{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HORY3FRMRRHHB35JWWSD27WULY","short_pith_number":"pith:HORY3FRM","canonical_record":{"source":{"id":"1308.0157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-01T11:32:11Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"7efd2b1f84719872b1a94af30d6164cb6cde20f4f782700634e9449a3399513b","abstract_canon_sha256":"e96d63caff691a4c290ada6b45b1816d5be7fcec044271534a34b2382d6dbcf5"},"schema_version":"1.0"},"canonical_sha256":"3ba38d962c8c4e70efa9b5a43d7ed45e2d2c380eb9c0929fd318b5092a2b9692","source":{"kind":"arxiv","id":"1308.0157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0157","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0157v1","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0157","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"HORY3FRMRRHH","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HORY3FRMRRHHB35J","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HORY3FRM","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HORY3FRMRRHHB35JWWSD27WULY","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-01T11:32:11Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"7efd2b1f84719872b1a94af30d6164cb6cde20f4f782700634e9449a3399513b","abstract_canon_sha256":"e96d63caff691a4c290ada6b45b1816d5be7fcec044271534a34b2382d6dbcf5"},"schema_version":"1.0"},"canonical_sha256":"3ba38d962c8c4e70efa9b5a43d7ed45e2d2c380eb9c0929fd318b5092a2b9692","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:59.674682Z","signature_b64":"umAPXetCenV617X+2D5Efl3zkXGv90itQtnx+rMaiRcyRIIr49ZVVk1PRu6YjR/afKzu5xzekY4GEW2wUthIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ba38d962c8c4e70efa9b5a43d7ed45e2d2c380eb9c0929fd318b5092a2b9692","last_reissued_at":"2026-05-18T03:16:59.674134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:59.674134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0157","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":"2026-05-18T03:16:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JMOrUfenj9ZuwPRv9oAOX/m5U9+C/QLa3G18MTPLWfziObtxHfI6DO95f1KA+2tvYCubGHygcJmXLqIOZlP3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:57:49.489674Z"},"content_sha256":"ac485d9b330b21229b1de067b9f1ebacb0cc08689e3da45cdafe774346ecc9eb","schema_version":"1.0","event_id":"sha256:ac485d9b330b21229b1de067b9f1ebacb0cc08689e3da45cdafe774346ecc9eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HORY3FRMRRHHB35JWWSD27WULY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuity in time of solutions of a phase-field model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Ibrahim Hoteit, Karl-Heinz Hoffmann, Nikolai D. Botkin, Thomas G. Amler","submitted_at":"2013-08-01T11:32:11Z","abstract_excerpt":"A phase field model proposed by G. Caginalp for the description of phase changes in materials is under consideration. It is assumed that the medium is located in a container with heat conductive walls that are not subjected to phase changes. Therefore, the temperature variable is defined both in the medium and wall regions, whereas the phase variable is only considered in the medium part. The case of Lipschitz domains in two and three dimensions is studied. We show that the temperature and phase variables are continuous in time functions with values in $L^2$ and $H^1$, respectively, provided t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0157","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":"2026-05-18T03:16:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRuMdTkjJsSp2cyjCz0slsVP8J83BMsbQEXuWcrygC7CmTC9aRW0KC82EpGU2PIwG54a7HLybDFz0qh6tPyCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:57:49.490379Z"},"content_sha256":"6f0b4b01a624efa65caa681b2bb738ed3e5c5179fca7ba73225e23bd36f0fdfd","schema_version":"1.0","event_id":"sha256:6f0b4b01a624efa65caa681b2bb738ed3e5c5179fca7ba73225e23bd36f0fdfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HORY3FRMRRHHB35JWWSD27WULY/bundle.json","state_url":"https://pith.science/pith/HORY3FRMRRHHB35JWWSD27WULY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HORY3FRMRRHHB35JWWSD27WULY/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":"2026-06-06T19:57:49Z","links":{"resolver":"https://pith.science/pith/HORY3FRMRRHHB35JWWSD27WULY","bundle":"https://pith.science/pith/HORY3FRMRRHHB35JWWSD27WULY/bundle.json","state":"https://pith.science/pith/HORY3FRMRRHHB35JWWSD27WULY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HORY3FRMRRHHB35JWWSD27WULY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HORY3FRMRRHHB35JWWSD27WULY","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":"e96d63caff691a4c290ada6b45b1816d5be7fcec044271534a34b2382d6dbcf5","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-01T11:32:11Z","title_canon_sha256":"7efd2b1f84719872b1a94af30d6164cb6cde20f4f782700634e9449a3399513b"},"schema_version":"1.0","source":{"id":"1308.0157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0157","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0157v1","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0157","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"HORY3FRMRRHH","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HORY3FRMRRHHB35J","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HORY3FRM","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:6f0b4b01a624efa65caa681b2bb738ed3e5c5179fca7ba73225e23bd36f0fdfd","target":"graph","created_at":"2026-05-18T03:16:59Z","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":"A phase field model proposed by G. Caginalp for the description of phase changes in materials is under consideration. It is assumed that the medium is located in a container with heat conductive walls that are not subjected to phase changes. Therefore, the temperature variable is defined both in the medium and wall regions, whereas the phase variable is only considered in the medium part. The case of Lipschitz domains in two and three dimensions is studied. We show that the temperature and phase variables are continuous in time functions with values in $L^2$ and $H^1$, respectively, provided t","authors_text":"Ibrahim Hoteit, Karl-Heinz Hoffmann, Nikolai D. Botkin, Thomas G. Amler","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-01T11:32:11Z","title":"Continuity in time of solutions of a phase-field model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0157","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:ac485d9b330b21229b1de067b9f1ebacb0cc08689e3da45cdafe774346ecc9eb","target":"record","created_at":"2026-05-18T03:16:59Z","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":"e96d63caff691a4c290ada6b45b1816d5be7fcec044271534a34b2382d6dbcf5","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-01T11:32:11Z","title_canon_sha256":"7efd2b1f84719872b1a94af30d6164cb6cde20f4f782700634e9449a3399513b"},"schema_version":"1.0","source":{"id":"1308.0157","kind":"arxiv","version":1}},"canonical_sha256":"3ba38d962c8c4e70efa9b5a43d7ed45e2d2c380eb9c0929fd318b5092a2b9692","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ba38d962c8c4e70efa9b5a43d7ed45e2d2c380eb9c0929fd318b5092a2b9692","first_computed_at":"2026-05-18T03:16:59.674134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:59.674134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"umAPXetCenV617X+2D5Efl3zkXGv90itQtnx+rMaiRcyRIIr49ZVVk1PRu6YjR/afKzu5xzekY4GEW2wUthIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:59.674682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac485d9b330b21229b1de067b9f1ebacb0cc08689e3da45cdafe774346ecc9eb","sha256:6f0b4b01a624efa65caa681b2bb738ed3e5c5179fca7ba73225e23bd36f0fdfd"],"state_sha256":"27851211600fc72a954c0125f662dcfb38d8c3b015df1c8f8710ea76dd50c7fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vJElBpi638SsFk6hY9r0oYkyHMYJvCRPsyLHHP4aAGivCLa5w6tyt70SSH/NOUmKWJ+aio9DwcZCNGBCipuOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:57:49.493984Z","bundle_sha256":"e785462aeb4d34ca5fa53da2ddd656246008e0aeaf0e5b97bdd6c3736376ff50"}}