{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BI3IQLMK2WXWM7OW2H75B2HDOX","short_pith_number":"pith:BI3IQLMK","canonical_record":{"source":{"id":"2608.01582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-08-03T01:34:13Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math-ph","math.MP"],"title_canon_sha256":"29b283aecf84cc09b0a5519cc1c595334a7c861d046aba62e5738a5e83144e4e","abstract_canon_sha256":"95e01248801c26a103e3b070aa209a75df3c32348acfbe71f682b6adec41fed8"},"schema_version":"1.0"},"canonical_sha256":"0a36882d8ad5af667dd6d1ffd0e8e375d40a478bfcf53dac21f7baf4af82fef2","source":{"kind":"arxiv","id":"2608.01582","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.01582","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"2608.01582v1","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01582","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"BI3IQLMK2WXW","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"pith_short_16","alias_value":"BI3IQLMK2WXWM7OW","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"pith_short_8","alias_value":"BI3IQLMK","created_at":"2026-08-04T02:06:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BI3IQLMK2WXWM7OW2H75B2HDOX","target":"record","payload":{"canonical_record":{"source":{"id":"2608.01582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-08-03T01:34:13Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math-ph","math.MP"],"title_canon_sha256":"29b283aecf84cc09b0a5519cc1c595334a7c861d046aba62e5738a5e83144e4e","abstract_canon_sha256":"95e01248801c26a103e3b070aa209a75df3c32348acfbe71f682b6adec41fed8"},"schema_version":"1.0"},"canonical_sha256":"0a36882d8ad5af667dd6d1ffd0e8e375d40a478bfcf53dac21f7baf4af82fef2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:06:04.617828Z","signature_b64":"pe256FGterAhiagtdNPjrQJHNuVwbrGtCtHZNK56B+kUmLO75uR3xJMT1tN37uCMyQAwzCyMCqOFiqh099V8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a36882d8ad5af667dd6d1ffd0e8e375d40a478bfcf53dac21f7baf4af82fef2","last_reissued_at":"2026-08-04T02:06:04.616345Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:06:04.616345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.01582","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":"2026-08-04T02:06:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mx4GWLtBz/vX+8VkXxLyYDIBeM7RWLRmhq6nYb+zdhMEMWsbCXHipuTkLgLNbQnAcK4DfExdHChVm4yfLVnrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:45:31.311121Z"},"content_sha256":"dad93c7523d475907d9c19fe040a870983e0d39067986890dcde958b91159132","schema_version":"1.0","event_id":"sha256:dad93c7523d475907d9c19fe040a870983e0d39067986890dcde958b91159132"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BI3IQLMK2WXWM7OW2H75B2HDOX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Abhishek Gupta, L. Mahadevan, Shida Liu, Sumit Sinha","submitted_at":"2026-08-03T01:34:13Z","abstract_excerpt":"Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems the relevant continuous symmetries are rarely known, and symmetry discovery for SDEs has remained essentially unexplored. We introduce \\textit{LieStoNet}, an end-to-end, \\emph{template-free} framework for discovering Lie-point symmetries of SDEs directly from spatiotemporal trajectories, without prespecifying symmetry groups, templates, or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01582","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.01582/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-04T02:06:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dt3nctuwBp7a+Q7LX0etVEjPsmk7zRgZB6v9JDTtdxqdOnbJULc2QJP7MewwvGyJpeVrEHgwYTdz9ZOGnqJmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:45:31.311505Z"},"content_sha256":"b234733d493a0de709dbf32084d47fb2a27a0c8056c4704f2905a2716225b0ac","schema_version":"1.0","event_id":"sha256:b234733d493a0de709dbf32084d47fb2a27a0c8056c4704f2905a2716225b0ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BI3IQLMK2WXWM7OW2H75B2HDOX/bundle.json","state_url":"https://pith.science/pith/BI3IQLMK2WXWM7OW2H75B2HDOX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BI3IQLMK2WXWM7OW2H75B2HDOX/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":"2026-08-05T14:45:31Z","links":{"resolver":"https://pith.science/pith/BI3IQLMK2WXWM7OW2H75B2HDOX","bundle":"https://pith.science/pith/BI3IQLMK2WXWM7OW2H75B2HDOX/bundle.json","state":"https://pith.science/pith/BI3IQLMK2WXWM7OW2H75B2HDOX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BI3IQLMK2WXWM7OW2H75B2HDOX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BI3IQLMK2WXWM7OW2H75B2HDOX","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":"95e01248801c26a103e3b070aa209a75df3c32348acfbe71f682b6adec41fed8","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-08-03T01:34:13Z","title_canon_sha256":"29b283aecf84cc09b0a5519cc1c595334a7c861d046aba62e5738a5e83144e4e"},"schema_version":"1.0","source":{"id":"2608.01582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.01582","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"2608.01582v1","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01582","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"BI3IQLMK2WXW","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"pith_short_16","alias_value":"BI3IQLMK2WXWM7OW","created_at":"2026-08-04T02:06:04Z"},{"alias_kind":"pith_short_8","alias_value":"BI3IQLMK","created_at":"2026-08-04T02:06:04Z"}],"graph_snapshots":[{"event_id":"sha256:b234733d493a0de709dbf32084d47fb2a27a0c8056c4704f2905a2716225b0ac","target":"graph","created_at":"2026-08-04T02:06:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.01582/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems the relevant continuous symmetries are rarely known, and symmetry discovery for SDEs has remained essentially unexplored. We introduce \\textit{LieStoNet}, an end-to-end, \\emph{template-free} framework for discovering Lie-point symmetries of SDEs directly from spatiotemporal trajectories, without prespecifying symmetry groups, templates, or","authors_text":"Abhishek Gupta, L. Mahadevan, Shida Liu, Sumit Sinha","cross_cats":["cond-mat.dis-nn","cs.LG","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-08-03T01:34:13Z","title":"LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01582","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:dad93c7523d475907d9c19fe040a870983e0d39067986890dcde958b91159132","target":"record","created_at":"2026-08-04T02:06:04Z","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":"95e01248801c26a103e3b070aa209a75df3c32348acfbe71f682b6adec41fed8","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-08-03T01:34:13Z","title_canon_sha256":"29b283aecf84cc09b0a5519cc1c595334a7c861d046aba62e5738a5e83144e4e"},"schema_version":"1.0","source":{"id":"2608.01582","kind":"arxiv","version":1}},"canonical_sha256":"0a36882d8ad5af667dd6d1ffd0e8e375d40a478bfcf53dac21f7baf4af82fef2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a36882d8ad5af667dd6d1ffd0e8e375d40a478bfcf53dac21f7baf4af82fef2","first_computed_at":"2026-08-04T02:06:04.616345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:06:04.616345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pe256FGterAhiagtdNPjrQJHNuVwbrGtCtHZNK56B+kUmLO75uR3xJMT1tN37uCMyQAwzCyMCqOFiqh099V8BA==","signature_status":"signed_v1","signed_at":"2026-08-04T02:06:04.617828Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.01582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dad93c7523d475907d9c19fe040a870983e0d39067986890dcde958b91159132","sha256:b234733d493a0de709dbf32084d47fb2a27a0c8056c4704f2905a2716225b0ac"],"state_sha256":"8f5aa238d3d84ceb7a174b586b31e745e1369f77ff8d96cf5e7436a93b69dd57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAhtLVDTUWyX56DLZsHrsZoqypi7I7X0j909PFvg76Lfgk3ahr3VbEtaog7yPvJ4CPUZjtm1aRni2TDU8xPvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T14:45:31.315243Z","bundle_sha256":"62ab24f0e61f4b89cc3a7cfc231e466deab0d001b636278d438667890f7f4bd0"}}