{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VKKMNB2QDGY3DG5XOR557YERFP","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":"7bca82f7dc707a98696260ef6e7c6772cf8d92661870f7649d1798faefb5da83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-21T12:03:13Z","title_canon_sha256":"4c44868904f50e2379df82b0df4f4dd52b4d153da64ae8bb03a8b1fec18c38a5"},"schema_version":"1.0","source":{"id":"1110.4767","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4767","created_at":"2026-05-18T04:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4767v1","created_at":"2026-05-18T04:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4767","created_at":"2026-05-18T04:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"VKKMNB2QDGY3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VKKMNB2QDGY3DG5X","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VKKMNB2Q","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:c90a3d0ab6784f09425f6c4e87cbcf7534c237d4d59716d9cb3a4e1f700118b6","target":"graph","created_at":"2026-05-18T04:10:35Z","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":"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.","authors_text":"A. Anantharaman, F. Legoll, X. Blanc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-21T12:03:13Z","title":"Asymptotic behaviour of Green functions of divergence form operators with periodic coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4767","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:e16bd8c2614825ca8f81630eb9b6dfe65d2a71e94c0acb147531459ede26efdf","target":"record","created_at":"2026-05-18T04:10:35Z","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":"7bca82f7dc707a98696260ef6e7c6772cf8d92661870f7649d1798faefb5da83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-21T12:03:13Z","title_canon_sha256":"4c44868904f50e2379df82b0df4f4dd52b4d153da64ae8bb03a8b1fec18c38a5"},"schema_version":"1.0","source":{"id":"1110.4767","kind":"arxiv","version":1}},"canonical_sha256":"aa94c6875019b1b19bb7747bdfe0912bd39f3589640dc8e26e06e007e31d04bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa94c6875019b1b19bb7747bdfe0912bd39f3589640dc8e26e06e007e31d04bc","first_computed_at":"2026-05-18T04:10:35.057268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:35.057268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UAk9I7+zMC0WRKehWeZ3kdpLBYi7BuP5ne+zjuMP1d2/PWb2V99gtvy5MoAyYanDtcA26I8sXdwG+UVBlwR9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:35.058102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4767","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e16bd8c2614825ca8f81630eb9b6dfe65d2a71e94c0acb147531459ede26efdf","sha256:c90a3d0ab6784f09425f6c4e87cbcf7534c237d4d59716d9cb3a4e1f700118b6"],"state_sha256":"8ec3bcf38b2759cdc0cbf1f49bd8c2a56d2a34a1d65fa59e83a976c75e197fa0"}