{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WTYDSQCYCBWENEAHWEW55PGEPM","short_pith_number":"pith:WTYDSQCY","canonical_record":{"source":{"id":"1510.00536","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-02T09:19:59Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"0c867b5ff3caf95cd3c8994df75051ae3dfe3972fc49acb3782fedd64b36f77e","abstract_canon_sha256":"cb764366639d85c608bc1e2c7172308e0f6a0998e5571a2dd14e01817c3c879a"},"schema_version":"1.0"},"canonical_sha256":"b4f0394058106c469007b12ddebcc47b1c7997b9ae354655ba87e447cca48c2f","source":{"kind":"arxiv","id":"1510.00536","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00536","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00536v2","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00536","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"pith_short_12","alias_value":"WTYDSQCYCBWE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WTYDSQCYCBWENEAH","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WTYDSQCY","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WTYDSQCYCBWENEAHWEW55PGEPM","target":"record","payload":{"canonical_record":{"source":{"id":"1510.00536","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-02T09:19:59Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"0c867b5ff3caf95cd3c8994df75051ae3dfe3972fc49acb3782fedd64b36f77e","abstract_canon_sha256":"cb764366639d85c608bc1e2c7172308e0f6a0998e5571a2dd14e01817c3c879a"},"schema_version":"1.0"},"canonical_sha256":"b4f0394058106c469007b12ddebcc47b1c7997b9ae354655ba87e447cca48c2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:19.784081Z","signature_b64":"LIfFAY9buoVNg2vAPuzE7CYbXJpw20zhtn9hhHlxiBEDhUjiP1axiJSzHvBNE872ffkWKRmdMpQ/lm0105SIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4f0394058106c469007b12ddebcc47b1c7997b9ae354655ba87e447cca48c2f","last_reissued_at":"2026-05-18T00:36:19.783485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:19.783485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.00536","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":"2026-05-18T00:36:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lIyx9UbPc7arZH4UYNHAA0ZNepa88lBREOkNsImE9XsgqUypT3M4gPq4HHNEt/iahLA3Z6y3HqZJIY7yjKQKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:39:38.920653Z"},"content_sha256":"6ddba808291a945d4f5bc8b6cb1f29a64c510660e492329a09007dc875b5104c","schema_version":"1.0","event_id":"sha256:6ddba808291a945d4f5bc8b6cb1f29a64c510660e492329a09007dc875b5104c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WTYDSQCYCBWENEAHWEW55PGEPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correlations between real conjugate algebraic numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.NT","authors_text":"Dmitry Zaporozhets, Dzianis Kaliada, Friedrich G\\\"otze","submitted_at":"2015-10-02T09:19:59Z","abstract_excerpt":"For $B\\subset\\mathbb{R}^k$ denote by $\\Phi_k(Q;B)$ the number of ordered $k$-tuples in $B$ of real conjugate algebraic numbers of degree $\\leq n$ and naive height $\\leq Q$. We show that $$ \\Phi_k(Q;B) = \\frac{(2Q)^{n+1}}{2\\zeta(n+1)} \\int_{B} \\rho_k(\\mathbf{x})\\,d\\mathbf{x} + O\\left(Q^n\\right),\\quad Q\\to \\infty, $$ where the function $\\rho_k$ will be given explicitly. If $n=2$, then an additional factor $\\log Q$ appears in the reminder term."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00536","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":"2026-05-18T00:36:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jvYf2cHm45wDRJ4ylcnwsXsvJohD3aIeMFw+S8Wv4mH4a7W7Yu49e+XzxTAJyE/QxbAqqfYBcTh8ufrL7EwgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:39:38.921362Z"},"content_sha256":"4c5b5bd78a5457b0916e6c756bdd67a085086b53d5280be45d581078aab72225","schema_version":"1.0","event_id":"sha256:4c5b5bd78a5457b0916e6c756bdd67a085086b53d5280be45d581078aab72225"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTYDSQCYCBWENEAHWEW55PGEPM/bundle.json","state_url":"https://pith.science/pith/WTYDSQCYCBWENEAHWEW55PGEPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTYDSQCYCBWENEAHWEW55PGEPM/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":"2026-05-26T16:39:38Z","links":{"resolver":"https://pith.science/pith/WTYDSQCYCBWENEAHWEW55PGEPM","bundle":"https://pith.science/pith/WTYDSQCYCBWENEAHWEW55PGEPM/bundle.json","state":"https://pith.science/pith/WTYDSQCYCBWENEAHWEW55PGEPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTYDSQCYCBWENEAHWEW55PGEPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WTYDSQCYCBWENEAHWEW55PGEPM","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":"cb764366639d85c608bc1e2c7172308e0f6a0998e5571a2dd14e01817c3c879a","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-02T09:19:59Z","title_canon_sha256":"0c867b5ff3caf95cd3c8994df75051ae3dfe3972fc49acb3782fedd64b36f77e"},"schema_version":"1.0","source":{"id":"1510.00536","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00536","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00536v2","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00536","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"pith_short_12","alias_value":"WTYDSQCYCBWE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WTYDSQCYCBWENEAH","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WTYDSQCY","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:4c5b5bd78a5457b0916e6c756bdd67a085086b53d5280be45d581078aab72225","target":"graph","created_at":"2026-05-18T00:36:19Z","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":"For $B\\subset\\mathbb{R}^k$ denote by $\\Phi_k(Q;B)$ the number of ordered $k$-tuples in $B$ of real conjugate algebraic numbers of degree $\\leq n$ and naive height $\\leq Q$. We show that $$ \\Phi_k(Q;B) = \\frac{(2Q)^{n+1}}{2\\zeta(n+1)} \\int_{B} \\rho_k(\\mathbf{x})\\,d\\mathbf{x} + O\\left(Q^n\\right),\\quad Q\\to \\infty, $$ where the function $\\rho_k$ will be given explicitly. If $n=2$, then an additional factor $\\log Q$ appears in the reminder term.","authors_text":"Dmitry Zaporozhets, Dzianis Kaliada, Friedrich G\\\"otze","cross_cats":["math.CA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-02T09:19:59Z","title":"Correlations between real conjugate algebraic numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00536","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":"sha256:6ddba808291a945d4f5bc8b6cb1f29a64c510660e492329a09007dc875b5104c","target":"record","created_at":"2026-05-18T00:36:19Z","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":"cb764366639d85c608bc1e2c7172308e0f6a0998e5571a2dd14e01817c3c879a","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-02T09:19:59Z","title_canon_sha256":"0c867b5ff3caf95cd3c8994df75051ae3dfe3972fc49acb3782fedd64b36f77e"},"schema_version":"1.0","source":{"id":"1510.00536","kind":"arxiv","version":2}},"canonical_sha256":"b4f0394058106c469007b12ddebcc47b1c7997b9ae354655ba87e447cca48c2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4f0394058106c469007b12ddebcc47b1c7997b9ae354655ba87e447cca48c2f","first_computed_at":"2026-05-18T00:36:19.783485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:19.783485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LIfFAY9buoVNg2vAPuzE7CYbXJpw20zhtn9hhHlxiBEDhUjiP1axiJSzHvBNE872ffkWKRmdMpQ/lm0105SIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:19.784081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00536","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ddba808291a945d4f5bc8b6cb1f29a64c510660e492329a09007dc875b5104c","sha256:4c5b5bd78a5457b0916e6c756bdd67a085086b53d5280be45d581078aab72225"],"state_sha256":"ec4ad790cc4517291247477e8ea19619a397e186646e023678098ea75ce8d4dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XagT6fHSJrW7obvKZkmYAJuuSmwJK0w46JpMX93QPwtfxAieSvPoyFKHuTj+pHHR/VC8jPvFc2ELQU25jCK9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:39:38.924770Z","bundle_sha256":"3cb6fbb32c61cbffa48fe3fc4c75cddfb9d5256fc351b70b5dda2f3d823b9078"}}