{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7L4HYGTIFLCFLH3AQ7DCXCUYQP","short_pith_number":"pith:7L4HYGTI","canonical_record":{"source":{"id":"1406.2884","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-11T12:30:55Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"81c06c14312bd35d6c5defbc0791037577d2bb4757a9ed2cff21c268a0180848","abstract_canon_sha256":"ab570439a81892ff4f03b0cca6a4ed903955be0b9d43bfe7cb05a73c5a96852f"},"schema_version":"1.0"},"canonical_sha256":"faf87c1a682ac4559f6087c62b8a9883ecf7dc465a0ef8e2af7a04c4aae51d29","source":{"kind":"arxiv","id":"1406.2884","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2884","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2884v2","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2884","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"7L4HYGTIFLCF","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7L4HYGTIFLCFLH3A","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7L4HYGTI","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7L4HYGTIFLCFLH3AQ7DCXCUYQP","target":"record","payload":{"canonical_record":{"source":{"id":"1406.2884","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-11T12:30:55Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"81c06c14312bd35d6c5defbc0791037577d2bb4757a9ed2cff21c268a0180848","abstract_canon_sha256":"ab570439a81892ff4f03b0cca6a4ed903955be0b9d43bfe7cb05a73c5a96852f"},"schema_version":"1.0"},"canonical_sha256":"faf87c1a682ac4559f6087c62b8a9883ecf7dc465a0ef8e2af7a04c4aae51d29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:53.310006Z","signature_b64":"fhVCchRyX5zBr3qZpeO4pC9yYAAPmI9VvFwLCw6365ssonZ46xP3rcyyHQXYi/kUg4PzO7wzcYsFtxyqrUj/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faf87c1a682ac4559f6087c62b8a9883ecf7dc465a0ef8e2af7a04c4aae51d29","last_reissued_at":"2026-05-18T02:49:53.309584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:53.309584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.2884","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":"2026-05-18T02:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cR3AkdvHTUjPbfHrBqfdhM877EkX42506pAqVRK7mwPx1julLcYTMeN9qofm0bQ+iAF/R7JIRtpRZanz2/HCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:29:20.193504Z"},"content_sha256":"3517f37ff3104bf45eece2019a4b5387335fb62f86b4df72cfba6bc5e89e43cf","schema_version":"1.0","event_id":"sha256:3517f37ff3104bf45eece2019a4b5387335fb62f86b4df72cfba6bc5e89e43cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7L4HYGTIFLCFLH3AQ7DCXCUYQP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Autonomous Maximal Regularity for Forms of Bounded Variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Dominik Dier","submitted_at":"2014-06-11T12:30:55Z","abstract_excerpt":"We consider a non-autonomous evolutionary problem \\[ u' (t)+\\mathcal A (t)u(t)=f(t), \\quad u(0)=u_0, \\] where $V, H$ are Hilbert spaces such that $V$ is continuously and densely embedded in $H$ and the operator $\\mathcal A (t)\\colon V\\to V^\\prime$ is associated with a coercive, bounded, symmetric form $\\mathfrak{a}(t,.,.)\\colon V\\times V \\to \\mathbb{C}$ for all $t \\in [0,T]$. Given $f \\in L^2(0,T;H)$, $u_0\\in V$ there exists always a unique solution $u \\in MR(V,V'):= L^2(0,T;V) \\cap H^1(0,T;V')$. The purpose of this article is to investigate when $u \\in H^1(0,T;H)$. This property of maximal re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2884","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":"2026-05-18T02:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bMDTsqS8s42M6Q3aF6l4MJ3ZvggZfehLdZ8TiB9pXcpH3f8fWVkUbelH4KaKVjaTgEUnsgc2MhVNnk9qgcmUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:29:20.193856Z"},"content_sha256":"cb530637f10d55b45fd4b95b5546ed0957cbde4aa004c0e243ba9291a2e37c2c","schema_version":"1.0","event_id":"sha256:cb530637f10d55b45fd4b95b5546ed0957cbde4aa004c0e243ba9291a2e37c2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7L4HYGTIFLCFLH3AQ7DCXCUYQP/bundle.json","state_url":"https://pith.science/pith/7L4HYGTIFLCFLH3AQ7DCXCUYQP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7L4HYGTIFLCFLH3AQ7DCXCUYQP/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":"2026-06-24T07:29:20Z","links":{"resolver":"https://pith.science/pith/7L4HYGTIFLCFLH3AQ7DCXCUYQP","bundle":"https://pith.science/pith/7L4HYGTIFLCFLH3AQ7DCXCUYQP/bundle.json","state":"https://pith.science/pith/7L4HYGTIFLCFLH3AQ7DCXCUYQP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7L4HYGTIFLCFLH3AQ7DCXCUYQP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7L4HYGTIFLCFLH3AQ7DCXCUYQP","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":"ab570439a81892ff4f03b0cca6a4ed903955be0b9d43bfe7cb05a73c5a96852f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-11T12:30:55Z","title_canon_sha256":"81c06c14312bd35d6c5defbc0791037577d2bb4757a9ed2cff21c268a0180848"},"schema_version":"1.0","source":{"id":"1406.2884","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2884","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2884v2","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2884","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"7L4HYGTIFLCF","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7L4HYGTIFLCFLH3A","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7L4HYGTI","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:cb530637f10d55b45fd4b95b5546ed0957cbde4aa004c0e243ba9291a2e37c2c","target":"graph","created_at":"2026-05-18T02:49:53Z","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":"We consider a non-autonomous evolutionary problem \\[ u' (t)+\\mathcal A (t)u(t)=f(t), \\quad u(0)=u_0, \\] where $V, H$ are Hilbert spaces such that $V$ is continuously and densely embedded in $H$ and the operator $\\mathcal A (t)\\colon V\\to V^\\prime$ is associated with a coercive, bounded, symmetric form $\\mathfrak{a}(t,.,.)\\colon V\\times V \\to \\mathbb{C}$ for all $t \\in [0,T]$. Given $f \\in L^2(0,T;H)$, $u_0\\in V$ there exists always a unique solution $u \\in MR(V,V'):= L^2(0,T;V) \\cap H^1(0,T;V')$. The purpose of this article is to investigate when $u \\in H^1(0,T;H)$. This property of maximal re","authors_text":"Dominik Dier","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-11T12:30:55Z","title":"Non-Autonomous Maximal Regularity for Forms of Bounded Variation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2884","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":"sha256:3517f37ff3104bf45eece2019a4b5387335fb62f86b4df72cfba6bc5e89e43cf","target":"record","created_at":"2026-05-18T02:49:53Z","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":"ab570439a81892ff4f03b0cca6a4ed903955be0b9d43bfe7cb05a73c5a96852f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-11T12:30:55Z","title_canon_sha256":"81c06c14312bd35d6c5defbc0791037577d2bb4757a9ed2cff21c268a0180848"},"schema_version":"1.0","source":{"id":"1406.2884","kind":"arxiv","version":2}},"canonical_sha256":"faf87c1a682ac4559f6087c62b8a9883ecf7dc465a0ef8e2af7a04c4aae51d29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faf87c1a682ac4559f6087c62b8a9883ecf7dc465a0ef8e2af7a04c4aae51d29","first_computed_at":"2026-05-18T02:49:53.309584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:53.309584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fhVCchRyX5zBr3qZpeO4pC9yYAAPmI9VvFwLCw6365ssonZ46xP3rcyyHQXYi/kUg4PzO7wzcYsFtxyqrUj/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:53.310006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2884","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3517f37ff3104bf45eece2019a4b5387335fb62f86b4df72cfba6bc5e89e43cf","sha256:cb530637f10d55b45fd4b95b5546ed0957cbde4aa004c0e243ba9291a2e37c2c"],"state_sha256":"ff871eac60f441452db2e4112b47a87933522a838e4baee391822171976a606f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nFwQkG365FxL5R67j7x6Q9iCtxO2ePrIikyIYrGtHgYVB/EZaAMBuJ50kjETCtw5pI4BQzcyOSxZziJmd6+0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:29:20.195940Z","bundle_sha256":"acdb28f80e0a5a6505c7613a7a7f5a8b9b8ea1d1ff600faad2f53bac75cff594"}}