087599e0754947e7c30d568770cc495260dedfb93eecede69aee0ea","abstract_canon_sha256":"93b087481e6c681b75c0e02eb6741e8861b5a3d7eb79912677fa9a0bbbccbdb2"},"schema_version":"1.0"},"canonical_sha256":"c1a42bde0cb39d6e46f192047c8c1ccc221a3cc1038495071a4a6ba9ed34678b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:58.393621Z","signature_b64":"LQfchxaE3YSKu70o9UNY8jCbE6g0keP9CrGGAAf3jIxtaD6cXtrL1sasn/S7rIMAMz5wUf5pNSktydqUjeu5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1a42bde0cb39d6e46f192047c8c1ccc221a3cc1038495071a4a6ba9ed34678b","last_reissued_at":"2026-05-17T23:55:58.392879Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:58.392879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.08304","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":"2026-05-17T23:55:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRfH0TNUbktRqxCBolrgvwAfLM3WHlTL91nOUHkYuI2B+iFPuUdRf3vyvuC8HjKVfoSE6jRKgLNkp2xgWUT9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T10:39:38.119308Z"},"content_sha256":"ed1a9a8ecd9ce1661b2c6eac2c676dca50a067bcfc1ebe91671c1f32f3dc8ed0","schema_version":"1.0","event_id":"sha256:ed1a9a8ecd9ce1661b2c6eac2c676dca50a067bcfc1ebe91671c1f32f3dc8ed0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YGSCXXQMWOOW4RXRSICHZDA4ZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypergraph Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.CT","authors_text":"Brendan Fong, David I Spivak","submitted_at":"2018-06-21T16:03:04Z","abstract_excerpt":"Hypergraph categories have been rediscovered at least five times, under various names, including well-supported compact closed categories, dgs-monoidal categories, and dungeon categories. Perhaps the reason they keep being reinvented is two-fold: there are many applications---including to automata, databases, circuits, linear relations, graph rewriting, and belief propagation---and yet the standard definition is so involved and ornate as to be difficult to find in the literature. Indeed, a hypergraph category is, roughly speaking, a \"symmetric monoidal category in which each object is equipped"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08304","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":"2026-05-17T23:55:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RcgzusKxshUjh87lvhRlLfg04t92YIkWFyWfZ4mmv5vNkSqKiTmePpKlbd+LhWMDfcVmLTt9cb9wd1MnlyzsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T10:39:38.119753Z"},"content_sha256":"f337bccd17eec268b4a30ecbc939bc178adf39f0a877f0c51238e42de41da164","schema_version":"1.0","event_id":"sha256:f337bccd17eec268b4a30ecbc939bc178adf39f0a877f0c51238e42de41da164"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YGSCXXQMWOOW4RXRSICHZDA4ZQ/bundle.json","state_url":"https://pith.science/pith/YGSCXXQMWOOW4RXRSICHZDA4ZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YGSCXXQMWOOW4RXRSICHZDA4ZQ/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":"2026-08-05T10:39:38Z","links":{"resolver":"https://pith.science/pith/YGSCXXQMWOOW4RXRSICHZDA4ZQ","bundle":"https://pith.science/pith/YGSCXXQMWOOW4RXRSICHZDA4ZQ/bundle.json","state":"https://pith.science/pith/YGSCXXQMWOOW4RXRSICHZDA4ZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YGSCXXQMWOOW4RXRSICHZDA4ZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YGSCXXQMWOOW4RXRSICHZDA4ZQ","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":"93b087481e6c681b75c0e02eb6741e8861b5a3d7eb79912677fa9a0bbbccbdb2","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-06-21T16:03:04Z","title_canon_sha256":"283f2f2c0087599e0754947e7c30d568770cc495260dedfb93eecede69aee0ea"},"schema_version":"1.0","source":{"id":"1806.08304","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08304","created_at":"2026-05-17T23:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08304v3","created_at":"2026-05-17T23:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08304","created_at":"2026-05-17T23:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"YGSCXXQMWOOW","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YGSCXXQMWOOW4RXR","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YGSCXXQM","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:f337bccd17eec268b4a30ecbc939bc178adf39f0a877f0c51238e42de41da164","target":"graph","created_at":"2026-05-17T23:55:58Z","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":"Hypergraph categories have been rediscovered at least five times, under various names, including well-supported compact closed categories, dgs-monoidal categories, and dungeon categories. Perhaps the reason they keep being reinvented is two-fold: there are many applications---including to automata, databases, circuits, linear relations, graph rewriting, and belief propagation---and yet the standard definition is so involved and ornate as to be difficult to find in the literature. Indeed, a hypergraph category is, roughly speaking, a \"symmetric monoidal category in which each object is equipped","authors_text":"Brendan Fong, David I Spivak","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-06-21T16:03:04Z","title":"Hypergraph Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08304","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:ed1a9a8ecd9ce1661b2c6eac2c676dca50a067bcfc1ebe91671c1f32f3dc8ed0","target":"record","created_at":"2026-05-17T23:55:58Z","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":"93b087481e6c681b75c0e02eb6741e8861b5a3d7eb79912677fa9a0bbbccbdb2","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-06-21T16:03:04Z","title_canon_sha256":"283f2f2c0087599e0754947e7c30d568770cc495260dedfb93eecede69aee0ea"},"schema_version":"1.0","source":{"id":"1806.08304","kind":"arxiv","version":3}},"canonical_sha256":"c1a42bde0cb39d6e46f192047c8c1ccc221a3cc1038495071a4a6ba9ed34678b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1a42bde0cb39d6e46f192047c8c1ccc221a3cc1038495071a4a6ba9ed34678b","first_computed_at":"2026-05-17T23:55:58.392879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:58.392879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LQfchxaE3YSKu70o9UNY8jCbE6g0keP9CrGGAAf3jIxtaD6cXtrL1sasn/S7rIMAMz5wUf5pNSktydqUjeu5Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:58.393621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.08304","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed1a9a8ecd9ce1661b2c6eac2c676dca50a067bcfc1ebe91671c1f32f3dc8ed0","sha256:f337bccd17eec268b4a30ecbc939bc178adf39f0a877f0c51238e42de41da164"],"state_sha256":"a7ca8c2b5a930f2265d0e8bf343ab8c69e2da94bd804a2bb15f3c7be3259aa65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzNyHdmhrB3fuqMx0olFEa9Km3vZ3aExxkAaziSC935qNrWyKxbHUU5Zfo/I5JluPE+D1loq32XqZSsSg+arAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T10:39:38.125820Z","bundle_sha256":"87ce32ef4edac49675e57383d60dc3d1995dac230a7d6bc16059ff593c1c985c"}}