{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3FG5USJ2GJGKTKRN4RC7LSAF5Y","short_pith_number":"pith:3FG5USJ2","canonical_record":{"source":{"id":"1310.0965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T12:59:27Z","cross_cats_sorted":[],"title_canon_sha256":"be457791671c182f43748db3caef7d95df967e02af79883a543794242ee4c7d4","abstract_canon_sha256":"9490df1a11f9d702b0bbcea95b8c78d63b5b0eda041a428f0af5040888a4a1a1"},"schema_version":"1.0"},"canonical_sha256":"d94dda493a324ca9aa2de445f5c805ee0e518e7ae16e49d6a21cfea2ddb95d1b","source":{"kind":"arxiv","id":"1310.0965","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0965","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0965v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0965","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"3FG5USJ2GJGK","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3FG5USJ2GJGKTKRN","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3FG5USJ2","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3FG5USJ2GJGKTKRN4RC7LSAF5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T12:59:27Z","cross_cats_sorted":[],"title_canon_sha256":"be457791671c182f43748db3caef7d95df967e02af79883a543794242ee4c7d4","abstract_canon_sha256":"9490df1a11f9d702b0bbcea95b8c78d63b5b0eda041a428f0af5040888a4a1a1"},"schema_version":"1.0"},"canonical_sha256":"d94dda493a324ca9aa2de445f5c805ee0e518e7ae16e49d6a21cfea2ddb95d1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:24.903174Z","signature_b64":"6FUTSkEXTWP0spowDTNx4eJnSPAxcQYlrhU7IjgUq/QgP4Jk6o52ooqdkkGWGA125WjtvDbf0qAjceGr3OnwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d94dda493a324ca9aa2de445f5c805ee0e518e7ae16e49d6a21cfea2ddb95d1b","last_reissued_at":"2026-05-18T03:11:24.902353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:24.902353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0965","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oPO73rDU7hb8cWk+0sGIk+63Yh3PzlAx7OeahSk4A/dYkDSbpC7p9NRzAqsi5XYlUufuly2aRlHsbkTfvW8hCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:26:26.669862Z"},"content_sha256":"8e2a317a3aeb75d04207747a862a75f42e3409cd7cbd2681d279f90d7b01a70e","schema_version":"1.0","event_id":"sha256:8e2a317a3aeb75d04207747a862a75f42e3409cd7cbd2681d279f90d7b01a70e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3FG5USJ2GJGKTKRN4RC7LSAF5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-isothermal viscous Cahn--Hilliard equation with inertial term and dynamic boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cecilia Cavaterra, Hao Wu, Maurizio Grasselli","submitted_at":"2013-10-03T12:59:27Z","abstract_excerpt":"We consider a non-isothermal modified Cahn--Hilliard equation which was previously analyzed by M. Grasselli et al. Such an equation is characterized by an inertial term and a viscous term and it is coupled with a hyperbolic heat equation. The resulting system was studied in the case of no-flux boundary conditions. Here we analyze the case in which the order parameter is subject to a dynamic boundary condition. This assumption requires a more refined strategy to extend the previous results to the present case. More precisely, we first prove the well-posedness for solutions with bounded energy a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0965","kind":"arxiv","version":1},"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":"2026-05-18T03:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2VB+oPeaLzpcIym47xEH5mgH5YmifHIKmbW0T5qlaoLdhFXRrup++/KxyEJl2WznWoWLmawwv+1k1xmy1w1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:26:26.670478Z"},"content_sha256":"8cd20a14c25a8fb871a77802a3e8dc8805654e180e9ea194b71693e204fd8f95","schema_version":"1.0","event_id":"sha256:8cd20a14c25a8fb871a77802a3e8dc8805654e180e9ea194b71693e204fd8f95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3FG5USJ2GJGKTKRN4RC7LSAF5Y/bundle.json","state_url":"https://pith.science/pith/3FG5USJ2GJGKTKRN4RC7LSAF5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3FG5USJ2GJGKTKRN4RC7LSAF5Y/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":"2026-05-26T01:26:26Z","links":{"resolver":"https://pith.science/pith/3FG5USJ2GJGKTKRN4RC7LSAF5Y","bundle":"https://pith.science/pith/3FG5USJ2GJGKTKRN4RC7LSAF5Y/bundle.json","state":"https://pith.science/pith/3FG5USJ2GJGKTKRN4RC7LSAF5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3FG5USJ2GJGKTKRN4RC7LSAF5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3FG5USJ2GJGKTKRN4RC7LSAF5Y","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":"9490df1a11f9d702b0bbcea95b8c78d63b5b0eda041a428f0af5040888a4a1a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T12:59:27Z","title_canon_sha256":"be457791671c182f43748db3caef7d95df967e02af79883a543794242ee4c7d4"},"schema_version":"1.0","source":{"id":"1310.0965","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0965","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0965v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0965","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"3FG5USJ2GJGK","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3FG5USJ2GJGKTKRN","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3FG5USJ2","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:8cd20a14c25a8fb871a77802a3e8dc8805654e180e9ea194b71693e204fd8f95","target":"graph","created_at":"2026-05-18T03:11:24Z","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-isothermal modified Cahn--Hilliard equation which was previously analyzed by M. Grasselli et al. Such an equation is characterized by an inertial term and a viscous term and it is coupled with a hyperbolic heat equation. The resulting system was studied in the case of no-flux boundary conditions. Here we analyze the case in which the order parameter is subject to a dynamic boundary condition. This assumption requires a more refined strategy to extend the previous results to the present case. More precisely, we first prove the well-posedness for solutions with bounded energy a","authors_text":"Cecilia Cavaterra, Hao Wu, Maurizio Grasselli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T12:59:27Z","title":"Non-isothermal viscous Cahn--Hilliard equation with inertial term and dynamic boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0965","kind":"arxiv","version":1},"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":"sha256:8e2a317a3aeb75d04207747a862a75f42e3409cd7cbd2681d279f90d7b01a70e","target":"record","created_at":"2026-05-18T03:11:24Z","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":"9490df1a11f9d702b0bbcea95b8c78d63b5b0eda041a428f0af5040888a4a1a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T12:59:27Z","title_canon_sha256":"be457791671c182f43748db3caef7d95df967e02af79883a543794242ee4c7d4"},"schema_version":"1.0","source":{"id":"1310.0965","kind":"arxiv","version":1}},"canonical_sha256":"d94dda493a324ca9aa2de445f5c805ee0e518e7ae16e49d6a21cfea2ddb95d1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d94dda493a324ca9aa2de445f5c805ee0e518e7ae16e49d6a21cfea2ddb95d1b","first_computed_at":"2026-05-18T03:11:24.902353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:24.902353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6FUTSkEXTWP0spowDTNx4eJnSPAxcQYlrhU7IjgUq/QgP4Jk6o52ooqdkkGWGA125WjtvDbf0qAjceGr3OnwCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:24.903174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0965","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e2a317a3aeb75d04207747a862a75f42e3409cd7cbd2681d279f90d7b01a70e","sha256:8cd20a14c25a8fb871a77802a3e8dc8805654e180e9ea194b71693e204fd8f95"],"state_sha256":"2585e14b38204c08eca9e26e78504bc7cb66a374432d1a32d17019a7f61cc747"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oW0mWTHeHoczTlYIGu59ksyOghJNoWaGfR3Yp3jImRhi2FeyLbOFjOoGuKYYxmUVUFqr47UuDoxD4e7qxTkUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:26:26.673566Z","bundle_sha256":"3fd68d25cb2414008a8f45a8cd9a87eb6dd33c5601dbebd5cf597645b1f65372"}}