{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:T3E3YW5AHJUYKUIQH2PK3IU27W","short_pith_number":"pith:T3E3YW5A","schema_version":"1.0","canonical_sha256":"9ec9bc5ba03a698551103e9eada29afdb557856f79e495b1c442a172723d91b4","source":{"kind":"arxiv","id":"1111.3703","version":1},"attestation_state":"computed","paper":{"title":"Existence of Rosseland equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"JunZhi Cui, QiaoFu Zhang","submitted_at":"2011-11-16T01:38:19Z","abstract_excerpt":"The global boundness, existence and uniqueness are presented for the kind of Rosseland equation with a small parameter. This problem comes from conduction-radiation coupled heat transfer in the composites; it's with coefficients of high order growth and mixed boundary conditions.\n  A linearized map is constructed by fixing the function variables in the coefficients and the right-hand side. The solution to the linearized problem is uniformly bounded based on De Giorgi iteration; it is bounded in the H\\\"older space from a Sobolev-Campanato estimate.\n  This linearized map is compact and continuou"},"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":"1111.3703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-16T01:38:19Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"34d5b8463b21bb49aa1bb17fbbc92a00ed32ef37eaf959ad9ea84b62baf70d73","abstract_canon_sha256":"12ebdc597a6ff7af3bd83862d9f4895635829c5bfde16f88b66d13c0ac8c660d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:13.250352Z","signature_b64":"4Kz8J6NPM7tCrfjui77GtJNX1hDLM96HwwkC/TSN+rHkBcPpaYbYEgS2wZ2lt2IL6LhLptLsIF37K7zkfuu2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ec9bc5ba03a698551103e9eada29afdb557856f79e495b1c442a172723d91b4","last_reissued_at":"2026-05-18T04:08:13.249877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:13.249877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of Rosseland equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"JunZhi Cui, QiaoFu Zhang","submitted_at":"2011-11-16T01:38:19Z","abstract_excerpt":"The global boundness, existence and uniqueness are presented for the kind of Rosseland equation with a small parameter. This problem comes from conduction-radiation coupled heat transfer in the composites; it's with coefficients of high order growth and mixed boundary conditions.\n  A linearized map is constructed by fixing the function variables in the coefficients and the right-hand side. The solution to the linearized problem is uniformly bounded based on De Giorgi iteration; it is bounded in the H\\\"older space from a Sobolev-Campanato estimate.\n  This linearized map is compact and continuou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3703","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":"1111.3703","created_at":"2026-05-18T04:08:13.249959+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.3703v1","created_at":"2026-05-18T04:08:13.249959+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3703","created_at":"2026-05-18T04:08:13.249959+00:00"},{"alias_kind":"pith_short_12","alias_value":"T3E3YW5AHJUY","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"T3E3YW5AHJUYKUIQ","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"T3E3YW5A","created_at":"2026-05-18T12:26:41.206345+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/T3E3YW5AHJUYKUIQH2PK3IU27W","json":"https://pith.science/pith/T3E3YW5AHJUYKUIQH2PK3IU27W.json","graph_json":"https://pith.science/api/pith-number/T3E3YW5AHJUYKUIQH2PK3IU27W/graph.json","events_json":"https://pith.science/api/pith-number/T3E3YW5AHJUYKUIQH2PK3IU27W/events.json","paper":"https://pith.science/paper/T3E3YW5A"},"agent_actions":{"view_html":"https://pith.science/pith/T3E3YW5AHJUYKUIQH2PK3IU27W","download_json":"https://pith.science/pith/T3E3YW5AHJUYKUIQH2PK3IU27W.json","view_paper":"https://pith.science/paper/T3E3YW5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.3703&json=true","fetch_graph":"https://pith.science/api/pith-number/T3E3YW5AHJUYKUIQH2PK3IU27W/graph.json","fetch_events":"https://pith.science/api/pith-number/T3E3YW5AHJUYKUIQH2PK3IU27W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T3E3YW5AHJUYKUIQH2PK3IU27W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T3E3YW5AHJUYKUIQH2PK3IU27W/action/storage_attestation","attest_author":"https://pith.science/pith/T3E3YW5AHJUYKUIQH2PK3IU27W/action/author_attestation","sign_citation":"https://pith.science/pith/T3E3YW5AHJUYKUIQH2PK3IU27W/action/citation_signature","submit_replication":"https://pith.science/pith/T3E3YW5AHJUYKUIQH2PK3IU27W/action/replication_record"}},"created_at":"2026-05-18T04:08:13.249959+00:00","updated_at":"2026-05-18T04:08:13.249959+00:00"}