{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:H5ZARMVQZRLHNGZ3WXG3LK3KAB","short_pith_number":"pith:H5ZARMVQ","canonical_record":{"source":{"id":"1607.04375","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-15T04:07:04Z","cross_cats_sorted":[],"title_canon_sha256":"bfc968cd09b2c6c1403a2276801baad6cbeff28d2072dedb33089547acc49134","abstract_canon_sha256":"9f842f0d21a0a867dc332061f208c0b2157eae8eb2d8b29aa4ebbd6ba3cd5ce2"},"schema_version":"1.0"},"canonical_sha256":"3f7208b2b0cc56769b3bb5cdb5ab6a0046aa5f8b5b5a077ae43e354b3cba813f","source":{"kind":"arxiv","id":"1607.04375","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04375","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04375v2","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04375","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"pith_short_12","alias_value":"H5ZARMVQZRLH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H5ZARMVQZRLHNGZ3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H5ZARMVQ","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:H5ZARMVQZRLHNGZ3WXG3LK3KAB","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04375","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-15T04:07:04Z","cross_cats_sorted":[],"title_canon_sha256":"bfc968cd09b2c6c1403a2276801baad6cbeff28d2072dedb33089547acc49134","abstract_canon_sha256":"9f842f0d21a0a867dc332061f208c0b2157eae8eb2d8b29aa4ebbd6ba3cd5ce2"},"schema_version":"1.0"},"canonical_sha256":"3f7208b2b0cc56769b3bb5cdb5ab6a0046aa5f8b5b5a077ae43e354b3cba813f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:24.354426Z","signature_b64":"ghFrNRI6ZZlH4yjqWdwv0smObbMTSjxbrjjiJKiuYGgTS0HpmbaNdhx5TuKZT66BLDyafw1+AMP2Q/m3jwfoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f7208b2b0cc56769b3bb5cdb5ab6a0046aa5f8b5b5a077ae43e354b3cba813f","last_reissued_at":"2026-05-18T00:59:24.353969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:24.353969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04375","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":"2026-05-18T00:59:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9LrCPdt0cQzIylJAL8R9EdmeferRHa0m5M2s+FB0GVR/lbVu/fn1Y65yPbjtoVuTVHds6LX7eL4XB18JDxrPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:35:20.152128Z"},"content_sha256":"718698881a613c7315165cbf4c099dcdba419b2687dcb2061d447accd112799a","schema_version":"1.0","event_id":"sha256:718698881a613c7315165cbf4c099dcdba419b2687dcb2061d447accd112799a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:H5ZARMVQZRLHNGZ3WXG3LK3KAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representation of functions on big data associated with directed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Charles K.Chui, H. N. Mhaskar, Xiaosheng Zhuang","submitted_at":"2016-07-15T04:07:04Z","abstract_excerpt":"This paper is an extension of the previous work of Chui, Filbir, and Mhaskar (Appl. Comput. Harm. Anal. 38 (3) 2015:489-509), not only from numeric data to include non-numeric data as in that paper, but also from undirected graphs to directed graphs (called digraphs, for simplicity). Besides theoretical development, this paper introduces effective mathematical tools in terms of certain data-dependent orthogonal systems for function representation and analysis directly on the digraphs. In addition, this paper also includes algorithmic development and discussion of various experimental results o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04375","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":""},"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":"2026-05-18T00:59:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wvY13IawKgs+hkmSMz34ftO3zUXR2I8cR+36i4Vu1ZW9RTBE5dk7XhRIzpnGbhnh2HeFXWIz22UHHqgY9bG6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:35:20.152498Z"},"content_sha256":"673b9c38d628a8bad21efdf70d72ece98d638710ebe09b10e5e8241598faeddc","schema_version":"1.0","event_id":"sha256:673b9c38d628a8bad21efdf70d72ece98d638710ebe09b10e5e8241598faeddc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5ZARMVQZRLHNGZ3WXG3LK3KAB/bundle.json","state_url":"https://pith.science/pith/H5ZARMVQZRLHNGZ3WXG3LK3KAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5ZARMVQZRLHNGZ3WXG3LK3KAB/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":"2026-05-31T07:35:20Z","links":{"resolver":"https://pith.science/pith/H5ZARMVQZRLHNGZ3WXG3LK3KAB","bundle":"https://pith.science/pith/H5ZARMVQZRLHNGZ3WXG3LK3KAB/bundle.json","state":"https://pith.science/pith/H5ZARMVQZRLHNGZ3WXG3LK3KAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5ZARMVQZRLHNGZ3WXG3LK3KAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H5ZARMVQZRLHNGZ3WXG3LK3KAB","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":"9f842f0d21a0a867dc332061f208c0b2157eae8eb2d8b29aa4ebbd6ba3cd5ce2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-15T04:07:04Z","title_canon_sha256":"bfc968cd09b2c6c1403a2276801baad6cbeff28d2072dedb33089547acc49134"},"schema_version":"1.0","source":{"id":"1607.04375","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04375","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04375v2","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04375","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"pith_short_12","alias_value":"H5ZARMVQZRLH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H5ZARMVQZRLHNGZ3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H5ZARMVQ","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:673b9c38d628a8bad21efdf70d72ece98d638710ebe09b10e5e8241598faeddc","target":"graph","created_at":"2026-05-18T00:59:24Z","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"},"paper":{"abstract_excerpt":"This paper is an extension of the previous work of Chui, Filbir, and Mhaskar (Appl. Comput. Harm. Anal. 38 (3) 2015:489-509), not only from numeric data to include non-numeric data as in that paper, but also from undirected graphs to directed graphs (called digraphs, for simplicity). Besides theoretical development, this paper introduces effective mathematical tools in terms of certain data-dependent orthogonal systems for function representation and analysis directly on the digraphs. In addition, this paper also includes algorithmic development and discussion of various experimental results o","authors_text":"Charles K.Chui, H. N. Mhaskar, Xiaosheng Zhuang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-15T04:07:04Z","title":"Representation of functions on big data associated with directed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04375","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":"sha256:718698881a613c7315165cbf4c099dcdba419b2687dcb2061d447accd112799a","target":"record","created_at":"2026-05-18T00:59:24Z","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":"9f842f0d21a0a867dc332061f208c0b2157eae8eb2d8b29aa4ebbd6ba3cd5ce2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-15T04:07:04Z","title_canon_sha256":"bfc968cd09b2c6c1403a2276801baad6cbeff28d2072dedb33089547acc49134"},"schema_version":"1.0","source":{"id":"1607.04375","kind":"arxiv","version":2}},"canonical_sha256":"3f7208b2b0cc56769b3bb5cdb5ab6a0046aa5f8b5b5a077ae43e354b3cba813f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f7208b2b0cc56769b3bb5cdb5ab6a0046aa5f8b5b5a077ae43e354b3cba813f","first_computed_at":"2026-05-18T00:59:24.353969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:24.353969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ghFrNRI6ZZlH4yjqWdwv0smObbMTSjxbrjjiJKiuYGgTS0HpmbaNdhx5TuKZT66BLDyafw1+AMP2Q/m3jwfoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:24.354426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04375","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:718698881a613c7315165cbf4c099dcdba419b2687dcb2061d447accd112799a","sha256:673b9c38d628a8bad21efdf70d72ece98d638710ebe09b10e5e8241598faeddc"],"state_sha256":"4056373033636338d726658f819bccbf9d29b237c0762324f1e1e94510340cca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yajHS3Rfu68tY30tqxQtUKKjuxrE0mNQBP9IXsENY4msP5IMPt4TtqlEyHCVJwL6jrHXvKoddVVJKSpl1jUiAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:35:20.154455Z","bundle_sha256":"c296b2255569f4de1d80997f670298fd794baafdaa810e10241096b5e05a39bd"}}