{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:LNNRKFCOEWH2JBKRO45K26NXCK","short_pith_number":"pith:LNNRKFCO","canonical_record":{"source":{"id":"2208.09515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-19T19:01:30Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"1d640ec3e84e783ae8590f11d086672cc9de9072a5079666d87af14bd6c729f0","abstract_canon_sha256":"e6425602b7146b8c6e21e349a7bbfd37ec6839d4b1e4f14c7349686302253fb4"},"schema_version":"1.0"},"canonical_sha256":"5b5b15144e258fa48551773aad79b712b39823dc8f51909302f08f7c6be625b0","source":{"kind":"arxiv","id":"2208.09515","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.09515","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"arxiv_version","alias_value":"2208.09515v2","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.09515","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"pith_short_12","alias_value":"LNNRKFCOEWH2","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"pith_short_16","alias_value":"LNNRKFCOEWH2JBKR","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"pith_short_8","alias_value":"LNNRKFCO","created_at":"2026-07-05T05:48:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:LNNRKFCOEWH2JBKRO45K26NXCK","target":"record","payload":{"canonical_record":{"source":{"id":"2208.09515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-19T19:01:30Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"1d640ec3e84e783ae8590f11d086672cc9de9072a5079666d87af14bd6c729f0","abstract_canon_sha256":"e6425602b7146b8c6e21e349a7bbfd37ec6839d4b1e4f14c7349686302253fb4"},"schema_version":"1.0"},"canonical_sha256":"5b5b15144e258fa48551773aad79b712b39823dc8f51909302f08f7c6be625b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:48:37.475726Z","signature_b64":"EvfRBWsKxLjuw45ZWev/fk1q0TCj3oaVbSbvqin7KUlwL7XxdkoBdcjFChLSThiYKAB0z31KOfXoQqoIGBu1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b5b15144e258fa48551773aad79b712b39823dc8f51909302f08f7c6be625b0","last_reissued_at":"2026-07-05T05:48:37.475275Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:48:37.475275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.09515","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:48:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MPHxcg1kxkxTbtI37ENp8GngMsFUshf/n+9x9/VAzw9jBRjwWVJq+4051UwscsBsU2x8hGgzcrlVgB/ihzN5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:24:52.134544Z"},"content_sha256":"928281929fc2277802ab0c59cd0683e1036ed956aa4b9bf4f72f3e216724a9df","schema_version":"1.0","event_id":"sha256:928281929fc2277802ab0c59cd0683e1036ed956aa4b9bf4f72f3e216724a9df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:LNNRKFCOEWH2JBKRO45K26NXCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Decomposition Representation for Reinforcement Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Bo Dai, Dale Schuurmans, Joseph E. Gonzalez, Lisa Lee, Tianjun Zhang, Tongzheng Ren","submitted_at":"2022-08-19T19:01:30Z","abstract_excerpt":"Representation learning often plays a critical role in reinforcement learning by managing the curse of dimensionality. A representative class of algorithms exploits a spectral decomposition of the stochastic transition dynamics to construct representations that enjoy strong theoretical properties in an idealized setting. However, current spectral methods suffer from limited applicability because they are constructed for state-only aggregation and derived from a policy-dependent transition kernel, without considering the issue of exploration. To address these issues, we propose an alternative s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.09515","kind":"arxiv","version":2},"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/2208.09515/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":"2026-07-05T05:48:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xXb32qE3cQ0ZNGP4MeGm3Y0th9aobmnjyur4yjax77Oy8Jafgp+N6uMhskLb1tztDRpRzef63OSjEY1pvBwwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:24:52.135418Z"},"content_sha256":"ec8d50093f58578cbeefa82fcf6484fa96ffa848984ae82e05fdf2bebbb4730d","schema_version":"1.0","event_id":"sha256:ec8d50093f58578cbeefa82fcf6484fa96ffa848984ae82e05fdf2bebbb4730d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LNNRKFCOEWH2JBKRO45K26NXCK/bundle.json","state_url":"https://pith.science/pith/LNNRKFCOEWH2JBKRO45K26NXCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LNNRKFCOEWH2JBKRO45K26NXCK/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":"2026-08-04T05:24:52Z","links":{"resolver":"https://pith.science/pith/LNNRKFCOEWH2JBKRO45K26NXCK","bundle":"https://pith.science/pith/LNNRKFCOEWH2JBKRO45K26NXCK/bundle.json","state":"https://pith.science/pith/LNNRKFCOEWH2JBKRO45K26NXCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LNNRKFCOEWH2JBKRO45K26NXCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:LNNRKFCOEWH2JBKRO45K26NXCK","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":"e6425602b7146b8c6e21e349a7bbfd37ec6839d4b1e4f14c7349686302253fb4","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-19T19:01:30Z","title_canon_sha256":"1d640ec3e84e783ae8590f11d086672cc9de9072a5079666d87af14bd6c729f0"},"schema_version":"1.0","source":{"id":"2208.09515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.09515","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"arxiv_version","alias_value":"2208.09515v2","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.09515","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"pith_short_12","alias_value":"LNNRKFCOEWH2","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"pith_short_16","alias_value":"LNNRKFCOEWH2JBKR","created_at":"2026-07-05T05:48:37Z"},{"alias_kind":"pith_short_8","alias_value":"LNNRKFCO","created_at":"2026-07-05T05:48:37Z"}],"graph_snapshots":[{"event_id":"sha256:ec8d50093f58578cbeefa82fcf6484fa96ffa848984ae82e05fdf2bebbb4730d","target":"graph","created_at":"2026-07-05T05:48:37Z","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/2208.09515/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Representation learning often plays a critical role in reinforcement learning by managing the curse of dimensionality. A representative class of algorithms exploits a spectral decomposition of the stochastic transition dynamics to construct representations that enjoy strong theoretical properties in an idealized setting. However, current spectral methods suffer from limited applicability because they are constructed for state-only aggregation and derived from a policy-dependent transition kernel, without considering the issue of exploration. To address these issues, we propose an alternative s","authors_text":"Bo Dai, Dale Schuurmans, Joseph E. Gonzalez, Lisa Lee, Tianjun Zhang, Tongzheng Ren","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-19T19:01:30Z","title":"Spectral Decomposition Representation for Reinforcement Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.09515","kind":"arxiv","version":2},"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":"sha256:928281929fc2277802ab0c59cd0683e1036ed956aa4b9bf4f72f3e216724a9df","target":"record","created_at":"2026-07-05T05:48:37Z","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":"e6425602b7146b8c6e21e349a7bbfd37ec6839d4b1e4f14c7349686302253fb4","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-19T19:01:30Z","title_canon_sha256":"1d640ec3e84e783ae8590f11d086672cc9de9072a5079666d87af14bd6c729f0"},"schema_version":"1.0","source":{"id":"2208.09515","kind":"arxiv","version":2}},"canonical_sha256":"5b5b15144e258fa48551773aad79b712b39823dc8f51909302f08f7c6be625b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b5b15144e258fa48551773aad79b712b39823dc8f51909302f08f7c6be625b0","first_computed_at":"2026-07-05T05:48:37.475275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:48:37.475275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EvfRBWsKxLjuw45ZWev/fk1q0TCj3oaVbSbvqin7KUlwL7XxdkoBdcjFChLSThiYKAB0z31KOfXoQqoIGBu1AA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:48:37.475726Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.09515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:928281929fc2277802ab0c59cd0683e1036ed956aa4b9bf4f72f3e216724a9df","sha256:ec8d50093f58578cbeefa82fcf6484fa96ffa848984ae82e05fdf2bebbb4730d"],"state_sha256":"a58216c3fd31e19dac641c24ae051544aeec7afd0b6c3a3a7c3e28348a8ff76d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npaHl9EeCi8ul9cGguzQrhalK4A5yfvmi85EZnte9V5bq2gD5yOu75KmS77WaObE/SUH74RpjDz7FEtUGTGECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T05:24:52.144167Z","bundle_sha256":"592d06063f6cd6e0f582b0095ef84d1cc75f6666e4ea42954ebbfc59d49cc6fe"}}