{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LJJFCQXKPKCFGLWNU3A4MDHBVH","short_pith_number":"pith:LJJFCQXK","canonical_record":{"source":{"id":"1603.07927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-25T14:40:14Z","cross_cats_sorted":["math-ph","math.MP","q-bio.MN"],"title_canon_sha256":"db65a5a52b5a90837158737abe2ef5ffd52eaaedafe29a67963e2bf3c11b65f8","abstract_canon_sha256":"787bce834b2b8827adfa0328520b47486f9388d36bf39f1bcb635677d8331c45"},"schema_version":"1.0"},"canonical_sha256":"5a525142ea7a84532ecda6c1c60ce1a9ea0fc3ed970aa883a027d97f82cf3c83","source":{"kind":"arxiv","id":"1603.07927","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07927","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07927v1","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07927","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"LJJFCQXKPKCF","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LJJFCQXKPKCFGLWN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LJJFCQXK","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LJJFCQXKPKCFGLWNU3A4MDHBVH","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-25T14:40:14Z","cross_cats_sorted":["math-ph","math.MP","q-bio.MN"],"title_canon_sha256":"db65a5a52b5a90837158737abe2ef5ffd52eaaedafe29a67963e2bf3c11b65f8","abstract_canon_sha256":"787bce834b2b8827adfa0328520b47486f9388d36bf39f1bcb635677d8331c45"},"schema_version":"1.0"},"canonical_sha256":"5a525142ea7a84532ecda6c1c60ce1a9ea0fc3ed970aa883a027d97f82cf3c83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:15.853544Z","signature_b64":"TPkmRwyhC6ggJQVcXd6AjEpeNFXnVbA/4RWGZn7V/B2xRwpfLV6k5BUwEcC32ORGDxiB4tUQLvhftpZoTF0iAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a525142ea7a84532ecda6c1c60ce1a9ea0fc3ed970aa883a027d97f82cf3c83","last_reissued_at":"2026-05-18T01:18:15.852843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:15.852843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07927","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":"2026-05-18T01:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlcBELixgTLAafsdrT0+yLUp5oTYTxOblijcJKftueBoUGSRDW9w9GKSiFvLNpubCEdjA/fRxlBaD1QkzcDMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:21:39.354888Z"},"content_sha256":"ccfda68d01f82aeb53814a6238f9948defaf7781ddd593a86d2e3a13d7e06888","schema_version":"1.0","event_id":"sha256:ccfda68d01f82aeb53814a6238f9948defaf7781ddd593a86d2e3a13d7e06888"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LJJFCQXKPKCFGLWNU3A4MDHBVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Uniqueness of \"SDE Decomposition\" in A-type Stochastic Integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","q-bio.MN"],"primary_cat":"cond-mat.stat-mech","authors_text":"Ping Ao, Ruoshi Yuan, Ying Tang","submitted_at":"2016-03-25T14:40:14Z","abstract_excerpt":"An innovative theoretical framework for stochastic dynamics based on a decomposition of a stochastic differential equation (SDE) has been developed with an evident advantage in connecting deterministic and stochastic dynamics, as well as useful applications in physics, engineering, chemistry and biology. It introduces the A-type stochastic integration for SDE beyond traditional Ito's or Stratonovich's interpretation. Serious question on its uniqueness was recently raised. We provide here both mathematical and physical demonstrations that the uniqueness is guaranteed. Such discussion leads to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07927","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":"2026-05-18T01:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sfXV2Gp41GFustOEjmWxN8jmdRtqQFY21JJE1Sk5fk+s4KTYPcTDF64MNy5/hH3wu1+sdjKmcC7L+Yo0cXj+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:21:39.355589Z"},"content_sha256":"e61a5ac9b78fde6787471255d0d8de6df8281ee969b1b310834e2c327990b83e","schema_version":"1.0","event_id":"sha256:e61a5ac9b78fde6787471255d0d8de6df8281ee969b1b310834e2c327990b83e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJJFCQXKPKCFGLWNU3A4MDHBVH/bundle.json","state_url":"https://pith.science/pith/LJJFCQXKPKCFGLWNU3A4MDHBVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJJFCQXKPKCFGLWNU3A4MDHBVH/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":"2026-06-11T17:21:39Z","links":{"resolver":"https://pith.science/pith/LJJFCQXKPKCFGLWNU3A4MDHBVH","bundle":"https://pith.science/pith/LJJFCQXKPKCFGLWNU3A4MDHBVH/bundle.json","state":"https://pith.science/pith/LJJFCQXKPKCFGLWNU3A4MDHBVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJJFCQXKPKCFGLWNU3A4MDHBVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LJJFCQXKPKCFGLWNU3A4MDHBVH","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":"787bce834b2b8827adfa0328520b47486f9388d36bf39f1bcb635677d8331c45","cross_cats_sorted":["math-ph","math.MP","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-25T14:40:14Z","title_canon_sha256":"db65a5a52b5a90837158737abe2ef5ffd52eaaedafe29a67963e2bf3c11b65f8"},"schema_version":"1.0","source":{"id":"1603.07927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07927","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07927v1","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07927","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"LJJFCQXKPKCF","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LJJFCQXKPKCFGLWN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LJJFCQXK","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:e61a5ac9b78fde6787471255d0d8de6df8281ee969b1b310834e2c327990b83e","target":"graph","created_at":"2026-05-18T01:18:15Z","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":"An innovative theoretical framework for stochastic dynamics based on a decomposition of a stochastic differential equation (SDE) has been developed with an evident advantage in connecting deterministic and stochastic dynamics, as well as useful applications in physics, engineering, chemistry and biology. It introduces the A-type stochastic integration for SDE beyond traditional Ito's or Stratonovich's interpretation. Serious question on its uniqueness was recently raised. We provide here both mathematical and physical demonstrations that the uniqueness is guaranteed. Such discussion leads to a","authors_text":"Ping Ao, Ruoshi Yuan, Ying Tang","cross_cats":["math-ph","math.MP","q-bio.MN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-25T14:40:14Z","title":"On Uniqueness of \"SDE Decomposition\" in A-type Stochastic Integration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07927","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:ccfda68d01f82aeb53814a6238f9948defaf7781ddd593a86d2e3a13d7e06888","target":"record","created_at":"2026-05-18T01:18:15Z","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":"787bce834b2b8827adfa0328520b47486f9388d36bf39f1bcb635677d8331c45","cross_cats_sorted":["math-ph","math.MP","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-25T14:40:14Z","title_canon_sha256":"db65a5a52b5a90837158737abe2ef5ffd52eaaedafe29a67963e2bf3c11b65f8"},"schema_version":"1.0","source":{"id":"1603.07927","kind":"arxiv","version":1}},"canonical_sha256":"5a525142ea7a84532ecda6c1c60ce1a9ea0fc3ed970aa883a027d97f82cf3c83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a525142ea7a84532ecda6c1c60ce1a9ea0fc3ed970aa883a027d97f82cf3c83","first_computed_at":"2026-05-18T01:18:15.852843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:15.852843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPkmRwyhC6ggJQVcXd6AjEpeNFXnVbA/4RWGZn7V/B2xRwpfLV6k5BUwEcC32ORGDxiB4tUQLvhftpZoTF0iAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:15.853544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccfda68d01f82aeb53814a6238f9948defaf7781ddd593a86d2e3a13d7e06888","sha256:e61a5ac9b78fde6787471255d0d8de6df8281ee969b1b310834e2c327990b83e"],"state_sha256":"455093fcfa280cfffc9d89369dc475be73504d4aa4cf2ca08dd362d4c408e0b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lSU/Scpou8dSkMtvZdyBjxW24scBJm+vPyk+j+3D0QRg/l627PeATED2tednM7cuW44rnwe9ozLZIBqfCcThAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T17:21:39.359730Z","bundle_sha256":"1099e54ed229f5e7efc2ad23dd6451846fd0e1478fccfd8faa3327657c9586f3"}}