{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TRR5ZJBO32VWLDVGIOAO3NHBEP","short_pith_number":"pith:TRR5ZJBO","canonical_record":{"source":{"id":"1601.01281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-06T19:17:01Z","cross_cats_sorted":[],"title_canon_sha256":"4cfad988da4d75de5feb7ceaf745578ccabd74c81e70b0723786f1f88cdf33a6","abstract_canon_sha256":"adf7c02fd83177c1f9201a7fe4bc85a7e6659ec7b7da25a49bbc027b9aee323b"},"schema_version":"1.0"},"canonical_sha256":"9c63dca42edeab658ea64380edb4e123c1f65e32c9024a1e23c6d55de08d6132","source":{"kind":"arxiv","id":"1601.01281","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01281","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01281v2","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01281","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"TRR5ZJBO32VW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TRR5ZJBO32VWLDVG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TRR5ZJBO","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TRR5ZJBO32VWLDVGIOAO3NHBEP","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-06T19:17:01Z","cross_cats_sorted":[],"title_canon_sha256":"4cfad988da4d75de5feb7ceaf745578ccabd74c81e70b0723786f1f88cdf33a6","abstract_canon_sha256":"adf7c02fd83177c1f9201a7fe4bc85a7e6659ec7b7da25a49bbc027b9aee323b"},"schema_version":"1.0"},"canonical_sha256":"9c63dca42edeab658ea64380edb4e123c1f65e32c9024a1e23c6d55de08d6132","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:23.974147Z","signature_b64":"BpMmfF2x6iZisjjfktuYZmEhgacff3HmuezmjuTZMcdEZsXN6AqbU6Qg8fiPuAIbqQ1y4qcamzPgklAQ+eN/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c63dca42edeab658ea64380edb4e123c1f65e32c9024a1e23c6d55de08d6132","last_reissued_at":"2026-05-18T01:20:23.973652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:23.973652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01281","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":"2026-05-18T01:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jA4oKlzAN7f8+lfsaFiYtS+LvbeqUH+2bTgSpojGWGK4go7VHGjohCI5qooFD7jiCJGwn6X25W/q1QhoTvj1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:04:21.721455Z"},"content_sha256":"04caa945a807c809edea2df51d159ec3a211984a0887089dc4a258fa645bb6ba","schema_version":"1.0","event_id":"sha256:04caa945a807c809edea2df51d159ec3a211984a0887089dc4a258fa645bb6ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TRR5ZJBO32VWLDVGIOAO3NHBEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absolute Continuity of the Laws of the Solutions to Parabolic SPDEs with Two Reflecting Walls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Wen Yue","submitted_at":"2016-01-06T19:17:01Z","abstract_excerpt":"In this paper, we focus on the existence of the density for the law of the solutions to parabolic stochastic partial differential equations with two reflecting walls. The main tool is Malliavin calculus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01281","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":"2026-05-18T01:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4OqFLHggyvTzOdw4lT+aAUKkA+eIvGAlZLRz9A3CyvXKcDjYY3NObfwx7WwDsmS5wxDNsPZB+fDX3fhnB+ZKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:04:21.721807Z"},"content_sha256":"62f65904d9b0500a8ff49425d72dbfe9ec5c86df38665329e1fdceb3accc6b9f","schema_version":"1.0","event_id":"sha256:62f65904d9b0500a8ff49425d72dbfe9ec5c86df38665329e1fdceb3accc6b9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRR5ZJBO32VWLDVGIOAO3NHBEP/bundle.json","state_url":"https://pith.science/pith/TRR5ZJBO32VWLDVGIOAO3NHBEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRR5ZJBO32VWLDVGIOAO3NHBEP/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":"2026-06-05T14:04:21Z","links":{"resolver":"https://pith.science/pith/TRR5ZJBO32VWLDVGIOAO3NHBEP","bundle":"https://pith.science/pith/TRR5ZJBO32VWLDVGIOAO3NHBEP/bundle.json","state":"https://pith.science/pith/TRR5ZJBO32VWLDVGIOAO3NHBEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRR5ZJBO32VWLDVGIOAO3NHBEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TRR5ZJBO32VWLDVGIOAO3NHBEP","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":"adf7c02fd83177c1f9201a7fe4bc85a7e6659ec7b7da25a49bbc027b9aee323b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-06T19:17:01Z","title_canon_sha256":"4cfad988da4d75de5feb7ceaf745578ccabd74c81e70b0723786f1f88cdf33a6"},"schema_version":"1.0","source":{"id":"1601.01281","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01281","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01281v2","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01281","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"TRR5ZJBO32VW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TRR5ZJBO32VWLDVG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TRR5ZJBO","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:62f65904d9b0500a8ff49425d72dbfe9ec5c86df38665329e1fdceb3accc6b9f","target":"graph","created_at":"2026-05-18T01:20:23Z","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 paper, we focus on the existence of the density for the law of the solutions to parabolic stochastic partial differential equations with two reflecting walls. The main tool is Malliavin calculus.","authors_text":"Wen Yue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-06T19:17:01Z","title":"Absolute Continuity of the Laws of the Solutions to Parabolic SPDEs with Two Reflecting Walls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01281","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":"sha256:04caa945a807c809edea2df51d159ec3a211984a0887089dc4a258fa645bb6ba","target":"record","created_at":"2026-05-18T01:20:23Z","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":"adf7c02fd83177c1f9201a7fe4bc85a7e6659ec7b7da25a49bbc027b9aee323b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-06T19:17:01Z","title_canon_sha256":"4cfad988da4d75de5feb7ceaf745578ccabd74c81e70b0723786f1f88cdf33a6"},"schema_version":"1.0","source":{"id":"1601.01281","kind":"arxiv","version":2}},"canonical_sha256":"9c63dca42edeab658ea64380edb4e123c1f65e32c9024a1e23c6d55de08d6132","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c63dca42edeab658ea64380edb4e123c1f65e32c9024a1e23c6d55de08d6132","first_computed_at":"2026-05-18T01:20:23.973652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:23.973652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BpMmfF2x6iZisjjfktuYZmEhgacff3HmuezmjuTZMcdEZsXN6AqbU6Qg8fiPuAIbqQ1y4qcamzPgklAQ+eN/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:23.974147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01281","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04caa945a807c809edea2df51d159ec3a211984a0887089dc4a258fa645bb6ba","sha256:62f65904d9b0500a8ff49425d72dbfe9ec5c86df38665329e1fdceb3accc6b9f"],"state_sha256":"85507c12b47b7302f86dae0f759e3a9d77135927b43a20685f037076e1040922"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bC3VR69Oz1qT92XwwAGlsfzZYDOn4qsZn29awbQ8QOCEKMp2yxL5+yHlk40lm0mkIykZFiLlfhWtNiLQPKDaCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:04:21.723951Z","bundle_sha256":"ebb40f4affec489504ac44fc44cce2ac03f295cd61544abb2810e309693cc375"}}