{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:SLLV2ACY3KZ5FI57KE4JSFNWAP","short_pith_number":"pith:SLLV2ACY","canonical_record":{"source":{"id":"2404.06583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-04-09T19:25:16Z","cross_cats_sorted":["math.PR","math.ST","stat.TH"],"title_canon_sha256":"ad291efd1ad90674a60b7826ac5a82cf6986a5a85bfb10b12fbe3134712847f4","abstract_canon_sha256":"b48a55ded13a10110c1355002960564e13af50ce55e553c990e46658ac318d6a"},"schema_version":"1.0"},"canonical_sha256":"92d75d0058dab3d2a3bf51389915b603d88da8a7b74fca11b4ff63d9aa1d8b1a","source":{"kind":"arxiv","id":"2404.06583","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.06583","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"arxiv_version","alias_value":"2404.06583v1","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06583","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"pith_short_12","alias_value":"SLLV2ACY3KZ5","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"pith_short_16","alias_value":"SLLV2ACY3KZ5FI57","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"pith_short_8","alias_value":"SLLV2ACY","created_at":"2026-07-05T08:06:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:SLLV2ACY3KZ5FI57KE4JSFNWAP","target":"record","payload":{"canonical_record":{"source":{"id":"2404.06583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-04-09T19:25:16Z","cross_cats_sorted":["math.PR","math.ST","stat.TH"],"title_canon_sha256":"ad291efd1ad90674a60b7826ac5a82cf6986a5a85bfb10b12fbe3134712847f4","abstract_canon_sha256":"b48a55ded13a10110c1355002960564e13af50ce55e553c990e46658ac318d6a"},"schema_version":"1.0"},"canonical_sha256":"92d75d0058dab3d2a3bf51389915b603d88da8a7b74fca11b4ff63d9aa1d8b1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:06:14.510069Z","signature_b64":"M1KpuHgU9hmFCmHWoja5IlcW5TeTknNUMqzh2zQjf90CaOS7RB00GUM0T6dYN6lCWl+yLPGKUmgdgaX/Jx5VAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92d75d0058dab3d2a3bf51389915b603d88da8a7b74fca11b4ff63d9aa1d8b1a","last_reissued_at":"2026-07-05T08:06:14.509652Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:06:14.509652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.06583","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":"2026-07-05T08:06:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GbLvy/THJnvHwDO+tWMmOwLPI8rZyfvyIjIzRNKaT4/ErnsJtbEPwhlrRUflN2MfehuNaVXpMmQ5tbuMxpyjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T10:34:10.050460Z"},"content_sha256":"2fd34467322dd7e44eab3729a084a3785a12c502d4a1ca6e35bbc17822a32ac0","schema_version":"1.0","event_id":"sha256:2fd34467322dd7e44eab3729a084a3785a12c502d4a1ca6e35bbc17822a32ac0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:SLLV2ACY3KZ5FI57KE4JSFNWAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lecture notes on rough paths and applications to machine learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Cristopher Salvi, Thomas Cass","submitted_at":"2024-04-09T19:25:16Z","abstract_excerpt":"These notes expound the recent use of the signature transform and rough path theory in data science and machine learning. We develop the core theory of the signature from first principles and then survey some recent popular applications of this approach, including signature-based kernel methods and neural rough differential equations. The notes are based on a course given by the two authors at Imperial College London."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06583","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/2404.06583/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":"2026-07-05T08:06:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xyYVKjBFZbmIKywsseMpHOcjD43NZnxLL7UWTCQjuV+jTjRQDs58zu8YMR6MgeBhWw19DNcE5S21KHO4nu3xBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T10:34:10.050838Z"},"content_sha256":"5bdbe4c2aad55f390fcd7cd6af65ac97c9c4964fdb676d631d2053b99c35195f","schema_version":"1.0","event_id":"sha256:5bdbe4c2aad55f390fcd7cd6af65ac97c9c4964fdb676d631d2053b99c35195f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SLLV2ACY3KZ5FI57KE4JSFNWAP/bundle.json","state_url":"https://pith.science/pith/SLLV2ACY3KZ5FI57KE4JSFNWAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SLLV2ACY3KZ5FI57KE4JSFNWAP/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":"2026-07-10T10:34:10Z","links":{"resolver":"https://pith.science/pith/SLLV2ACY3KZ5FI57KE4JSFNWAP","bundle":"https://pith.science/pith/SLLV2ACY3KZ5FI57KE4JSFNWAP/bundle.json","state":"https://pith.science/pith/SLLV2ACY3KZ5FI57KE4JSFNWAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SLLV2ACY3KZ5FI57KE4JSFNWAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SLLV2ACY3KZ5FI57KE4JSFNWAP","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":"b48a55ded13a10110c1355002960564e13af50ce55e553c990e46658ac318d6a","cross_cats_sorted":["math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-04-09T19:25:16Z","title_canon_sha256":"ad291efd1ad90674a60b7826ac5a82cf6986a5a85bfb10b12fbe3134712847f4"},"schema_version":"1.0","source":{"id":"2404.06583","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.06583","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"arxiv_version","alias_value":"2404.06583v1","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06583","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"pith_short_12","alias_value":"SLLV2ACY3KZ5","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"pith_short_16","alias_value":"SLLV2ACY3KZ5FI57","created_at":"2026-07-05T08:06:14Z"},{"alias_kind":"pith_short_8","alias_value":"SLLV2ACY","created_at":"2026-07-05T08:06:14Z"}],"graph_snapshots":[{"event_id":"sha256:5bdbe4c2aad55f390fcd7cd6af65ac97c9c4964fdb676d631d2053b99c35195f","target":"graph","created_at":"2026-07-05T08:06:14Z","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/2404.06583/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These notes expound the recent use of the signature transform and rough path theory in data science and machine learning. We develop the core theory of the signature from first principles and then survey some recent popular applications of this approach, including signature-based kernel methods and neural rough differential equations. The notes are based on a course given by the two authors at Imperial College London.","authors_text":"Cristopher Salvi, Thomas Cass","cross_cats":["math.PR","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-04-09T19:25:16Z","title":"Lecture notes on rough paths and applications to machine learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06583","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":"sha256:2fd34467322dd7e44eab3729a084a3785a12c502d4a1ca6e35bbc17822a32ac0","target":"record","created_at":"2026-07-05T08:06:14Z","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":"b48a55ded13a10110c1355002960564e13af50ce55e553c990e46658ac318d6a","cross_cats_sorted":["math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-04-09T19:25:16Z","title_canon_sha256":"ad291efd1ad90674a60b7826ac5a82cf6986a5a85bfb10b12fbe3134712847f4"},"schema_version":"1.0","source":{"id":"2404.06583","kind":"arxiv","version":1}},"canonical_sha256":"92d75d0058dab3d2a3bf51389915b603d88da8a7b74fca11b4ff63d9aa1d8b1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92d75d0058dab3d2a3bf51389915b603d88da8a7b74fca11b4ff63d9aa1d8b1a","first_computed_at":"2026-07-05T08:06:14.509652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:06:14.509652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M1KpuHgU9hmFCmHWoja5IlcW5TeTknNUMqzh2zQjf90CaOS7RB00GUM0T6dYN6lCWl+yLPGKUmgdgaX/Jx5VAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:06:14.510069Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.06583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fd34467322dd7e44eab3729a084a3785a12c502d4a1ca6e35bbc17822a32ac0","sha256:5bdbe4c2aad55f390fcd7cd6af65ac97c9c4964fdb676d631d2053b99c35195f"],"state_sha256":"4bb24965a27fe445c65d40c266d0499896c92ab3b0efc9b8d958f018cb9280a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OqsRP+uJaNhCWgS8Dhrip7koxSxJe/1N5dGogJ42/KfLD/YJjYzm4E4pY2tHniea7g2Llg10mEO70rnIySqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-10T10:34:10.053234Z","bundle_sha256":"37df3b71996bb2f57d31f936575d90f8cfe8e9421636dca7d419c422d9676595"}}