{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:LM6PVD7O63CGGCGL2DDSPDNPIK","short_pith_number":"pith:LM6PVD7O","canonical_record":{"source":{"id":"2212.14641","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-30T11:33:20Z","cross_cats_sorted":[],"title_canon_sha256":"82150f25c403a193534718a387f6074061077990f26c32f9f814a86afd7411a1","abstract_canon_sha256":"9bd19c58400fe0fd917838fe75c22f98379583edd77264d9d5b5be949aae80a0"},"schema_version":"1.0"},"canonical_sha256":"5b3cfa8feef6c46308cbd0c7278daf42b56367dd4d60f06f0c4ce64b1d0741fc","source":{"kind":"arxiv","id":"2212.14641","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.14641","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2212.14641v2","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.14641","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"LM6PVD7O63CG","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"LM6PVD7O63CGGCGL","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"LM6PVD7O","created_at":"2026-07-05T12:04:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:LM6PVD7O63CGGCGL2DDSPDNPIK","target":"record","payload":{"canonical_record":{"source":{"id":"2212.14641","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-30T11:33:20Z","cross_cats_sorted":[],"title_canon_sha256":"82150f25c403a193534718a387f6074061077990f26c32f9f814a86afd7411a1","abstract_canon_sha256":"9bd19c58400fe0fd917838fe75c22f98379583edd77264d9d5b5be949aae80a0"},"schema_version":"1.0"},"canonical_sha256":"5b3cfa8feef6c46308cbd0c7278daf42b56367dd4d60f06f0c4ce64b1d0741fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:04:24.773664Z","signature_b64":"GTEw/WfOMUwdLymh8khQhpeTEW8uvEVsCnqfdxILyMrUaGWQDFwiImCJt3sfAGe/w+rdK7p7786ARM4UbymlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b3cfa8feef6c46308cbd0c7278daf42b56367dd4d60f06f0c4ce64b1d0741fc","last_reissued_at":"2026-07-05T12:04:24.772940Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:04:24.772940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.14641","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":"2026-07-05T12:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPKmq86N3I8KykS8oycNHqMnKO8a9O/S0C4TEoI14iTYKuKOk+Fk5ZvQrZBU9Zi7QmY5TZxvtNsl3v4VJGdZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:22:27.225171Z"},"content_sha256":"23b5c2f9f81eeeaa8c76f46709a4acd1648e41af1037da6408a77871fcf3497d","schema_version":"1.0","event_id":"sha256:23b5c2f9f81eeeaa8c76f46709a4acd1648e41af1037da6408a77871fcf3497d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:LM6PVD7O63CGGCGL2DDSPDNPIK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reservoir kernels and Volterra series","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Juan-Pablo Ortega, Lukas Gonon, Lyudmila Grigoryeva","submitted_at":"2022-12-30T11:33:20Z","abstract_excerpt":"A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using the reservoir functional associated with a state-space representation of the Volterra series expansion available for any analytic fading memory filter, and it is hence called the Volterra reservoir kernel. Even though the state-space representation and the corresponding reservoir feature map are defined on an infinite-dimensional tensor algebra space, the kernel map is characte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.14641","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/2212.14641/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":"2026-07-05T12:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qfpBQRqhnxoATM03jrh+l+VhLRuff3lKvR6r49MxXeV4mwCeBwqqi0jDvacCXdlSIx3SNuERkIQfXUa0Wn8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:22:27.225656Z"},"content_sha256":"911439b9ea5d881f94bf3c24d359cbc6b6dd3c7a8407aee703746beffb6ed979","schema_version":"1.0","event_id":"sha256:911439b9ea5d881f94bf3c24d359cbc6b6dd3c7a8407aee703746beffb6ed979"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LM6PVD7O63CGGCGL2DDSPDNPIK/bundle.json","state_url":"https://pith.science/pith/LM6PVD7O63CGGCGL2DDSPDNPIK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LM6PVD7O63CGGCGL2DDSPDNPIK/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":"2026-08-08T12:22:27Z","links":{"resolver":"https://pith.science/pith/LM6PVD7O63CGGCGL2DDSPDNPIK","bundle":"https://pith.science/pith/LM6PVD7O63CGGCGL2DDSPDNPIK/bundle.json","state":"https://pith.science/pith/LM6PVD7O63CGGCGL2DDSPDNPIK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LM6PVD7O63CGGCGL2DDSPDNPIK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:LM6PVD7O63CGGCGL2DDSPDNPIK","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":"9bd19c58400fe0fd917838fe75c22f98379583edd77264d9d5b5be949aae80a0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-30T11:33:20Z","title_canon_sha256":"82150f25c403a193534718a387f6074061077990f26c32f9f814a86afd7411a1"},"schema_version":"1.0","source":{"id":"2212.14641","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.14641","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2212.14641v2","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.14641","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"LM6PVD7O63CG","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"LM6PVD7O63CGGCGL","created_at":"2026-07-05T12:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"LM6PVD7O","created_at":"2026-07-05T12:04:24Z"}],"graph_snapshots":[{"event_id":"sha256:911439b9ea5d881f94bf3c24d359cbc6b6dd3c7a8407aee703746beffb6ed979","target":"graph","created_at":"2026-07-05T12:04:24Z","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/2212.14641/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using the reservoir functional associated with a state-space representation of the Volterra series expansion available for any analytic fading memory filter, and it is hence called the Volterra reservoir kernel. Even though the state-space representation and the corresponding reservoir feature map are defined on an infinite-dimensional tensor algebra space, the kernel map is characte","authors_text":"Juan-Pablo Ortega, Lukas Gonon, Lyudmila Grigoryeva","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-30T11:33:20Z","title":"Reservoir kernels and Volterra series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.14641","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":"sha256:23b5c2f9f81eeeaa8c76f46709a4acd1648e41af1037da6408a77871fcf3497d","target":"record","created_at":"2026-07-05T12:04:24Z","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":"9bd19c58400fe0fd917838fe75c22f98379583edd77264d9d5b5be949aae80a0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2022-12-30T11:33:20Z","title_canon_sha256":"82150f25c403a193534718a387f6074061077990f26c32f9f814a86afd7411a1"},"schema_version":"1.0","source":{"id":"2212.14641","kind":"arxiv","version":2}},"canonical_sha256":"5b3cfa8feef6c46308cbd0c7278daf42b56367dd4d60f06f0c4ce64b1d0741fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b3cfa8feef6c46308cbd0c7278daf42b56367dd4d60f06f0c4ce64b1d0741fc","first_computed_at":"2026-07-05T12:04:24.772940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:24.772940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GTEw/WfOMUwdLymh8khQhpeTEW8uvEVsCnqfdxILyMrUaGWQDFwiImCJt3sfAGe/w+rdK7p7786ARM4UbymlBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:24.773664Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.14641","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23b5c2f9f81eeeaa8c76f46709a4acd1648e41af1037da6408a77871fcf3497d","sha256:911439b9ea5d881f94bf3c24d359cbc6b6dd3c7a8407aee703746beffb6ed979"],"state_sha256":"df4d567f0f60059037e5eadc38edbb1e04d1b925059e0cf39734fb552c8a41cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z7D2Eae9z6Zs0gBrJth6my4QkWZW2cms5G48znk31dRkp2BdSgQcWas7QFIB4ucravrHHrI9F4Yy3a/hZJP8DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T12:22:27.229169Z","bundle_sha256":"2f4c4e4c3291eccebfd24279a5ee6583156987d39ace96668582426e2e97e753"}}