{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NGOSDXQMY52FP4P43N2SYUKV6H","short_pith_number":"pith:NGOSDXQM","canonical_record":{"source":{"id":"1501.02310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-10T04:24:58Z","cross_cats_sorted":[],"title_canon_sha256":"b397e53eabafff4c468ce43d8349c1486ef48b1a16b0629a2b1d20c44f043d2e","abstract_canon_sha256":"5fc819a77a78c74c57592e392c4d450e85b92b7f2c83f97f710eb8f9b51c9a74"},"schema_version":"1.0"},"canonical_sha256":"699d21de0cc77457f1fcdb752c5155f1c7c994ba9b65b5c8268ccc01de0a781b","source":{"kind":"arxiv","id":"1501.02310","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02310","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02310v1","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02310","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"NGOSDXQMY52F","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGOSDXQMY52FP4P4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGOSDXQM","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NGOSDXQMY52FP4P43N2SYUKV6H","target":"record","payload":{"canonical_record":{"source":{"id":"1501.02310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-10T04:24:58Z","cross_cats_sorted":[],"title_canon_sha256":"b397e53eabafff4c468ce43d8349c1486ef48b1a16b0629a2b1d20c44f043d2e","abstract_canon_sha256":"5fc819a77a78c74c57592e392c4d450e85b92b7f2c83f97f710eb8f9b51c9a74"},"schema_version":"1.0"},"canonical_sha256":"699d21de0cc77457f1fcdb752c5155f1c7c994ba9b65b5c8268ccc01de0a781b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:38.273255Z","signature_b64":"PbJu+72+nGTmvVh0j+5BPF6P4Wl09C56q4PKR/OLAgMhte+CJgkxqcRAbJ/6D5dsOrbp/g9p88/6ZQ+3QipbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"699d21de0cc77457f1fcdb752c5155f1c7c994ba9b65b5c8268ccc01de0a781b","last_reissued_at":"2026-05-18T02:29:38.272806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:38.272806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.02310","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":"2026-05-18T02:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PTh1dturZUlq0DqytjUqP/+3mo+6qFS/4Q6VHdUB/uOWcreXgIp4lFBLpMdjuYfYWiJattr+zOZ4JaAfGjQXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T23:58:12.802299Z"},"content_sha256":"3608e8870778e9614f63ba4ad87cd0c131ab659e59abbfba897dc8167b34f08c","schema_version":"1.0","event_id":"sha256:3608e8870778e9614f63ba4ad87cd0c131ab659e59abbfba897dc8167b34f08c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NGOSDXQMY52FP4P43N2SYUKV6H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete reproducing kernel Hilbert spaces: Sampling and distribution of Dirac-masses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Feng Tian, Palle Jorgensen","submitted_at":"2015-01-10T04:24:58Z","abstract_excerpt":"We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) $\\mathscr{H}$ over infinite, discrete and countable sets $V$. In this setting we analyze in detail the distributions of the corresponding Dirac point-masses of $V$. Illustrations include certain models from neural networks: An Extreme Learning Machine (ELM) is a neural network-configuration in which a hidden layer of weights are randomly sampled, and where the object is then to compute resulting output. For RKHSs $\\mathscr{H}$ of functions defined on a prescribed countable infinite discrete set $V$, we chara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02310","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":""},"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":"2026-05-18T02:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c4cLa/1AxTpGI/uZvzMcnbJc4FLDcS61YwUOrQ7a1DL4uDy/krPg24zZxLchzr2pjWaP3kF2tow985UmkhxOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T23:58:12.802687Z"},"content_sha256":"358d691b3d5e040f26ea121e5708b447c9170d83911454f5b12b5482b5e6251c","schema_version":"1.0","event_id":"sha256:358d691b3d5e040f26ea121e5708b447c9170d83911454f5b12b5482b5e6251c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGOSDXQMY52FP4P43N2SYUKV6H/bundle.json","state_url":"https://pith.science/pith/NGOSDXQMY52FP4P43N2SYUKV6H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGOSDXQMY52FP4P43N2SYUKV6H/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":"2026-05-29T23:58:12Z","links":{"resolver":"https://pith.science/pith/NGOSDXQMY52FP4P43N2SYUKV6H","bundle":"https://pith.science/pith/NGOSDXQMY52FP4P43N2SYUKV6H/bundle.json","state":"https://pith.science/pith/NGOSDXQMY52FP4P43N2SYUKV6H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGOSDXQMY52FP4P43N2SYUKV6H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NGOSDXQMY52FP4P43N2SYUKV6H","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":"5fc819a77a78c74c57592e392c4d450e85b92b7f2c83f97f710eb8f9b51c9a74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-10T04:24:58Z","title_canon_sha256":"b397e53eabafff4c468ce43d8349c1486ef48b1a16b0629a2b1d20c44f043d2e"},"schema_version":"1.0","source":{"id":"1501.02310","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02310","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02310v1","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02310","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"NGOSDXQMY52F","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGOSDXQMY52FP4P4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGOSDXQM","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:358d691b3d5e040f26ea121e5708b447c9170d83911454f5b12b5482b5e6251c","target":"graph","created_at":"2026-05-18T02:29:38Z","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"},"paper":{"abstract_excerpt":"We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) $\\mathscr{H}$ over infinite, discrete and countable sets $V$. In this setting we analyze in detail the distributions of the corresponding Dirac point-masses of $V$. Illustrations include certain models from neural networks: An Extreme Learning Machine (ELM) is a neural network-configuration in which a hidden layer of weights are randomly sampled, and where the object is then to compute resulting output. For RKHSs $\\mathscr{H}$ of functions defined on a prescribed countable infinite discrete set $V$, we chara","authors_text":"Feng Tian, Palle Jorgensen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-10T04:24:58Z","title":"Discrete reproducing kernel Hilbert spaces: Sampling and distribution of Dirac-masses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02310","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":"sha256:3608e8870778e9614f63ba4ad87cd0c131ab659e59abbfba897dc8167b34f08c","target":"record","created_at":"2026-05-18T02:29:38Z","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":"5fc819a77a78c74c57592e392c4d450e85b92b7f2c83f97f710eb8f9b51c9a74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-10T04:24:58Z","title_canon_sha256":"b397e53eabafff4c468ce43d8349c1486ef48b1a16b0629a2b1d20c44f043d2e"},"schema_version":"1.0","source":{"id":"1501.02310","kind":"arxiv","version":1}},"canonical_sha256":"699d21de0cc77457f1fcdb752c5155f1c7c994ba9b65b5c8268ccc01de0a781b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"699d21de0cc77457f1fcdb752c5155f1c7c994ba9b65b5c8268ccc01de0a781b","first_computed_at":"2026-05-18T02:29:38.272806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:38.272806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PbJu+72+nGTmvVh0j+5BPF6P4Wl09C56q4PKR/OLAgMhte+CJgkxqcRAbJ/6D5dsOrbp/g9p88/6ZQ+3QipbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:38.273255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02310","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3608e8870778e9614f63ba4ad87cd0c131ab659e59abbfba897dc8167b34f08c","sha256:358d691b3d5e040f26ea121e5708b447c9170d83911454f5b12b5482b5e6251c"],"state_sha256":"6ee8f28b0a700f79bfb491276e2d77d7698cf74ab38c7f384fa65d0efeb1d149"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mbYn3B4B1uCuFFuiLbIQnFdwxV7HrpBRXpOPyCP5V5WMoKLKxUmh9uB6fyCAY4kjszCPQ2HOtpgIEVDP+WKlAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T23:58:12.805165Z","bundle_sha256":"4d7b4175c6023c08b5c057ff6b7c1bc61a9020a25ab03542b23a47e5e66522e3"}}