{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4X7IDHBDW37OEJPFOL4Q5MXKU7","short_pith_number":"pith:4X7IDHBD","canonical_record":{"source":{"id":"1401.1340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-07T11:09:19Z","cross_cats_sorted":[],"title_canon_sha256":"22852a62e52ad648c76834ed7a898a9b97720917e9f485f78cfeb7a0c551e033","abstract_canon_sha256":"911d90ad4eb7d3633a101b3553ff107170d522e80e1845be3e3f7a7d2c558e5d"},"schema_version":"1.0"},"canonical_sha256":"e5fe819c23b6fee225e572f90eb2eaa7d7da86d4251c8db8eff87f0344e6223c","source":{"kind":"arxiv","id":"1401.1340","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1340","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1340v1","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1340","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"pith_short_12","alias_value":"4X7IDHBDW37O","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4X7IDHBDW37OEJPF","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4X7IDHBD","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4X7IDHBDW37OEJPFOL4Q5MXKU7","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-07T11:09:19Z","cross_cats_sorted":[],"title_canon_sha256":"22852a62e52ad648c76834ed7a898a9b97720917e9f485f78cfeb7a0c551e033","abstract_canon_sha256":"911d90ad4eb7d3633a101b3553ff107170d522e80e1845be3e3f7a7d2c558e5d"},"schema_version":"1.0"},"canonical_sha256":"e5fe819c23b6fee225e572f90eb2eaa7d7da86d4251c8db8eff87f0344e6223c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:08.903639Z","signature_b64":"on6BMboCGxpwILRU+j0K4NPeNOcDCUt0Dk5+0FDWksfeWJ+dMnkSEIcr5NcFwu7nvxdnp5L+IOFoARX/CHqUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5fe819c23b6fee225e572f90eb2eaa7d7da86d4251c8db8eff87f0344e6223c","last_reissued_at":"2026-05-18T03:03:08.902972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:08.902972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1340","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":"2026-05-18T03:03:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cM2B28QRTlFgTDZ2R5sfmn+RRFbvNOXpuf2EMkDEdm0bfpi2gJyTRbL9RJPoPbm65syf5MI60ZOSWKCzH/X5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T00:08:36.468006Z"},"content_sha256":"584c33c98208767ccfe203ce9f750392e9a84522782364a119f2a81666ea2035","schema_version":"1.0","event_id":"sha256:584c33c98208767ccfe203ce9f750392e9a84522782364a119f2a81666ea2035"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4X7IDHBDW37OEJPFOL4Q5MXKU7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The n-point correlation of quadratic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Oliver Sargent","submitted_at":"2014-01-07T11:09:19Z","abstract_excerpt":"In this paper we investigate the distribution of the set of values of a quadratic form Q, at integral points. In particular we are interested in the n-point correlations of the this set. The asymptotic behaviour of the counting function that counts the number of n-tuples of integral points $\\left(v_{1},\\dots,v_{n}\\right)$, with bounded norm, such that the n-1 differences $Q\\left(v_{1}\\right)-Q\\left(v_{2}\\right),\\dots Q\\left(v_{n-1}\\right)-Q\\left(v_{n}\\right)$, lie in prescribed intervals is obtained. The results are valid provided that the quadratic form has rank at least 5, is not a multiple "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1340","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":"2026-05-18T03:03:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i9RWL9JhgkmRZuYtoglP0jYUrmNdmpIQwK4AbrTkr3DrT6yoBPinh3iJyM306IRfctXI4rasx+LWn53i/9c/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T00:08:36.468369Z"},"content_sha256":"7d6479e2fb1bb0c602df5b61ab738a1e2e964b20ba1e01ac8d9b1bda4c52ff09","schema_version":"1.0","event_id":"sha256:7d6479e2fb1bb0c602df5b61ab738a1e2e964b20ba1e01ac8d9b1bda4c52ff09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4X7IDHBDW37OEJPFOL4Q5MXKU7/bundle.json","state_url":"https://pith.science/pith/4X7IDHBDW37OEJPFOL4Q5MXKU7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4X7IDHBDW37OEJPFOL4Q5MXKU7/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":"2026-06-25T00:08:36Z","links":{"resolver":"https://pith.science/pith/4X7IDHBDW37OEJPFOL4Q5MXKU7","bundle":"https://pith.science/pith/4X7IDHBDW37OEJPFOL4Q5MXKU7/bundle.json","state":"https://pith.science/pith/4X7IDHBDW37OEJPFOL4Q5MXKU7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4X7IDHBDW37OEJPFOL4Q5MXKU7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4X7IDHBDW37OEJPFOL4Q5MXKU7","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":"911d90ad4eb7d3633a101b3553ff107170d522e80e1845be3e3f7a7d2c558e5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-07T11:09:19Z","title_canon_sha256":"22852a62e52ad648c76834ed7a898a9b97720917e9f485f78cfeb7a0c551e033"},"schema_version":"1.0","source":{"id":"1401.1340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1340","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1340v1","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1340","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"pith_short_12","alias_value":"4X7IDHBDW37O","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4X7IDHBDW37OEJPF","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4X7IDHBD","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:7d6479e2fb1bb0c602df5b61ab738a1e2e964b20ba1e01ac8d9b1bda4c52ff09","target":"graph","created_at":"2026-05-18T03:03:08Z","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":"In this paper we investigate the distribution of the set of values of a quadratic form Q, at integral points. In particular we are interested in the n-point correlations of the this set. The asymptotic behaviour of the counting function that counts the number of n-tuples of integral points $\\left(v_{1},\\dots,v_{n}\\right)$, with bounded norm, such that the n-1 differences $Q\\left(v_{1}\\right)-Q\\left(v_{2}\\right),\\dots Q\\left(v_{n-1}\\right)-Q\\left(v_{n}\\right)$, lie in prescribed intervals is obtained. The results are valid provided that the quadratic form has rank at least 5, is not a multiple ","authors_text":"Oliver Sargent","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-07T11:09:19Z","title":"The n-point correlation of quadratic forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1340","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":"sha256:584c33c98208767ccfe203ce9f750392e9a84522782364a119f2a81666ea2035","target":"record","created_at":"2026-05-18T03:03:08Z","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":"911d90ad4eb7d3633a101b3553ff107170d522e80e1845be3e3f7a7d2c558e5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-07T11:09:19Z","title_canon_sha256":"22852a62e52ad648c76834ed7a898a9b97720917e9f485f78cfeb7a0c551e033"},"schema_version":"1.0","source":{"id":"1401.1340","kind":"arxiv","version":1}},"canonical_sha256":"e5fe819c23b6fee225e572f90eb2eaa7d7da86d4251c8db8eff87f0344e6223c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5fe819c23b6fee225e572f90eb2eaa7d7da86d4251c8db8eff87f0344e6223c","first_computed_at":"2026-05-18T03:03:08.902972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:08.902972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"on6BMboCGxpwILRU+j0K4NPeNOcDCUt0Dk5+0FDWksfeWJ+dMnkSEIcr5NcFwu7nvxdnp5L+IOFoARX/CHqUBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:08.903639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:584c33c98208767ccfe203ce9f750392e9a84522782364a119f2a81666ea2035","sha256:7d6479e2fb1bb0c602df5b61ab738a1e2e964b20ba1e01ac8d9b1bda4c52ff09"],"state_sha256":"fadf81cb19e48989706a53225f5ee649caab4f0caebef2b67e332ef96749b90b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4SYe3fJHTtPnf/GQ09YesJ5jqsm/y9pOZNpTXKZptPbuycnh3Gf3V7865impVQgsgx5GTm8RBU56ve/dT7IEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T00:08:36.470497Z","bundle_sha256":"6ef38c3b5316c2fb710b875d7abb3d79e61d47dc128325147e7d6bc2ebcf9a86"}}