{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OXBE3Q2Z7NALOCRPCYVSELHRI4","short_pith_number":"pith:OXBE3Q2Z","schema_version":"1.0","canonical_sha256":"75c24dc359fb40b70a2f162b222cf1471ebb058521c44626ea63ea2a57c4063c","source":{"kind":"arxiv","id":"1401.1740","version":2},"attestation_state":"computed","paper":{"title":"Heat Kernel Asymptotic Expansion on Unbounded Domains with Polynomially Confining Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Guglielmo Fucci","submitted_at":"2014-01-08T16:20:21Z","abstract_excerpt":"In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean space. To conduct this study, the trace of the heat kernel is expressed in terms of its partially resummed form which is then represented as a Mellin-Barnes integral. A suitable contour deformation then provides, through the use of Cauchy's residue theorem, closed formulas for the coefficients of the asymptotic expansion. The general expression for the asymptot"},"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":"1401.1740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-08T16:20:21Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"0976d795e2944e956d909c639afff28f85e5e423b60a73d340fe4f38ebbcbfc2","abstract_canon_sha256":"e5fd5670019e7f0e7acd3dcd8d29385f23409d1f03646a1351f740e4143e27d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:56.734879Z","signature_b64":"08kdVw9dUMGVLDjjTDMUK+bEcneuMPaG7VCwhCUbxJ45SeLepUXS3Uo/krfKggZ1/Tf74mcrILP9SZw9E+UpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75c24dc359fb40b70a2f162b222cf1471ebb058521c44626ea63ea2a57c4063c","last_reissued_at":"2026-05-18T02:51:56.734392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:56.734392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heat Kernel Asymptotic Expansion on Unbounded Domains with Polynomially Confining Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Guglielmo Fucci","submitted_at":"2014-01-08T16:20:21Z","abstract_excerpt":"In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean space. To conduct this study, the trace of the heat kernel is expressed in terms of its partially resummed form which is then represented as a Mellin-Barnes integral. A suitable contour deformation then provides, through the use of Cauchy's residue theorem, closed formulas for the coefficients of the asymptotic expansion. The general expression for the asymptot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1740","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":""},"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":"1401.1740","created_at":"2026-05-18T02:51:56.734465+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.1740v2","created_at":"2026-05-18T02:51:56.734465+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1740","created_at":"2026-05-18T02:51:56.734465+00:00"},{"alias_kind":"pith_short_12","alias_value":"OXBE3Q2Z7NAL","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OXBE3Q2Z7NALOCRP","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OXBE3Q2Z","created_at":"2026-05-18T12:28:43.426989+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/OXBE3Q2Z7NALOCRPCYVSELHRI4","json":"https://pith.science/pith/OXBE3Q2Z7NALOCRPCYVSELHRI4.json","graph_json":"https://pith.science/api/pith-number/OXBE3Q2Z7NALOCRPCYVSELHRI4/graph.json","events_json":"https://pith.science/api/pith-number/OXBE3Q2Z7NALOCRPCYVSELHRI4/events.json","paper":"https://pith.science/paper/OXBE3Q2Z"},"agent_actions":{"view_html":"https://pith.science/pith/OXBE3Q2Z7NALOCRPCYVSELHRI4","download_json":"https://pith.science/pith/OXBE3Q2Z7NALOCRPCYVSELHRI4.json","view_paper":"https://pith.science/paper/OXBE3Q2Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.1740&json=true","fetch_graph":"https://pith.science/api/pith-number/OXBE3Q2Z7NALOCRPCYVSELHRI4/graph.json","fetch_events":"https://pith.science/api/pith-number/OXBE3Q2Z7NALOCRPCYVSELHRI4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OXBE3Q2Z7NALOCRPCYVSELHRI4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OXBE3Q2Z7NALOCRPCYVSELHRI4/action/storage_attestation","attest_author":"https://pith.science/pith/OXBE3Q2Z7NALOCRPCYVSELHRI4/action/author_attestation","sign_citation":"https://pith.science/pith/OXBE3Q2Z7NALOCRPCYVSELHRI4/action/citation_signature","submit_replication":"https://pith.science/pith/OXBE3Q2Z7NALOCRPCYVSELHRI4/action/replication_record"}},"created_at":"2026-05-18T02:51:56.734465+00:00","updated_at":"2026-05-18T02:51:56.734465+00:00"}