{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:573UHXQOSNDBU62OSMVCHFAHUK","short_pith_number":"pith:573UHXQO","canonical_record":{"source":{"id":"1306.3851","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-17T13:29:20Z","cross_cats_sorted":[],"title_canon_sha256":"f8ca349ff72a4c769abe21e771223ce1996d3b176e33e4c15cc38598e14c4c21","abstract_canon_sha256":"9f9e1a1126151940a3cc60321c68006f807ee76bfaef6db56741d79587f3b0be"},"schema_version":"1.0"},"canonical_sha256":"eff743de0e93461a7b4e932a239407a2b7fabfe99325569b924b82ab7b6f188e","source":{"kind":"arxiv","id":"1306.3851","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3851","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3851v3","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3851","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"573UHXQOSNDB","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"573UHXQOSNDBU62O","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"573UHXQO","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:573UHXQOSNDBU62OSMVCHFAHUK","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3851","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-17T13:29:20Z","cross_cats_sorted":[],"title_canon_sha256":"f8ca349ff72a4c769abe21e771223ce1996d3b176e33e4c15cc38598e14c4c21","abstract_canon_sha256":"9f9e1a1126151940a3cc60321c68006f807ee76bfaef6db56741d79587f3b0be"},"schema_version":"1.0"},"canonical_sha256":"eff743de0e93461a7b4e932a239407a2b7fabfe99325569b924b82ab7b6f188e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:51.976101Z","signature_b64":"rnEom9DllL4j0AWA/bAOZYcbsXZfd6xnNGSezZT+JeG1JNLk8RSpwW8uhRC/fkUlAe5+m6KIQzqBoxepEmbmCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eff743de0e93461a7b4e932a239407a2b7fabfe99325569b924b82ab7b6f188e","last_reissued_at":"2026-05-18T02:56:51.975503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:51.975503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3851","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":"2026-05-18T02:56:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3ecQVgiswOVentyP/k78H8UIc+7lK+XueGxdS7xHYn/wnuVMozequpr5rHxX3FhgzughKk3AHF90Mou+wqYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T11:06:41.435188Z"},"content_sha256":"a4d724c0d75019e4bb9c524dfdc094edeced6c4831ea94255b0baa2d8e21a72d","schema_version":"1.0","event_id":"sha256:a4d724c0d75019e4bb9c524dfdc094edeced6c4831ea94255b0baa2d8e21a72d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:573UHXQOSNDBU62OSMVCHFAHUK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on causality in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marcus Waurick","submitted_at":"2013-06-17T13:29:20Z","abstract_excerpt":"In this note we provide examples that show that a common notion of causality for linear operators on Banach spaces does not carry over to the closure of the respective operators. We provide an alternative definition for causality, which is equivalent to the usual definition for closed linear operators but does carry over to the closure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3851","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":"2026-05-18T02:56:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v8AE9E37a4MxpxKLlS+SrpUBcfWm6RimXx9llIdar+kDKF+D5EfbKJ8czwr2KMwDBKayi1C+zzZHhDkZQIBGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T11:06:41.435564Z"},"content_sha256":"b8216c226e89951603b708d8725e64b170faf5e57bbe27770db5969f71ad997d","schema_version":"1.0","event_id":"sha256:b8216c226e89951603b708d8725e64b170faf5e57bbe27770db5969f71ad997d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/573UHXQOSNDBU62OSMVCHFAHUK/bundle.json","state_url":"https://pith.science/pith/573UHXQOSNDBU62OSMVCHFAHUK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/573UHXQOSNDBU62OSMVCHFAHUK/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":"2026-05-21T11:06:41Z","links":{"resolver":"https://pith.science/pith/573UHXQOSNDBU62OSMVCHFAHUK","bundle":"https://pith.science/pith/573UHXQOSNDBU62OSMVCHFAHUK/bundle.json","state":"https://pith.science/pith/573UHXQOSNDBU62OSMVCHFAHUK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/573UHXQOSNDBU62OSMVCHFAHUK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:573UHXQOSNDBU62OSMVCHFAHUK","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":"9f9e1a1126151940a3cc60321c68006f807ee76bfaef6db56741d79587f3b0be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-17T13:29:20Z","title_canon_sha256":"f8ca349ff72a4c769abe21e771223ce1996d3b176e33e4c15cc38598e14c4c21"},"schema_version":"1.0","source":{"id":"1306.3851","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3851","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3851v3","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3851","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"573UHXQOSNDB","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"573UHXQOSNDBU62O","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"573UHXQO","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:b8216c226e89951603b708d8725e64b170faf5e57bbe27770db5969f71ad997d","target":"graph","created_at":"2026-05-18T02:56:51Z","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":"In this note we provide examples that show that a common notion of causality for linear operators on Banach spaces does not carry over to the closure of the respective operators. We provide an alternative definition for causality, which is equivalent to the usual definition for closed linear operators but does carry over to the closure.","authors_text":"Marcus Waurick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-17T13:29:20Z","title":"A note on causality in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3851","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:a4d724c0d75019e4bb9c524dfdc094edeced6c4831ea94255b0baa2d8e21a72d","target":"record","created_at":"2026-05-18T02:56:51Z","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":"9f9e1a1126151940a3cc60321c68006f807ee76bfaef6db56741d79587f3b0be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-17T13:29:20Z","title_canon_sha256":"f8ca349ff72a4c769abe21e771223ce1996d3b176e33e4c15cc38598e14c4c21"},"schema_version":"1.0","source":{"id":"1306.3851","kind":"arxiv","version":3}},"canonical_sha256":"eff743de0e93461a7b4e932a239407a2b7fabfe99325569b924b82ab7b6f188e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eff743de0e93461a7b4e932a239407a2b7fabfe99325569b924b82ab7b6f188e","first_computed_at":"2026-05-18T02:56:51.975503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:51.975503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rnEom9DllL4j0AWA/bAOZYcbsXZfd6xnNGSezZT+JeG1JNLk8RSpwW8uhRC/fkUlAe5+m6KIQzqBoxepEmbmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:51.976101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3851","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4d724c0d75019e4bb9c524dfdc094edeced6c4831ea94255b0baa2d8e21a72d","sha256:b8216c226e89951603b708d8725e64b170faf5e57bbe27770db5969f71ad997d"],"state_sha256":"e8d45a1c094abe242f57fe30d83c39067cfc667eae70a92844d986e9c8f15a0e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6qxhiUK9b+6abGN24Y/TWPFeXijIB3o81QXmLAEnwSabwpt01UsYDYER76EDEGn98ICUgxU6F93e/yBGZb6ACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T11:06:41.437614Z","bundle_sha256":"a51c0a4d1d22ae9ac91d4d5f5e283387b305c22be57592c41fdce28dcbcd7ce8"}}