{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OGH272EJJ37M2MIXSKCUSYVDIY","short_pith_number":"pith:OGH272EJ","canonical_record":{"source":{"id":"1510.07643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-26T20:20:09Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c7dab938729128224f0a15715b4a3c17f27ba1f1f50bf487d5ffa0f401e3fe78","abstract_canon_sha256":"5e542ae7a9a770126ba18289ff5eb210333d62f7c58df93e774e7cd73f867b5f"},"schema_version":"1.0"},"canonical_sha256":"718fafe8894efecd311792854962a34637ef471739937f5bd18d59d5b4c050c5","source":{"kind":"arxiv","id":"1510.07643","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07643","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07643v2","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07643","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"OGH272EJJ37M","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OGH272EJJ37M2MIX","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OGH272EJ","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OGH272EJJ37M2MIXSKCUSYVDIY","target":"record","payload":{"canonical_record":{"source":{"id":"1510.07643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-26T20:20:09Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c7dab938729128224f0a15715b4a3c17f27ba1f1f50bf487d5ffa0f401e3fe78","abstract_canon_sha256":"5e542ae7a9a770126ba18289ff5eb210333d62f7c58df93e774e7cd73f867b5f"},"schema_version":"1.0"},"canonical_sha256":"718fafe8894efecd311792854962a34637ef471739937f5bd18d59d5b4c050c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:22.559289Z","signature_b64":"MaXg6ghOm2kidSL8NbiJrFcT+LwJf3oYTPqhW/sq3cL+g/R0Y4tjRHMuUeLxPr7LCyS4viPPqLrULWZn+2qWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"718fafe8894efecd311792854962a34637ef471739937f5bd18d59d5b4c050c5","last_reissued_at":"2026-05-18T01:11:22.558705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:22.558705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.07643","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f2Rb9F9EnGX1DwNqqqbknYbz40uDmkbNFuQZv63MfsCZ7h/BnfDnXitaa3dSHHlyJ953wbljfU4s24B4PCaBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:46:39.068243Z"},"content_sha256":"a06ae0a4a9b69f6dc5481a90188408c6adff3e957f88abc770354adcd68b7b99","schema_version":"1.0","event_id":"sha256:a06ae0a4a9b69f6dc5481a90188408c6adff3e957f88abc770354adcd68b7b99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OGH272EJJ37M2MIXSKCUSYVDIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolution families and maximal regularity for systems of parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Chiara Gallarati, Mark Veraar","submitted_at":"2015-10-26T20:20:09Z","abstract_excerpt":"In this paper we prove maximal $L^p$-regularity for a system of parabolic PDEs, where the elliptic operator $A$ has coefficients which depend on time in a measurable way and are continuous in the space variable. The proof is based on operator-theoretic methods and one of the main ingredients in the proof is the construction of an evolution family on weighted $L^q$-spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07643","kind":"arxiv","version":2},"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":"2026-05-18T01:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6bBkkbkzJwjWlTDwYn/D9gVC9BMDzyrfnuqP44TWB27vRMVXvCGKPMnuDJKXCNUhH9gdwRm31Qom2usZ1Q9ZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:46:39.068617Z"},"content_sha256":"ca62323ed0ca60f403c86bebb16420f9310844eb51e30f40eaeb28bb05249709","schema_version":"1.0","event_id":"sha256:ca62323ed0ca60f403c86bebb16420f9310844eb51e30f40eaeb28bb05249709"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGH272EJJ37M2MIXSKCUSYVDIY/bundle.json","state_url":"https://pith.science/pith/OGH272EJJ37M2MIXSKCUSYVDIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGH272EJJ37M2MIXSKCUSYVDIY/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":"2026-06-25T09:46:39Z","links":{"resolver":"https://pith.science/pith/OGH272EJJ37M2MIXSKCUSYVDIY","bundle":"https://pith.science/pith/OGH272EJJ37M2MIXSKCUSYVDIY/bundle.json","state":"https://pith.science/pith/OGH272EJJ37M2MIXSKCUSYVDIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGH272EJJ37M2MIXSKCUSYVDIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OGH272EJJ37M2MIXSKCUSYVDIY","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":"5e542ae7a9a770126ba18289ff5eb210333d62f7c58df93e774e7cd73f867b5f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-26T20:20:09Z","title_canon_sha256":"c7dab938729128224f0a15715b4a3c17f27ba1f1f50bf487d5ffa0f401e3fe78"},"schema_version":"1.0","source":{"id":"1510.07643","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07643","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07643v2","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07643","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"OGH272EJJ37M","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OGH272EJJ37M2MIX","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OGH272EJ","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:ca62323ed0ca60f403c86bebb16420f9310844eb51e30f40eaeb28bb05249709","target":"graph","created_at":"2026-05-18T01:11:22Z","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 paper we prove maximal $L^p$-regularity for a system of parabolic PDEs, where the elliptic operator $A$ has coefficients which depend on time in a measurable way and are continuous in the space variable. The proof is based on operator-theoretic methods and one of the main ingredients in the proof is the construction of an evolution family on weighted $L^q$-spaces.","authors_text":"Chiara Gallarati, Mark Veraar","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-26T20:20:09Z","title":"Evolution families and maximal regularity for systems of parabolic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07643","kind":"arxiv","version":2},"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:a06ae0a4a9b69f6dc5481a90188408c6adff3e957f88abc770354adcd68b7b99","target":"record","created_at":"2026-05-18T01:11:22Z","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":"5e542ae7a9a770126ba18289ff5eb210333d62f7c58df93e774e7cd73f867b5f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-26T20:20:09Z","title_canon_sha256":"c7dab938729128224f0a15715b4a3c17f27ba1f1f50bf487d5ffa0f401e3fe78"},"schema_version":"1.0","source":{"id":"1510.07643","kind":"arxiv","version":2}},"canonical_sha256":"718fafe8894efecd311792854962a34637ef471739937f5bd18d59d5b4c050c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"718fafe8894efecd311792854962a34637ef471739937f5bd18d59d5b4c050c5","first_computed_at":"2026-05-18T01:11:22.558705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:22.558705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MaXg6ghOm2kidSL8NbiJrFcT+LwJf3oYTPqhW/sq3cL+g/R0Y4tjRHMuUeLxPr7LCyS4viPPqLrULWZn+2qWAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:22.559289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07643","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a06ae0a4a9b69f6dc5481a90188408c6adff3e957f88abc770354adcd68b7b99","sha256:ca62323ed0ca60f403c86bebb16420f9310844eb51e30f40eaeb28bb05249709"],"state_sha256":"3986a08f3f3eed79b027307b4253c9411edb5946431e50d927aed23376569b03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nt1ZtjDtatXBFYcv8IUlZaGcuzNWOOL6tfi3+mFtdOKyIOjk+2kWGYI4H5TPGDgbUACAfCBtiK7sLJJZ62DlCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:46:39.070538Z","bundle_sha256":"0545efa07ef9c144e05bb62081c0990f2dc4ed8bff639fdd26024649ff199851"}}