{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YLEWXUMLOSV4ALQ6QAIFBFJL2Q","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":"a177f6c469508e1879e70a5011d5f3aa0587160d8a18f489538a8efb7337fb84","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-12T10:10:57Z","title_canon_sha256":"5c408868b31a54b2210b636dd7a692819e1a6a921e43b231a9aec67ed063ac4d"},"schema_version":"1.0","source":{"id":"1709.03772","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03772","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03772v1","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03772","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"pith_short_12","alias_value":"YLEWXUMLOSV4","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YLEWXUMLOSV4ALQ6","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YLEWXUML","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:f1eed72f848d1a41c34652b511527097c517ac9d4cfcf6231bd4239015ba288d","target":"graph","created_at":"2026-05-18T00:35:29Z","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":"In this short note we outline a simple probabilistic proof of the Gauss-Bonnet formula for compact Riemannian manifolds with boundary, which adapts to this setting an argument due to Hsu \\cite{Hs1,Hs2} in the closed case. The new technical ingredient is the Feynman-Kac formula for differential forms satisfying absolute boundary conditions proved in \\cite{dL}. Combined with the so-called supersymmetric aproach to index theory, this leads to a path integral representation of the Euler characteristic of the manifold in terms of normally reflected Brownian motion whose short time asymptotics clari","authors_text":"Levi Lopes de Lima","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-12T10:10:57Z","title":"A probabilistic proof of the Gauss-Bonnet formula for manifolds with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03772","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":"sha256:21439072fdd5018932c9449fbfadb8a80b6e11d1c386817d3d585803ebe71056","target":"record","created_at":"2026-05-18T00:35:29Z","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":"a177f6c469508e1879e70a5011d5f3aa0587160d8a18f489538a8efb7337fb84","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-12T10:10:57Z","title_canon_sha256":"5c408868b31a54b2210b636dd7a692819e1a6a921e43b231a9aec67ed063ac4d"},"schema_version":"1.0","source":{"id":"1709.03772","kind":"arxiv","version":1}},"canonical_sha256":"c2c96bd18b74abc02e1e801050952bd40002616be2efd5546141d65cc9c19fd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2c96bd18b74abc02e1e801050952bd40002616be2efd5546141d65cc9c19fd0","first_computed_at":"2026-05-18T00:35:29.522467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:29.522467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qPtRs/i1PfBIsZMk2sMp2mBrKPkSPZhCKD06LDfdHueTGF5/VmoWFkEJMPStlbTgenLPzagREl5Pvbf9MYRMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:29.523016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03772","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21439072fdd5018932c9449fbfadb8a80b6e11d1c386817d3d585803ebe71056","sha256:f1eed72f848d1a41c34652b511527097c517ac9d4cfcf6231bd4239015ba288d"],"state_sha256":"3ef6bfbc5af1f1fa8dc8a93f1c1d47f8fc5740e6c1f1776782df4d760253fe25"}