{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VY3ZQRITOYIQXGC35FUDJRSTJ6","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":"09a9b743c510e4415e317e2ebc482b211c400da86104e9d485818064dd74313e","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-10-09T13:28:25Z","title_canon_sha256":"87624284d52e37f75329935d55e90c08833e9d56df4a47dbf0f3df6c64280279"},"schema_version":"1.0","source":{"id":"1710.03080","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03080","created_at":"2026-05-18T00:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03080v2","created_at":"2026-05-18T00:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03080","created_at":"2026-05-18T00:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"VY3ZQRITOYIQ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VY3ZQRITOYIQXGC3","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VY3ZQRIT","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:a4613eb0333e3a376e37314583a54ecacb92e46f57522cd8716a111089f6f07a","target":"graph","created_at":"2026-05-18T00:27:18Z","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":"Let $\\Delta_{\\Omega_\\varepsilon}$ be the Dirichlet Laplacian in the domain $\\Omega_\\varepsilon:=\\Omega\\setminus\\left(\\cup_i D_{i \\varepsilon}\\right)$. Here $\\Omega\\subset\\mathbb{R}^n$ and $\\{D_{i \\varepsilon}\\}_{i}$ is a family of tiny identical holes (\"ice pieces\") distributed periodically in $\\mathbb{R}^n$ with period $\\varepsilon$. We denote by $\\mathrm{cap}(D_{i \\varepsilon})$ the capacity of a single hole. It was known for a long time that $-\\Delta_{\\Omega_\\varepsilon}$ converges to the operator $-\\Delta_{\\Omega}+q$ in strong resolvent sense provided the limit $q:=\\lim_{\\varepsilon\\to 0} ","authors_text":"Andrii Khrabustovskyi, Olaf Post","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-10-09T13:28:25Z","title":"Operator estimates for the crushed ice problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03080","kind":"arxiv","version":2},"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:db8fd7643acd30568e3f67e25a482190224b61417000ae0f676681036047c5f0","target":"record","created_at":"2026-05-18T00:27:18Z","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":"09a9b743c510e4415e317e2ebc482b211c400da86104e9d485818064dd74313e","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-10-09T13:28:25Z","title_canon_sha256":"87624284d52e37f75329935d55e90c08833e9d56df4a47dbf0f3df6c64280279"},"schema_version":"1.0","source":{"id":"1710.03080","kind":"arxiv","version":2}},"canonical_sha256":"ae3798451376110b985be96834c6534f948f25d133e790334268e0e78e9353ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae3798451376110b985be96834c6534f948f25d133e790334268e0e78e9353ef","first_computed_at":"2026-05-18T00:27:18.768004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:18.768004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vwt8qrPEJd+v+9gIiSARLXWPHGWEPKzi9hI5HbIT/1TXsnCjQgf0QqtdmVdBu2Uptf1HwQl0jrYeKWeSxPF5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:18.768504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03080","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db8fd7643acd30568e3f67e25a482190224b61417000ae0f676681036047c5f0","sha256:a4613eb0333e3a376e37314583a54ecacb92e46f57522cd8716a111089f6f07a"],"state_sha256":"27ba5565702aab8fdb9646d82c9e441b19771a15e0b5eea0d8ef5d6cf100720b"}