{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:C74S4IW5WO2GYGZYLDGWOSDGVC","short_pith_number":"pith:C74S4IW5","canonical_record":{"source":{"id":"2504.20375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-04-29T02:38:44Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"4cf796854567f6db96b56123d36033ac910354a45f1886336326164510cde906","abstract_canon_sha256":"17c8a2487fc8a9504482316c3d16531c721710f63ca14165cdff9644001145e2"},"schema_version":"1.0"},"canonical_sha256":"17f92e22ddb3b46c1b3858cd674866a88f7e35cb7039264ede9a387bb9ddbd45","source":{"kind":"arxiv","id":"2504.20375","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.20375","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"arxiv_version","alias_value":"2504.20375v1","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.20375","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"pith_short_12","alias_value":"C74S4IW5WO2G","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"pith_short_16","alias_value":"C74S4IW5WO2GYGZY","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"pith_short_8","alias_value":"C74S4IW5","created_at":"2026-07-05T10:55:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:C74S4IW5WO2GYGZYLDGWOSDGVC","target":"record","payload":{"canonical_record":{"source":{"id":"2504.20375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-04-29T02:38:44Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"4cf796854567f6db96b56123d36033ac910354a45f1886336326164510cde906","abstract_canon_sha256":"17c8a2487fc8a9504482316c3d16531c721710f63ca14165cdff9644001145e2"},"schema_version":"1.0"},"canonical_sha256":"17f92e22ddb3b46c1b3858cd674866a88f7e35cb7039264ede9a387bb9ddbd45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:55:41.506248Z","signature_b64":"xlZMizWPt2BrmxxBBIDZVYxWWRpy0YEZFrF6xWVyOkCXDEBiQKxuRrs401e8IKerSHUwh8/Iv8ZEpUHMr733Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17f92e22ddb3b46c1b3858cd674866a88f7e35cb7039264ede9a387bb9ddbd45","last_reissued_at":"2026-07-05T10:55:41.505753Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:55:41.505753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.20375","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":"2026-07-05T10:55:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"biT+FjZRT1Bx7t7jwznd+7D2tBmfbLKz4/nFPozJsRmvK7q3JSXe4xbHYypKEblf00OhBowPnkt2UhTzJW+IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:49:12.194690Z"},"content_sha256":"04bdae2a6ca2691cbae4402b34f5122964b773a4a12b2be35a4d1904a50a8aa2","schema_version":"1.0","event_id":"sha256:04bdae2a6ca2691cbae4402b34f5122964b773a4a12b2be35a4d1904a50a8aa2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:C74S4IW5WO2GYGZYLDGWOSDGVC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generative Learning for Slow Manifolds and Bifurcation Diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.LG","authors_text":"Dimitris G. Giovanis, Ellis R. Crabtree, Ioannis G. Kevrekidis, Juan M. Bello-Rivas, Nikolaos Evangelou","submitted_at":"2025-04-29T02:38:44Z","abstract_excerpt":"In dynamical systems characterized by separation of time scales, the approximation of so called ``slow manifolds'', on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams. Sampling th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.20375","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/2504.20375/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":"2026-07-05T10:55:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4obipF9aUGz1pSsZOOAvHqvRn/PI6egUwGwEPF85W6AJUafyKjb5BMLPnmeFVOPhbM704GlDgRmumYP9FLZFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:49:12.195183Z"},"content_sha256":"2b92112494bf2b892cfd4fd661159f6a519336fffaa922d5182840ca1705ba16","schema_version":"1.0","event_id":"sha256:2b92112494bf2b892cfd4fd661159f6a519336fffaa922d5182840ca1705ba16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C74S4IW5WO2GYGZYLDGWOSDGVC/bundle.json","state_url":"https://pith.science/pith/C74S4IW5WO2GYGZYLDGWOSDGVC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C74S4IW5WO2GYGZYLDGWOSDGVC/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":"2026-08-08T03:49:12Z","links":{"resolver":"https://pith.science/pith/C74S4IW5WO2GYGZYLDGWOSDGVC","bundle":"https://pith.science/pith/C74S4IW5WO2GYGZYLDGWOSDGVC/bundle.json","state":"https://pith.science/pith/C74S4IW5WO2GYGZYLDGWOSDGVC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C74S4IW5WO2GYGZYLDGWOSDGVC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:C74S4IW5WO2GYGZYLDGWOSDGVC","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":"17c8a2487fc8a9504482316c3d16531c721710f63ca14165cdff9644001145e2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-04-29T02:38:44Z","title_canon_sha256":"4cf796854567f6db96b56123d36033ac910354a45f1886336326164510cde906"},"schema_version":"1.0","source":{"id":"2504.20375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.20375","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"arxiv_version","alias_value":"2504.20375v1","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.20375","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"pith_short_12","alias_value":"C74S4IW5WO2G","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"pith_short_16","alias_value":"C74S4IW5WO2GYGZY","created_at":"2026-07-05T10:55:41Z"},{"alias_kind":"pith_short_8","alias_value":"C74S4IW5","created_at":"2026-07-05T10:55:41Z"}],"graph_snapshots":[{"event_id":"sha256:2b92112494bf2b892cfd4fd661159f6a519336fffaa922d5182840ca1705ba16","target":"graph","created_at":"2026-07-05T10:55:41Z","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/2504.20375/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In dynamical systems characterized by separation of time scales, the approximation of so called ``slow manifolds'', on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams. Sampling th","authors_text":"Dimitris G. Giovanis, Ellis R. Crabtree, Ioannis G. Kevrekidis, Juan M. Bello-Rivas, Nikolaos Evangelou","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-04-29T02:38:44Z","title":"Generative Learning for Slow Manifolds and Bifurcation Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.20375","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":"sha256:04bdae2a6ca2691cbae4402b34f5122964b773a4a12b2be35a4d1904a50a8aa2","target":"record","created_at":"2026-07-05T10:55:41Z","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":"17c8a2487fc8a9504482316c3d16531c721710f63ca14165cdff9644001145e2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-04-29T02:38:44Z","title_canon_sha256":"4cf796854567f6db96b56123d36033ac910354a45f1886336326164510cde906"},"schema_version":"1.0","source":{"id":"2504.20375","kind":"arxiv","version":1}},"canonical_sha256":"17f92e22ddb3b46c1b3858cd674866a88f7e35cb7039264ede9a387bb9ddbd45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17f92e22ddb3b46c1b3858cd674866a88f7e35cb7039264ede9a387bb9ddbd45","first_computed_at":"2026-07-05T10:55:41.505753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:55:41.505753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xlZMizWPt2BrmxxBBIDZVYxWWRpy0YEZFrF6xWVyOkCXDEBiQKxuRrs401e8IKerSHUwh8/Iv8ZEpUHMr733Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:55:41.506248Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.20375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04bdae2a6ca2691cbae4402b34f5122964b773a4a12b2be35a4d1904a50a8aa2","sha256:2b92112494bf2b892cfd4fd661159f6a519336fffaa922d5182840ca1705ba16"],"state_sha256":"2c5e677a0627acf35e2c1276797cd28ed9eed17b5a3bdf1b35371bff779e8f74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mOqIRcXzz/cuEKnsW1txhbkZBGglNfcwte7ycmguHf+u96WzaY7g4zE3KF57ESQWBdTMlqslBMXzlSbPc18bDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T03:49:12.198593Z","bundle_sha256":"408d7a0d528403061ee165e8fcd7243b6ee2adeba179a45271c1cdaa99a97a72"}}