{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SM7F4YBXISVWMP277GB7XZMO7C","short_pith_number":"pith:SM7F4YBX","canonical_record":{"source":{"id":"2509.01432","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-01T12:42:43Z","cross_cats_sorted":[],"title_canon_sha256":"dfaf80a3d59fedf4c83fac0fe17f1cf65435981e1442510f3bdf6244fa9aeb42","abstract_canon_sha256":"1c7ae4474741785a1730f20e2d81203178821f09cbd699bba3d4bd8484f650b9"},"schema_version":"1.0"},"canonical_sha256":"933e5e603744ab663f5ff983fbe58ef8903e1bedf52c86a9bb007fe358ce5d59","source":{"kind":"arxiv","id":"2509.01432","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.01432","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"arxiv_version","alias_value":"2509.01432v1","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01432","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"pith_short_12","alias_value":"SM7F4YBXISVW","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"pith_short_16","alias_value":"SM7F4YBXISVWMP27","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"pith_short_8","alias_value":"SM7F4YBX","created_at":"2026-07-05T12:03:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SM7F4YBXISVWMP277GB7XZMO7C","target":"record","payload":{"canonical_record":{"source":{"id":"2509.01432","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-01T12:42:43Z","cross_cats_sorted":[],"title_canon_sha256":"dfaf80a3d59fedf4c83fac0fe17f1cf65435981e1442510f3bdf6244fa9aeb42","abstract_canon_sha256":"1c7ae4474741785a1730f20e2d81203178821f09cbd699bba3d4bd8484f650b9"},"schema_version":"1.0"},"canonical_sha256":"933e5e603744ab663f5ff983fbe58ef8903e1bedf52c86a9bb007fe358ce5d59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:03:00.849695Z","signature_b64":"t/8WeixLcY7PpGnL/+yGWHFoLdTrNudoXAtfhY61xXRBPIW9Glta3lWucZuNS+dAzThdC79o8kpj5Z9u9k+yAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"933e5e603744ab663f5ff983fbe58ef8903e1bedf52c86a9bb007fe358ce5d59","last_reissued_at":"2026-07-05T12:03:00.849197Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:03:00.849197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.01432","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":"2026-07-05T12:03:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"208sEjk6L8cTCIJcue8IGGNJQAkWhj7SrGd/JRe7cgRAx68DVAouXBVn3YaIRyBYn9c+PbtIBPiMuNSv0XrGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:45:19.737595Z"},"content_sha256":"86cd7b1e133a107f7f311742831bc0e0b260d7b25dfc90f6b2a9730fb9700661","schema_version":"1.0","event_id":"sha256:86cd7b1e133a107f7f311742831bc0e0b260d7b25dfc90f6b2a9730fb9700661"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SM7F4YBXISVWMP277GB7XZMO7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Geometry of Nonlinear Reinforcement Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Nico Scherf, Nikola Milosevic","submitted_at":"2025-09-01T12:42:43Z","abstract_excerpt":"Reward maximization, safe exploration, and intrinsic motivation are often studied as separate objectives in reinforcement learning (RL). We present a unified geometric framework, that views these goals as instances of a single optimization problem on the space of achievable long-term behavior in an environment. Within this framework, classical methods such as policy mirror descent, natural policy gradient, and trust-region algorithms naturally generalize to nonlinear utilities and convex constraints. We illustrate how this perspective captures robustness, safety, exploration, and diversity obj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01432","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/2509.01432/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":"2026-07-05T12:03:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/3rprFFqN/2wPazpsTiZkvra+a/kgXVPqCYJRR8B1p36qiTmsMiNL86P9EHE3GV1kMfpEi7EuhGveVayAuzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:45:19.738150Z"},"content_sha256":"c5a0c33850dc0224c8de289c354136b7f2847dcfde779a70798bfefb0880d040","schema_version":"1.0","event_id":"sha256:c5a0c33850dc0224c8de289c354136b7f2847dcfde779a70798bfefb0880d040"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SM7F4YBXISVWMP277GB7XZMO7C/bundle.json","state_url":"https://pith.science/pith/SM7F4YBXISVWMP277GB7XZMO7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SM7F4YBXISVWMP277GB7XZMO7C/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":"2026-08-13T18:45:19Z","links":{"resolver":"https://pith.science/pith/SM7F4YBXISVWMP277GB7XZMO7C","bundle":"https://pith.science/pith/SM7F4YBXISVWMP277GB7XZMO7C/bundle.json","state":"https://pith.science/pith/SM7F4YBXISVWMP277GB7XZMO7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SM7F4YBXISVWMP277GB7XZMO7C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SM7F4YBXISVWMP277GB7XZMO7C","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":"1c7ae4474741785a1730f20e2d81203178821f09cbd699bba3d4bd8484f650b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-01T12:42:43Z","title_canon_sha256":"dfaf80a3d59fedf4c83fac0fe17f1cf65435981e1442510f3bdf6244fa9aeb42"},"schema_version":"1.0","source":{"id":"2509.01432","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.01432","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"arxiv_version","alias_value":"2509.01432v1","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01432","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"pith_short_12","alias_value":"SM7F4YBXISVW","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"pith_short_16","alias_value":"SM7F4YBXISVWMP27","created_at":"2026-07-05T12:03:00Z"},{"alias_kind":"pith_short_8","alias_value":"SM7F4YBX","created_at":"2026-07-05T12:03:00Z"}],"graph_snapshots":[{"event_id":"sha256:c5a0c33850dc0224c8de289c354136b7f2847dcfde779a70798bfefb0880d040","target":"graph","created_at":"2026-07-05T12:03:00Z","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/2509.01432/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Reward maximization, safe exploration, and intrinsic motivation are often studied as separate objectives in reinforcement learning (RL). We present a unified geometric framework, that views these goals as instances of a single optimization problem on the space of achievable long-term behavior in an environment. Within this framework, classical methods such as policy mirror descent, natural policy gradient, and trust-region algorithms naturally generalize to nonlinear utilities and convex constraints. We illustrate how this perspective captures robustness, safety, exploration, and diversity obj","authors_text":"Nico Scherf, Nikola Milosevic","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-01T12:42:43Z","title":"The Geometry of Nonlinear Reinforcement Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01432","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":"sha256:86cd7b1e133a107f7f311742831bc0e0b260d7b25dfc90f6b2a9730fb9700661","target":"record","created_at":"2026-07-05T12:03:00Z","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":"1c7ae4474741785a1730f20e2d81203178821f09cbd699bba3d4bd8484f650b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-01T12:42:43Z","title_canon_sha256":"dfaf80a3d59fedf4c83fac0fe17f1cf65435981e1442510f3bdf6244fa9aeb42"},"schema_version":"1.0","source":{"id":"2509.01432","kind":"arxiv","version":1}},"canonical_sha256":"933e5e603744ab663f5ff983fbe58ef8903e1bedf52c86a9bb007fe358ce5d59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"933e5e603744ab663f5ff983fbe58ef8903e1bedf52c86a9bb007fe358ce5d59","first_computed_at":"2026-07-05T12:03:00.849197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:03:00.849197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t/8WeixLcY7PpGnL/+yGWHFoLdTrNudoXAtfhY61xXRBPIW9Glta3lWucZuNS+dAzThdC79o8kpj5Z9u9k+yAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:03:00.849695Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.01432","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86cd7b1e133a107f7f311742831bc0e0b260d7b25dfc90f6b2a9730fb9700661","sha256:c5a0c33850dc0224c8de289c354136b7f2847dcfde779a70798bfefb0880d040"],"state_sha256":"21e9aafe505db5f8985fe66d57ff200f4ea81591c9d3c50a21598f370aa89166"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BrOgArowmumAlGkyrIiSaEh0i2Qrna5MqwGNo3DOiBqOh/7nm9Dw+PI/dOLh96JCsbXcac9BL0qLnjj1AvGnAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T18:45:19.744156Z","bundle_sha256":"220dd5fb9dcf681de968a1f73e230ee84fd0cd2dc28849f1553ed910f25c0d04"}}