{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MKJJTKRQ2WITUI3OCTTQQVJQGE","short_pith_number":"pith:MKJJTKRQ","canonical_record":{"source":{"id":"1712.09495","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-12-27T05:15:21Z","cross_cats_sorted":[],"title_canon_sha256":"5252b03f47cca53180e6d084c88c98a977c5339dab73da9b65fe1adc0c6cb16e","abstract_canon_sha256":"2b1c1b3da0fc1b1e878d73082f707b964701c594061dc6c3f9d19cf5cf32e2d9"},"schema_version":"1.0"},"canonical_sha256":"629299aa30d5913a236e14e708553031047362e655292eaad5ceeb6b6d6141a0","source":{"kind":"arxiv","id":"1712.09495","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09495","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09495v2","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09495","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"pith_short_12","alias_value":"MKJJTKRQ2WIT","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MKJJTKRQ2WITUI3O","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MKJJTKRQ","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MKJJTKRQ2WITUI3OCTTQQVJQGE","target":"record","payload":{"canonical_record":{"source":{"id":"1712.09495","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-12-27T05:15:21Z","cross_cats_sorted":[],"title_canon_sha256":"5252b03f47cca53180e6d084c88c98a977c5339dab73da9b65fe1adc0c6cb16e","abstract_canon_sha256":"2b1c1b3da0fc1b1e878d73082f707b964701c594061dc6c3f9d19cf5cf32e2d9"},"schema_version":"1.0"},"canonical_sha256":"629299aa30d5913a236e14e708553031047362e655292eaad5ceeb6b6d6141a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:48.890149Z","signature_b64":"PN+cbjt3e1sJRWeF1tg5cfqEFn/qlUAjZvCP8jZygpv44NjV8xBW3Q/R3tpBhjjqS87BJBcliUsqAG2wS1XzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"629299aa30d5913a236e14e708553031047362e655292eaad5ceeb6b6d6141a0","last_reissued_at":"2026-05-18T00:26:48.889512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:48.889512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.09495","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":"2026-05-18T00:26:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"22zrikDEWnjse90a1zD4sk+Jf9YJbjGgGfDc2eDT625qKDdR37vPmEGNK2+pDEGIVcA8ZjRWk/NmqbkB/YCZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:25:44.868510Z"},"content_sha256":"2c141ef21b702e1785289bbe0da4e7eeff80dbf1caa6e94ccd1ce55d0a3e7d1a","schema_version":"1.0","event_id":"sha256:2c141ef21b702e1785289bbe0da4e7eeff80dbf1caa6e94ccd1ce55d0a3e7d1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MKJJTKRQ2WITUI3OCTTQQVJQGE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rewriting in Free Hypergraph Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Fabio Zanasi (University College London)","submitted_at":"2017-12-27T05:15:21Z","abstract_excerpt":"We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. These categories, also called hypergraph categories, are increasingly relevant: Frobenius structures recently appeared in cross-disciplinary applications, including the study of quantum processes, dynamical systems and natural language processing. In this work we give a combinatorial characterisation of arrows of a free hypergraph category as cospans of labelled hypergraphs and establish a precise correspondence between rewriting modulo Frobeniu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09495","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":"2026-05-18T00:26:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w89XkQD1rV/A7TawOTZUqkdfgnhCSBhmmdbLUckmcmEKARo/P+nvLuMM6ZpMi435K5zbewriCevxTB3ICJPoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:25:44.868860Z"},"content_sha256":"172496ad4058a968cd44c01769eef622329a303811c7e2977edf8e1440a7d496","schema_version":"1.0","event_id":"sha256:172496ad4058a968cd44c01769eef622329a303811c7e2977edf8e1440a7d496"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MKJJTKRQ2WITUI3OCTTQQVJQGE/bundle.json","state_url":"https://pith.science/pith/MKJJTKRQ2WITUI3OCTTQQVJQGE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MKJJTKRQ2WITUI3OCTTQQVJQGE/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":"2026-05-30T13:25:44Z","links":{"resolver":"https://pith.science/pith/MKJJTKRQ2WITUI3OCTTQQVJQGE","bundle":"https://pith.science/pith/MKJJTKRQ2WITUI3OCTTQQVJQGE/bundle.json","state":"https://pith.science/pith/MKJJTKRQ2WITUI3OCTTQQVJQGE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MKJJTKRQ2WITUI3OCTTQQVJQGE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MKJJTKRQ2WITUI3OCTTQQVJQGE","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":"2b1c1b3da0fc1b1e878d73082f707b964701c594061dc6c3f9d19cf5cf32e2d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-12-27T05:15:21Z","title_canon_sha256":"5252b03f47cca53180e6d084c88c98a977c5339dab73da9b65fe1adc0c6cb16e"},"schema_version":"1.0","source":{"id":"1712.09495","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09495","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09495v2","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09495","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"pith_short_12","alias_value":"MKJJTKRQ2WIT","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MKJJTKRQ2WITUI3O","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MKJJTKRQ","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:172496ad4058a968cd44c01769eef622329a303811c7e2977edf8e1440a7d496","target":"graph","created_at":"2026-05-18T00:26:48Z","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 study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. These categories, also called hypergraph categories, are increasingly relevant: Frobenius structures recently appeared in cross-disciplinary applications, including the study of quantum processes, dynamical systems and natural language processing. In this work we give a combinatorial characterisation of arrows of a free hypergraph category as cospans of labelled hypergraphs and establish a precise correspondence between rewriting modulo Frobeniu","authors_text":"Fabio Zanasi (University College London)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-12-27T05:15:21Z","title":"Rewriting in Free Hypergraph Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09495","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":"sha256:2c141ef21b702e1785289bbe0da4e7eeff80dbf1caa6e94ccd1ce55d0a3e7d1a","target":"record","created_at":"2026-05-18T00:26:48Z","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":"2b1c1b3da0fc1b1e878d73082f707b964701c594061dc6c3f9d19cf5cf32e2d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-12-27T05:15:21Z","title_canon_sha256":"5252b03f47cca53180e6d084c88c98a977c5339dab73da9b65fe1adc0c6cb16e"},"schema_version":"1.0","source":{"id":"1712.09495","kind":"arxiv","version":2}},"canonical_sha256":"629299aa30d5913a236e14e708553031047362e655292eaad5ceeb6b6d6141a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"629299aa30d5913a236e14e708553031047362e655292eaad5ceeb6b6d6141a0","first_computed_at":"2026-05-18T00:26:48.889512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:48.889512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PN+cbjt3e1sJRWeF1tg5cfqEFn/qlUAjZvCP8jZygpv44NjV8xBW3Q/R3tpBhjjqS87BJBcliUsqAG2wS1XzAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:48.890149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09495","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c141ef21b702e1785289bbe0da4e7eeff80dbf1caa6e94ccd1ce55d0a3e7d1a","sha256:172496ad4058a968cd44c01769eef622329a303811c7e2977edf8e1440a7d496"],"state_sha256":"9a5537d9bd81d10d7140e3818b08e7a3c7b17d5c04fd247659a50c8aaf90820d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UcCu/FkPw7lG5tUwAW7WHBqmrdvOWBN2nrUvWGBwcDUGGdeJ0cDonDqudZy7iOVPaIQpE1ZVOuZ9jq2txFR0DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:25:44.870707Z","bundle_sha256":"1aa074238fffd2fb46b82dfb03d283045fe29bdcc928e135db953761693971c2"}}