{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GNR6OEJLXR5GLE3RIQEXDX5S3W","short_pith_number":"pith:GNR6OEJL","canonical_record":{"source":{"id":"1412.3975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-12T12:46:58Z","cross_cats_sorted":[],"title_canon_sha256":"454bffe1e3fa95c2104a377bc6a2c578a5f4fbf0b5500a5d18b2d9bf691c2036","abstract_canon_sha256":"2b7e6af06187de276a465c13ffd40a73af6bbf156d8696a8f857b3f77d05cc2a"},"schema_version":"1.0"},"canonical_sha256":"3363e7112bbc7a659371440971dfb2dd8f673e247755fc9da54cc7d14238ec8e","source":{"kind":"arxiv","id":"1412.3975","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3975","created_at":"2026-05-18T02:29:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3975v2","created_at":"2026-05-18T02:29:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3975","created_at":"2026-05-18T02:29:31Z"},{"alias_kind":"pith_short_12","alias_value":"GNR6OEJLXR5G","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GNR6OEJLXR5GLE3R","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GNR6OEJL","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GNR6OEJLXR5GLE3RIQEXDX5S3W","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-12T12:46:58Z","cross_cats_sorted":[],"title_canon_sha256":"454bffe1e3fa95c2104a377bc6a2c578a5f4fbf0b5500a5d18b2d9bf691c2036","abstract_canon_sha256":"2b7e6af06187de276a465c13ffd40a73af6bbf156d8696a8f857b3f77d05cc2a"},"schema_version":"1.0"},"canonical_sha256":"3363e7112bbc7a659371440971dfb2dd8f673e247755fc9da54cc7d14238ec8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:31.225326Z","signature_b64":"6uQ6+QfMXTTcFADeb0ZIBAp3akslVuIuPceEhJ0MjvauJkkv7eugW6up5o3Mv0jkcbbbSxeZJkKihVGNI54GCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3363e7112bbc7a659371440971dfb2dd8f673e247755fc9da54cc7d14238ec8e","last_reissued_at":"2026-05-18T02:29:31.224804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:31.224804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3975","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X0ykOP1OwWE2ffcVHsgG30T1wceCzwqlvPZ1TyRm788H1zGKveRL6XbEsogVnUkfAqvXwOgCzmoTh6OGluk/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:43:17.838642Z"},"content_sha256":"4d635ae8bc256f457e2cd9063a974fa31b8a3c0eda25c4be1ff92705363b3023","schema_version":"1.0","event_id":"sha256:4d635ae8bc256f457e2cd9063a974fa31b8a3c0eda25c4be1ff92705363b3023"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GNR6OEJLXR5GLE3RIQEXDX5S3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction and analysis of sticky reflected diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Martin Grothaus, Robert Vo{\\ss}hall","submitted_at":"2014-12-12T12:46:58Z","abstract_excerpt":"We give a Dirichlet form approach for the construction of distorted Brownian motion in a bounded domain $\\Omega$ of $\\mathbb{R}^d$, $d \\geq 1$, with boundary $\\Gamma$, where the behavior at the boundary is sticky. The construction covers the case of a static boundary behavior as well as the case of a diffusion on the hypersurface $\\Gamma$ (for $d \\geq 2)$. More precisely, we consider the state space $\\overline{\\Omega}=\\Omega \\stackrel{.}{\\cup} \\Gamma$, the process is a diffusion process inside $\\Omega$, the occupation time of the process on the boundary $\\Gamma$ is positive and the process may"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3975","kind":"arxiv","version":2},"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":"2026-05-18T02:29:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7fIT/zrMvebmgAGtDAqAQ7GVkZ3EyN15BIrNbe+hAqelrt8jrMism5rahZFJYTUFLdmXNbWcfZLqubKXUqguBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:43:17.838983Z"},"content_sha256":"a3139844963d7e1c480e41a0787f4c867053bd7be549eeef0a1f0c24858124cb","schema_version":"1.0","event_id":"sha256:a3139844963d7e1c480e41a0787f4c867053bd7be549eeef0a1f0c24858124cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GNR6OEJLXR5GLE3RIQEXDX5S3W/bundle.json","state_url":"https://pith.science/pith/GNR6OEJLXR5GLE3RIQEXDX5S3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GNR6OEJLXR5GLE3RIQEXDX5S3W/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":"2026-06-27T11:43:17Z","links":{"resolver":"https://pith.science/pith/GNR6OEJLXR5GLE3RIQEXDX5S3W","bundle":"https://pith.science/pith/GNR6OEJLXR5GLE3RIQEXDX5S3W/bundle.json","state":"https://pith.science/pith/GNR6OEJLXR5GLE3RIQEXDX5S3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GNR6OEJLXR5GLE3RIQEXDX5S3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GNR6OEJLXR5GLE3RIQEXDX5S3W","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":"2b7e6af06187de276a465c13ffd40a73af6bbf156d8696a8f857b3f77d05cc2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-12T12:46:58Z","title_canon_sha256":"454bffe1e3fa95c2104a377bc6a2c578a5f4fbf0b5500a5d18b2d9bf691c2036"},"schema_version":"1.0","source":{"id":"1412.3975","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3975","created_at":"2026-05-18T02:29:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3975v2","created_at":"2026-05-18T02:29:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3975","created_at":"2026-05-18T02:29:31Z"},{"alias_kind":"pith_short_12","alias_value":"GNR6OEJLXR5G","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GNR6OEJLXR5GLE3R","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GNR6OEJL","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:a3139844963d7e1c480e41a0787f4c867053bd7be549eeef0a1f0c24858124cb","target":"graph","created_at":"2026-05-18T02:29:31Z","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 give a Dirichlet form approach for the construction of distorted Brownian motion in a bounded domain $\\Omega$ of $\\mathbb{R}^d$, $d \\geq 1$, with boundary $\\Gamma$, where the behavior at the boundary is sticky. The construction covers the case of a static boundary behavior as well as the case of a diffusion on the hypersurface $\\Gamma$ (for $d \\geq 2)$. More precisely, we consider the state space $\\overline{\\Omega}=\\Omega \\stackrel{.}{\\cup} \\Gamma$, the process is a diffusion process inside $\\Omega$, the occupation time of the process on the boundary $\\Gamma$ is positive and the process may","authors_text":"Martin Grothaus, Robert Vo{\\ss}hall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-12T12:46:58Z","title":"Construction and analysis of sticky reflected diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3975","kind":"arxiv","version":2},"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":"sha256:4d635ae8bc256f457e2cd9063a974fa31b8a3c0eda25c4be1ff92705363b3023","target":"record","created_at":"2026-05-18T02:29:31Z","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":"2b7e6af06187de276a465c13ffd40a73af6bbf156d8696a8f857b3f77d05cc2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-12T12:46:58Z","title_canon_sha256":"454bffe1e3fa95c2104a377bc6a2c578a5f4fbf0b5500a5d18b2d9bf691c2036"},"schema_version":"1.0","source":{"id":"1412.3975","kind":"arxiv","version":2}},"canonical_sha256":"3363e7112bbc7a659371440971dfb2dd8f673e247755fc9da54cc7d14238ec8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3363e7112bbc7a659371440971dfb2dd8f673e247755fc9da54cc7d14238ec8e","first_computed_at":"2026-05-18T02:29:31.224804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:31.224804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6uQ6+QfMXTTcFADeb0ZIBAp3akslVuIuPceEhJ0MjvauJkkv7eugW6up5o3Mv0jkcbbbSxeZJkKihVGNI54GCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:31.225326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3975","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d635ae8bc256f457e2cd9063a974fa31b8a3c0eda25c4be1ff92705363b3023","sha256:a3139844963d7e1c480e41a0787f4c867053bd7be549eeef0a1f0c24858124cb"],"state_sha256":"219d7ba2c5464c7cb2d0bf9983bc6eff884cbd972dfe9010a7ef87487fbec577"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LdHJ4ZNAk53hDnIGaksVqawOWstMbC0ULKBF0UtU6LQBQa41VN0bHuZcqCEldPc7PFhc51t2ky+TT6Xcl24vAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T11:43:17.840971Z","bundle_sha256":"b4bccb93122992f642f2f5ad66edfd626e3aeef836288cf444400c18b9a9dd70"}}