{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WCBG2NDMWRDWSEI6DASKOJZR3O","short_pith_number":"pith:WCBG2NDM","canonical_record":{"source":{"id":"1702.04033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-14T00:51:23Z","cross_cats_sorted":[],"title_canon_sha256":"e519e478b5c9dcc46b6ffe2ec6a0ec83f7da07d76df9d8ec2b164839894dc5d1","abstract_canon_sha256":"e208584cadc0d3f3c5ed39cb64cace606ef481c7c753a874a9da6956366d2c80"},"schema_version":"1.0"},"canonical_sha256":"b0826d346cb44769111e1824a72731db9b0e60f75d89e8c25203514b1758429d","source":{"kind":"arxiv","id":"1702.04033","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04033","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04033v1","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04033","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"WCBG2NDMWRDW","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WCBG2NDMWRDWSEI6","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WCBG2NDM","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WCBG2NDMWRDWSEI6DASKOJZR3O","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-14T00:51:23Z","cross_cats_sorted":[],"title_canon_sha256":"e519e478b5c9dcc46b6ffe2ec6a0ec83f7da07d76df9d8ec2b164839894dc5d1","abstract_canon_sha256":"e208584cadc0d3f3c5ed39cb64cace606ef481c7c753a874a9da6956366d2c80"},"schema_version":"1.0"},"canonical_sha256":"b0826d346cb44769111e1824a72731db9b0e60f75d89e8c25203514b1758429d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:37.026659Z","signature_b64":"Iabttv9dUD67UN2qxftwbjl8xV8I7sR2di98XoeXP6YZgRObVaMjv0xQW1w39quPZ2wT4JZBpK+hg+a52kv6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0826d346cb44769111e1824a72731db9b0e60f75d89e8c25203514b1758429d","last_reissued_at":"2026-05-18T00:41:37.026191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:37.026191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04033","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":"2026-05-18T00:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bsiXHXPTG6CaeCTbHW73X38qHZSMT3dINAoWEUXIOlf6sgOW15GMaNApRKISXfFdshmjHst9Yfv3NTi+nfz7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:27:03.943893Z"},"content_sha256":"8eaa8d540c11b9a216be9666d7762bf8b3fa90304605780604d14ce83b746291","schema_version":"1.0","event_id":"sha256:8eaa8d540c11b9a216be9666d7762bf8b3fa90304605780604d14ce83b746291"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WCBG2NDMWRDWSEI6DASKOJZR3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy dissipative solutions to the Kobayashi-Warren-Carter system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroshi Watanabe, Ken Shirakawa, Salvador Moll","submitted_at":"2017-02-14T00:51:23Z","abstract_excerpt":"In this paper we study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of the study is the existence of solutions to this system which dissipate the associated energy functional. We obtain existence of this type of solutions via a suitable approximation of the energy functional with Laplacians and an extra regularization of the weighted total variation term of the energy. As a byproduct of this result, we also prove some $\\Gamma$-convergence results concerning weighted total variations and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04033","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":"2026-05-18T00:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Um0+I/p9PtbxtJJjAODPrjo6Mwh+8FxeQ/Ap31Vad8xdM5hmSwxTxMGTetWeCj2+TicVtYpYABb9WjrxzyLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:27:03.944733Z"},"content_sha256":"db1a4c497382a3ee9b2a89444f50622a09b50f6d80f1d32868a60e4a85fe5d21","schema_version":"1.0","event_id":"sha256:db1a4c497382a3ee9b2a89444f50622a09b50f6d80f1d32868a60e4a85fe5d21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WCBG2NDMWRDWSEI6DASKOJZR3O/bundle.json","state_url":"https://pith.science/pith/WCBG2NDMWRDWSEI6DASKOJZR3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WCBG2NDMWRDWSEI6DASKOJZR3O/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":"2026-05-31T12:27:03Z","links":{"resolver":"https://pith.science/pith/WCBG2NDMWRDWSEI6DASKOJZR3O","bundle":"https://pith.science/pith/WCBG2NDMWRDWSEI6DASKOJZR3O/bundle.json","state":"https://pith.science/pith/WCBG2NDMWRDWSEI6DASKOJZR3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WCBG2NDMWRDWSEI6DASKOJZR3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WCBG2NDMWRDWSEI6DASKOJZR3O","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":"e208584cadc0d3f3c5ed39cb64cace606ef481c7c753a874a9da6956366d2c80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-14T00:51:23Z","title_canon_sha256":"e519e478b5c9dcc46b6ffe2ec6a0ec83f7da07d76df9d8ec2b164839894dc5d1"},"schema_version":"1.0","source":{"id":"1702.04033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04033","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04033v1","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04033","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"WCBG2NDMWRDW","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WCBG2NDMWRDWSEI6","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WCBG2NDM","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:db1a4c497382a3ee9b2a89444f50622a09b50f6d80f1d32868a60e4a85fe5d21","target":"graph","created_at":"2026-05-18T00:41:37Z","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 study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of the study is the existence of solutions to this system which dissipate the associated energy functional. We obtain existence of this type of solutions via a suitable approximation of the energy functional with Laplacians and an extra regularization of the weighted total variation term of the energy. As a byproduct of this result, we also prove some $\\Gamma$-convergence results concerning weighted total variations and","authors_text":"Hiroshi Watanabe, Ken Shirakawa, Salvador Moll","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-14T00:51:23Z","title":"Energy dissipative solutions to the Kobayashi-Warren-Carter system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04033","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":"sha256:8eaa8d540c11b9a216be9666d7762bf8b3fa90304605780604d14ce83b746291","target":"record","created_at":"2026-05-18T00:41:37Z","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":"e208584cadc0d3f3c5ed39cb64cace606ef481c7c753a874a9da6956366d2c80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-14T00:51:23Z","title_canon_sha256":"e519e478b5c9dcc46b6ffe2ec6a0ec83f7da07d76df9d8ec2b164839894dc5d1"},"schema_version":"1.0","source":{"id":"1702.04033","kind":"arxiv","version":1}},"canonical_sha256":"b0826d346cb44769111e1824a72731db9b0e60f75d89e8c25203514b1758429d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0826d346cb44769111e1824a72731db9b0e60f75d89e8c25203514b1758429d","first_computed_at":"2026-05-18T00:41:37.026191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:37.026191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Iabttv9dUD67UN2qxftwbjl8xV8I7sR2di98XoeXP6YZgRObVaMjv0xQW1w39quPZ2wT4JZBpK+hg+a52kv6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:37.026659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8eaa8d540c11b9a216be9666d7762bf8b3fa90304605780604d14ce83b746291","sha256:db1a4c497382a3ee9b2a89444f50622a09b50f6d80f1d32868a60e4a85fe5d21"],"state_sha256":"55838ab0458fff0ad890a05f3308eefbab7b2de90a6be9b937d25d1425c6ecf1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nrZI2LT5NVQRRsjAdV8dey4vMdOZvyqV8tiK5FHsnW34RkcADO3atgrLue1LxpD6kMByy6MD/BNmxi4xUuVTCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:27:03.949698Z","bundle_sha256":"40a07e8cc06210da8daa00d334e09e989847c6f1f53c1225bb759162255889f9"}}