{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4RGNYV6KO2DZCFH66CQSPCXYTE","short_pith_number":"pith:4RGNYV6K","schema_version":"1.0","canonical_sha256":"e44cdc57ca76879114fef0a1278af899397494878c3c12f77c6ee04817352a50","source":{"kind":"arxiv","id":"1312.3170","version":1},"attestation_state":"computed","paper":{"title":"Heat trace asymptotics and compactness of isospectral potentials for the Dirichlet Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eric Soccorsi (CPT), Laurent Kayser (IECL), Mourad Choulli (IECL), Yavar Kian (CPT)","submitted_at":"2013-12-11T14:06:44Z","abstract_excerpt":"Let $\\Omega$ be a $C^\\infty$-smooth bounded domain of $\\mathbb{R}^n$, $n \\geq 1$, and let the matrix ${\\bf a} \\in C^\\infty (\\overline{\\Omega};\\R^{n^2})$ be symmetric and uniformly elliptic. We consider the $L^2(\\Omega)$-realization $A$ of the operator $-\\mydiv ( {\\bf a} \\nabla \\cdot)$ with Dirichlet boundary conditions. We perturb $A$ by some real valued potential $V \\in C_0^\\infty (\\Omega)$ and note $A_V=A+V$. We compute the asymptotic expansion of $\\mbox{tr}\\left( e^{-t A_V}-e^{-t A}\\right)$ as $t \\downarrow 0$ for any matrix ${\\bf a}$ whose coefficients are homogeneous of degree $0$. In the"},"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":"1312.3170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-11T14:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"e0b9298362c10bb65bb0ef6e0c1ef7dde3d94c78783b8f88ec9687995b5862d3","abstract_canon_sha256":"e5326863c9e1a1e973cbea6be83a41df1f572c5a527c87a02d81dad653800492"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:00.305603Z","signature_b64":"5P4odSscdAAtS9WUxX6UMs+tYHzGlnkcqpBDgAJ9GT5tIHjYdQjsb9zUIbPPls2h++LVvJJ5Qzvwq1kx/jKxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e44cdc57ca76879114fef0a1278af899397494878c3c12f77c6ee04817352a50","last_reissued_at":"2026-05-18T03:05:00.305122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:00.305122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heat trace asymptotics and compactness of isospectral potentials for the Dirichlet Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eric Soccorsi (CPT), Laurent Kayser (IECL), Mourad Choulli (IECL), Yavar Kian (CPT)","submitted_at":"2013-12-11T14:06:44Z","abstract_excerpt":"Let $\\Omega$ be a $C^\\infty$-smooth bounded domain of $\\mathbb{R}^n$, $n \\geq 1$, and let the matrix ${\\bf a} \\in C^\\infty (\\overline{\\Omega};\\R^{n^2})$ be symmetric and uniformly elliptic. We consider the $L^2(\\Omega)$-realization $A$ of the operator $-\\mydiv ( {\\bf a} \\nabla \\cdot)$ with Dirichlet boundary conditions. We perturb $A$ by some real valued potential $V \\in C_0^\\infty (\\Omega)$ and note $A_V=A+V$. We compute the asymptotic expansion of $\\mbox{tr}\\left( e^{-t A_V}-e^{-t A}\\right)$ as $t \\downarrow 0$ for any matrix ${\\bf a}$ whose coefficients are homogeneous of degree $0$. In the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3170","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":"1312.3170","created_at":"2026-05-18T03:05:00.305191+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.3170v1","created_at":"2026-05-18T03:05:00.305191+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3170","created_at":"2026-05-18T03:05:00.305191+00:00"},{"alias_kind":"pith_short_12","alias_value":"4RGNYV6KO2DZ","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"4RGNYV6KO2DZCFH6","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"4RGNYV6K","created_at":"2026-05-18T12:27:34.582898+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/4RGNYV6KO2DZCFH66CQSPCXYTE","json":"https://pith.science/pith/4RGNYV6KO2DZCFH66CQSPCXYTE.json","graph_json":"https://pith.science/api/pith-number/4RGNYV6KO2DZCFH66CQSPCXYTE/graph.json","events_json":"https://pith.science/api/pith-number/4RGNYV6KO2DZCFH66CQSPCXYTE/events.json","paper":"https://pith.science/paper/4RGNYV6K"},"agent_actions":{"view_html":"https://pith.science/pith/4RGNYV6KO2DZCFH66CQSPCXYTE","download_json":"https://pith.science/pith/4RGNYV6KO2DZCFH66CQSPCXYTE.json","view_paper":"https://pith.science/paper/4RGNYV6K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.3170&json=true","fetch_graph":"https://pith.science/api/pith-number/4RGNYV6KO2DZCFH66CQSPCXYTE/graph.json","fetch_events":"https://pith.science/api/pith-number/4RGNYV6KO2DZCFH66CQSPCXYTE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4RGNYV6KO2DZCFH66CQSPCXYTE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4RGNYV6KO2DZCFH66CQSPCXYTE/action/storage_attestation","attest_author":"https://pith.science/pith/4RGNYV6KO2DZCFH66CQSPCXYTE/action/author_attestation","sign_citation":"https://pith.science/pith/4RGNYV6KO2DZCFH66CQSPCXYTE/action/citation_signature","submit_replication":"https://pith.science/pith/4RGNYV6KO2DZCFH66CQSPCXYTE/action/replication_record"}},"created_at":"2026-05-18T03:05:00.305191+00:00","updated_at":"2026-05-18T03:05:00.305191+00:00"}