{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6RESOQZU5CANHOWFAEGNSMHAM5","short_pith_number":"pith:6RESOQZU","schema_version":"1.0","canonical_sha256":"f449274334e880d3bac5010cd930e0677107672ee6cbb4b7283038dd05382b71","source":{"kind":"arxiv","id":"1705.02546","version":1},"attestation_state":"computed","paper":{"title":"Weak formulation for singular diffusion equation with dynamic boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ken Shirakawa, Ryota Nakayashiki","submitted_at":"2017-05-07T02:08:45Z","abstract_excerpt":"In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.02546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-07T02:08:45Z","cross_cats_sorted":[],"title_canon_sha256":"ab2e53491d5e2464a17e8314cccb23685737ca20b42d1418ba0a952aee79e79d","abstract_canon_sha256":"c4af2e7c06c4c6380b53ab6d85e2cfd4f67a64caa7bd9ee5ec52f2021f7f199f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:56.231908Z","signature_b64":"JPBZc2fGmAT2yuDkNrBetzaOTVQXEmwSYjo0C4WEb2NKC0pLVKs+qh808Pvqx5oPR+Hf3/nqGlnKh0RsMC98BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f449274334e880d3bac5010cd930e0677107672ee6cbb4b7283038dd05382b71","last_reissued_at":"2026-05-18T00:44:56.231348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:56.231348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak formulation for singular diffusion equation with dynamic boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ken Shirakawa, Ryota Nakayashiki","submitted_at":"2017-05-07T02:08:45Z","abstract_excerpt":"In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02546","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.02546","created_at":"2026-05-18T00:44:56.231442+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.02546v1","created_at":"2026-05-18T00:44:56.231442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02546","created_at":"2026-05-18T00:44:56.231442+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RESOQZU5CAN","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RESOQZU5CANHOWF","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RESOQZU","created_at":"2026-05-18T12:31:03.183658+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6RESOQZU5CANHOWFAEGNSMHAM5","json":"https://pith.science/pith/6RESOQZU5CANHOWFAEGNSMHAM5.json","graph_json":"https://pith.science/api/pith-number/6RESOQZU5CANHOWFAEGNSMHAM5/graph.json","events_json":"https://pith.science/api/pith-number/6RESOQZU5CANHOWFAEGNSMHAM5/events.json","paper":"https://pith.science/paper/6RESOQZU"},"agent_actions":{"view_html":"https://pith.science/pith/6RESOQZU5CANHOWFAEGNSMHAM5","download_json":"https://pith.science/pith/6RESOQZU5CANHOWFAEGNSMHAM5.json","view_paper":"https://pith.science/paper/6RESOQZU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.02546&json=true","fetch_graph":"https://pith.science/api/pith-number/6RESOQZU5CANHOWFAEGNSMHAM5/graph.json","fetch_events":"https://pith.science/api/pith-number/6RESOQZU5CANHOWFAEGNSMHAM5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RESOQZU5CANHOWFAEGNSMHAM5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RESOQZU5CANHOWFAEGNSMHAM5/action/storage_attestation","attest_author":"https://pith.science/pith/6RESOQZU5CANHOWFAEGNSMHAM5/action/author_attestation","sign_citation":"https://pith.science/pith/6RESOQZU5CANHOWFAEGNSMHAM5/action/citation_signature","submit_replication":"https://pith.science/pith/6RESOQZU5CANHOWFAEGNSMHAM5/action/replication_record"}},"created_at":"2026-05-18T00:44:56.231442+00:00","updated_at":"2026-05-18T00:44:56.231442+00:00"}