{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:G7TETBTMRYCEIFB4CX42GVYNPZ","short_pith_number":"pith:G7TETBTM","canonical_record":{"source":{"id":"2412.14723","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-19T10:46:12Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"dc3ec3c55e4bfea5ba89ef96aec5045904f64b253b45a99cd312ce4f190a1a62","abstract_canon_sha256":"db3d8d8c24a6b17a802bd85c5e0e2ff1de3b5db328cb3e4a34ddce237030e8c7"},"schema_version":"1.0"},"canonical_sha256":"37e649866c8e0444143c15f9a3570d7e54588d717b1ed99526d0511efb352e64","source":{"kind":"arxiv","id":"2412.14723","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.14723","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"arxiv_version","alias_value":"2412.14723v3","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.14723","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"pith_short_12","alias_value":"G7TETBTMRYCE","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"pith_short_16","alias_value":"G7TETBTMRYCEIFB4","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"pith_short_8","alias_value":"G7TETBTM","created_at":"2026-07-22T01:23:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:G7TETBTMRYCEIFB4CX42GVYNPZ","target":"record","payload":{"canonical_record":{"source":{"id":"2412.14723","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-19T10:46:12Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"dc3ec3c55e4bfea5ba89ef96aec5045904f64b253b45a99cd312ce4f190a1a62","abstract_canon_sha256":"db3d8d8c24a6b17a802bd85c5e0e2ff1de3b5db328cb3e4a34ddce237030e8c7"},"schema_version":"1.0"},"canonical_sha256":"37e649866c8e0444143c15f9a3570d7e54588d717b1ed99526d0511efb352e64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T01:23:29.714183Z","signature_b64":"E0V6i5G+CKc52HjbvX62lgmoCq9PVcokc7BI/MwLKP6UqxOKJkOu36w0JGD48qrSpY5HGMCYKnpOwMFpvKh0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37e649866c8e0444143c15f9a3570d7e54588d717b1ed99526d0511efb352e64","last_reissued_at":"2026-07-22T01:23:29.713277Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T01:23:29.713277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.14723","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-22T01:23:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DhLsidAjUBiBefWxnynmjtzojsuMFigyuobUf/vRdAXME/IVL3QRh5vlGUUlkid9iElVWUyMhmYfslFbFVMLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:11:01.249127Z"},"content_sha256":"3410582c6cf8b78583768c9f346c42d428fa73d9292a4ceac3f88deeb10430c1","schema_version":"1.0","event_id":"sha256:3410582c6cf8b78583768c9f346c42d428fa73d9292a4ceac3f88deeb10430c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:G7TETBTMRYCEIFB4CX42GVYNPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension reduction for path signatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Christian Bayer, Martin Redmann","submitted_at":"2024-12-19T10:46:12Z","abstract_excerpt":"This paper focuses on the mathematical framework for reducing the complexity of models using path signatures. The structure of these signatures, which can be interpreted as collections of iterated integrals along paths, is discussed and their applications in areas such as stochastic differential equations (SDEs) and financial modeling are pointed out. In particular, exploiting the rough paths view, solutions of SDEs continuously depend on the lift of the driver. Such continuous mappings can be approximated using (truncated) signatures, which are solutions of high-dimensional linear systems. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14723","kind":"arxiv","version":3},"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/2412.14723/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":"2026-07-22T01:23:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U3ZEPHHc5HnHK8TZ8Y6QG8XYUlfLONCpP51bbnudeG0oLwpEDlADjbM1NnMbdPiITxtgE1hkpAHEIVLPH0l2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:11:01.250101Z"},"content_sha256":"0772f27287350aee931fdd0fc0560027453e900f5d8acba912d61c3d96c9ea93","schema_version":"1.0","event_id":"sha256:0772f27287350aee931fdd0fc0560027453e900f5d8acba912d61c3d96c9ea93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G7TETBTMRYCEIFB4CX42GVYNPZ/bundle.json","state_url":"https://pith.science/pith/G7TETBTMRYCEIFB4CX42GVYNPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G7TETBTMRYCEIFB4CX42GVYNPZ/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":"2026-08-17T18:11:01Z","links":{"resolver":"https://pith.science/pith/G7TETBTMRYCEIFB4CX42GVYNPZ","bundle":"https://pith.science/pith/G7TETBTMRYCEIFB4CX42GVYNPZ/bundle.json","state":"https://pith.science/pith/G7TETBTMRYCEIFB4CX42GVYNPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G7TETBTMRYCEIFB4CX42GVYNPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:G7TETBTMRYCEIFB4CX42GVYNPZ","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":"db3d8d8c24a6b17a802bd85c5e0e2ff1de3b5db328cb3e4a34ddce237030e8c7","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-19T10:46:12Z","title_canon_sha256":"dc3ec3c55e4bfea5ba89ef96aec5045904f64b253b45a99cd312ce4f190a1a62"},"schema_version":"1.0","source":{"id":"2412.14723","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.14723","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"arxiv_version","alias_value":"2412.14723v3","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.14723","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"pith_short_12","alias_value":"G7TETBTMRYCE","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"pith_short_16","alias_value":"G7TETBTMRYCEIFB4","created_at":"2026-07-22T01:23:29Z"},{"alias_kind":"pith_short_8","alias_value":"G7TETBTM","created_at":"2026-07-22T01:23:29Z"}],"graph_snapshots":[{"event_id":"sha256:0772f27287350aee931fdd0fc0560027453e900f5d8acba912d61c3d96c9ea93","target":"graph","created_at":"2026-07-22T01:23:29Z","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/2412.14723/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper focuses on the mathematical framework for reducing the complexity of models using path signatures. The structure of these signatures, which can be interpreted as collections of iterated integrals along paths, is discussed and their applications in areas such as stochastic differential equations (SDEs) and financial modeling are pointed out. In particular, exploiting the rough paths view, solutions of SDEs continuously depend on the lift of the driver. Such continuous mappings can be approximated using (truncated) signatures, which are solutions of high-dimensional linear systems. In","authors_text":"Christian Bayer, Martin Redmann","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-19T10:46:12Z","title":"Dimension reduction for path signatures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14723","kind":"arxiv","version":3},"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":"sha256:3410582c6cf8b78583768c9f346c42d428fa73d9292a4ceac3f88deeb10430c1","target":"record","created_at":"2026-07-22T01:23:29Z","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":"db3d8d8c24a6b17a802bd85c5e0e2ff1de3b5db328cb3e4a34ddce237030e8c7","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-19T10:46:12Z","title_canon_sha256":"dc3ec3c55e4bfea5ba89ef96aec5045904f64b253b45a99cd312ce4f190a1a62"},"schema_version":"1.0","source":{"id":"2412.14723","kind":"arxiv","version":3}},"canonical_sha256":"37e649866c8e0444143c15f9a3570d7e54588d717b1ed99526d0511efb352e64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37e649866c8e0444143c15f9a3570d7e54588d717b1ed99526d0511efb352e64","first_computed_at":"2026-07-22T01:23:29.713277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T01:23:29.713277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E0V6i5G+CKc52HjbvX62lgmoCq9PVcokc7BI/MwLKP6UqxOKJkOu36w0JGD48qrSpY5HGMCYKnpOwMFpvKh0DA==","signature_status":"signed_v1","signed_at":"2026-07-22T01:23:29.714183Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.14723","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3410582c6cf8b78583768c9f346c42d428fa73d9292a4ceac3f88deeb10430c1","sha256:0772f27287350aee931fdd0fc0560027453e900f5d8acba912d61c3d96c9ea93"],"state_sha256":"bbd74c64238a45651c543e0826681f8fbcd638d8567d9e6fb8601076a845bae6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fmLplIktV3DD5M5nKW5yGY9IpCPbdjzD3+Lx6p6BDr3HeXl7nxImvYPm5NlLPjnslCTiJYEMlrHO9j9XvlvtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T18:11:01.270733Z","bundle_sha256":"e1bd73d60074edb7b5b95619576260b5f64eb2110745430ca6f73721b3a3af9b"}}