{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FICU6F6TY33LH5SBSQSSTASLSQ","short_pith_number":"pith:FICU6F6T","canonical_record":{"source":{"id":"2506.14113","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-17T02:11:06Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"b7617ae29b87e979c5cf38fcd8d333ff80dfc253f6c2fe2015233ddf519c1d08","abstract_canon_sha256":"6899bb93fd0d39e3803cb57e12f8431ec37eb594d47ae16ee9cf966587645359"},"schema_version":"1.0"},"canonical_sha256":"2a054f17d3c6f6b3f641942529824b9420251c130934fa3fd01e6bfcdee92ef3","source":{"kind":"arxiv","id":"2506.14113","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.14113","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.14113v1","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.14113","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"FICU6F6TY33L","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"pith_short_16","alias_value":"FICU6F6TY33LH5SB","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"pith_short_8","alias_value":"FICU6F6T","created_at":"2026-07-05T11:22:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FICU6F6TY33LH5SBSQSSTASLSQ","target":"record","payload":{"canonical_record":{"source":{"id":"2506.14113","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-17T02:11:06Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"b7617ae29b87e979c5cf38fcd8d333ff80dfc253f6c2fe2015233ddf519c1d08","abstract_canon_sha256":"6899bb93fd0d39e3803cb57e12f8431ec37eb594d47ae16ee9cf966587645359"},"schema_version":"1.0"},"canonical_sha256":"2a054f17d3c6f6b3f641942529824b9420251c130934fa3fd01e6bfcdee92ef3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:49.305689Z","signature_b64":"ZgvpTyz9Ys0S9ECmYQjUHxun4KsJ2apCZsq0novmA8DLuE33JLzF+aQ423sd1VmyxKEnAAouftO47s3MmIXBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a054f17d3c6f6b3f641942529824b9420251c130934fa3fd01e6bfcdee92ef3","last_reissued_at":"2026-07-05T11:22:49.305096Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:49.305096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.14113","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":"2026-07-05T11:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W9Tr4qMbZIHu3zYMpMNM99G9Pm0dGckL2/Tf7n27j3Gf+BTJ7Y4Vxm5D5DcKdkf3T3HEdQ44LCIwGg1Wzot4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T19:38:36.559242Z"},"content_sha256":"84caa76f7c6afac839ca569be760def1ef5dec5d17cfe6296143c83cabc5e2ee","schema_version":"1.0","event_id":"sha256:84caa76f7c6afac839ca569be760def1ef5dec5d17cfe6296143c83cabc5e2ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FICU6F6TY33LH5SBSQSSTASLSQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Antonios Valkanas, Boris N. Oreshkin, Liheng Ma, Mark Coates, Yitian Zhang","submitted_at":"2025-06-17T02:11:06Z","abstract_excerpt":"Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14113","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/2506.14113/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":"2026-07-05T11:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8sa1moRAK+qnfV6pRt8GzAaPiFi8v7DkhDWOXGC27cNZk5sSbgwTI/PK4toJAtStc8+mwAelIgvPJ224xzUnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T19:38:36.559650Z"},"content_sha256":"68fb430891d951b58df4516a87f68c11e93f22fb73dbfd1be009470ada3f8d89","schema_version":"1.0","event_id":"sha256:68fb430891d951b58df4516a87f68c11e93f22fb73dbfd1be009470ada3f8d89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FICU6F6TY33LH5SBSQSSTASLSQ/bundle.json","state_url":"https://pith.science/pith/FICU6F6TY33LH5SBSQSSTASLSQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FICU6F6TY33LH5SBSQSSTASLSQ/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":"2026-07-08T19:38:36Z","links":{"resolver":"https://pith.science/pith/FICU6F6TY33LH5SBSQSSTASLSQ","bundle":"https://pith.science/pith/FICU6F6TY33LH5SBSQSSTASLSQ/bundle.json","state":"https://pith.science/pith/FICU6F6TY33LH5SBSQSSTASLSQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FICU6F6TY33LH5SBSQSSTASLSQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FICU6F6TY33LH5SBSQSSTASLSQ","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":"6899bb93fd0d39e3803cb57e12f8431ec37eb594d47ae16ee9cf966587645359","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-17T02:11:06Z","title_canon_sha256":"b7617ae29b87e979c5cf38fcd8d333ff80dfc253f6c2fe2015233ddf519c1d08"},"schema_version":"1.0","source":{"id":"2506.14113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.14113","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.14113v1","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.14113","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"FICU6F6TY33L","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"pith_short_16","alias_value":"FICU6F6TY33LH5SB","created_at":"2026-07-05T11:22:49Z"},{"alias_kind":"pith_short_8","alias_value":"FICU6F6T","created_at":"2026-07-05T11:22:49Z"}],"graph_snapshots":[{"event_id":"sha256:68fb430891d951b58df4516a87f68c11e93f22fb73dbfd1be009470ada3f8d89","target":"graph","created_at":"2026-07-05T11:22:49Z","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/2506.14113/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated r","authors_text":"Antonios Valkanas, Boris N. Oreshkin, Liheng Ma, Mark Coates, Yitian Zhang","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-17T02:11:06Z","title":"SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14113","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":"sha256:84caa76f7c6afac839ca569be760def1ef5dec5d17cfe6296143c83cabc5e2ee","target":"record","created_at":"2026-07-05T11:22:49Z","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":"6899bb93fd0d39e3803cb57e12f8431ec37eb594d47ae16ee9cf966587645359","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-17T02:11:06Z","title_canon_sha256":"b7617ae29b87e979c5cf38fcd8d333ff80dfc253f6c2fe2015233ddf519c1d08"},"schema_version":"1.0","source":{"id":"2506.14113","kind":"arxiv","version":1}},"canonical_sha256":"2a054f17d3c6f6b3f641942529824b9420251c130934fa3fd01e6bfcdee92ef3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a054f17d3c6f6b3f641942529824b9420251c130934fa3fd01e6bfcdee92ef3","first_computed_at":"2026-07-05T11:22:49.305096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:22:49.305096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgvpTyz9Ys0S9ECmYQjUHxun4KsJ2apCZsq0novmA8DLuE33JLzF+aQ423sd1VmyxKEnAAouftO47s3MmIXBDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:22:49.305689Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.14113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84caa76f7c6afac839ca569be760def1ef5dec5d17cfe6296143c83cabc5e2ee","sha256:68fb430891d951b58df4516a87f68c11e93f22fb73dbfd1be009470ada3f8d89"],"state_sha256":"cba8922b157016070d6472fc07d62705357d247c2a25d21df1730b432af42550"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2ECsNfOgRDNfbQ1pJa/NE7mU2P+WMUSgbBcvK/bSHDL07xKbfasur5FMAl6ZSllYmRcziRv4xQtyQTosWWICg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T19:38:36.561723Z","bundle_sha256":"02532410c26e26d04db0394003e86364ad9096bf03ca22484b7278adab2d2d90"}}