{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PRYX4Q2MBLWEP2XXFODG7HJM7D","short_pith_number":"pith:PRYX4Q2M","schema_version":"1.0","canonical_sha256":"7c717e434c0aec47eaf72b866f9d2cf8fee41080036c9c525374328c58d08459","source":{"kind":"arxiv","id":"2603.25094","version":2},"attestation_state":"computed","paper":{"title":"Homogenization and operator estimates for Steklov problems in perforated domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Andrii Khrabustovskyi, Jari Taskinen","submitted_at":"2026-03-26T06:59:16Z","abstract_excerpt":"Let the set $\\Omega_\\varepsilon$ be obtained from the bounded domain $\\Omega$ by removing a family of $\\varepsilon$-periodically distributed identical balls. In $\\Omega_\\varepsilon$ one considers the Steklov spectral problem. It is known from [Girouard-Henrot-Lagac\\'e, ARMA (2021)] that, if the radii of the holes shrink at a critical rate such that the surface area of a single hole is comparable to the volume of a periodicity cell, then, in the limit $\\varepsilon \\to 0$, the Steklov spectrum converges to the spectrum of the problem $-\\Delta u=\\lambda Q u$ on $\\Omega$ with some weight $Q>0$. In"},"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":"2603.25094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-03-26T06:59:16Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"cc399f76d4ffbca920711c081c1b08dd1a45e765de0d34616ff7dd7e014a2026","abstract_canon_sha256":"26eb1a9238122d983c9b4b835b1cfc751605d603e10ed8f5ad33cf74b8cb0a49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:25.249041Z","signature_b64":"f4CP5eptpZ2JCA+FD8dd8N1G0TZA+ZaU7LwAxQM2r/E2csJw/+psU2Nzja+3vIiXLOduBEFKMyT3Kq6sZ5KIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c717e434c0aec47eaf72b866f9d2cf8fee41080036c9c525374328c58d08459","last_reissued_at":"2026-06-09T02:07:25.248004Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:25.248004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogenization and operator estimates for Steklov problems in perforated domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Andrii Khrabustovskyi, Jari Taskinen","submitted_at":"2026-03-26T06:59:16Z","abstract_excerpt":"Let the set $\\Omega_\\varepsilon$ be obtained from the bounded domain $\\Omega$ by removing a family of $\\varepsilon$-periodically distributed identical balls. In $\\Omega_\\varepsilon$ one considers the Steklov spectral problem. It is known from [Girouard-Henrot-Lagac\\'e, ARMA (2021)] that, if the radii of the holes shrink at a critical rate such that the surface area of a single hole is comparable to the volume of a periodicity cell, then, in the limit $\\varepsilon \\to 0$, the Steklov spectrum converges to the spectrum of the problem $-\\Delta u=\\lambda Q u$ on $\\Omega$ with some weight $Q>0$. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.25094","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.25094/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2603.25094","created_at":"2026-06-09T02:07:25.248139+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.25094v2","created_at":"2026-06-09T02:07:25.248139+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.25094","created_at":"2026-06-09T02:07:25.248139+00:00"},{"alias_kind":"pith_short_12","alias_value":"PRYX4Q2MBLWE","created_at":"2026-06-09T02:07:25.248139+00:00"},{"alias_kind":"pith_short_16","alias_value":"PRYX4Q2MBLWEP2XX","created_at":"2026-06-09T02:07:25.248139+00:00"},{"alias_kind":"pith_short_8","alias_value":"PRYX4Q2M","created_at":"2026-06-09T02:07:25.248139+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/PRYX4Q2MBLWEP2XXFODG7HJM7D","json":"https://pith.science/pith/PRYX4Q2MBLWEP2XXFODG7HJM7D.json","graph_json":"https://pith.science/api/pith-number/PRYX4Q2MBLWEP2XXFODG7HJM7D/graph.json","events_json":"https://pith.science/api/pith-number/PRYX4Q2MBLWEP2XXFODG7HJM7D/events.json","paper":"https://pith.science/paper/PRYX4Q2M"},"agent_actions":{"view_html":"https://pith.science/pith/PRYX4Q2MBLWEP2XXFODG7HJM7D","download_json":"https://pith.science/pith/PRYX4Q2MBLWEP2XXFODG7HJM7D.json","view_paper":"https://pith.science/paper/PRYX4Q2M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.25094&json=true","fetch_graph":"https://pith.science/api/pith-number/PRYX4Q2MBLWEP2XXFODG7HJM7D/graph.json","fetch_events":"https://pith.science/api/pith-number/PRYX4Q2MBLWEP2XXFODG7HJM7D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PRYX4Q2MBLWEP2XXFODG7HJM7D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PRYX4Q2MBLWEP2XXFODG7HJM7D/action/storage_attestation","attest_author":"https://pith.science/pith/PRYX4Q2MBLWEP2XXFODG7HJM7D/action/author_attestation","sign_citation":"https://pith.science/pith/PRYX4Q2MBLWEP2XXFODG7HJM7D/action/citation_signature","submit_replication":"https://pith.science/pith/PRYX4Q2MBLWEP2XXFODG7HJM7D/action/replication_record"}},"created_at":"2026-06-09T02:07:25.248139+00:00","updated_at":"2026-06-09T02:07:25.248139+00:00"}