{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VKKMNB2QDGY3DG5XOR557YERFP","short_pith_number":"pith:VKKMNB2Q","schema_version":"1.0","canonical_sha256":"aa94c6875019b1b19bb7747bdfe0912bd39f3589640dc8e26e06e007e31d04bc","source":{"kind":"arxiv","id":"1110.4767","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic behaviour of Green functions of divergence form operators with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Anantharaman, F. Legoll, X. Blanc","submitted_at":"2011-10-21T12:03:13Z","abstract_excerpt":"This article is concerned with the asymptotic behaviour, at infinity and at the origin, of Green functions of operators of the form $Lu = -\\text{div} (A \\nabla u),$ where $A$ is a periodic, coercive and bounded matrix."},"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":"1110.4767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-21T12:03:13Z","cross_cats_sorted":[],"title_canon_sha256":"4c44868904f50e2379df82b0df4f4dd52b4d153da64ae8bb03a8b1fec18c38a5","abstract_canon_sha256":"7bca82f7dc707a98696260ef6e7c6772cf8d92661870f7649d1798faefb5da83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:35.058102Z","signature_b64":"UAk9I7+zMC0WRKehWeZ3kdpLBYi7BuP5ne+zjuMP1d2/PWb2V99gtvy5MoAyYanDtcA26I8sXdwG+UVBlwR9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa94c6875019b1b19bb7747bdfe0912bd39f3589640dc8e26e06e007e31d04bc","last_reissued_at":"2026-05-18T04:10:35.057268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:35.057268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic behaviour of Green functions of divergence form operators with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Anantharaman, F. Legoll, X. Blanc","submitted_at":"2011-10-21T12:03:13Z","abstract_excerpt":"This article is concerned with the asymptotic behaviour, at infinity and at the origin, of Green functions of operators of the form $Lu = -\\text{div} (A \\nabla u),$ where $A$ is a periodic, coercive and bounded matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4767","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":"1110.4767","created_at":"2026-05-18T04:10:35.057427+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.4767v1","created_at":"2026-05-18T04:10:35.057427+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4767","created_at":"2026-05-18T04:10:35.057427+00:00"},{"alias_kind":"pith_short_12","alias_value":"VKKMNB2QDGY3","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VKKMNB2QDGY3DG5X","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VKKMNB2Q","created_at":"2026-05-18T12:26:44.992195+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/VKKMNB2QDGY3DG5XOR557YERFP","json":"https://pith.science/pith/VKKMNB2QDGY3DG5XOR557YERFP.json","graph_json":"https://pith.science/api/pith-number/VKKMNB2QDGY3DG5XOR557YERFP/graph.json","events_json":"https://pith.science/api/pith-number/VKKMNB2QDGY3DG5XOR557YERFP/events.json","paper":"https://pith.science/paper/VKKMNB2Q"},"agent_actions":{"view_html":"https://pith.science/pith/VKKMNB2QDGY3DG5XOR557YERFP","download_json":"https://pith.science/pith/VKKMNB2QDGY3DG5XOR557YERFP.json","view_paper":"https://pith.science/paper/VKKMNB2Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.4767&json=true","fetch_graph":"https://pith.science/api/pith-number/VKKMNB2QDGY3DG5XOR557YERFP/graph.json","fetch_events":"https://pith.science/api/pith-number/VKKMNB2QDGY3DG5XOR557YERFP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VKKMNB2QDGY3DG5XOR557YERFP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VKKMNB2QDGY3DG5XOR557YERFP/action/storage_attestation","attest_author":"https://pith.science/pith/VKKMNB2QDGY3DG5XOR557YERFP/action/author_attestation","sign_citation":"https://pith.science/pith/VKKMNB2QDGY3DG5XOR557YERFP/action/citation_signature","submit_replication":"https://pith.science/pith/VKKMNB2QDGY3DG5XOR557YERFP/action/replication_record"}},"created_at":"2026-05-18T04:10:35.057427+00:00","updated_at":"2026-05-18T04:10:35.057427+00:00"}