{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NE4MMFHINSFB6Q3H3UU6WEZHIY","short_pith_number":"pith:NE4MMFHI","canonical_record":{"source":{"id":"2601.01175","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-03T12:37:20Z","cross_cats_sorted":[],"title_canon_sha256":"c33176b9f017adb11355171efe7a81221ac3f31f2519827d124356743bffef29","abstract_canon_sha256":"3f552f0e4114f293e9530cd16e7bb073e60d368a0faa561f2a82d4f04062d1eb"},"schema_version":"1.0"},"canonical_sha256":"6938c614e86c8a1f4367dd29eb132746313e1acb09947dc377f40d6ac8538909","source":{"kind":"arxiv","id":"2601.01175","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.01175","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"2601.01175v2","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.01175","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"NE4MMFHINSFB","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"pith_short_16","alias_value":"NE4MMFHINSFB6Q3H","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"pith_short_8","alias_value":"NE4MMFHI","created_at":"2026-05-25T02:01:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NE4MMFHINSFB6Q3H3UU6WEZHIY","target":"record","payload":{"canonical_record":{"source":{"id":"2601.01175","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-03T12:37:20Z","cross_cats_sorted":[],"title_canon_sha256":"c33176b9f017adb11355171efe7a81221ac3f31f2519827d124356743bffef29","abstract_canon_sha256":"3f552f0e4114f293e9530cd16e7bb073e60d368a0faa561f2a82d4f04062d1eb"},"schema_version":"1.0"},"canonical_sha256":"6938c614e86c8a1f4367dd29eb132746313e1acb09947dc377f40d6ac8538909","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:11.704435Z","signature_b64":"N1kYVbOGh0BzKEgYvSdkLg0lYQWUp/l2z8g1e+FY0EemcA99ktd4zAs0KO6S8taYwDeGToM7Y8S0bvkPy1ABCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6938c614e86c8a1f4367dd29eb132746313e1acb09947dc377f40d6ac8538909","last_reissued_at":"2026-05-25T02:01:11.703633Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:11.703633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.01175","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":"2026-05-25T02:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVrcb/ggWkPz+Ca3j/YN/N0RmPZaP9FIhW+w9milheU1W9j5gjOVaPLf+FPT428oynmsc1KyvosI7oXemC3CDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:12:03.903482Z"},"content_sha256":"30cfc1bf6e2ba0931780dc20a4f4e824d5f6c25aa991e7684d14fe0b485e15ee","schema_version":"1.0","event_id":"sha256:30cfc1bf6e2ba0931780dc20a4f4e824d5f6c25aa991e7684d14fe0b485e15ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NE4MMFHINSFB6Q3H3UU6WEZHIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scalable method for mean field control with kernel interactions via random Fourier features","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kaustav Das, Mathieu Lauri\\`ere, Nicolas Langren\\'e, Zhongyuan Cao","submitted_at":"2026-01-03T12:37:20Z","abstract_excerpt":"We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by linear-time estimates, enabling efficient stochastic gradient descent for training feedback controls in large populations. We provide theoretical complexity bounds and demonstrate through crowd motion and flocking examples that the approach preserves control performance while substantially reducing computational cost. The results indicate that random feature appr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.01175","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/2601.01175/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":"2026-05-25T02:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yvbfRqg21o4Scf8MPhUdvIVVLai7qvocQfkRIx+Ph7mcuKQ2eLuM4gSo94gPNyvbn5Usb4YOqobeVz3hnG4hDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:12:03.903856Z"},"content_sha256":"cd15c2118ca8c658a9be5d3371f01560f556fe5c7488c1e06cf36c75ea1e2cfd","schema_version":"1.0","event_id":"sha256:cd15c2118ca8c658a9be5d3371f01560f556fe5c7488c1e06cf36c75ea1e2cfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NE4MMFHINSFB6Q3H3UU6WEZHIY/bundle.json","state_url":"https://pith.science/pith/NE4MMFHINSFB6Q3H3UU6WEZHIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NE4MMFHINSFB6Q3H3UU6WEZHIY/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":"2026-06-22T16:12:03Z","links":{"resolver":"https://pith.science/pith/NE4MMFHINSFB6Q3H3UU6WEZHIY","bundle":"https://pith.science/pith/NE4MMFHINSFB6Q3H3UU6WEZHIY/bundle.json","state":"https://pith.science/pith/NE4MMFHINSFB6Q3H3UU6WEZHIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NE4MMFHINSFB6Q3H3UU6WEZHIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NE4MMFHINSFB6Q3H3UU6WEZHIY","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":"3f552f0e4114f293e9530cd16e7bb073e60d368a0faa561f2a82d4f04062d1eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-03T12:37:20Z","title_canon_sha256":"c33176b9f017adb11355171efe7a81221ac3f31f2519827d124356743bffef29"},"schema_version":"1.0","source":{"id":"2601.01175","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.01175","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"2601.01175v2","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.01175","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"NE4MMFHINSFB","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"pith_short_16","alias_value":"NE4MMFHINSFB6Q3H","created_at":"2026-05-25T02:01:11Z"},{"alias_kind":"pith_short_8","alias_value":"NE4MMFHI","created_at":"2026-05-25T02:01:11Z"}],"graph_snapshots":[{"event_id":"sha256:cd15c2118ca8c658a9be5d3371f01560f556fe5c7488c1e06cf36c75ea1e2cfd","target":"graph","created_at":"2026-05-25T02:01:11Z","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/2601.01175/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by linear-time estimates, enabling efficient stochastic gradient descent for training feedback controls in large populations. We provide theoretical complexity bounds and demonstrate through crowd motion and flocking examples that the approach preserves control performance while substantially reducing computational cost. The results indicate that random feature appr","authors_text":"Kaustav Das, Mathieu Lauri\\`ere, Nicolas Langren\\'e, Zhongyuan Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-03T12:37:20Z","title":"Scalable method for mean field control with kernel interactions via random Fourier features"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.01175","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":"sha256:30cfc1bf6e2ba0931780dc20a4f4e824d5f6c25aa991e7684d14fe0b485e15ee","target":"record","created_at":"2026-05-25T02:01:11Z","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":"3f552f0e4114f293e9530cd16e7bb073e60d368a0faa561f2a82d4f04062d1eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-03T12:37:20Z","title_canon_sha256":"c33176b9f017adb11355171efe7a81221ac3f31f2519827d124356743bffef29"},"schema_version":"1.0","source":{"id":"2601.01175","kind":"arxiv","version":2}},"canonical_sha256":"6938c614e86c8a1f4367dd29eb132746313e1acb09947dc377f40d6ac8538909","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6938c614e86c8a1f4367dd29eb132746313e1acb09947dc377f40d6ac8538909","first_computed_at":"2026-05-25T02:01:11.703633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:11.703633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N1kYVbOGh0BzKEgYvSdkLg0lYQWUp/l2z8g1e+FY0EemcA99ktd4zAs0KO6S8taYwDeGToM7Y8S0bvkPy1ABCA==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:11.704435Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.01175","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30cfc1bf6e2ba0931780dc20a4f4e824d5f6c25aa991e7684d14fe0b485e15ee","sha256:cd15c2118ca8c658a9be5d3371f01560f556fe5c7488c1e06cf36c75ea1e2cfd"],"state_sha256":"113ca252eaae1243e8becf56b357a1bdca5b57d7c77a397c16e6ec679efa18a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G0tanCLUSARq67MyI1tmmn1TrmrjeecSl9T78VT8TohWmFLVSbIJHjwa/RMUNdeId+Pc4miHJiXgFm97qAF5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:12:03.905905Z","bundle_sha256":"a94775180fd85e9473161bc9a5d896c47920f7d773dce81b971d255009ba6585"}}