{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QKVHMLUJEZILJPA2EKEDBZYJ54","short_pith_number":"pith:QKVHMLUJ","canonical_record":{"source":{"id":"1805.03032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-05-04T08:17:24Z","cross_cats_sorted":["cs.LO","math.RA"],"title_canon_sha256":"f967674316c145f7d475fbaa7dfe775b15d9c2c48e51d28a568ff413701faca8","abstract_canon_sha256":"77e2a8b6518802aae622d95f23d7f12287e55a53995b4f37c2e42875a58059c8"},"schema_version":"1.0"},"canonical_sha256":"82aa762e892650b4bc1a228830e709ef016c11df0616ab54bd6f408b649d85c4","source":{"kind":"arxiv","id":"1805.03032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03032","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03032v1","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03032","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"pith_short_12","alias_value":"QKVHMLUJEZIL","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QKVHMLUJEZILJPA2","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QKVHMLUJ","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QKVHMLUJEZILJPA2EKEDBZYJ54","target":"record","payload":{"canonical_record":{"source":{"id":"1805.03032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-05-04T08:17:24Z","cross_cats_sorted":["cs.LO","math.RA"],"title_canon_sha256":"f967674316c145f7d475fbaa7dfe775b15d9c2c48e51d28a568ff413701faca8","abstract_canon_sha256":"77e2a8b6518802aae622d95f23d7f12287e55a53995b4f37c2e42875a58059c8"},"schema_version":"1.0"},"canonical_sha256":"82aa762e892650b4bc1a228830e709ef016c11df0616ab54bd6f408b649d85c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:34.853978Z","signature_b64":"jcL4ZidFVRx+wbg+ZA2enWS1cAaDJgkXIigebNa/JLEYaKlSaupVwXKJWsuSAifiZrEzqDZJgDJH2dA8ei8LCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82aa762e892650b4bc1a228830e709ef016c11df0616ab54bd6f408b649d85c4","last_reissued_at":"2026-05-18T00:16:34.853360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:34.853360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.03032","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":"2026-05-18T00:16:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7FADMC4zlC4ut+4DCO1wZjG//rXFAcefwY7BsPqHvv5EntlirItI+cEnHL0G6ufxUhgrvVu8EXJbUgTYzt6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:43:43.250971Z"},"content_sha256":"48c6d68ac1bc75266de547bdc4c8a871f524c2379848372514ed32c9d9f11f97","schema_version":"1.0","event_id":"sha256:48c6d68ac1bc75266de547bdc4c8a871f524c2379848372514ed32c9d9f11f97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QKVHMLUJEZILJPA2EKEDBZYJ54","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interacting Hopf Algebras: the theory of linear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.RA"],"primary_cat":"math.CT","authors_text":"Fabio Zanasi","submitted_at":"2018-05-04T08:17:24Z","abstract_excerpt":"As first main contribution, this thesis characterises the PROP SVk of linear subspaces over a field k - an important domain of interpretation for circuit diagrams appearing in diverse research areas. We present by generators and equations the PROP IH of string diagrams whose free model is SVk. IH stands for interacting Hopf algebras: its equations arise by distributive laws between Hopf algebras, which we obtain using Lack's technique for composing PROPs. The significance of the result is two-fold. First, it offers a canonical diagrammatic syntax for linear algebra: linear maps, kernels, subsp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03032","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":"2026-05-18T00:16:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tqT6SHWV8nbD8ktUPeugaIyCFXSnAF0TcrCe6ihZRKAQjFz6U0sH9eMNPgTvtjKHyFXgFuVR368t+EQTYiVVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:43:43.251727Z"},"content_sha256":"11b3fe355a34254249e94f10aca7ae4620218a536111009aec9bc52a80b87975","schema_version":"1.0","event_id":"sha256:11b3fe355a34254249e94f10aca7ae4620218a536111009aec9bc52a80b87975"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QKVHMLUJEZILJPA2EKEDBZYJ54/bundle.json","state_url":"https://pith.science/pith/QKVHMLUJEZILJPA2EKEDBZYJ54/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QKVHMLUJEZILJPA2EKEDBZYJ54/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":"2026-06-10T01:43:43Z","links":{"resolver":"https://pith.science/pith/QKVHMLUJEZILJPA2EKEDBZYJ54","bundle":"https://pith.science/pith/QKVHMLUJEZILJPA2EKEDBZYJ54/bundle.json","state":"https://pith.science/pith/QKVHMLUJEZILJPA2EKEDBZYJ54/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QKVHMLUJEZILJPA2EKEDBZYJ54/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QKVHMLUJEZILJPA2EKEDBZYJ54","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":"77e2a8b6518802aae622d95f23d7f12287e55a53995b4f37c2e42875a58059c8","cross_cats_sorted":["cs.LO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-05-04T08:17:24Z","title_canon_sha256":"f967674316c145f7d475fbaa7dfe775b15d9c2c48e51d28a568ff413701faca8"},"schema_version":"1.0","source":{"id":"1805.03032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03032","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03032v1","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03032","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"pith_short_12","alias_value":"QKVHMLUJEZIL","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QKVHMLUJEZILJPA2","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QKVHMLUJ","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:11b3fe355a34254249e94f10aca7ae4620218a536111009aec9bc52a80b87975","target":"graph","created_at":"2026-05-18T00:16:34Z","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":"As first main contribution, this thesis characterises the PROP SVk of linear subspaces over a field k - an important domain of interpretation for circuit diagrams appearing in diverse research areas. We present by generators and equations the PROP IH of string diagrams whose free model is SVk. IH stands for interacting Hopf algebras: its equations arise by distributive laws between Hopf algebras, which we obtain using Lack's technique for composing PROPs. The significance of the result is two-fold. First, it offers a canonical diagrammatic syntax for linear algebra: linear maps, kernels, subsp","authors_text":"Fabio Zanasi","cross_cats":["cs.LO","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-05-04T08:17:24Z","title":"Interacting Hopf Algebras: the theory of linear systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03032","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":"sha256:48c6d68ac1bc75266de547bdc4c8a871f524c2379848372514ed32c9d9f11f97","target":"record","created_at":"2026-05-18T00:16:34Z","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":"77e2a8b6518802aae622d95f23d7f12287e55a53995b4f37c2e42875a58059c8","cross_cats_sorted":["cs.LO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-05-04T08:17:24Z","title_canon_sha256":"f967674316c145f7d475fbaa7dfe775b15d9c2c48e51d28a568ff413701faca8"},"schema_version":"1.0","source":{"id":"1805.03032","kind":"arxiv","version":1}},"canonical_sha256":"82aa762e892650b4bc1a228830e709ef016c11df0616ab54bd6f408b649d85c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82aa762e892650b4bc1a228830e709ef016c11df0616ab54bd6f408b649d85c4","first_computed_at":"2026-05-18T00:16:34.853360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:34.853360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jcL4ZidFVRx+wbg+ZA2enWS1cAaDJgkXIigebNa/JLEYaKlSaupVwXKJWsuSAifiZrEzqDZJgDJH2dA8ei8LCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:34.853978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.03032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48c6d68ac1bc75266de547bdc4c8a871f524c2379848372514ed32c9d9f11f97","sha256:11b3fe355a34254249e94f10aca7ae4620218a536111009aec9bc52a80b87975"],"state_sha256":"c6f4f1a0b211a75b89e16811949e717e8bcc8a81f0682e02a69c5c04c80e99d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/nZeFOLgq2HNr+VF1q5jTD2GxjFvl9NCqYtQD7GVbBrTkK5dtkAQVF2w2C6uKquPevVk7/MJtdbAIvsodthAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:43:43.256787Z","bundle_sha256":"60537e9810ad456b50020cea8333c8f6588997c20c953830872ee70eb6900655"}}