{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YZWBC5GGUNACT2WTG3S33PAZRG","short_pith_number":"pith:YZWBC5GG","schema_version":"1.0","canonical_sha256":"c66c1174c6a34029ead336e5bdbc1989b930de70dbce2ca68773fd6134d5463f","source":{"kind":"arxiv","id":"2606.04225","version":1},"attestation_state":"computed","paper":{"title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.CV","authors_text":"Bart Rosenzweig, Jonathan Stanfill","submitted_at":"2026-06-02T21:23:05Z","abstract_excerpt":"We answer in the affirmative a question posed by V. Maz'ya of whether one can continue as a meromorphic function of $t$ the series representation of the fundamental solution of a certain nonlocal parabolic equation associated to a logarithmic Laplacian on the circle, which arises in the study of boundary value problems associated to the ordinary Laplacian on domains with thin cavities. The $a\\ln(n) +O(1)$ growth of the eigenvalues of the integral operator, together with explicit formulas for the eigenfunctions and the subleading asymptotic behavior of the eigenvalues, allows us to show that th"},"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":"2606.04225","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-06-02T21:23:05Z","cross_cats_sorted":["math.AP","math.SP"],"title_canon_sha256":"9e1594b9381c9cffd1e1c9f5d3034d073b5b6b6fe0155aed8c98645b7836defc","abstract_canon_sha256":"2804a1d6806f66b010674497a0ef259a53a3174659d646962864182a96991d64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:08:59.189591Z","signature_b64":"u4lqZcRFU0fOe5PoqxMYYK+JnV1VNl6Ol5xZpWBssAWe3XQS2hLx9VSBpZTYEUf7n3MttlOr9Zs9z+rf0+E9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c66c1174c6a34029ead336e5bdbc1989b930de70dbce2ca68773fd6134d5463f","last_reissued_at":"2026-06-04T01:08:59.189059Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:08:59.189059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.CV","authors_text":"Bart Rosenzweig, Jonathan Stanfill","submitted_at":"2026-06-02T21:23:05Z","abstract_excerpt":"We answer in the affirmative a question posed by V. Maz'ya of whether one can continue as a meromorphic function of $t$ the series representation of the fundamental solution of a certain nonlocal parabolic equation associated to a logarithmic Laplacian on the circle, which arises in the study of boundary value problems associated to the ordinary Laplacian on domains with thin cavities. The $a\\ln(n) +O(1)$ growth of the eigenvalues of the integral operator, together with explicit formulas for the eigenfunctions and the subleading asymptotic behavior of the eigenvalues, allows us to show that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04225","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04225/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":"2606.04225","created_at":"2026-06-04T01:08:59.189123+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04225v1","created_at":"2026-06-04T01:08:59.189123+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04225","created_at":"2026-06-04T01:08:59.189123+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZWBC5GGUNAC","created_at":"2026-06-04T01:08:59.189123+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZWBC5GGUNACT2WT","created_at":"2026-06-04T01:08:59.189123+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZWBC5GG","created_at":"2026-06-04T01:08:59.189123+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/YZWBC5GGUNACT2WTG3S33PAZRG","json":"https://pith.science/pith/YZWBC5GGUNACT2WTG3S33PAZRG.json","graph_json":"https://pith.science/api/pith-number/YZWBC5GGUNACT2WTG3S33PAZRG/graph.json","events_json":"https://pith.science/api/pith-number/YZWBC5GGUNACT2WTG3S33PAZRG/events.json","paper":"https://pith.science/paper/YZWBC5GG"},"agent_actions":{"view_html":"https://pith.science/pith/YZWBC5GGUNACT2WTG3S33PAZRG","download_json":"https://pith.science/pith/YZWBC5GGUNACT2WTG3S33PAZRG.json","view_paper":"https://pith.science/paper/YZWBC5GG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04225&json=true","fetch_graph":"https://pith.science/api/pith-number/YZWBC5GGUNACT2WTG3S33PAZRG/graph.json","fetch_events":"https://pith.science/api/pith-number/YZWBC5GGUNACT2WTG3S33PAZRG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZWBC5GGUNACT2WTG3S33PAZRG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZWBC5GGUNACT2WTG3S33PAZRG/action/storage_attestation","attest_author":"https://pith.science/pith/YZWBC5GGUNACT2WTG3S33PAZRG/action/author_attestation","sign_citation":"https://pith.science/pith/YZWBC5GGUNACT2WTG3S33PAZRG/action/citation_signature","submit_replication":"https://pith.science/pith/YZWBC5GGUNACT2WTG3S33PAZRG/action/replication_record"}},"created_at":"2026-06-04T01:08:59.189123+00:00","updated_at":"2026-06-04T01:08:59.189123+00:00"}