{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WTCBZEN6JPARBTINUJQ2NF5EGK","short_pith_number":"pith:WTCBZEN6","canonical_record":{"source":{"id":"1405.0372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-02T10:26:28Z","cross_cats_sorted":[],"title_canon_sha256":"c21627baf2cb48b44beab6e0b116b2f1c671da80c260a26952bf6651c8b912c0","abstract_canon_sha256":"4b6a7c66dcf1fd461236083a58dfbafde22d1a5b932dfed6a9d2b1d55a76bfde"},"schema_version":"1.0"},"canonical_sha256":"b4c41c91be4bc110cd0da261a697a432b4579d58a3c6d677dd680e7d20392478","source":{"kind":"arxiv","id":"1405.0372","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0372","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0372v1","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0372","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"pith_short_12","alias_value":"WTCBZEN6JPAR","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WTCBZEN6JPARBTIN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WTCBZEN6","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WTCBZEN6JPARBTINUJQ2NF5EGK","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-02T10:26:28Z","cross_cats_sorted":[],"title_canon_sha256":"c21627baf2cb48b44beab6e0b116b2f1c671da80c260a26952bf6651c8b912c0","abstract_canon_sha256":"4b6a7c66dcf1fd461236083a58dfbafde22d1a5b932dfed6a9d2b1d55a76bfde"},"schema_version":"1.0"},"canonical_sha256":"b4c41c91be4bc110cd0da261a697a432b4579d58a3c6d677dd680e7d20392478","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:48.106760Z","signature_b64":"p4gL8qdrK7lK3xR2MNFwfSS31d8maBhdYbzVFZdajL5OcvNtx6uzt/FP+ONYvLRDnXV0evwjVENR8WX66PTXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4c41c91be4bc110cd0da261a697a432b4579d58a3c6d677dd680e7d20392478","last_reissued_at":"2026-05-18T02:52:48.106341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:48.106341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0372","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":"2026-05-18T02:52:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GSpgeKbujVv/BCqXRDWKATODwuXmjRdv2Vo213mIM85foaKK9aGE+OuKHk5TXzeT2u8Cmg6Ti/xprsN/tHJUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:48:58.386621Z"},"content_sha256":"1152409b885b35f74eccc46ddf177b958a4062eff1a2a45e857ad275a12072a8","schema_version":"1.0","event_id":"sha256:1152409b885b35f74eccc46ddf177b958a4062eff1a2a45e857ad275a12072a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WTCBZEN6JPARBTINUJQ2NF5EGK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of a Feller semigroup with atomic measure in nonlocal boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pavel Gurevich","submitted_at":"2014-05-02T10:26:28Z","abstract_excerpt":"The existence of Feller semigroups arising in the theory of multidimensional diffusion processes is studied. An elliptic operator of second order is considered on a plane bounded region $G$. Its domain of definition consists of continuous functions satisfying a nonlocal condition on the boundary of the region. In general, the nonlocal term is an integral of a function over the closure of the region $G$ with respect to a nonnegative Borel measure $\\mu(y,d\\eta)$, $y\\in\\partial G$. It is proved that the operator is a generator of a Feller semigroup in the case where the measure is atomic. The sma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0372","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":"2026-05-18T02:52:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qk+/fbI1KtiDkyXSD1KzxnvceiF8KVRQpSse/8o6NdCXe0+eZukuyA0mCtqkCXfLNKm8y6zYag52hpf5RqomCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:48:58.387304Z"},"content_sha256":"4c1a27348a77bf56150d3e5f7f4092504a0ed44729ef1a642daab9c668cb5534","schema_version":"1.0","event_id":"sha256:4c1a27348a77bf56150d3e5f7f4092504a0ed44729ef1a642daab9c668cb5534"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTCBZEN6JPARBTINUJQ2NF5EGK/bundle.json","state_url":"https://pith.science/pith/WTCBZEN6JPARBTINUJQ2NF5EGK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTCBZEN6JPARBTINUJQ2NF5EGK/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":"2026-06-06T22:48:58Z","links":{"resolver":"https://pith.science/pith/WTCBZEN6JPARBTINUJQ2NF5EGK","bundle":"https://pith.science/pith/WTCBZEN6JPARBTINUJQ2NF5EGK/bundle.json","state":"https://pith.science/pith/WTCBZEN6JPARBTINUJQ2NF5EGK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTCBZEN6JPARBTINUJQ2NF5EGK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WTCBZEN6JPARBTINUJQ2NF5EGK","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":"4b6a7c66dcf1fd461236083a58dfbafde22d1a5b932dfed6a9d2b1d55a76bfde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-02T10:26:28Z","title_canon_sha256":"c21627baf2cb48b44beab6e0b116b2f1c671da80c260a26952bf6651c8b912c0"},"schema_version":"1.0","source":{"id":"1405.0372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0372","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0372v1","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0372","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"pith_short_12","alias_value":"WTCBZEN6JPAR","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WTCBZEN6JPARBTIN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WTCBZEN6","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:4c1a27348a77bf56150d3e5f7f4092504a0ed44729ef1a642daab9c668cb5534","target":"graph","created_at":"2026-05-18T02:52:48Z","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":"The existence of Feller semigroups arising in the theory of multidimensional diffusion processes is studied. An elliptic operator of second order is considered on a plane bounded region $G$. Its domain of definition consists of continuous functions satisfying a nonlocal condition on the boundary of the region. In general, the nonlocal term is an integral of a function over the closure of the region $G$ with respect to a nonnegative Borel measure $\\mu(y,d\\eta)$, $y\\in\\partial G$. It is proved that the operator is a generator of a Feller semigroup in the case where the measure is atomic. The sma","authors_text":"Pavel Gurevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-02T10:26:28Z","title":"On the existence of a Feller semigroup with atomic measure in nonlocal boundary condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0372","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":"sha256:1152409b885b35f74eccc46ddf177b958a4062eff1a2a45e857ad275a12072a8","target":"record","created_at":"2026-05-18T02:52:48Z","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":"4b6a7c66dcf1fd461236083a58dfbafde22d1a5b932dfed6a9d2b1d55a76bfde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-02T10:26:28Z","title_canon_sha256":"c21627baf2cb48b44beab6e0b116b2f1c671da80c260a26952bf6651c8b912c0"},"schema_version":"1.0","source":{"id":"1405.0372","kind":"arxiv","version":1}},"canonical_sha256":"b4c41c91be4bc110cd0da261a697a432b4579d58a3c6d677dd680e7d20392478","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4c41c91be4bc110cd0da261a697a432b4579d58a3c6d677dd680e7d20392478","first_computed_at":"2026-05-18T02:52:48.106341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:48.106341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p4gL8qdrK7lK3xR2MNFwfSS31d8maBhdYbzVFZdajL5OcvNtx6uzt/FP+ONYvLRDnXV0evwjVENR8WX66PTXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:48.106760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1152409b885b35f74eccc46ddf177b958a4062eff1a2a45e857ad275a12072a8","sha256:4c1a27348a77bf56150d3e5f7f4092504a0ed44729ef1a642daab9c668cb5534"],"state_sha256":"02ce3bcdd3f27a8a834612afeac7fe853d90d0967cb773f56024244b8fa033b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f0up8JJv18u42Sg5Z9irRBTPlcVDAmBlc65TnwFOYOcbjBmGPkX/mgB8mYheGNN+YTa/VrMwLgsKDL2qRAZhCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:48:58.391002Z","bundle_sha256":"71ea48b08474b69598d64f4d7cb2aadc482a7e34d95a3152b9284446fb574f38"}}