{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JZRWI2ED5FVS5NOZGPRBHS7YN3","short_pith_number":"pith:JZRWI2ED","schema_version":"1.0","canonical_sha256":"4e63646883e96b2eb5d933e213cbf86eec2bbaa24862803a7aac8a12faa319ca","source":{"kind":"arxiv","id":"1501.01072","version":1},"attestation_state":"computed","paper":{"title":"Unidirectional evolution equations of diffusion type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Goro Akagi, Masato Kimura","submitted_at":"2015-01-06T04:14:48Z","abstract_excerpt":"This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in Damage\n  Mechanics due to the strong irreversibility of crack propagation or damage evolution. The existence of solutions is proved in an L^2-framework by introducing a peculiar discretization of the unidirectional diffusion equation by means of variational inequities of obstacle type and by developing a regularity theory for such variational inequalities. The"},"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":"1501.01072","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-06T04:14:48Z","cross_cats_sorted":[],"title_canon_sha256":"4fa1f95695a24de3c0c5852df36896b59212903dad09b7857d86362fb364859e","abstract_canon_sha256":"e2af499f0cdc1514a2fb0b878d3057459dad48c47216bf56f1ca3d521b08e236"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:00.347447Z","signature_b64":"6/SJZp881i83LYkRazbz7kwvfjcRl8/FslRvTOh/Yw2rHvCBEEvjkowDGnYCv3eSWTV+SH1B7ZRrGcp6VZ4eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e63646883e96b2eb5d933e213cbf86eec2bbaa24862803a7aac8a12faa319ca","last_reissued_at":"2026-05-18T02:30:00.347042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:00.347042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unidirectional evolution equations of diffusion type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Goro Akagi, Masato Kimura","submitted_at":"2015-01-06T04:14:48Z","abstract_excerpt":"This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in Damage\n  Mechanics due to the strong irreversibility of crack propagation or damage evolution. The existence of solutions is proved in an L^2-framework by introducing a peculiar discretization of the unidirectional diffusion equation by means of variational inequities of obstacle type and by developing a regularity theory for such variational inequalities. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01072","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":"1501.01072","created_at":"2026-05-18T02:30:00.347105+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.01072v1","created_at":"2026-05-18T02:30:00.347105+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01072","created_at":"2026-05-18T02:30:00.347105+00:00"},{"alias_kind":"pith_short_12","alias_value":"JZRWI2ED5FVS","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JZRWI2ED5FVS5NOZ","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JZRWI2ED","created_at":"2026-05-18T12:29:27.538025+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/JZRWI2ED5FVS5NOZGPRBHS7YN3","json":"https://pith.science/pith/JZRWI2ED5FVS5NOZGPRBHS7YN3.json","graph_json":"https://pith.science/api/pith-number/JZRWI2ED5FVS5NOZGPRBHS7YN3/graph.json","events_json":"https://pith.science/api/pith-number/JZRWI2ED5FVS5NOZGPRBHS7YN3/events.json","paper":"https://pith.science/paper/JZRWI2ED"},"agent_actions":{"view_html":"https://pith.science/pith/JZRWI2ED5FVS5NOZGPRBHS7YN3","download_json":"https://pith.science/pith/JZRWI2ED5FVS5NOZGPRBHS7YN3.json","view_paper":"https://pith.science/paper/JZRWI2ED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.01072&json=true","fetch_graph":"https://pith.science/api/pith-number/JZRWI2ED5FVS5NOZGPRBHS7YN3/graph.json","fetch_events":"https://pith.science/api/pith-number/JZRWI2ED5FVS5NOZGPRBHS7YN3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JZRWI2ED5FVS5NOZGPRBHS7YN3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JZRWI2ED5FVS5NOZGPRBHS7YN3/action/storage_attestation","attest_author":"https://pith.science/pith/JZRWI2ED5FVS5NOZGPRBHS7YN3/action/author_attestation","sign_citation":"https://pith.science/pith/JZRWI2ED5FVS5NOZGPRBHS7YN3/action/citation_signature","submit_replication":"https://pith.science/pith/JZRWI2ED5FVS5NOZGPRBHS7YN3/action/replication_record"}},"created_at":"2026-05-18T02:30:00.347105+00:00","updated_at":"2026-05-18T02:30:00.347105+00:00"}