{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:UPXDYZZQH5JWA3YJ6F5SU6GL6A","short_pith_number":"pith:UPXDYZZQ","canonical_record":{"source":{"id":"0812.3813","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2008-12-19T15:29:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ad3cf45e14ab8b3b833abd583260c60d17900282fedfae992f007d473a6ef69b","abstract_canon_sha256":"a635dfa7913667705cbe4ac724baa1be5e3d6ddcd81854229735e68087d9a171"},"schema_version":"1.0"},"canonical_sha256":"a3ee3c67303f53606f09f17b2a78cbf0392f47b1564aecc2b7e304b307256829","source":{"kind":"arxiv","id":"0812.3813","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3813","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3813v2","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3813","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"UPXDYZZQH5JW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UPXDYZZQH5JWA3YJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UPXDYZZQ","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:UPXDYZZQH5JWA3YJ6F5SU6GL6A","target":"record","payload":{"canonical_record":{"source":{"id":"0812.3813","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2008-12-19T15:29:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ad3cf45e14ab8b3b833abd583260c60d17900282fedfae992f007d473a6ef69b","abstract_canon_sha256":"a635dfa7913667705cbe4ac724baa1be5e3d6ddcd81854229735e68087d9a171"},"schema_version":"1.0"},"canonical_sha256":"a3ee3c67303f53606f09f17b2a78cbf0392f47b1564aecc2b7e304b307256829","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:54.603434Z","signature_b64":"2ppVIcVkoXwW+2Q220dYJsbNtDOz1a+90GMcBQ9FkichHFrHFw8QP/RxYpSurw+6BnSsGNakgs3MhbI+7KeZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3ee3c67303f53606f09f17b2a78cbf0392f47b1564aecc2b7e304b307256829","last_reissued_at":"2026-05-17T23:57:54.602722Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:54.602722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.3813","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":"2026-05-17T23:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R0aj1Hc77t/lZIPpF5CHFyrYHPfqtoSjrzAbDRfyiFSNbku/ZSkyJB7wnMpvVhZyPxBMy51LeonxJ6WlyvvyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:18:39.645691Z"},"content_sha256":"495fc77e131a1e09781ae63738871e5d2a3a4dc0f91d745bd8eb1fab874289ac","schema_version":"1.0","event_id":"sha256:495fc77e131a1e09781ae63738871e5d2a3a4dc0f91d745bd8eb1fab874289ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:UPXDYZZQH5JWA3YJ6F5SU6GL6A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parabolic systems with coupled boundary conditions","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Delio Mugnolo, Stefano Cardanobile","submitted_at":"2008-12-19T15:29:51Z","abstract_excerpt":"We consider elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space $W$. The system is equipped with a general class of coupled boundary conditions of the form $f_{|\\partial\\Omega}\\in \\mathcal Y$ and $\\frac{\\partial f}{\\partial \\nu}\\in {\\mathcal Y}^\\perp$, where $\\mathcal Y$ is a closed subspace of $L^2(\\partial\\Omega;W)$. We discuss well-posedness and further qualitative properties, systematically reducing features of the parabolic system to operator-theoretical properties of the orthogonal p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3813","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":"2026-05-17T23:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H/Uc6BjKBoAN9jilkambvB8+F6k1Y+wwhOXMMTSw5ichCJ19OxwY/q1O4KMeBsJtCuBnb7o9GYfpg3NDOE0LCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:18:39.646038Z"},"content_sha256":"3f7e2777fa60a5ad5073db227165900f13e91c9061544c8f7b231172467d16a9","schema_version":"1.0","event_id":"sha256:3f7e2777fa60a5ad5073db227165900f13e91c9061544c8f7b231172467d16a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPXDYZZQH5JWA3YJ6F5SU6GL6A/bundle.json","state_url":"https://pith.science/pith/UPXDYZZQH5JWA3YJ6F5SU6GL6A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPXDYZZQH5JWA3YJ6F5SU6GL6A/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":"2026-06-11T14:18:39Z","links":{"resolver":"https://pith.science/pith/UPXDYZZQH5JWA3YJ6F5SU6GL6A","bundle":"https://pith.science/pith/UPXDYZZQH5JWA3YJ6F5SU6GL6A/bundle.json","state":"https://pith.science/pith/UPXDYZZQH5JWA3YJ6F5SU6GL6A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPXDYZZQH5JWA3YJ6F5SU6GL6A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:UPXDYZZQH5JWA3YJ6F5SU6GL6A","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":"a635dfa7913667705cbe4ac724baa1be5e3d6ddcd81854229735e68087d9a171","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2008-12-19T15:29:51Z","title_canon_sha256":"ad3cf45e14ab8b3b833abd583260c60d17900282fedfae992f007d473a6ef69b"},"schema_version":"1.0","source":{"id":"0812.3813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3813","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3813v2","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3813","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"UPXDYZZQH5JW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UPXDYZZQH5JWA3YJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UPXDYZZQ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:3f7e2777fa60a5ad5073db227165900f13e91c9061544c8f7b231172467d16a9","target":"graph","created_at":"2026-05-17T23:57:54Z","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 elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space $W$. The system is equipped with a general class of coupled boundary conditions of the form $f_{|\\partial\\Omega}\\in \\mathcal Y$ and $\\frac{\\partial f}{\\partial \\nu}\\in {\\mathcal Y}^\\perp$, where $\\mathcal Y$ is a closed subspace of $L^2(\\partial\\Omega;W)$. We discuss well-posedness and further qualitative properties, systematically reducing features of the parabolic system to operator-theoretical properties of the orthogonal p","authors_text":"Delio Mugnolo, Stefano Cardanobile","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2008-12-19T15:29:51Z","title":"Parabolic systems with coupled boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3813","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":"sha256:495fc77e131a1e09781ae63738871e5d2a3a4dc0f91d745bd8eb1fab874289ac","target":"record","created_at":"2026-05-17T23:57:54Z","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":"a635dfa7913667705cbe4ac724baa1be5e3d6ddcd81854229735e68087d9a171","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2008-12-19T15:29:51Z","title_canon_sha256":"ad3cf45e14ab8b3b833abd583260c60d17900282fedfae992f007d473a6ef69b"},"schema_version":"1.0","source":{"id":"0812.3813","kind":"arxiv","version":2}},"canonical_sha256":"a3ee3c67303f53606f09f17b2a78cbf0392f47b1564aecc2b7e304b307256829","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3ee3c67303f53606f09f17b2a78cbf0392f47b1564aecc2b7e304b307256829","first_computed_at":"2026-05-17T23:57:54.602722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:54.602722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ppVIcVkoXwW+2Q220dYJsbNtDOz1a+90GMcBQ9FkichHFrHFw8QP/RxYpSurw+6BnSsGNakgs3MhbI+7KeZDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:54.603434Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:495fc77e131a1e09781ae63738871e5d2a3a4dc0f91d745bd8eb1fab874289ac","sha256:3f7e2777fa60a5ad5073db227165900f13e91c9061544c8f7b231172467d16a9"],"state_sha256":"979784e810bda838acc3afd4352cd859a83f2c29519e793ac0e0c5f6c221ef84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eaNsdogCUdzYCwr3raASKHJENQSCDb4oGeSJxU6wvgLt4rpqNe183aiPXKA/dcKQNNF3EToaBnTjdOxHmpanDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:18:39.648332Z","bundle_sha256":"c63fa1dbeff9ee62c98a02c7d59590099b95dd4ea60a2ce584a180ad87018983"}}