{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RHJ5ABFTHRHP5TD2YTEOKFBTDF","short_pith_number":"pith:RHJ5ABFT","canonical_record":{"source":{"id":"1709.08379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-25T08:54:08Z","cross_cats_sorted":[],"title_canon_sha256":"285dfe9d94a17556e005e66a18f037bb2d5bf165be4ea65b528e43cf4e77c2b5","abstract_canon_sha256":"4a15d033406bc6703ae281d2a19696886a8ef007e403d8c1ee19cd298b2b863a"},"schema_version":"1.0"},"canonical_sha256":"89d3d004b33c4efecc7ac4c8e5143319578b2c59efcdcdf21b810b606b7b3472","source":{"kind":"arxiv","id":"1709.08379","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08379","created_at":"2026-05-17T23:59:39Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08379v3","created_at":"2026-05-17T23:59:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08379","created_at":"2026-05-17T23:59:39Z"},{"alias_kind":"pith_short_12","alias_value":"RHJ5ABFTHRHP","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RHJ5ABFTHRHP5TD2","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RHJ5ABFT","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RHJ5ABFTHRHP5TD2YTEOKFBTDF","target":"record","payload":{"canonical_record":{"source":{"id":"1709.08379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-25T08:54:08Z","cross_cats_sorted":[],"title_canon_sha256":"285dfe9d94a17556e005e66a18f037bb2d5bf165be4ea65b528e43cf4e77c2b5","abstract_canon_sha256":"4a15d033406bc6703ae281d2a19696886a8ef007e403d8c1ee19cd298b2b863a"},"schema_version":"1.0"},"canonical_sha256":"89d3d004b33c4efecc7ac4c8e5143319578b2c59efcdcdf21b810b606b7b3472","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:39.523970Z","signature_b64":"Rq45d8IJ3txpJJVzymD6DgWaiEGBoszeGvvWTf385bS3u4DBFcWkG2mD9lSVo53Z9mx8A7M/Ln9GEQacNoZxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89d3d004b33c4efecc7ac4c8e5143319578b2c59efcdcdf21b810b606b7b3472","last_reissued_at":"2026-05-17T23:59:39.523286Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:39.523286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.08379","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iNrO2N80q+IVMBkcLc9xHQ70TpQdfIshAFBpFEzQOVHVlCI9o+gvzo8Doymq9m5eMzZXKNVzcZum7Jb8tYWYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:37:56.646594Z"},"content_sha256":"89b40c150153f982b2c4e34685458f26b6917c2508edef5f61e9dab4a8ebb7b0","schema_version":"1.0","event_id":"sha256:89b40c150153f982b2c4e34685458f26b6917c2508edef5f61e9dab4a8ebb7b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RHJ5ABFTHRHP5TD2YTEOKFBTDF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Dirichlet form of three-dimensional Brownian motion conditioned to hit the origin","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Liping Li, Patrick J. Fitzsimmons","submitted_at":"2017-09-25T08:54:08Z","abstract_excerpt":"Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to $C_c^\\infty(\\mathbf{R}^3\\setminus \\{0\\})$. We will prove that this energy form is a regular Dirichlet form with core $C_c^\\infty(\\mathbf{R}^3)$. The associated diffusion $X$ behaves like a $3$-dimensional Brownian motion with a mild radial drift when far from $0$, subject to an ever-stronger push toward $0$ near that point. In particular $\\{0\\}$ is not a polar set with respect to $X$. The diffusion $X$ is rotation invariant, and admits a skew-produc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08379","kind":"arxiv","version":3},"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":"2026-05-17T23:59:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rzARf+GHVOwjg9a8QC1FB/Fj0fT+SXyd9qMYOAh/NUeJBozpFGYEyy6v86siP0S48MFTsFd46Zrhbv00B0oVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:37:56.647129Z"},"content_sha256":"593703606f3c006b3427fa81fee5c1c0c02af9f55c9ee176c2049f0e916c1fc0","schema_version":"1.0","event_id":"sha256:593703606f3c006b3427fa81fee5c1c0c02af9f55c9ee176c2049f0e916c1fc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHJ5ABFTHRHP5TD2YTEOKFBTDF/bundle.json","state_url":"https://pith.science/pith/RHJ5ABFTHRHP5TD2YTEOKFBTDF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHJ5ABFTHRHP5TD2YTEOKFBTDF/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":"2026-05-25T12:37:56Z","links":{"resolver":"https://pith.science/pith/RHJ5ABFTHRHP5TD2YTEOKFBTDF","bundle":"https://pith.science/pith/RHJ5ABFTHRHP5TD2YTEOKFBTDF/bundle.json","state":"https://pith.science/pith/RHJ5ABFTHRHP5TD2YTEOKFBTDF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHJ5ABFTHRHP5TD2YTEOKFBTDF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RHJ5ABFTHRHP5TD2YTEOKFBTDF","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":"4a15d033406bc6703ae281d2a19696886a8ef007e403d8c1ee19cd298b2b863a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-25T08:54:08Z","title_canon_sha256":"285dfe9d94a17556e005e66a18f037bb2d5bf165be4ea65b528e43cf4e77c2b5"},"schema_version":"1.0","source":{"id":"1709.08379","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08379","created_at":"2026-05-17T23:59:39Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08379v3","created_at":"2026-05-17T23:59:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08379","created_at":"2026-05-17T23:59:39Z"},{"alias_kind":"pith_short_12","alias_value":"RHJ5ABFTHRHP","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RHJ5ABFTHRHP5TD2","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RHJ5ABFT","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:593703606f3c006b3427fa81fee5c1c0c02af9f55c9ee176c2049f0e916c1fc0","target":"graph","created_at":"2026-05-17T23:59:39Z","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":"Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to $C_c^\\infty(\\mathbf{R}^3\\setminus \\{0\\})$. We will prove that this energy form is a regular Dirichlet form with core $C_c^\\infty(\\mathbf{R}^3)$. The associated diffusion $X$ behaves like a $3$-dimensional Brownian motion with a mild radial drift when far from $0$, subject to an ever-stronger push toward $0$ near that point. In particular $\\{0\\}$ is not a polar set with respect to $X$. The diffusion $X$ is rotation invariant, and admits a skew-produc","authors_text":"Liping Li, Patrick J. Fitzsimmons","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-25T08:54:08Z","title":"On the Dirichlet form of three-dimensional Brownian motion conditioned to hit the origin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08379","kind":"arxiv","version":3},"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":"sha256:89b40c150153f982b2c4e34685458f26b6917c2508edef5f61e9dab4a8ebb7b0","target":"record","created_at":"2026-05-17T23:59:39Z","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":"4a15d033406bc6703ae281d2a19696886a8ef007e403d8c1ee19cd298b2b863a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-25T08:54:08Z","title_canon_sha256":"285dfe9d94a17556e005e66a18f037bb2d5bf165be4ea65b528e43cf4e77c2b5"},"schema_version":"1.0","source":{"id":"1709.08379","kind":"arxiv","version":3}},"canonical_sha256":"89d3d004b33c4efecc7ac4c8e5143319578b2c59efcdcdf21b810b606b7b3472","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89d3d004b33c4efecc7ac4c8e5143319578b2c59efcdcdf21b810b606b7b3472","first_computed_at":"2026-05-17T23:59:39.523286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:39.523286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rq45d8IJ3txpJJVzymD6DgWaiEGBoszeGvvWTf385bS3u4DBFcWkG2mD9lSVo53Z9mx8A7M/Ln9GEQacNoZxBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:39.523970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08379","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89b40c150153f982b2c4e34685458f26b6917c2508edef5f61e9dab4a8ebb7b0","sha256:593703606f3c006b3427fa81fee5c1c0c02af9f55c9ee176c2049f0e916c1fc0"],"state_sha256":"d9fa8203736161c3e7930086f2b348e30dd0e39f5ba3d8b0619520dee6dc2f52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5bcU6hUqeDZ4Bxys1vTjQpLT7jPcY5QZyZPNQgEGBtFwLwa/uXaqPPk0V8cgpPIb3j2EjDUvGvl0V2c6lQ7JBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:37:56.650379Z","bundle_sha256":"6b6405c82d4a21f40512f732dc60cc1051f8fb796eace0fd06f50426a2a79eaa"}}