{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HIHN2X6AMO4NMCGDUQXAATC2QJ","short_pith_number":"pith:HIHN2X6A","canonical_record":{"source":{"id":"1110.0715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-10-04T15:11:29Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"f3eb7ca382bbb2e4f1bfe94519a6ba32951d8ca6902daeb2aefcb6054697d491","abstract_canon_sha256":"a45b52d696700f1e080b48401b1c5509db2b4f1000fb15275a0828d10bf580a2"},"schema_version":"1.0"},"canonical_sha256":"3a0edd5fc063b8d608c3a42e004c5a8249bd05d8678778eb7830ea5160397702","source":{"kind":"arxiv","id":"1110.0715","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0715","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0715v1","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0715","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"HIHN2X6AMO4N","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HIHN2X6AMO4NMCGD","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HIHN2X6A","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HIHN2X6AMO4NMCGDUQXAATC2QJ","target":"record","payload":{"canonical_record":{"source":{"id":"1110.0715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-10-04T15:11:29Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"f3eb7ca382bbb2e4f1bfe94519a6ba32951d8ca6902daeb2aefcb6054697d491","abstract_canon_sha256":"a45b52d696700f1e080b48401b1c5509db2b4f1000fb15275a0828d10bf580a2"},"schema_version":"1.0"},"canonical_sha256":"3a0edd5fc063b8d608c3a42e004c5a8249bd05d8678778eb7830ea5160397702","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:41.163298Z","signature_b64":"/7Vuu+yEAI/fDb0Lj4G0ysSvUo/fj2B7yw4PVdqKPby/tSpdrHyyuv3Fj3AIdnawkFXkj80NxObmqvUPuuDNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a0edd5fc063b8d608c3a42e004c5a8249bd05d8678778eb7830ea5160397702","last_reissued_at":"2026-05-18T04:11:41.162813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:41.162813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.0715","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GcUr80nWDFdusuo15v2qZAsk9rmn9VTUMfixJeYYCS1MdvqS0GAQceJvhTTj24pM7tyq4AQQkWpxR+aJDGZsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T07:52:52.042675Z"},"content_sha256":"ffdfae7f78be3778347a368becee1204b0e1a53149eff31675528505c37faccb","schema_version":"1.0","event_id":"sha256:ffdfae7f78be3778347a368becee1204b0e1a53149eff31675528505c37faccb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HIHN2X6AMO4NMCGDUQXAATC2QJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tangled Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.CT","authors_text":"N. Sabadini, R.F.C. Walters, R. Rosebrugh","submitted_at":"2011-10-04T15:11:29Z","abstract_excerpt":"The theme of the paper is the use of commutative Frobenius algebras in braided strict monoidal categories in the study of varieties of circuits and communicating systems which occur in Computer Science, including circuits in which the wires are tangled. We indicate also some possible novel geometric interest in such algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0715","kind":"arxiv","version":1},"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":"2026-05-18T04:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qpMeMklxs/qtu/w8km55LhHvoIKTrc8Iq05ticRuNcT8BGW5YUmP7/C4SgMgoXm4tEob736DpSQKttqFJd0tDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T07:52:52.043188Z"},"content_sha256":"0f8b304f2062bb3f66add38fe7104789a8113d827e5fba4eccd30b0a8365c63b","schema_version":"1.0","event_id":"sha256:0f8b304f2062bb3f66add38fe7104789a8113d827e5fba4eccd30b0a8365c63b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HIHN2X6AMO4NMCGDUQXAATC2QJ/bundle.json","state_url":"https://pith.science/pith/HIHN2X6AMO4NMCGDUQXAATC2QJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HIHN2X6AMO4NMCGDUQXAATC2QJ/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":"2026-08-17T07:52:52Z","links":{"resolver":"https://pith.science/pith/HIHN2X6AMO4NMCGDUQXAATC2QJ","bundle":"https://pith.science/pith/HIHN2X6AMO4NMCGDUQXAATC2QJ/bundle.json","state":"https://pith.science/pith/HIHN2X6AMO4NMCGDUQXAATC2QJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HIHN2X6AMO4NMCGDUQXAATC2QJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HIHN2X6AMO4NMCGDUQXAATC2QJ","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":"a45b52d696700f1e080b48401b1c5509db2b4f1000fb15275a0828d10bf580a2","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-10-04T15:11:29Z","title_canon_sha256":"f3eb7ca382bbb2e4f1bfe94519a6ba32951d8ca6902daeb2aefcb6054697d491"},"schema_version":"1.0","source":{"id":"1110.0715","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0715","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0715v1","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0715","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"HIHN2X6AMO4N","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HIHN2X6AMO4NMCGD","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HIHN2X6A","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:0f8b304f2062bb3f66add38fe7104789a8113d827e5fba4eccd30b0a8365c63b","target":"graph","created_at":"2026-05-18T04:11:41Z","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"},"paper":{"abstract_excerpt":"The theme of the paper is the use of commutative Frobenius algebras in braided strict monoidal categories in the study of varieties of circuits and communicating systems which occur in Computer Science, including circuits in which the wires are tangled. We indicate also some possible novel geometric interest in such algebras.","authors_text":"N. Sabadini, R.F.C. Walters, R. Rosebrugh","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-10-04T15:11:29Z","title":"Tangled Circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0715","kind":"arxiv","version":1},"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:ffdfae7f78be3778347a368becee1204b0e1a53149eff31675528505c37faccb","target":"record","created_at":"2026-05-18T04:11:41Z","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":"a45b52d696700f1e080b48401b1c5509db2b4f1000fb15275a0828d10bf580a2","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-10-04T15:11:29Z","title_canon_sha256":"f3eb7ca382bbb2e4f1bfe94519a6ba32951d8ca6902daeb2aefcb6054697d491"},"schema_version":"1.0","source":{"id":"1110.0715","kind":"arxiv","version":1}},"canonical_sha256":"3a0edd5fc063b8d608c3a42e004c5a8249bd05d8678778eb7830ea5160397702","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a0edd5fc063b8d608c3a42e004c5a8249bd05d8678778eb7830ea5160397702","first_computed_at":"2026-05-18T04:11:41.162813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:41.162813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/7Vuu+yEAI/fDb0Lj4G0ysSvUo/fj2B7yw4PVdqKPby/tSpdrHyyuv3Fj3AIdnawkFXkj80NxObmqvUPuuDNCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:41.163298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0715","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffdfae7f78be3778347a368becee1204b0e1a53149eff31675528505c37faccb","sha256:0f8b304f2062bb3f66add38fe7104789a8113d827e5fba4eccd30b0a8365c63b"],"state_sha256":"5d468d227f42374b14bbefe248ab6b661a3468ffc0be6f50e3e1d0ccaf10bc85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hQ1FJAAmMDXb5/QLD93LQOA4hwHqKqdjteZF1xNZcung2ROsoLt3QOgQ0jIoThLPD5j9IvU7xxM5QpBHwALnBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T07:52:52.046463Z","bundle_sha256":"5168e72e332af5c8f8c75f04789bee9d9b534ecdbf7514319ac0113963eb55f2"}}