{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZD3PZIU4H6HUQUIOAYULBI3VJM","short_pith_number":"pith:ZD3PZIU4","canonical_record":{"source":{"id":"2605.26416","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2026-05-26T00:48:12Z","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"title_canon_sha256":"7f2074646c93bbdc8b2a25572796e8f41e4d987bbb44bdd50b1036222c46b90b","abstract_canon_sha256":"a88a98072f7d692687a709ee15c04c0a1e794c7af831fa8dc1332a3dca760e50"},"schema_version":"1.0"},"canonical_sha256":"c8f6fca29c3f8f48510e0628b0a3754b3fd9d43ddf4c0c58fa43a4414e16f2cf","source":{"kind":"arxiv","id":"2605.26416","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26416","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26416v1","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26416","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"ZD3PZIU4H6HU","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"pith_short_16","alias_value":"ZD3PZIU4H6HUQUIO","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"pith_short_8","alias_value":"ZD3PZIU4","created_at":"2026-05-27T01:05:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZD3PZIU4H6HUQUIOAYULBI3VJM","target":"record","payload":{"canonical_record":{"source":{"id":"2605.26416","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2026-05-26T00:48:12Z","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"title_canon_sha256":"7f2074646c93bbdc8b2a25572796e8f41e4d987bbb44bdd50b1036222c46b90b","abstract_canon_sha256":"a88a98072f7d692687a709ee15c04c0a1e794c7af831fa8dc1332a3dca760e50"},"schema_version":"1.0"},"canonical_sha256":"c8f6fca29c3f8f48510e0628b0a3754b3fd9d43ddf4c0c58fa43a4414e16f2cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:05:16.762487Z","signature_b64":"vXlS8aYwtYNZgOWWJLoRO7SkjPnnVq+wWGANiqnrRMWpvh7pY/qBjZfNDwmR6pt3VNgjU/FRBA+uILuh4Z0xCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8f6fca29c3f8f48510e0628b0a3754b3fd9d43ddf4c0c58fa43a4414e16f2cf","last_reissued_at":"2026-05-27T01:05:16.761674Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:05:16.761674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.26416","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":"2026-05-27T01:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CUm90xSgxdMguhRL2blwLcdSIk2fgt9q90IX8Ol9GGIkB6PnKVUg5/rj5a0i2TG8r5kMt6knwV9L+M1BB2TmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T04:36:33.335963Z"},"content_sha256":"147b2b91bbdce37b4a0c8866f6bed7759c27151cc5722a7014eeff86bbbb7952","schema_version":"1.0","event_id":"sha256:147b2b91bbdce37b4a0c8866f6bed7759c27151cc5722a7014eeff86bbbb7952"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZD3PZIU4H6HUQUIOAYULBI3VJM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Differentiable Programming Framework for Accurate and Stable Reduced-Order Modeling of Chaotic Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD","physics.flu-dyn"],"primary_cat":"physics.comp-ph","authors_text":"Anant Kumar, Oliver Morales, Rohit Deshmukh","submitted_at":"2026-05-26T00:48:12Z","abstract_excerpt":"Classical Proper Orthogonal Decomposition (POD)-based Galerkin projection models of chaotic flows typically require a large number of modes as well as stabilization or closure terms to achieve adequate accuracy and long-term stability. We present a novel differentiable programming framework that stabilizes low-rank POD-Galerkin models without increasing the number of modes or introducing additional closure terms, thereby delivering both high efficiency and high accuracy. Model stabilization is achieved by tuning the linear and quadratic tensors in the POD-Galerkin using differentiable programm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26416","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/2605.26416/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":"2026-05-27T01:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YJKAyzf1MfCJjaUxWR/krdpmkaDcHaqF/paDdWhMJsv435PHIz1S+jRPrAD3jF83uSXPc6Oiqy8MFCYMJUO9Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T04:36:33.336527Z"},"content_sha256":"c3a69b4a8d25c6b79eff7f4f157418abbeb641c4f72054ae2709f03f396a7e10","schema_version":"1.0","event_id":"sha256:c3a69b4a8d25c6b79eff7f4f157418abbeb641c4f72054ae2709f03f396a7e10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZD3PZIU4H6HUQUIOAYULBI3VJM/bundle.json","state_url":"https://pith.science/pith/ZD3PZIU4H6HUQUIOAYULBI3VJM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZD3PZIU4H6HUQUIOAYULBI3VJM/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":"2026-08-11T04:36:33Z","links":{"resolver":"https://pith.science/pith/ZD3PZIU4H6HUQUIOAYULBI3VJM","bundle":"https://pith.science/pith/ZD3PZIU4H6HUQUIOAYULBI3VJM/bundle.json","state":"https://pith.science/pith/ZD3PZIU4H6HUQUIOAYULBI3VJM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZD3PZIU4H6HUQUIOAYULBI3VJM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZD3PZIU4H6HUQUIOAYULBI3VJM","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":"a88a98072f7d692687a709ee15c04c0a1e794c7af831fa8dc1332a3dca760e50","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2026-05-26T00:48:12Z","title_canon_sha256":"7f2074646c93bbdc8b2a25572796e8f41e4d987bbb44bdd50b1036222c46b90b"},"schema_version":"1.0","source":{"id":"2605.26416","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26416","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26416v1","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26416","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"ZD3PZIU4H6HU","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"pith_short_16","alias_value":"ZD3PZIU4H6HUQUIO","created_at":"2026-05-27T01:05:16Z"},{"alias_kind":"pith_short_8","alias_value":"ZD3PZIU4","created_at":"2026-05-27T01:05:16Z"}],"graph_snapshots":[{"event_id":"sha256:c3a69b4a8d25c6b79eff7f4f157418abbeb641c4f72054ae2709f03f396a7e10","target":"graph","created_at":"2026-05-27T01:05:16Z","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/2605.26416/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Classical Proper Orthogonal Decomposition (POD)-based Galerkin projection models of chaotic flows typically require a large number of modes as well as stabilization or closure terms to achieve adequate accuracy and long-term stability. We present a novel differentiable programming framework that stabilizes low-rank POD-Galerkin models without increasing the number of modes or introducing additional closure terms, thereby delivering both high efficiency and high accuracy. Model stabilization is achieved by tuning the linear and quadratic tensors in the POD-Galerkin using differentiable programm","authors_text":"Anant Kumar, Oliver Morales, Rohit Deshmukh","cross_cats":["nlin.CD","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2026-05-26T00:48:12Z","title":"A Differentiable Programming Framework for Accurate and Stable Reduced-Order Modeling of Chaotic Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26416","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":"sha256:147b2b91bbdce37b4a0c8866f6bed7759c27151cc5722a7014eeff86bbbb7952","target":"record","created_at":"2026-05-27T01:05:16Z","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":"a88a98072f7d692687a709ee15c04c0a1e794c7af831fa8dc1332a3dca760e50","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2026-05-26T00:48:12Z","title_canon_sha256":"7f2074646c93bbdc8b2a25572796e8f41e4d987bbb44bdd50b1036222c46b90b"},"schema_version":"1.0","source":{"id":"2605.26416","kind":"arxiv","version":1}},"canonical_sha256":"c8f6fca29c3f8f48510e0628b0a3754b3fd9d43ddf4c0c58fa43a4414e16f2cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8f6fca29c3f8f48510e0628b0a3754b3fd9d43ddf4c0c58fa43a4414e16f2cf","first_computed_at":"2026-05-27T01:05:16.761674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:05:16.761674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vXlS8aYwtYNZgOWWJLoRO7SkjPnnVq+wWGANiqnrRMWpvh7pY/qBjZfNDwmR6pt3VNgjU/FRBA+uILuh4Z0xCQ==","signature_status":"signed_v1","signed_at":"2026-05-27T01:05:16.762487Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26416","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:147b2b91bbdce37b4a0c8866f6bed7759c27151cc5722a7014eeff86bbbb7952","sha256:c3a69b4a8d25c6b79eff7f4f157418abbeb641c4f72054ae2709f03f396a7e10"],"state_sha256":"2f2b872f7adade1b8a09db6ac6af8b0a8c78b6b996112431f13c89ad8d29e116"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YzW8omxOpTtIuwwtuVVYtJfqvYt/BRYA+jqwLabz+X1CVK4aETg/vuX1PDDgvvGzvC2Jd2maIreysPUIm9ZKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T04:36:33.340651Z","bundle_sha256":"961f9ed9e7fc3dfe2f665fda5dc8f3921c6d126e69bd47af23d7e25607767aca"}}