{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HL3PWH3BO7UNJFKMWZ4TDPZGZY","short_pith_number":"pith:HL3PWH3B","canonical_record":{"source":{"id":"2605.16747","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T02:03:20Z","cross_cats_sorted":["math.AP","math.OC","math.PR","math.ST","stat.TH"],"title_canon_sha256":"5fd3a623f34f363407e3d4d72356d76f357b62346441e5963b0f3794533f43c6","abstract_canon_sha256":"79c9dc5f2d925f46e75e1b95dbfbae7560e5fedfd991ccadeb2d40a8f56dcfa7"},"schema_version":"1.0"},"canonical_sha256":"3af6fb1f6177e8d4954cb67931bf26ce00271e6f1c3115f59895937bf63972e3","source":{"kind":"arxiv","id":"2605.16747","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16747","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16747v1","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16747","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"HL3PWH3BO7UN","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"pith_short_16","alias_value":"HL3PWH3BO7UNJFKM","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"pith_short_8","alias_value":"HL3PWH3B","created_at":"2026-05-20T00:03:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HL3PWH3BO7UNJFKMWZ4TDPZGZY","target":"record","payload":{"canonical_record":{"source":{"id":"2605.16747","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T02:03:20Z","cross_cats_sorted":["math.AP","math.OC","math.PR","math.ST","stat.TH"],"title_canon_sha256":"5fd3a623f34f363407e3d4d72356d76f357b62346441e5963b0f3794533f43c6","abstract_canon_sha256":"79c9dc5f2d925f46e75e1b95dbfbae7560e5fedfd991ccadeb2d40a8f56dcfa7"},"schema_version":"1.0"},"canonical_sha256":"3af6fb1f6177e8d4954cb67931bf26ce00271e6f1c3115f59895937bf63972e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:19.481296Z","signature_b64":"TZE+NFKUUKwi7CneQCZlPjHc7aSSUoR4AcVZibhsFEg6zDLc+ZKi6xxOCVan8VQKS5z5V9sKzgjPaAOYt8vsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3af6fb1f6177e8d4954cb67931bf26ce00271e6f1c3115f59895937bf63972e3","last_reissued_at":"2026-05-20T00:03:19.480239Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:19.480239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.16747","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":"2026-05-20T00:03:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkIZgsbnNYFUPKN8VtoGe8jb0dXzK4Zv8ZTyfT9bRcpUSaxn6QmrYZP8s4LFZflL5UcFXIX0MIn6l8BMrBp/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:40:41.538228Z"},"content_sha256":"673e0749b04b367449621eef17f601fa49349322c9b5751ffa5a77c6e9529769","schema_version":"1.0","event_id":"sha256:673e0749b04b367449621eef17f601fa49349322c9b5751ffa5a77c6e9529769"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HL3PWH3BO7UNJFKMWZ4TDPZGZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Propagation of Chaos in Contextual Flow Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Finite-context models converge to infinite-context versions uniformly in depth and training steps at optimal Wasserstein rates.","cross_cats":["math.AP","math.OC","math.PR","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Kaizhao Liu, Philippe Rigollet, Shi Chen, Zhengjiang Lin","submitted_at":"2026-05-16T02:03:20Z","abstract_excerpt":"We develop a quantitative statistical theory of transformers in the large-context regime by adopting the abstraction of contextual flow maps (CFMs): dynamical systems that evolve a distinguished token in the presence of a contextual measure across a stack of attention blocks. Within this framework, the finite-context model approximates an idealized infinite-context system in which the contextual measure is replaced by its underlying population, so that the context length $n$ becomes a statistical resource. Exploiting the McKean--Vlasov structure of the dynamics and the classical machinery of p"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish a forward bound controlling the deviation between the finite- and infinite-context CFMs uniformly along depth, and a backward bound controlling the deviation between the corresponding training trajectories uniformly across iterations of online gradient descent. Both bounds achieve the optimal Wasserstein rate n^{-1/d} for general CFMs and parametric rate n^{-1/2} for a restricted class of CFMs that includes transformers as a special case.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The dynamics of the attention blocks admit a McKean-Vlasov structure so that the finite-context empirical measure converges to a population measure in the large-n limit; this is invoked to apply classical propagation-of-chaos machinery (abstract, paragraph on McKean-Vlasov structure).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives forward and backward propagation-of-chaos bounds for finite vs. infinite-context transformers modeled as contextual flow maps, achieving Wasserstein rate n^{-1/d} generally and n^{-1/2} for transformer-like cases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Finite-context models converge to infinite-context versions uniformly in depth and training steps at optimal Wasserstein rates.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4b1696ea3d5175fd5b9a23981ff54ee7bd313e6513acf15eac02af4d313263bd"},"source":{"id":"2605.16747","kind":"arxiv","version":1},"verdict":{"id":"9491591e-e120-4485-9bee-b853e3fc8d04","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:15:44.139730Z","strongest_claim":"We establish a forward bound controlling the deviation between the finite- and infinite-context CFMs uniformly along depth, and a backward bound controlling the deviation between the corresponding training trajectories uniformly across iterations of online gradient descent. Both bounds achieve the optimal Wasserstein rate n^{-1/d} for general CFMs and parametric rate n^{-1/2} for a restricted class of CFMs that includes transformers as a special case.","one_line_summary":"Derives forward and backward propagation-of-chaos bounds for finite vs. infinite-context transformers modeled as contextual flow maps, achieving Wasserstein rate n^{-1/d} generally and n^{-1/2} for transformer-like cases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The dynamics of the attention blocks admit a McKean-Vlasov structure so that the finite-context empirical measure converges to a population measure in the large-n limit; this is invoked to apply classical propagation-of-chaos machinery (abstract, paragraph on McKean-Vlasov structure).","pith_extraction_headline":"Finite-context models converge to infinite-context versions uniformly in depth and training steps at optimal Wasserstein rates."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16747/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.163510Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:22:11.512694Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.329523Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.459780Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6303bd8a460a220a3ff93483a6cd5fc147a16daacf37cb5c4b5df01fe11acdd7"},"references":{"count":21,"sample":[{"doi":"","year":null,"title":"[ÁLGRB26] Antonio Álvarez-López, Borjan Geshkovski, and Domènec Ruiz-Balet","work_id":"04dcc830-26c9-4d53-a03a-9610389db975","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Perceptrons and localization of attention’s mean-field landscape","work_id":"9fa6df2f-3410-4bf8-9e33-0ba750fb8576","ref_index":2,"cited_arxiv_id":"2601.21366","is_internal_anchor":true},{"doi":"","year":null,"title":"[BCL+26] Giuseppe Bruno, Shi Chen, Zhengjiang Lin, Yury Polyanskiy, and Philippe Rigollet","work_id":"dd1dccbe-d10b-4755-a09d-154d6b7a49b0","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Scaling Limits of Long-Context Transformers","work_id":"a43dad01-bd2f-4ec0-a7fb-6fe560c35c34","ref_index":4,"cited_arxiv_id":"2605.08505","is_internal_anchor":true},{"doi":"","year":null,"title":"[BO20] Tom B","work_id":"990fb2ff-4f53-40a4-8805-541835999e17","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":21,"snapshot_sha256":"4a8a7d006c96f7534755a2dd51241ede42cc0ed174d6806b03d5cf8fb7e4560f","internal_anchors":6},"formal_canon":{"evidence_count":1,"snapshot_sha256":"bcc4a03d1502d975e7a32e3bdd0bdc3e5d74aad94837da5ba10b65d479e9a36a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"9491591e-e120-4485-9bee-b853e3fc8d04"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:03:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2K6QXiKhrx0i5+Z6DDu9SdcWbOHWYtlXQqsRFMK6fxcgeojNT0vfGrhod3hWgxInmS6VRRhK+PZTnTq1+Tq/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:40:41.539660Z"},"content_sha256":"e7db57c1c3f17083ea3c9bf5a5d92278591405f3329ad268547fd7bcaece2dde","schema_version":"1.0","event_id":"sha256:e7db57c1c3f17083ea3c9bf5a5d92278591405f3329ad268547fd7bcaece2dde"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HL3PWH3BO7UNJFKMWZ4TDPZGZY/bundle.json","state_url":"https://pith.science/pith/HL3PWH3BO7UNJFKMWZ4TDPZGZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HL3PWH3BO7UNJFKMWZ4TDPZGZY/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":"2026-05-25T20:40:41Z","links":{"resolver":"https://pith.science/pith/HL3PWH3BO7UNJFKMWZ4TDPZGZY","bundle":"https://pith.science/pith/HL3PWH3BO7UNJFKMWZ4TDPZGZY/bundle.json","state":"https://pith.science/pith/HL3PWH3BO7UNJFKMWZ4TDPZGZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HL3PWH3BO7UNJFKMWZ4TDPZGZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HL3PWH3BO7UNJFKMWZ4TDPZGZY","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":"79c9dc5f2d925f46e75e1b95dbfbae7560e5fedfd991ccadeb2d40a8f56dcfa7","cross_cats_sorted":["math.AP","math.OC","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T02:03:20Z","title_canon_sha256":"5fd3a623f34f363407e3d4d72356d76f357b62346441e5963b0f3794533f43c6"},"schema_version":"1.0","source":{"id":"2605.16747","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16747","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16747v1","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16747","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"HL3PWH3BO7UN","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"pith_short_16","alias_value":"HL3PWH3BO7UNJFKM","created_at":"2026-05-20T00:03:19Z"},{"alias_kind":"pith_short_8","alias_value":"HL3PWH3B","created_at":"2026-05-20T00:03:19Z"}],"graph_snapshots":[{"event_id":"sha256:e7db57c1c3f17083ea3c9bf5a5d92278591405f3329ad268547fd7bcaece2dde","target":"graph","created_at":"2026-05-20T00:03:19Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We establish a forward bound controlling the deviation between the finite- and infinite-context CFMs uniformly along depth, and a backward bound controlling the deviation between the corresponding training trajectories uniformly across iterations of online gradient descent. Both bounds achieve the optimal Wasserstein rate n^{-1/d} for general CFMs and parametric rate n^{-1/2} for a restricted class of CFMs that includes transformers as a special case."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The dynamics of the attention blocks admit a McKean-Vlasov structure so that the finite-context empirical measure converges to a population measure in the large-n limit; this is invoked to apply classical propagation-of-chaos machinery (abstract, paragraph on McKean-Vlasov structure)."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Derives forward and backward propagation-of-chaos bounds for finite vs. infinite-context transformers modeled as contextual flow maps, achieving Wasserstein rate n^{-1/d} generally and n^{-1/2} for transformer-like cases."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Finite-context models converge to infinite-context versions uniformly in depth and training steps at optimal Wasserstein rates."}],"snapshot_sha256":"4b1696ea3d5175fd5b9a23981ff54ee7bd313e6513acf15eac02af4d313263bd"},"formal_canon":{"evidence_count":1,"snapshot_sha256":"bcc4a03d1502d975e7a32e3bdd0bdc3e5d74aad94837da5ba10b65d479e9a36a"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.163510Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T20:22:11.512694Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.329523Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.459780Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.16747/integrity.json","findings":[],"snapshot_sha256":"6303bd8a460a220a3ff93483a6cd5fc147a16daacf37cb5c4b5df01fe11acdd7","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a quantitative statistical theory of transformers in the large-context regime by adopting the abstraction of contextual flow maps (CFMs): dynamical systems that evolve a distinguished token in the presence of a contextual measure across a stack of attention blocks. Within this framework, the finite-context model approximates an idealized infinite-context system in which the contextual measure is replaced by its underlying population, so that the context length $n$ becomes a statistical resource. Exploiting the McKean--Vlasov structure of the dynamics and the classical machinery of p","authors_text":"Kaizhao Liu, Philippe Rigollet, Shi Chen, Zhengjiang Lin","cross_cats":["math.AP","math.OC","math.PR","math.ST","stat.TH"],"headline":"Finite-context models converge to infinite-context versions uniformly in depth and training steps at optimal Wasserstein rates.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T02:03:20Z","title":"Propagation of Chaos in Contextual Flow Maps"},"references":{"count":21,"internal_anchors":6,"resolved_work":21,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"[ÁLGRB26] Antonio Álvarez-López, Borjan Geshkovski, and Domènec Ruiz-Balet","work_id":"04dcc830-26c9-4d53-a03a-9610389db975","year":null},{"cited_arxiv_id":"2601.21366","doi":"","is_internal_anchor":true,"ref_index":2,"title":"Perceptrons and localization of attention’s mean-field landscape","work_id":"9fa6df2f-3410-4bf8-9e33-0ba750fb8576","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"[BCL+26] Giuseppe Bruno, Shi Chen, Zhengjiang Lin, Yury Polyanskiy, and Philippe Rigollet","work_id":"dd1dccbe-d10b-4755-a09d-154d6b7a49b0","year":null},{"cited_arxiv_id":"2605.08505","doi":"","is_internal_anchor":true,"ref_index":4,"title":"Scaling Limits of Long-Context Transformers","work_id":"a43dad01-bd2f-4ec0-a7fb-6fe560c35c34","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"[BO20] Tom B","work_id":"990fb2ff-4f53-40a4-8805-541835999e17","year":null}],"snapshot_sha256":"4a8a7d006c96f7534755a2dd51241ede42cc0ed174d6806b03d5cf8fb7e4560f"},"source":{"id":"2605.16747","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T20:15:44.139730Z","id":"9491591e-e120-4485-9bee-b853e3fc8d04","model_set":{"reader":"grok-4.3"},"one_line_summary":"Derives forward and backward propagation-of-chaos bounds for finite vs. infinite-context transformers modeled as contextual flow maps, achieving Wasserstein rate n^{-1/d} generally and n^{-1/2} for transformer-like cases.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Finite-context models converge to infinite-context versions uniformly in depth and training steps at optimal Wasserstein rates.","strongest_claim":"We establish a forward bound controlling the deviation between the finite- and infinite-context CFMs uniformly along depth, and a backward bound controlling the deviation between the corresponding training trajectories uniformly across iterations of online gradient descent. Both bounds achieve the optimal Wasserstein rate n^{-1/d} for general CFMs and parametric rate n^{-1/2} for a restricted class of CFMs that includes transformers as a special case.","weakest_assumption":"The dynamics of the attention blocks admit a McKean-Vlasov structure so that the finite-context empirical measure converges to a population measure in the large-n limit; this is invoked to apply classical propagation-of-chaos machinery (abstract, paragraph on McKean-Vlasov structure)."}},"verdict_id":"9491591e-e120-4485-9bee-b853e3fc8d04"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:673e0749b04b367449621eef17f601fa49349322c9b5751ffa5a77c6e9529769","target":"record","created_at":"2026-05-20T00:03:19Z","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":"79c9dc5f2d925f46e75e1b95dbfbae7560e5fedfd991ccadeb2d40a8f56dcfa7","cross_cats_sorted":["math.AP","math.OC","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T02:03:20Z","title_canon_sha256":"5fd3a623f34f363407e3d4d72356d76f357b62346441e5963b0f3794533f43c6"},"schema_version":"1.0","source":{"id":"2605.16747","kind":"arxiv","version":1}},"canonical_sha256":"3af6fb1f6177e8d4954cb67931bf26ce00271e6f1c3115f59895937bf63972e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3af6fb1f6177e8d4954cb67931bf26ce00271e6f1c3115f59895937bf63972e3","first_computed_at":"2026-05-20T00:03:19.480239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:19.480239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZE+NFKUUKwi7CneQCZlPjHc7aSSUoR4AcVZibhsFEg6zDLc+ZKi6xxOCVan8VQKS5z5V9sKzgjPaAOYt8vsCA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:19.481296Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16747","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:673e0749b04b367449621eef17f601fa49349322c9b5751ffa5a77c6e9529769","sha256:e7db57c1c3f17083ea3c9bf5a5d92278591405f3329ad268547fd7bcaece2dde"],"state_sha256":"9a153839744350cae1f380bf63990a852c4abd6626eefc0c310b8621cf4f26bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cnr2acfZZC9nz0m+ZCVIDB6ijGgzOvMnEXv/m1hly71+lB1Hcpzt84DR9uPnHN2rk4e0gLSQpb7SKqf/hOW7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:40:41.545897Z","bundle_sha256":"aef226bd444ce584b8ef02967446b240887edf8e0092dc4241b38cf02b302c7e"}}