{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:J7PPCBV3WMVAL5F6SH6GRUZHJR","short_pith_number":"pith:J7PPCBV3","canonical_record":{"source":{"id":"2507.16915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-22T18:01:05Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.SP","stat.ML"],"title_canon_sha256":"31676c3bddfa101f6fd20940f615054e5a93ca0d32007e790eff5b71bb04e11b","abstract_canon_sha256":"baf3a8f425c74430bf5690532fc5cf17eebf147241c83793be17a2c9826b067d"},"schema_version":"1.0"},"canonical_sha256":"4fdef106bbb32a05f4be91fc68d3274c604829bf2382c2fd18b05ef66c6f5f61","source":{"kind":"arxiv","id":"2507.16915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.16915","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"2507.16915v1","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.16915","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"J7PPCBV3WMVA","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"pith_short_16","alias_value":"J7PPCBV3WMVAL5F6","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"pith_short_8","alias_value":"J7PPCBV3","created_at":"2026-07-05T11:41:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:J7PPCBV3WMVAL5F6SH6GRUZHJR","target":"record","payload":{"canonical_record":{"source":{"id":"2507.16915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-22T18:01:05Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.SP","stat.ML"],"title_canon_sha256":"31676c3bddfa101f6fd20940f615054e5a93ca0d32007e790eff5b71bb04e11b","abstract_canon_sha256":"baf3a8f425c74430bf5690532fc5cf17eebf147241c83793be17a2c9826b067d"},"schema_version":"1.0"},"canonical_sha256":"4fdef106bbb32a05f4be91fc68d3274c604829bf2382c2fd18b05ef66c6f5f61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:41:58.213289Z","signature_b64":"5XUkDuBOoYJOXj9a7RNI2KEAMcsBqe1QztrMOhn0Jh9nqe+RsGwjv2oLtfppKKcVFudj0nkWug2VuYbo5dXiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fdef106bbb32a05f4be91fc68d3274c604829bf2382c2fd18b05ef66c6f5f61","last_reissued_at":"2026-07-05T11:41:58.212786Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:41:58.212786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.16915","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":"2026-07-05T11:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WT2MvWzPPMu2+El0zN41+eK05dsSMOC24V84p49WNap7+1NTtsKeVX2aC+a+PRJBj0skLZD6d+fQes8eWc5vDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:21:05.158502Z"},"content_sha256":"0d9a59f1f3e0a1b23ee56f7b1df11603dc2c6b07c606e5e619f5c868e87712de","schema_version":"1.0","event_id":"sha256:0d9a59f1f3e0a1b23ee56f7b1df11603dc2c6b07c606e5e619f5c868e87712de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:J7PPCBV3WMVAL5F6SH6GRUZHJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Avoiding spectral pollution for transfer operators using residuals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","math.SP","stat.ML"],"primary_cat":"math.DS","authors_text":"April Herwig, Julia Slipantschuk, Matthew J. Colbrook, Oliver Junge, P\\'eter Koltai","submitted_at":"2025-07-22T18:01:05Z","abstract_excerpt":"Koopman operator theory enables linear analysis of nonlinear dynamical systems by lifting their evolution to infinite-dimensional function spaces. However, finite-dimensional approximations of Koopman and transfer (Frobenius--Perron) operators are prone to spectral pollution, introducing spurious eigenvalues that can compromise spectral computations. While recent advances have yielded provably convergent methods for Koopman operators, analogous tools for general transfer operators remain limited. In this paper, we present algorithms for computing spectral properties of transfer operators witho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16915","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/2507.16915/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":"2026-07-05T11:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EeFKa6uEwgqY8XjdTOz5rXHFmbdTG9m+VfvITaXT0rbjuiTpzyyJaPhORwydH+p6m7WcPSC/r2E2cJkQW/Y5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:21:05.159036Z"},"content_sha256":"179db8fcae0c70ccde1a2b80e03eb65c3565173fc2c55f6d55202a3274fd5e6b","schema_version":"1.0","event_id":"sha256:179db8fcae0c70ccde1a2b80e03eb65c3565173fc2c55f6d55202a3274fd5e6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7PPCBV3WMVAL5F6SH6GRUZHJR/bundle.json","state_url":"https://pith.science/pith/J7PPCBV3WMVAL5F6SH6GRUZHJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7PPCBV3WMVAL5F6SH6GRUZHJR/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":"2026-08-09T12:21:05Z","links":{"resolver":"https://pith.science/pith/J7PPCBV3WMVAL5F6SH6GRUZHJR","bundle":"https://pith.science/pith/J7PPCBV3WMVAL5F6SH6GRUZHJR/bundle.json","state":"https://pith.science/pith/J7PPCBV3WMVAL5F6SH6GRUZHJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7PPCBV3WMVAL5F6SH6GRUZHJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:J7PPCBV3WMVAL5F6SH6GRUZHJR","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":"baf3a8f425c74430bf5690532fc5cf17eebf147241c83793be17a2c9826b067d","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.SP","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-22T18:01:05Z","title_canon_sha256":"31676c3bddfa101f6fd20940f615054e5a93ca0d32007e790eff5b71bb04e11b"},"schema_version":"1.0","source":{"id":"2507.16915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.16915","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"2507.16915v1","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.16915","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"J7PPCBV3WMVA","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"pith_short_16","alias_value":"J7PPCBV3WMVAL5F6","created_at":"2026-07-05T11:41:58Z"},{"alias_kind":"pith_short_8","alias_value":"J7PPCBV3","created_at":"2026-07-05T11:41:58Z"}],"graph_snapshots":[{"event_id":"sha256:179db8fcae0c70ccde1a2b80e03eb65c3565173fc2c55f6d55202a3274fd5e6b","target":"graph","created_at":"2026-07-05T11:41:58Z","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/2507.16915/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Koopman operator theory enables linear analysis of nonlinear dynamical systems by lifting their evolution to infinite-dimensional function spaces. However, finite-dimensional approximations of Koopman and transfer (Frobenius--Perron) operators are prone to spectral pollution, introducing spurious eigenvalues that can compromise spectral computations. While recent advances have yielded provably convergent methods for Koopman operators, analogous tools for general transfer operators remain limited. In this paper, we present algorithms for computing spectral properties of transfer operators witho","authors_text":"April Herwig, Julia Slipantschuk, Matthew J. Colbrook, Oliver Junge, P\\'eter Koltai","cross_cats":["cs.LG","cs.NA","math.NA","math.SP","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-22T18:01:05Z","title":"Avoiding spectral pollution for transfer operators using residuals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16915","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":"sha256:0d9a59f1f3e0a1b23ee56f7b1df11603dc2c6b07c606e5e619f5c868e87712de","target":"record","created_at":"2026-07-05T11:41:58Z","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":"baf3a8f425c74430bf5690532fc5cf17eebf147241c83793be17a2c9826b067d","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.SP","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-22T18:01:05Z","title_canon_sha256":"31676c3bddfa101f6fd20940f615054e5a93ca0d32007e790eff5b71bb04e11b"},"schema_version":"1.0","source":{"id":"2507.16915","kind":"arxiv","version":1}},"canonical_sha256":"4fdef106bbb32a05f4be91fc68d3274c604829bf2382c2fd18b05ef66c6f5f61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fdef106bbb32a05f4be91fc68d3274c604829bf2382c2fd18b05ef66c6f5f61","first_computed_at":"2026-07-05T11:41:58.212786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:41:58.212786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5XUkDuBOoYJOXj9a7RNI2KEAMcsBqe1QztrMOhn0Jh9nqe+RsGwjv2oLtfppKKcVFudj0nkWug2VuYbo5dXiAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:41:58.213289Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.16915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d9a59f1f3e0a1b23ee56f7b1df11603dc2c6b07c606e5e619f5c868e87712de","sha256:179db8fcae0c70ccde1a2b80e03eb65c3565173fc2c55f6d55202a3274fd5e6b"],"state_sha256":"0418928f3798fa60823169225bbc0d6464815998d92f0db70aa77c701edf4844"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4e9dG7dboqM/n8+RQd5ToO7ZK0n1hzVwJr5MuetWmTJ225LpJPLu62m2Iox2SKXCOilu6/m45OuQnzHQiZEWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T12:21:05.164123Z","bundle_sha256":"c9445864f3bb55bfe1f9d183a6e3fe1f2d5bb94a619952bbb65a8f24b10c56cc"}}