{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YZWBC5GGUNACT2WTG3S33PAZRG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2804a1d6806f66b010674497a0ef259a53a3174659d646962864182a96991d64","cross_cats_sorted":["math.AP","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-06-02T21:23:05Z","title_canon_sha256":"9e1594b9381c9cffd1e1c9f5d3034d073b5b6b6fe0155aed8c98645b7836defc"},"schema_version":"1.0","source":{"id":"2606.04225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04225","created_at":"2026-06-04T01:08:59Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04225v1","created_at":"2026-06-04T01:08:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04225","created_at":"2026-06-04T01:08:59Z"},{"alias_kind":"pith_short_12","alias_value":"YZWBC5GGUNAC","created_at":"2026-06-04T01:08:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZWBC5GGUNACT2WT","created_at":"2026-06-04T01:08:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZWBC5GG","created_at":"2026-06-04T01:08:59Z"}],"graph_snapshots":[{"event_id":"sha256:3dbeef103d796b2d77b0ed13b9ce2429258124f00ed4469f26885add05ba9b47","target":"graph","created_at":"2026-06-04T01:08:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.04225/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Bart Rosenzweig, Jonathan Stanfill","cross_cats":["math.AP","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04225","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b74a7e95ca845116f4da7a6bf8b4286430ce326e82fa57290b887bedeedec0f8","target":"record","created_at":"2026-06-04T01:08:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2804a1d6806f66b010674497a0ef259a53a3174659d646962864182a96991d64","cross_cats_sorted":["math.AP","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-06-02T21:23:05Z","title_canon_sha256":"9e1594b9381c9cffd1e1c9f5d3034d073b5b6b6fe0155aed8c98645b7836defc"},"schema_version":"1.0","source":{"id":"2606.04225","kind":"arxiv","version":1}},"canonical_sha256":"c66c1174c6a34029ead336e5bdbc1989b930de70dbce2ca68773fd6134d5463f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c66c1174c6a34029ead336e5bdbc1989b930de70dbce2ca68773fd6134d5463f","first_computed_at":"2026-06-04T01:08:59.189059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:08:59.189059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u4lqZcRFU0fOe5PoqxMYYK+JnV1VNl6Ol5xZpWBssAWe3XQS2hLx9VSBpZTYEUf7n3MttlOr9Zs9z+rf0+E9CA==","signature_status":"signed_v1","signed_at":"2026-06-04T01:08:59.189591Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b74a7e95ca845116f4da7a6bf8b4286430ce326e82fa57290b887bedeedec0f8","sha256:3dbeef103d796b2d77b0ed13b9ce2429258124f00ed4469f26885add05ba9b47"],"state_sha256":"99fc8c557d9cc9248deae5358c9579712c8833f587a79ec513dc8d7504b5d85b"}