{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7OASPE6RC5GPWSBH4ET7IBE2SF","short_pith_number":"pith:7OASPE6R","canonical_record":{"source":{"id":"1203.4700","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-21T10:21:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fc6c394ff6f4248e06f1494ec2d5be98333486e79933358f56b153bd4958cd53","abstract_canon_sha256":"3888e591fdefe139f9aa9ca3ce6b0a9778724595c9b05bba9ff26371c11cc71d"},"schema_version":"1.0"},"canonical_sha256":"fb812793d1174cfb4827e127f4049a91415baf35f8fc9cb5380f2dccfa327c03","source":{"kind":"arxiv","id":"1203.4700","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4700","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4700v3","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4700","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"7OASPE6RC5GP","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7OASPE6RC5GPWSBH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7OASPE6R","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7OASPE6RC5GPWSBH4ET7IBE2SF","target":"record","payload":{"canonical_record":{"source":{"id":"1203.4700","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-21T10:21:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fc6c394ff6f4248e06f1494ec2d5be98333486e79933358f56b153bd4958cd53","abstract_canon_sha256":"3888e591fdefe139f9aa9ca3ce6b0a9778724595c9b05bba9ff26371c11cc71d"},"schema_version":"1.0"},"canonical_sha256":"fb812793d1174cfb4827e127f4049a91415baf35f8fc9cb5380f2dccfa327c03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:18.701367Z","signature_b64":"xrxAvBIWFbTfEH6aIytiMfz4UaMp8KzLtFicLJ3HqPLmaPULi2xzZDQcy9aJXtHQQ/H8kKgqZ+UM4DYq3BJeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb812793d1174cfb4827e127f4049a91415baf35f8fc9cb5380f2dccfa327c03","last_reissued_at":"2026-05-18T02:49:18.700787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:18.700787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.4700","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":"2026-05-18T02:49:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fp6//SUM2j0OD40jxhZUor+VjRH7ErtmIBYw4xd4mQjUhIKlGtIknuuxrssJ9UVvdjZAb9Q0LebOP0U02PfgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:48:15.064879Z"},"content_sha256":"cfc25b44457d0d1aced988fcde447e5a0c6fa0f3added28a59a62907500a916b","schema_version":"1.0","event_id":"sha256:cfc25b44457d0d1aced988fcde447e5a0c6fa0f3added28a59a62907500a916b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7OASPE6RC5GPWSBH4ET7IBE2SF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kato's theorem on the integration of non-autonomous linear evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Jochen Schmid, Marcel Griesemer","submitted_at":"2012-03-21T10:21:27Z","abstract_excerpt":"This paper is devoted to a comparison of early works of Kato and Yosida on the integration of non-autonomous linear evolution equations $\\dot{x} = A(t)x$ in Banach space, where the domain $D$ of $A(t)$ is independent of $t$. Our focus is on the regularity assumed of $t\\mapsto A(t)$ and our main objective is to clarify the meaning of the rather involved set of assumptions given in Yosida's classic and highly influential \\emph{Functional Analysis}. We prove Yosida's assumptions to be equivalent to Kato's condition that $t\\mapsto A(t)x$ is continuously differentiable for each $x\\in D$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4700","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":"2026-05-18T02:49:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ZwLHvGxBJNxRmyQs7vKCBQ8JXIr6nb/xCa1beKm1AAorwKkJPBFRuXKjwOdNCsANzhJGu5IQis2YQvJp1g5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:48:15.065228Z"},"content_sha256":"55d031dd7260b62fc99ee000bcc674ab5c09d8ebae76d6002db455b17eaa9824","schema_version":"1.0","event_id":"sha256:55d031dd7260b62fc99ee000bcc674ab5c09d8ebae76d6002db455b17eaa9824"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7OASPE6RC5GPWSBH4ET7IBE2SF/bundle.json","state_url":"https://pith.science/pith/7OASPE6RC5GPWSBH4ET7IBE2SF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7OASPE6RC5GPWSBH4ET7IBE2SF/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":"2026-05-28T13:48:15Z","links":{"resolver":"https://pith.science/pith/7OASPE6RC5GPWSBH4ET7IBE2SF","bundle":"https://pith.science/pith/7OASPE6RC5GPWSBH4ET7IBE2SF/bundle.json","state":"https://pith.science/pith/7OASPE6RC5GPWSBH4ET7IBE2SF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7OASPE6RC5GPWSBH4ET7IBE2SF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7OASPE6RC5GPWSBH4ET7IBE2SF","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":"3888e591fdefe139f9aa9ca3ce6b0a9778724595c9b05bba9ff26371c11cc71d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-21T10:21:27Z","title_canon_sha256":"fc6c394ff6f4248e06f1494ec2d5be98333486e79933358f56b153bd4958cd53"},"schema_version":"1.0","source":{"id":"1203.4700","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4700","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4700v3","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4700","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"7OASPE6RC5GP","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7OASPE6RC5GPWSBH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7OASPE6R","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:55d031dd7260b62fc99ee000bcc674ab5c09d8ebae76d6002db455b17eaa9824","target":"graph","created_at":"2026-05-18T02:49:18Z","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":"This paper is devoted to a comparison of early works of Kato and Yosida on the integration of non-autonomous linear evolution equations $\\dot{x} = A(t)x$ in Banach space, where the domain $D$ of $A(t)$ is independent of $t$. Our focus is on the regularity assumed of $t\\mapsto A(t)$ and our main objective is to clarify the meaning of the rather involved set of assumptions given in Yosida's classic and highly influential \\emph{Functional Analysis}. We prove Yosida's assumptions to be equivalent to Kato's condition that $t\\mapsto A(t)x$ is continuously differentiable for each $x\\in D$.","authors_text":"Jochen Schmid, Marcel Griesemer","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-21T10:21:27Z","title":"Kato's theorem on the integration of non-autonomous linear evolution equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4700","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:cfc25b44457d0d1aced988fcde447e5a0c6fa0f3added28a59a62907500a916b","target":"record","created_at":"2026-05-18T02:49:18Z","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":"3888e591fdefe139f9aa9ca3ce6b0a9778724595c9b05bba9ff26371c11cc71d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-21T10:21:27Z","title_canon_sha256":"fc6c394ff6f4248e06f1494ec2d5be98333486e79933358f56b153bd4958cd53"},"schema_version":"1.0","source":{"id":"1203.4700","kind":"arxiv","version":3}},"canonical_sha256":"fb812793d1174cfb4827e127f4049a91415baf35f8fc9cb5380f2dccfa327c03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb812793d1174cfb4827e127f4049a91415baf35f8fc9cb5380f2dccfa327c03","first_computed_at":"2026-05-18T02:49:18.700787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:18.700787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xrxAvBIWFbTfEH6aIytiMfz4UaMp8KzLtFicLJ3HqPLmaPULi2xzZDQcy9aJXtHQQ/H8kKgqZ+UM4DYq3BJeBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:18.701367Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4700","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfc25b44457d0d1aced988fcde447e5a0c6fa0f3added28a59a62907500a916b","sha256:55d031dd7260b62fc99ee000bcc674ab5c09d8ebae76d6002db455b17eaa9824"],"state_sha256":"b81d48470a6e7eb89251d4668c1a42bf20f96ce1ca634f47c0b22f61c6f9eea6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Bbl5AiwVnAyh7p7RPh0JYDA+mmQDTyH3YEiGt/q1XG21YDfxludLUUOHgufsUiNAnp+XMC78/qCulbuqV8dBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:48:15.067309Z","bundle_sha256":"c141efddee6636a23fc9bb4250daf8003601923d61fba3abea92011c2b11dfd8"}}