{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2XWWDI37AF6RX2KFQFYHNNM5ZW","short_pith_number":"pith:2XWWDI37","schema_version":"1.0","canonical_sha256":"d5ed61a37f017d1be945817076b59dcd91b74ca2a0cf2573cf80eae9d19ce058","source":{"kind":"arxiv","id":"1008.4092","version":1},"attestation_state":"computed","paper":{"title":"An Asymptotic Faber-Krahn Inequality for the Combinatorial Laplacian on Z^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.SP","authors_text":"Yakov Shlapentokh-Rothman","submitted_at":"2010-08-24T17:29:16Z","abstract_excerpt":"The Faber-Krahn inequality states that among all open domains with a fixed volume in R^n, the ball minimizes the first Dirichlet eigenvalue of the Laplacian. We study an asymptotic discrete analogue of this for the combinatorial Dirichlet Laplacian acting on induced subgraphs of Z^2. Namely, an induced subgraph G with n vertices is called a minimizing subgraph if it minimizes the first eigenvalue of the combinatorial Dirichlet Laplacian among all induced subgraphs with n vertices. Consider an induced subgraph G and take the interior of the union of closed squares of area 1 about each point of "},"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":"1008.4092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-08-24T17:29:16Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bf2f646eb5600ae18a7a049a1c05bdc0075dda7d59cfc1269550eea9050f1586","abstract_canon_sha256":"56bd1044c96be03e5b32ac7e493c98b036abd197a21a193a611ce5f4e01cd248"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:54.168178Z","signature_b64":"+YKl6WDUIeQHknbi89uNYrRXRLelr7rytHy69NpCkmOA1P9BvsET+DWybLPAOiZNOkEgaisNiplSCrgY1FlMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5ed61a37f017d1be945817076b59dcd91b74ca2a0cf2573cf80eae9d19ce058","last_reissued_at":"2026-05-18T04:41:54.167601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:54.167601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Asymptotic Faber-Krahn Inequality for the Combinatorial Laplacian on Z^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.SP","authors_text":"Yakov Shlapentokh-Rothman","submitted_at":"2010-08-24T17:29:16Z","abstract_excerpt":"The Faber-Krahn inequality states that among all open domains with a fixed volume in R^n, the ball minimizes the first Dirichlet eigenvalue of the Laplacian. We study an asymptotic discrete analogue of this for the combinatorial Dirichlet Laplacian acting on induced subgraphs of Z^2. Namely, an induced subgraph G with n vertices is called a minimizing subgraph if it minimizes the first eigenvalue of the combinatorial Dirichlet Laplacian among all induced subgraphs with n vertices. Consider an induced subgraph G and take the interior of the union of closed squares of area 1 about each point of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4092","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":"1008.4092","created_at":"2026-05-18T04:41:54.167687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.4092v1","created_at":"2026-05-18T04:41:54.167687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4092","created_at":"2026-05-18T04:41:54.167687+00:00"},{"alias_kind":"pith_short_12","alias_value":"2XWWDI37AF6R","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2XWWDI37AF6RX2KF","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2XWWDI37","created_at":"2026-05-18T12:26:03.138858+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/2XWWDI37AF6RX2KFQFYHNNM5ZW","json":"https://pith.science/pith/2XWWDI37AF6RX2KFQFYHNNM5ZW.json","graph_json":"https://pith.science/api/pith-number/2XWWDI37AF6RX2KFQFYHNNM5ZW/graph.json","events_json":"https://pith.science/api/pith-number/2XWWDI37AF6RX2KFQFYHNNM5ZW/events.json","paper":"https://pith.science/paper/2XWWDI37"},"agent_actions":{"view_html":"https://pith.science/pith/2XWWDI37AF6RX2KFQFYHNNM5ZW","download_json":"https://pith.science/pith/2XWWDI37AF6RX2KFQFYHNNM5ZW.json","view_paper":"https://pith.science/paper/2XWWDI37","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.4092&json=true","fetch_graph":"https://pith.science/api/pith-number/2XWWDI37AF6RX2KFQFYHNNM5ZW/graph.json","fetch_events":"https://pith.science/api/pith-number/2XWWDI37AF6RX2KFQFYHNNM5ZW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2XWWDI37AF6RX2KFQFYHNNM5ZW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2XWWDI37AF6RX2KFQFYHNNM5ZW/action/storage_attestation","attest_author":"https://pith.science/pith/2XWWDI37AF6RX2KFQFYHNNM5ZW/action/author_attestation","sign_citation":"https://pith.science/pith/2XWWDI37AF6RX2KFQFYHNNM5ZW/action/citation_signature","submit_replication":"https://pith.science/pith/2XWWDI37AF6RX2KFQFYHNNM5ZW/action/replication_record"}},"created_at":"2026-05-18T04:41:54.167687+00:00","updated_at":"2026-05-18T04:41:54.167687+00:00"}