{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NBOZ3EIXQ32LNYVES7I6UMJ3UW","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":"fa8e35a7e75e9c7f96fcc44f207572834482493d7617c318aa53110f28e12537","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T22:07:13Z","title_canon_sha256":"4faa5c63adffe1eb1a2cbde65d3a17c55f7fed759c8695ef0dd373512fa6224c"},"schema_version":"1.0","source":{"id":"1404.5342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5342","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5342v1","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5342","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"NBOZ3EIXQ32L","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NBOZ3EIXQ32LNYVE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NBOZ3EIX","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:9f1cc3faeddb60b5cae7b6c480eaa7fe1bb063fc642d2d31c7a6bcbbbe8b8570","target":"graph","created_at":"2026-05-18T01:31:46Z","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":"We study the asymptotic behaviour of the resolvents $({\\mathcal A}^\\varepsilon+I)^{-1}$ of elliptic second-order differential operators ${\\mathcal A}^\\varepsilon$ in ${\\mathbb R}^d$ with periodic rapidly oscillating coefficients, as the period $\\varepsilon$ goes to zero. The class of operators covered by our analysis includes both the \"classical\" case of uniformly elliptic families (where the ellipticity constant does not depend on $\\varepsilon$) and the \"double-porosity\" case of coefficients that take contrasting values of order one and of order $\\varepsilon^2$ in different parts of the perio","authors_text":"Kirill Cherednichenko, Shane Cooper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T22:07:13Z","title":"Resolvent estimates for high-contrast elliptic problems with periodic coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5342","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":"sha256:460f6fe7d1729990944ecd092a393ae038553059fc9848ea57d6572efb6ad07d","target":"record","created_at":"2026-05-18T01:31:46Z","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":"fa8e35a7e75e9c7f96fcc44f207572834482493d7617c318aa53110f28e12537","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T22:07:13Z","title_canon_sha256":"4faa5c63adffe1eb1a2cbde65d3a17c55f7fed759c8695ef0dd373512fa6224c"},"schema_version":"1.0","source":{"id":"1404.5342","kind":"arxiv","version":1}},"canonical_sha256":"685d9d911786f4b6e2a497d1ea313ba5bae85d30edda1663a62a98a7ea3be92c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"685d9d911786f4b6e2a497d1ea313ba5bae85d30edda1663a62a98a7ea3be92c","first_computed_at":"2026-05-18T01:31:46.667053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:46.667053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g3ctwqWA5HTFRi/k/Jx7PLSKGbfWiGCAggBK6B1nQ/0MK131IDhGhOWGhHO8KtNwuBqw4u1esTPnFPw+zutABg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:46.667605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:460f6fe7d1729990944ecd092a393ae038553059fc9848ea57d6572efb6ad07d","sha256:9f1cc3faeddb60b5cae7b6c480eaa7fe1bb063fc642d2d31c7a6bcbbbe8b8570"],"state_sha256":"1313cd5d86590390fbe862e565e5c63e724444e4deabce2f7c8d44f4581687e2"}