{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BXC5NQET7RHLTIVPT2SOLZCVQT","short_pith_number":"pith:BXC5NQET","canonical_record":{"source":{"id":"1503.01763","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-05T20:41:56Z","cross_cats_sorted":[],"title_canon_sha256":"e807384fe48c259dbb723b5734f9564fd9d6f12df706d0712b8290f12a353eee","abstract_canon_sha256":"557d41d501f66fd297ba888fb5dc04410aa85226cae0660b8f5048003cde7945"},"schema_version":"1.0"},"canonical_sha256":"0dc5d6c093fc4eb9a2af9ea4e5e45584fc8abe86aa0eb7bf66dc62537ad5fa71","source":{"kind":"arxiv","id":"1503.01763","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01763","created_at":"2026-05-18T02:25:32Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01763v1","created_at":"2026-05-18T02:25:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01763","created_at":"2026-05-18T02:25:32Z"},{"alias_kind":"pith_short_12","alias_value":"BXC5NQET7RHL","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BXC5NQET7RHLTIVP","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BXC5NQET","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BXC5NQET7RHLTIVPT2SOLZCVQT","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01763","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-05T20:41:56Z","cross_cats_sorted":[],"title_canon_sha256":"e807384fe48c259dbb723b5734f9564fd9d6f12df706d0712b8290f12a353eee","abstract_canon_sha256":"557d41d501f66fd297ba888fb5dc04410aa85226cae0660b8f5048003cde7945"},"schema_version":"1.0"},"canonical_sha256":"0dc5d6c093fc4eb9a2af9ea4e5e45584fc8abe86aa0eb7bf66dc62537ad5fa71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:32.986970Z","signature_b64":"ihp2z5/fSkdJq1rSzzmpQNZXVgXSC7hxEZqfEeuIszRoPFcywSDo7/ZkqT2E2QCw6rHno8UPOHV48rZMjWVkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dc5d6c093fc4eb9a2af9ea4e5e45584fc8abe86aa0eb7bf66dc62537ad5fa71","last_reissued_at":"2026-05-18T02:25:32.985803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:32.985803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01763","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":"2026-05-18T02:25:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hG0TXK3Pin6Et1/kOds3dnLKOa+FFejLZDbXHRDzLvuDibez9vmhDRNjqDh5WaYP5uvjtePLGqBZw3lhCG1LCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:19:20.801425Z"},"content_sha256":"a33d4194d529599819fbc5a32cee302aec5d842d49cdcc55b3636010fe7345fc","schema_version":"1.0","event_id":"sha256:a33d4194d529599819fbc5a32cee302aec5d842d49cdcc55b3636010fe7345fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BXC5NQET7RHLTIVPT2SOLZCVQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourier Frames for the Cantor-4 Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eric S. Weber, Gabriel Picioroaga","submitted_at":"2015-03-05T20:41:56Z","abstract_excerpt":"The measure supported on the Cantor-4 set constructed by Jorgensen-Pedersen is known to have a Fourier basis, i.e. that it possess a sequence of exponentials which form an orthonormal basis. We construct Fourier frames for this measure via a dilation theory type construction. We expand the Cantor-4 set to a 2 dimensional fractal which admits a representation of a Cuntz algebra. Using the action of this algebra, an orthonormal set is generated on the larger fractal, which is then projected onto the Cantor-4 set to produce a Fourier frame."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01763","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":"2026-05-18T02:25:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fWy3jvAp/4C0+LUHzUlRg0CBKsh/5kl6BozzCOyBaqsq3M5bpVgPxp9sToU6wW611IHHSL1fV42/6cN8QNdgAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:19:20.802090Z"},"content_sha256":"1b0bb4a1886089f6334afef6d4fbaf1ccae5571d9947efa48e75583f0865d8b4","schema_version":"1.0","event_id":"sha256:1b0bb4a1886089f6334afef6d4fbaf1ccae5571d9947efa48e75583f0865d8b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXC5NQET7RHLTIVPT2SOLZCVQT/bundle.json","state_url":"https://pith.science/pith/BXC5NQET7RHLTIVPT2SOLZCVQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXC5NQET7RHLTIVPT2SOLZCVQT/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":"2026-05-27T02:19:20Z","links":{"resolver":"https://pith.science/pith/BXC5NQET7RHLTIVPT2SOLZCVQT","bundle":"https://pith.science/pith/BXC5NQET7RHLTIVPT2SOLZCVQT/bundle.json","state":"https://pith.science/pith/BXC5NQET7RHLTIVPT2SOLZCVQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXC5NQET7RHLTIVPT2SOLZCVQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BXC5NQET7RHLTIVPT2SOLZCVQT","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":"557d41d501f66fd297ba888fb5dc04410aa85226cae0660b8f5048003cde7945","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-05T20:41:56Z","title_canon_sha256":"e807384fe48c259dbb723b5734f9564fd9d6f12df706d0712b8290f12a353eee"},"schema_version":"1.0","source":{"id":"1503.01763","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01763","created_at":"2026-05-18T02:25:32Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01763v1","created_at":"2026-05-18T02:25:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01763","created_at":"2026-05-18T02:25:32Z"},{"alias_kind":"pith_short_12","alias_value":"BXC5NQET7RHL","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BXC5NQET7RHLTIVP","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BXC5NQET","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:1b0bb4a1886089f6334afef6d4fbaf1ccae5571d9947efa48e75583f0865d8b4","target":"graph","created_at":"2026-05-18T02:25:32Z","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":"The measure supported on the Cantor-4 set constructed by Jorgensen-Pedersen is known to have a Fourier basis, i.e. that it possess a sequence of exponentials which form an orthonormal basis. We construct Fourier frames for this measure via a dilation theory type construction. We expand the Cantor-4 set to a 2 dimensional fractal which admits a representation of a Cuntz algebra. Using the action of this algebra, an orthonormal set is generated on the larger fractal, which is then projected onto the Cantor-4 set to produce a Fourier frame.","authors_text":"Eric S. Weber, Gabriel Picioroaga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-05T20:41:56Z","title":"Fourier Frames for the Cantor-4 Set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01763","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:a33d4194d529599819fbc5a32cee302aec5d842d49cdcc55b3636010fe7345fc","target":"record","created_at":"2026-05-18T02:25:32Z","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":"557d41d501f66fd297ba888fb5dc04410aa85226cae0660b8f5048003cde7945","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-05T20:41:56Z","title_canon_sha256":"e807384fe48c259dbb723b5734f9564fd9d6f12df706d0712b8290f12a353eee"},"schema_version":"1.0","source":{"id":"1503.01763","kind":"arxiv","version":1}},"canonical_sha256":"0dc5d6c093fc4eb9a2af9ea4e5e45584fc8abe86aa0eb7bf66dc62537ad5fa71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dc5d6c093fc4eb9a2af9ea4e5e45584fc8abe86aa0eb7bf66dc62537ad5fa71","first_computed_at":"2026-05-18T02:25:32.985803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:32.985803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ihp2z5/fSkdJq1rSzzmpQNZXVgXSC7hxEZqfEeuIszRoPFcywSDo7/ZkqT2E2QCw6rHno8UPOHV48rZMjWVkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:32.986970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01763","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a33d4194d529599819fbc5a32cee302aec5d842d49cdcc55b3636010fe7345fc","sha256:1b0bb4a1886089f6334afef6d4fbaf1ccae5571d9947efa48e75583f0865d8b4"],"state_sha256":"a9ae535d7106a161d5e29c738653b7d86b4c8b32e729db966f5db094ea0dab07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WPZViP7uq7xkyqEr3qisMCNpa1C8rZIkXxNF4oyYvnQCVaENslXwgwCDYcpha1Y6VGzG7+KyvrGwGMyynj1hAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:19:20.805513Z","bundle_sha256":"730d6491a866751c2521d6597a8d2b319f4d7fca1d273af5a4c29fce7315b692"}}