{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:O65XC64XUN5EOTFKU5RLHGVLMT","short_pith_number":"pith:O65XC64X","canonical_record":{"source":{"id":"1105.2626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-13T07:21:27Z","cross_cats_sorted":["cond-mat.other","math-ph","math.AP","math.MP"],"title_canon_sha256":"7a089a344ba6e7e63372c813f8246177c07ac236a05a837fa355e8533dca097b","abstract_canon_sha256":"e956ce237124856a0f972e15d97f35d38c32f63db130bb45706f4c13ee0aad4e"},"schema_version":"1.0"},"canonical_sha256":"77bb717b97a37a474caaa762b39aab64d1c4340e1c0d2c6399ae23774d8337b0","source":{"kind":"arxiv","id":"1105.2626","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2626","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2626v1","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2626","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"O65XC64XUN5E","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O65XC64XUN5EOTFK","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O65XC64X","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:O65XC64XUN5EOTFKU5RLHGVLMT","target":"record","payload":{"canonical_record":{"source":{"id":"1105.2626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-13T07:21:27Z","cross_cats_sorted":["cond-mat.other","math-ph","math.AP","math.MP"],"title_canon_sha256":"7a089a344ba6e7e63372c813f8246177c07ac236a05a837fa355e8533dca097b","abstract_canon_sha256":"e956ce237124856a0f972e15d97f35d38c32f63db130bb45706f4c13ee0aad4e"},"schema_version":"1.0"},"canonical_sha256":"77bb717b97a37a474caaa762b39aab64d1c4340e1c0d2c6399ae23774d8337b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:33.274899Z","signature_b64":"KnS2CtQ9Oqvd8/NK7pTFAm0Calx4OG1HDpLP9Ezl1ge/wnjIfmFS2fZ13FxgqTAf1C3k0Sjjw59uYZNmcW89CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77bb717b97a37a474caaa762b39aab64d1c4340e1c0d2c6399ae23774d8337b0","last_reissued_at":"2026-05-18T04:19:33.274422Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:33.274422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.2626","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:19:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9E0nS10K25ZV74gFVxxmb0Xf0DCOKfpvFcppj2AUHR/5yL//G4yIQZU+YDXBK/qkq9jBXBYdXCNjbDFNoEckBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:20:04.911235Z"},"content_sha256":"05e69e116f7f4ab6832f89b0f4a8428a7c6bcb8da939ffc46e545c5fe15e7733","schema_version":"1.0","event_id":"sha256:05e69e116f7f4ab6832f89b0f4a8428a7c6bcb8da939ffc46e545c5fe15e7733"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:O65XC64XUN5EOTFKU5RLHGVLMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Survival probability (heat content) and the lowest eigenvalue of Dirichlet Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"I. Travenec, L. Samaj, P. Kalinay","submitted_at":"2011-05-13T07:21:27Z","abstract_excerpt":"We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary \"star-shaped\" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2626","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:19:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPVEbQ6hCmfrEZRO3H1VFP4EvsjKWDvqLoQwVeHTpvMVunIY70+PNRFF6NCTDzJcEYgXaPMO5CH3ch/Gn8jqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:20:04.912019Z"},"content_sha256":"b4f04ef0f212d1ac2342d809f2e433fc47a620fe78c4cb8d4a91c3fef71dd558","schema_version":"1.0","event_id":"sha256:b4f04ef0f212d1ac2342d809f2e433fc47a620fe78c4cb8d4a91c3fef71dd558"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O65XC64XUN5EOTFKU5RLHGVLMT/bundle.json","state_url":"https://pith.science/pith/O65XC64XUN5EOTFKU5RLHGVLMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O65XC64XUN5EOTFKU5RLHGVLMT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T18:20:04Z","links":{"resolver":"https://pith.science/pith/O65XC64XUN5EOTFKU5RLHGVLMT","bundle":"https://pith.science/pith/O65XC64XUN5EOTFKU5RLHGVLMT/bundle.json","state":"https://pith.science/pith/O65XC64XUN5EOTFKU5RLHGVLMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O65XC64XUN5EOTFKU5RLHGVLMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:O65XC64XUN5EOTFKU5RLHGVLMT","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":"e956ce237124856a0f972e15d97f35d38c32f63db130bb45706f4c13ee0aad4e","cross_cats_sorted":["cond-mat.other","math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-13T07:21:27Z","title_canon_sha256":"7a089a344ba6e7e63372c813f8246177c07ac236a05a837fa355e8533dca097b"},"schema_version":"1.0","source":{"id":"1105.2626","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2626","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2626v1","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2626","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"O65XC64XUN5E","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O65XC64XUN5EOTFK","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O65XC64X","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:b4f04ef0f212d1ac2342d809f2e433fc47a620fe78c4cb8d4a91c3fef71dd558","target":"graph","created_at":"2026-05-18T04:19:33Z","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"},"paper":{"abstract_excerpt":"We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary \"star-shaped\" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this ex","authors_text":"I. Travenec, L. Samaj, P. Kalinay","cross_cats":["cond-mat.other","math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-13T07:21:27Z","title":"Survival probability (heat content) and the lowest eigenvalue of Dirichlet Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2626","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":"sha256:05e69e116f7f4ab6832f89b0f4a8428a7c6bcb8da939ffc46e545c5fe15e7733","target":"record","created_at":"2026-05-18T04:19:33Z","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":"e956ce237124856a0f972e15d97f35d38c32f63db130bb45706f4c13ee0aad4e","cross_cats_sorted":["cond-mat.other","math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-13T07:21:27Z","title_canon_sha256":"7a089a344ba6e7e63372c813f8246177c07ac236a05a837fa355e8533dca097b"},"schema_version":"1.0","source":{"id":"1105.2626","kind":"arxiv","version":1}},"canonical_sha256":"77bb717b97a37a474caaa762b39aab64d1c4340e1c0d2c6399ae23774d8337b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77bb717b97a37a474caaa762b39aab64d1c4340e1c0d2c6399ae23774d8337b0","first_computed_at":"2026-05-18T04:19:33.274422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:33.274422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KnS2CtQ9Oqvd8/NK7pTFAm0Calx4OG1HDpLP9Ezl1ge/wnjIfmFS2fZ13FxgqTAf1C3k0Sjjw59uYZNmcW89CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:33.274899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2626","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05e69e116f7f4ab6832f89b0f4a8428a7c6bcb8da939ffc46e545c5fe15e7733","sha256:b4f04ef0f212d1ac2342d809f2e433fc47a620fe78c4cb8d4a91c3fef71dd558"],"state_sha256":"98ba05414ac31ce1e99445074fab3fa51dc3ffabb825fcca9a5bcc5a92dd1b07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"56ydGON/ypefuFMzg5zmPcRiXu3CO6g9jrKbhdpBLfnPERd8ELvbwTtgkcJppG+aiJvNlyEp5AX325Lb+uDpBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:20:04.915704Z","bundle_sha256":"399d8f5babb0616df8d11f1e83eec789a886b2306039fb8619a26dea410b2e18"}}