{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:DNVTFMQ6SNBJ5NWWF5AGYZQTPB","short_pith_number":"pith:DNVTFMQ6","canonical_record":{"source":{"id":"2402.12589","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-19T22:55:56Z","cross_cats_sorted":["cs.DM","math.PR","stat.TH"],"title_canon_sha256":"c66a28baaa06c61182fd0671f610cd078c8ac52b4ce4322649c150cbb419e2fd","abstract_canon_sha256":"d8f5cd5b500bc65f255ea503a5069e6b0a943739fdbebfd8e9fc8a8217cbeeb6"},"schema_version":"1.0"},"canonical_sha256":"1b6b32b21e93429eb6d62f406c66137848c7b70d795419c1e323e162b2af3dfa","source":{"kind":"arxiv","id":"2402.12589","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.12589","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"2402.12589v1","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.12589","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"DNVTFMQ6SNBJ","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"pith_short_16","alias_value":"DNVTFMQ6SNBJ5NWW","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"pith_short_8","alias_value":"DNVTFMQ6","created_at":"2026-07-05T07:47:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:DNVTFMQ6SNBJ5NWWF5AGYZQTPB","target":"record","payload":{"canonical_record":{"source":{"id":"2402.12589","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-19T22:55:56Z","cross_cats_sorted":["cs.DM","math.PR","stat.TH"],"title_canon_sha256":"c66a28baaa06c61182fd0671f610cd078c8ac52b4ce4322649c150cbb419e2fd","abstract_canon_sha256":"d8f5cd5b500bc65f255ea503a5069e6b0a943739fdbebfd8e9fc8a8217cbeeb6"},"schema_version":"1.0"},"canonical_sha256":"1b6b32b21e93429eb6d62f406c66137848c7b70d795419c1e323e162b2af3dfa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:47:13.330983Z","signature_b64":"iLu/Z4Hnj0J1iyERQGt5qPjhWslh6QVX2387jTTHB75kQm5MDV1yVDhATnXrrvowju8Pt7DPgvRxOzLdigIKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b6b32b21e93429eb6d62f406c66137848c7b70d795419c1e323e162b2af3dfa","last_reissued_at":"2026-07-05T07:47:13.330613Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:47:13.330613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.12589","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":"2026-07-05T07:47:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kk4GaG/LG3jFqxo2qUFvqdlxH/52e09NKdZDeUMrcXYDpU1hRJqoHnzGjZ5Hfph16EDCNyVO0zpPcCgeBnZ6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:05:53.399163Z"},"content_sha256":"4f48289c22a49e782c84941c3df40e95ec57cf981aced0a0f349a386c6950c31","schema_version":"1.0","event_id":"sha256:4f48289c22a49e782c84941c3df40e95ec57cf981aced0a0f349a386c6950c31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:DNVTFMQ6SNBJ5NWWF5AGYZQTPB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On The Fourier Coefficients of High-Dimensional Random Geometric Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Guy Bresler, Kiril Bangachev","submitted_at":"2024-02-19T22:55:56Z","abstract_excerpt":"The random geometric graph $\\mathsf{RGG}(n,\\mathbb{S}^{d-1}, p)$ is formed by sampling $n$ i.i.d. vectors $\\{V_i\\}_{i = 1}^n$ uniformly on $\\mathbb{S}^{d-1}$ and placing an edge between pairs of vertices $i$ and $j$ for which $\\langle V_i,V_j\\rangle \\ge \\tau^p_d,$ where $\\tau^p_d$ is such that the expected density is $p.$ We study the low-degree Fourier coefficients of the distribution $\\mathsf{RGG}(n,\\mathbb{S}^{d-1}, p)$ and its Gaussian analogue.\n  Our main conceptual contribution is a novel two-step strategy for bounding Fourier coefficients which we believe is more widely applicable to st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.12589","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.12589/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":"2026-07-05T07:47:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E6eMpzjBxBPa/zNxgVaCCyEVpBuExrP3NtPka6XeEnPYDUg2To9SvmOZy7PDxFLQmpQ1Lx7QsFhcyI/0IGuYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:05:53.400166Z"},"content_sha256":"3da0d98bdf0e29e94ae4ce9eab485c8da93ca584bcfc97b8171a0dd13b91f913","schema_version":"1.0","event_id":"sha256:3da0d98bdf0e29e94ae4ce9eab485c8da93ca584bcfc97b8171a0dd13b91f913"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNVTFMQ6SNBJ5NWWF5AGYZQTPB/bundle.json","state_url":"https://pith.science/pith/DNVTFMQ6SNBJ5NWWF5AGYZQTPB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNVTFMQ6SNBJ5NWWF5AGYZQTPB/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":"2026-08-04T17:05:53Z","links":{"resolver":"https://pith.science/pith/DNVTFMQ6SNBJ5NWWF5AGYZQTPB","bundle":"https://pith.science/pith/DNVTFMQ6SNBJ5NWWF5AGYZQTPB/bundle.json","state":"https://pith.science/pith/DNVTFMQ6SNBJ5NWWF5AGYZQTPB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNVTFMQ6SNBJ5NWWF5AGYZQTPB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DNVTFMQ6SNBJ5NWWF5AGYZQTPB","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":"d8f5cd5b500bc65f255ea503a5069e6b0a943739fdbebfd8e9fc8a8217cbeeb6","cross_cats_sorted":["cs.DM","math.PR","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-19T22:55:56Z","title_canon_sha256":"c66a28baaa06c61182fd0671f610cd078c8ac52b4ce4322649c150cbb419e2fd"},"schema_version":"1.0","source":{"id":"2402.12589","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.12589","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"2402.12589v1","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.12589","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"DNVTFMQ6SNBJ","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"pith_short_16","alias_value":"DNVTFMQ6SNBJ5NWW","created_at":"2026-07-05T07:47:13Z"},{"alias_kind":"pith_short_8","alias_value":"DNVTFMQ6","created_at":"2026-07-05T07:47:13Z"}],"graph_snapshots":[{"event_id":"sha256:3da0d98bdf0e29e94ae4ce9eab485c8da93ca584bcfc97b8171a0dd13b91f913","target":"graph","created_at":"2026-07-05T07:47:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.12589/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The random geometric graph $\\mathsf{RGG}(n,\\mathbb{S}^{d-1}, p)$ is formed by sampling $n$ i.i.d. vectors $\\{V_i\\}_{i = 1}^n$ uniformly on $\\mathbb{S}^{d-1}$ and placing an edge between pairs of vertices $i$ and $j$ for which $\\langle V_i,V_j\\rangle \\ge \\tau^p_d,$ where $\\tau^p_d$ is such that the expected density is $p.$ We study the low-degree Fourier coefficients of the distribution $\\mathsf{RGG}(n,\\mathbb{S}^{d-1}, p)$ and its Gaussian analogue.\n  Our main conceptual contribution is a novel two-step strategy for bounding Fourier coefficients which we believe is more widely applicable to st","authors_text":"Guy Bresler, Kiril Bangachev","cross_cats":["cs.DM","math.PR","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-19T22:55:56Z","title":"On The Fourier Coefficients of High-Dimensional Random Geometric Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.12589","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":"sha256:4f48289c22a49e782c84941c3df40e95ec57cf981aced0a0f349a386c6950c31","target":"record","created_at":"2026-07-05T07:47:13Z","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":"d8f5cd5b500bc65f255ea503a5069e6b0a943739fdbebfd8e9fc8a8217cbeeb6","cross_cats_sorted":["cs.DM","math.PR","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-02-19T22:55:56Z","title_canon_sha256":"c66a28baaa06c61182fd0671f610cd078c8ac52b4ce4322649c150cbb419e2fd"},"schema_version":"1.0","source":{"id":"2402.12589","kind":"arxiv","version":1}},"canonical_sha256":"1b6b32b21e93429eb6d62f406c66137848c7b70d795419c1e323e162b2af3dfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b6b32b21e93429eb6d62f406c66137848c7b70d795419c1e323e162b2af3dfa","first_computed_at":"2026-07-05T07:47:13.330613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:47:13.330613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iLu/Z4Hnj0J1iyERQGt5qPjhWslh6QVX2387jTTHB75kQm5MDV1yVDhATnXrrvowju8Pt7DPgvRxOzLdigIKCw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:47:13.330983Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.12589","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f48289c22a49e782c84941c3df40e95ec57cf981aced0a0f349a386c6950c31","sha256:3da0d98bdf0e29e94ae4ce9eab485c8da93ca584bcfc97b8171a0dd13b91f913"],"state_sha256":"067a30f05d3e4a06246ac105e143596b515308a8957fa914d7c58d052fd548c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RLpHY9o0oO9Uo89LCtJaNR4M6HyVmUCOaKy30xZ8S6ApkmL9NgapBOAEHiZnSpBgyK4dspYDB5vPvxAgBnd7CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:05:53.406518Z","bundle_sha256":"dcb80605777bf92d6966b4777f0a998bc4f6bfcbcd834ec4d7150160a35ecd3f"}}