{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:WZSZME72LU5XJAYHYOUDRJ5MWN","short_pith_number":"pith:WZSZME72","schema_version":"1.0","canonical_sha256":"b6659613fa5d3b748307c3a838a7acb37ac37a72099f70367a6817588ee342ff","source":{"kind":"arxiv","id":"1108.3191","version":1},"attestation_state":"computed","paper":{"title":"The Brownian traveller on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","math.SP"],"primary_cat":"math.AP","authors_text":"David Krejcirik, Martin Kolb","submitted_at":"2011-08-16T09:48:19Z","abstract_excerpt":"We study the influence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the flat case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the flat case. The proof employs the existence "},"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":"1108.3191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-16T09:48:19Z","cross_cats_sorted":["math-ph","math.MP","math.PR","math.SP"],"title_canon_sha256":"e0ce578e64cdb3e4a1f15a2fbce7d54cf28c3b7aad699899f62391df5c161ae0","abstract_canon_sha256":"9f3b6834457eedd400ba083f3d3cd753b54e19d88321b742aa6fe62016d53428"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:31.692733Z","signature_b64":"LUTTBWRNuGb6KyV8FMGhCdFpuKDpDU7kGgiIZAHcUfq+Fj9+Sda0QIj6Wkx5lUiiAVrqbF6iGMAwwHiJFMTvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6659613fa5d3b748307c3a838a7acb37ac37a72099f70367a6817588ee342ff","last_reissued_at":"2026-05-18T02:46:31.692190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:31.692190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Brownian traveller on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","math.SP"],"primary_cat":"math.AP","authors_text":"David Krejcirik, Martin Kolb","submitted_at":"2011-08-16T09:48:19Z","abstract_excerpt":"We study the influence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the flat case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the flat case. The proof employs the existence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3191","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":"1108.3191","created_at":"2026-05-18T02:46:31.692277+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.3191v1","created_at":"2026-05-18T02:46:31.692277+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3191","created_at":"2026-05-18T02:46:31.692277+00:00"},{"alias_kind":"pith_short_12","alias_value":"WZSZME72LU5X","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"WZSZME72LU5XJAYH","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"WZSZME72","created_at":"2026-05-18T12:26:44.992195+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/WZSZME72LU5XJAYHYOUDRJ5MWN","json":"https://pith.science/pith/WZSZME72LU5XJAYHYOUDRJ5MWN.json","graph_json":"https://pith.science/api/pith-number/WZSZME72LU5XJAYHYOUDRJ5MWN/graph.json","events_json":"https://pith.science/api/pith-number/WZSZME72LU5XJAYHYOUDRJ5MWN/events.json","paper":"https://pith.science/paper/WZSZME72"},"agent_actions":{"view_html":"https://pith.science/pith/WZSZME72LU5XJAYHYOUDRJ5MWN","download_json":"https://pith.science/pith/WZSZME72LU5XJAYHYOUDRJ5MWN.json","view_paper":"https://pith.science/paper/WZSZME72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.3191&json=true","fetch_graph":"https://pith.science/api/pith-number/WZSZME72LU5XJAYHYOUDRJ5MWN/graph.json","fetch_events":"https://pith.science/api/pith-number/WZSZME72LU5XJAYHYOUDRJ5MWN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WZSZME72LU5XJAYHYOUDRJ5MWN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WZSZME72LU5XJAYHYOUDRJ5MWN/action/storage_attestation","attest_author":"https://pith.science/pith/WZSZME72LU5XJAYHYOUDRJ5MWN/action/author_attestation","sign_citation":"https://pith.science/pith/WZSZME72LU5XJAYHYOUDRJ5MWN/action/citation_signature","submit_replication":"https://pith.science/pith/WZSZME72LU5XJAYHYOUDRJ5MWN/action/replication_record"}},"created_at":"2026-05-18T02:46:31.692277+00:00","updated_at":"2026-05-18T02:46:31.692277+00:00"}