{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:J5QJ54TE74HK6LLZ2P2XJGICNV","short_pith_number":"pith:J5QJ54TE","schema_version":"1.0","canonical_sha256":"4f609ef264ff0eaf2d79d3f57499026d5070ca548e1b0e7f07de5f51de09ebcf","source":{"kind":"arxiv","id":"1604.00784","version":1},"attestation_state":"computed","paper":{"title":"Heat Kernel estimates for general boundary problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Alexander Strohmaier, Liangpan Li","submitted_at":"2016-04-04T09:26:49Z","abstract_excerpt":"We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in $\\mathbb{R}^d$. They are therefore valid for any choice of boundary condition and we show that the implied constants can be chosen independent of the self-adjoint extension. The method of proof is very general and is based on finite propagation speed estimates and explicit Fourier Tauberian theorems obtained by Y. Safarov."},"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":"1604.00784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-04T09:26:49Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"51e0a201a7ab8b87e47e458958e8c03acc9b8c711cf14cc8269d0b743d4e15fe","abstract_canon_sha256":"9e7d49fc83cd3dca62f56a40258b936954a8bc42855a5d80b83687a2f76069bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:48.315110Z","signature_b64":"WW/DJVuop9ApV1sZW5yIG+vOi2qzg7UTsueSvPfhUVGuRMc8dXRyxojqHfu3N+Cwzaho6xCO8b9p8XTmQSwhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f609ef264ff0eaf2d79d3f57499026d5070ca548e1b0e7f07de5f51de09ebcf","last_reissued_at":"2026-05-18T01:17:48.314402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:48.314402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heat Kernel estimates for general boundary problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Alexander Strohmaier, Liangpan Li","submitted_at":"2016-04-04T09:26:49Z","abstract_excerpt":"We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in $\\mathbb{R}^d$. They are therefore valid for any choice of boundary condition and we show that the implied constants can be chosen independent of the self-adjoint extension. The method of proof is very general and is based on finite propagation speed estimates and explicit Fourier Tauberian theorems obtained by Y. Safarov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00784","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":"1604.00784","created_at":"2026-05-18T01:17:48.314512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.00784v1","created_at":"2026-05-18T01:17:48.314512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00784","created_at":"2026-05-18T01:17:48.314512+00:00"},{"alias_kind":"pith_short_12","alias_value":"J5QJ54TE74HK","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"J5QJ54TE74HK6LLZ","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"J5QJ54TE","created_at":"2026-05-18T12:30:22.444734+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/J5QJ54TE74HK6LLZ2P2XJGICNV","json":"https://pith.science/pith/J5QJ54TE74HK6LLZ2P2XJGICNV.json","graph_json":"https://pith.science/api/pith-number/J5QJ54TE74HK6LLZ2P2XJGICNV/graph.json","events_json":"https://pith.science/api/pith-number/J5QJ54TE74HK6LLZ2P2XJGICNV/events.json","paper":"https://pith.science/paper/J5QJ54TE"},"agent_actions":{"view_html":"https://pith.science/pith/J5QJ54TE74HK6LLZ2P2XJGICNV","download_json":"https://pith.science/pith/J5QJ54TE74HK6LLZ2P2XJGICNV.json","view_paper":"https://pith.science/paper/J5QJ54TE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.00784&json=true","fetch_graph":"https://pith.science/api/pith-number/J5QJ54TE74HK6LLZ2P2XJGICNV/graph.json","fetch_events":"https://pith.science/api/pith-number/J5QJ54TE74HK6LLZ2P2XJGICNV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J5QJ54TE74HK6LLZ2P2XJGICNV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J5QJ54TE74HK6LLZ2P2XJGICNV/action/storage_attestation","attest_author":"https://pith.science/pith/J5QJ54TE74HK6LLZ2P2XJGICNV/action/author_attestation","sign_citation":"https://pith.science/pith/J5QJ54TE74HK6LLZ2P2XJGICNV/action/citation_signature","submit_replication":"https://pith.science/pith/J5QJ54TE74HK6LLZ2P2XJGICNV/action/replication_record"}},"created_at":"2026-05-18T01:17:48.314512+00:00","updated_at":"2026-05-18T01:17:48.314512+00:00"}