{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:73HK4JOY2WR7GCIHC23VIYVJ2Q","short_pith_number":"pith:73HK4JOY","canonical_record":{"source":{"id":"1701.07958","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-27T07:11:46Z","cross_cats_sorted":[],"title_canon_sha256":"51340d2cdc6cef99b3fbbcbab267d71017406000da80be04a71b7addffb03b73","abstract_canon_sha256":"8c5dc96424a756d5b8b8b034b5478f9f1099a1f628cccb3b588d9cca39acad48"},"schema_version":"1.0"},"canonical_sha256":"feceae25d8d5a3f3090716b75462a9d422dc330f4745504c6030204c3a8dc1de","source":{"kind":"arxiv","id":"1701.07958","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07958","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07958v2","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07958","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"73HK4JOY2WR7","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"73HK4JOY2WR7GCIH","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"73HK4JOY","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:73HK4JOY2WR7GCIHC23VIYVJ2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1701.07958","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-27T07:11:46Z","cross_cats_sorted":[],"title_canon_sha256":"51340d2cdc6cef99b3fbbcbab267d71017406000da80be04a71b7addffb03b73","abstract_canon_sha256":"8c5dc96424a756d5b8b8b034b5478f9f1099a1f628cccb3b588d9cca39acad48"},"schema_version":"1.0"},"canonical_sha256":"feceae25d8d5a3f3090716b75462a9d422dc330f4745504c6030204c3a8dc1de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:13.373892Z","signature_b64":"7vymbNR5Jh9HpCqEJNiGCxZTUSbhga9xOh2LARsbqU+vT3wduyTycjfrZ/gCwF3GqroHBV27DFoLRxfUZvWBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"feceae25d8d5a3f3090716b75462a9d422dc330f4745504c6030204c3a8dc1de","last_reissued_at":"2026-05-18T00:50:13.373437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:13.373437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.07958","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":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BcoqUnjnu+jnm82VGN1Jj3UaiA3MI6KvNypwMk1dVi3G7dNQpULM2LG/A2zKEnJGbAyFGYCa1i0nAK2BUejNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:43:14.191724Z"},"content_sha256":"15d17ba675726f73fd94a1e2a71510393494331ecd6dc3b66ae42ee2b1da0905","schema_version":"1.0","event_id":"sha256:15d17ba675726f73fd94a1e2a71510393494331ecd6dc3b66ae42ee2b1da0905"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:73HK4JOY2WR7GCIHC23VIYVJ2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Salem sets in vector spaces over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Changhao Chen","submitted_at":"2017-01-27T07:11:46Z","abstract_excerpt":"We prove that almost all random subsets of a finite vector space are weak Salem sets (small Fourier coefficient), which extends a result of Hayes to a different probability model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07958","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":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YJGfPxKk8X/HL81Cub8S7gjzTyVFN+3AVBF71BSeKI7P8tAJ+oSO+SakW7NLPTRaXYa9jPxh96PeinoZ0sU4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:43:14.192459Z"},"content_sha256":"b02028150798e33e96487e5f9afc58004c07acd1d30ea995bf259915a007e498","schema_version":"1.0","event_id":"sha256:b02028150798e33e96487e5f9afc58004c07acd1d30ea995bf259915a007e498"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/73HK4JOY2WR7GCIHC23VIYVJ2Q/bundle.json","state_url":"https://pith.science/pith/73HK4JOY2WR7GCIHC23VIYVJ2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/73HK4JOY2WR7GCIHC23VIYVJ2Q/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":"2026-05-29T14:43:14Z","links":{"resolver":"https://pith.science/pith/73HK4JOY2WR7GCIHC23VIYVJ2Q","bundle":"https://pith.science/pith/73HK4JOY2WR7GCIHC23VIYVJ2Q/bundle.json","state":"https://pith.science/pith/73HK4JOY2WR7GCIHC23VIYVJ2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/73HK4JOY2WR7GCIHC23VIYVJ2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:73HK4JOY2WR7GCIHC23VIYVJ2Q","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":"8c5dc96424a756d5b8b8b034b5478f9f1099a1f628cccb3b588d9cca39acad48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-27T07:11:46Z","title_canon_sha256":"51340d2cdc6cef99b3fbbcbab267d71017406000da80be04a71b7addffb03b73"},"schema_version":"1.0","source":{"id":"1701.07958","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07958","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07958v2","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07958","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"73HK4JOY2WR7","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"73HK4JOY2WR7GCIH","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"73HK4JOY","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:b02028150798e33e96487e5f9afc58004c07acd1d30ea995bf259915a007e498","target":"graph","created_at":"2026-05-18T00:50:13Z","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 prove that almost all random subsets of a finite vector space are weak Salem sets (small Fourier coefficient), which extends a result of Hayes to a different probability model.","authors_text":"Changhao Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-27T07:11:46Z","title":"Salem sets in vector spaces over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07958","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":"sha256:15d17ba675726f73fd94a1e2a71510393494331ecd6dc3b66ae42ee2b1da0905","target":"record","created_at":"2026-05-18T00:50:13Z","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":"8c5dc96424a756d5b8b8b034b5478f9f1099a1f628cccb3b588d9cca39acad48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-27T07:11:46Z","title_canon_sha256":"51340d2cdc6cef99b3fbbcbab267d71017406000da80be04a71b7addffb03b73"},"schema_version":"1.0","source":{"id":"1701.07958","kind":"arxiv","version":2}},"canonical_sha256":"feceae25d8d5a3f3090716b75462a9d422dc330f4745504c6030204c3a8dc1de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"feceae25d8d5a3f3090716b75462a9d422dc330f4745504c6030204c3a8dc1de","first_computed_at":"2026-05-18T00:50:13.373437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:13.373437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7vymbNR5Jh9HpCqEJNiGCxZTUSbhga9xOh2LARsbqU+vT3wduyTycjfrZ/gCwF3GqroHBV27DFoLRxfUZvWBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:13.373892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07958","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15d17ba675726f73fd94a1e2a71510393494331ecd6dc3b66ae42ee2b1da0905","sha256:b02028150798e33e96487e5f9afc58004c07acd1d30ea995bf259915a007e498"],"state_sha256":"2646907cc85c10c0608cd8d08454ba8bb347db549cae7d912633c10acd00fb3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"41NZR7BlOY023AYah0UI35qiA81cKYqI+sZvCPvn51YpTq40Bjm3C1mSuqwiuyJf0DnWddanSxlNb3mPQFRgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:43:14.196096Z","bundle_sha256":"0c78609c70a1073a32148ca3a8229e502f566534be9aed23c912fcd5a108c34c"}}