{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:LQA6XIXD4LDOXWVEMQA4IZOY6T","short_pith_number":"pith:LQA6XIXD","canonical_record":{"source":{"id":"2004.02472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-04-06T08:20:52Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"c33296042c0826aa536fdf69988150d3286642e01da3b4274e9de046c14ad6b4","abstract_canon_sha256":"7081b8b36381b8d46053bab134fc1a9bfddc423df89881222ef36109f711f475"},"schema_version":"1.0"},"canonical_sha256":"5c01eba2e3e2c6ebdaa46401c465d8f4f2d314b8b94b00eabc2b7555214bc0d7","source":{"kind":"arxiv","id":"2004.02472","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.02472","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"2004.02472v1","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.02472","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"LQA6XIXD4LDO","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"pith_short_16","alias_value":"LQA6XIXD4LDOXWVE","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"pith_short_8","alias_value":"LQA6XIXD","created_at":"2026-07-05T01:03:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:LQA6XIXD4LDOXWVEMQA4IZOY6T","target":"record","payload":{"canonical_record":{"source":{"id":"2004.02472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-04-06T08:20:52Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"c33296042c0826aa536fdf69988150d3286642e01da3b4274e9de046c14ad6b4","abstract_canon_sha256":"7081b8b36381b8d46053bab134fc1a9bfddc423df89881222ef36109f711f475"},"schema_version":"1.0"},"canonical_sha256":"5c01eba2e3e2c6ebdaa46401c465d8f4f2d314b8b94b00eabc2b7555214bc0d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:03:24.392266Z","signature_b64":"2uuiDT/VNmPdvIrvx88K8nWB7tzwS0eSIIinkZgu2Z6+nXxKOZVmlXGhJfhT/eilEVXsxfIHJNdzdooD+djzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c01eba2e3e2c6ebdaa46401c465d8f4f2d314b8b94b00eabc2b7555214bc0d7","last_reissued_at":"2026-07-05T01:03:24.391872Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:03:24.391872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.02472","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":"2026-07-05T01:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gGovSuIomPSlnFQ9oRXVfXp23hIQplH9kzuiW/Pn+WFjB99UL/buGf41bBRh5mGZh0FaAygsjqDzAbyaRl9UBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:16:15.321252Z"},"content_sha256":"3a6db94d74f2d6e93a255741a147aa2ccbba90f068a4486e36205e1d77f0a0ac","schema_version":"1.0","event_id":"sha256:3a6db94d74f2d6e93a255741a147aa2ccbba90f068a4486e36205e1d77f0a0ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:LQA6XIXD4LDOXWVEMQA4IZOY6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schwinger's Picture of Quantum Mechanics IV: Composition and independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Alberto Ibort, Fabio Di Cosmo, Florio M. Ciaglia, Giuseppe Marmo","submitted_at":"2020-04-06T08:20:52Z","abstract_excerpt":"The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic description as subgroupoids of the Schwinger's groupoid of the system. The groupoids picture offers two natural notions of composition of systems: Direct and free products of groupoids, that will be analyzed in depth as well as their universal character. Finally, the notion of independence of subsystems will be reviewed, finding that the usual notion of independence, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.02472","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.02472/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GHDRpp5PGkyfRyb7lqP7LKYsDxlTQl8879N1Fz147YwP4b1L5Qc8dIJBvEF3evP+MsQirD5UGx+dBVkCl8jcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:16:15.321756Z"},"content_sha256":"cf3cef68670d1fe4f5f9fcd4d05268ba2108b41933c78f5b2e6adea81a4e95f5","schema_version":"1.0","event_id":"sha256:cf3cef68670d1fe4f5f9fcd4d05268ba2108b41933c78f5b2e6adea81a4e95f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQA6XIXD4LDOXWVEMQA4IZOY6T/bundle.json","state_url":"https://pith.science/pith/LQA6XIXD4LDOXWVEMQA4IZOY6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQA6XIXD4LDOXWVEMQA4IZOY6T/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":"2026-08-08T13:16:15Z","links":{"resolver":"https://pith.science/pith/LQA6XIXD4LDOXWVEMQA4IZOY6T","bundle":"https://pith.science/pith/LQA6XIXD4LDOXWVEMQA4IZOY6T/bundle.json","state":"https://pith.science/pith/LQA6XIXD4LDOXWVEMQA4IZOY6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQA6XIXD4LDOXWVEMQA4IZOY6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:LQA6XIXD4LDOXWVEMQA4IZOY6T","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":"7081b8b36381b8d46053bab134fc1a9bfddc423df89881222ef36109f711f475","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-04-06T08:20:52Z","title_canon_sha256":"c33296042c0826aa536fdf69988150d3286642e01da3b4274e9de046c14ad6b4"},"schema_version":"1.0","source":{"id":"2004.02472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.02472","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"2004.02472v1","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.02472","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"LQA6XIXD4LDO","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"pith_short_16","alias_value":"LQA6XIXD4LDOXWVE","created_at":"2026-07-05T01:03:24Z"},{"alias_kind":"pith_short_8","alias_value":"LQA6XIXD","created_at":"2026-07-05T01:03:24Z"}],"graph_snapshots":[{"event_id":"sha256:cf3cef68670d1fe4f5f9fcd4d05268ba2108b41933c78f5b2e6adea81a4e95f5","target":"graph","created_at":"2026-07-05T01:03:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.02472/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic description as subgroupoids of the Schwinger's groupoid of the system. The groupoids picture offers two natural notions of composition of systems: Direct and free products of groupoids, that will be analyzed in depth as well as their universal character. Finally, the notion of independence of subsystems will be reviewed, finding that the usual notion of independence, ","authors_text":"Alberto Ibort, Fabio Di Cosmo, Florio M. Ciaglia, Giuseppe Marmo","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-04-06T08:20:52Z","title":"Schwinger's Picture of Quantum Mechanics IV: Composition and independence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.02472","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":"sha256:3a6db94d74f2d6e93a255741a147aa2ccbba90f068a4486e36205e1d77f0a0ac","target":"record","created_at":"2026-07-05T01:03:24Z","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":"7081b8b36381b8d46053bab134fc1a9bfddc423df89881222ef36109f711f475","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-04-06T08:20:52Z","title_canon_sha256":"c33296042c0826aa536fdf69988150d3286642e01da3b4274e9de046c14ad6b4"},"schema_version":"1.0","source":{"id":"2004.02472","kind":"arxiv","version":1}},"canonical_sha256":"5c01eba2e3e2c6ebdaa46401c465d8f4f2d314b8b94b00eabc2b7555214bc0d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c01eba2e3e2c6ebdaa46401c465d8f4f2d314b8b94b00eabc2b7555214bc0d7","first_computed_at":"2026-07-05T01:03:24.391872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:03:24.391872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2uuiDT/VNmPdvIrvx88K8nWB7tzwS0eSIIinkZgu2Z6+nXxKOZVmlXGhJfhT/eilEVXsxfIHJNdzdooD+djzBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:03:24.392266Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.02472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a6db94d74f2d6e93a255741a147aa2ccbba90f068a4486e36205e1d77f0a0ac","sha256:cf3cef68670d1fe4f5f9fcd4d05268ba2108b41933c78f5b2e6adea81a4e95f5"],"state_sha256":"5ca305e218255711871c6a4ae370c866e43bbce561ec74b8ef8f8ed4154ccdad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yrpAYYgCfhLfkeBhbL2zaC56SQE0WGdxo17faM3xNWh8Z46BrLP+KvHPSwKLz9VMoFtk/wx0yWEz00owWqWdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T13:16:15.326652Z","bundle_sha256":"1ddb97200fc8cadc76c54070a147ca29a8eb476c383cd33f3bccea995d05270f"}}