{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QVZUYNFBUNYGTQETJKGMAVHGMS","short_pith_number":"pith:QVZUYNFB","canonical_record":{"source":{"id":"1412.1611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-04T10:38:15Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"3c7891e284975f3ac29ce58ec9ad10a0cddaec1825570548cdef202c44aff149","abstract_canon_sha256":"af82865ced27038f5bcfc55b1c23b25d16f180361c1168fa4559b73199cbc023"},"schema_version":"1.0"},"canonical_sha256":"85734c34a1a37069c0934a8cc054e664b6122e18edd6ef292a74e9c688f8f4cf","source":{"kind":"arxiv","id":"1412.1611","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1611","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1611v2","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1611","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"pith_short_12","alias_value":"QVZUYNFBUNYG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QVZUYNFBUNYGTQET","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QVZUYNFB","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QVZUYNFBUNYGTQETJKGMAVHGMS","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-04T10:38:15Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"3c7891e284975f3ac29ce58ec9ad10a0cddaec1825570548cdef202c44aff149","abstract_canon_sha256":"af82865ced27038f5bcfc55b1c23b25d16f180361c1168fa4559b73199cbc023"},"schema_version":"1.0"},"canonical_sha256":"85734c34a1a37069c0934a8cc054e664b6122e18edd6ef292a74e9c688f8f4cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:18.554048Z","signature_b64":"g5nb1ArbUOlS7ge2mtn9qK/CZKaIUOtiWwD7Xe1wO2OxXCw+Fx1Isc1LrGZ4ryT8STaxZ7oAbZ7QRTboWW8FCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85734c34a1a37069c0934a8cc054e664b6122e18edd6ef292a74e9c688f8f4cf","last_reissued_at":"2026-05-18T01:10:18.553139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:18.553139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1611","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":"2026-05-18T01:10:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zm9uZnLk39niGVvOaT8DWurG8j/xBdpqiwuNJ3knMfGRwd5jUHpIP50DSSuqIeIrBFgvRLyakyznWECpyZlECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:44:20.266975Z"},"content_sha256":"8ef4571c60d786e8d0f0bc6e116f1eb38460785367312749584d0d725f7a0994","schema_version":"1.0","event_id":"sha256:8ef4571c60d786e8d0f0bc6e116f1eb38460785367312749584d0d725f7a0994"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QVZUYNFBUNYGTQETJKGMAVHGMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On distinct perpendicular bisectors and pinned distances in finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Ben Lund, Brandon Hanson, Oliver Roche-Newton","submitted_at":"2014-12-04T10:38:15Z","abstract_excerpt":"Given a set of points $P \\subset \\mathbb F_q^2$ such that $|P|\\geq q^{3/2}$ it is established that $|P|$ determines $\\Omega(q^2)$ distinct perpendicular bisectors. It is also proven that, if $|P| \\geq q^{4/3}$, then for a positive proportion of points $a \\in P$, we have $$|\\{\\| a- b\\|: b \\in P\\}|=\\Omega(q),$$ where $\\|a- b\\|$ is the distance between points $a$ and $b$. The latter result represents an improvement on a result of Chapman et al. (arxiv:0903.4218)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1611","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":"2026-05-18T01:10:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0k0D0Wxhec6IekEXNTy1PmNlOvDMJkSZ8qccvLg08BrhSmyykBxleCCUfw4hRywb2NLawlMd7Wcx6XCz/flADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:44:20.267330Z"},"content_sha256":"397c065d4bb61c1ac1aa6f125284eb1397ff8103d4bfb75c8a71cd6c5e33c833","schema_version":"1.0","event_id":"sha256:397c065d4bb61c1ac1aa6f125284eb1397ff8103d4bfb75c8a71cd6c5e33c833"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVZUYNFBUNYGTQETJKGMAVHGMS/bundle.json","state_url":"https://pith.science/pith/QVZUYNFBUNYGTQETJKGMAVHGMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVZUYNFBUNYGTQETJKGMAVHGMS/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":"2026-06-26T12:44:20Z","links":{"resolver":"https://pith.science/pith/QVZUYNFBUNYGTQETJKGMAVHGMS","bundle":"https://pith.science/pith/QVZUYNFBUNYGTQETJKGMAVHGMS/bundle.json","state":"https://pith.science/pith/QVZUYNFBUNYGTQETJKGMAVHGMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVZUYNFBUNYGTQETJKGMAVHGMS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QVZUYNFBUNYGTQETJKGMAVHGMS","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":"af82865ced27038f5bcfc55b1c23b25d16f180361c1168fa4559b73199cbc023","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-04T10:38:15Z","title_canon_sha256":"3c7891e284975f3ac29ce58ec9ad10a0cddaec1825570548cdef202c44aff149"},"schema_version":"1.0","source":{"id":"1412.1611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1611","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1611v2","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1611","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"pith_short_12","alias_value":"QVZUYNFBUNYG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QVZUYNFBUNYGTQET","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QVZUYNFB","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:397c065d4bb61c1ac1aa6f125284eb1397ff8103d4bfb75c8a71cd6c5e33c833","target":"graph","created_at":"2026-05-18T01:10:18Z","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":"Given a set of points $P \\subset \\mathbb F_q^2$ such that $|P|\\geq q^{3/2}$ it is established that $|P|$ determines $\\Omega(q^2)$ distinct perpendicular bisectors. It is also proven that, if $|P| \\geq q^{4/3}$, then for a positive proportion of points $a \\in P$, we have $$|\\{\\| a- b\\|: b \\in P\\}|=\\Omega(q),$$ where $\\|a- b\\|$ is the distance between points $a$ and $b$. The latter result represents an improvement on a result of Chapman et al. (arxiv:0903.4218).","authors_text":"Ben Lund, Brandon Hanson, Oliver Roche-Newton","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-04T10:38:15Z","title":"On distinct perpendicular bisectors and pinned distances in finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1611","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":"sha256:8ef4571c60d786e8d0f0bc6e116f1eb38460785367312749584d0d725f7a0994","target":"record","created_at":"2026-05-18T01:10:18Z","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":"af82865ced27038f5bcfc55b1c23b25d16f180361c1168fa4559b73199cbc023","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-04T10:38:15Z","title_canon_sha256":"3c7891e284975f3ac29ce58ec9ad10a0cddaec1825570548cdef202c44aff149"},"schema_version":"1.0","source":{"id":"1412.1611","kind":"arxiv","version":2}},"canonical_sha256":"85734c34a1a37069c0934a8cc054e664b6122e18edd6ef292a74e9c688f8f4cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85734c34a1a37069c0934a8cc054e664b6122e18edd6ef292a74e9c688f8f4cf","first_computed_at":"2026-05-18T01:10:18.553139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:18.553139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g5nb1ArbUOlS7ge2mtn9qK/CZKaIUOtiWwD7Xe1wO2OxXCw+Fx1Isc1LrGZ4ryT8STaxZ7oAbZ7QRTboWW8FCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:18.554048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ef4571c60d786e8d0f0bc6e116f1eb38460785367312749584d0d725f7a0994","sha256:397c065d4bb61c1ac1aa6f125284eb1397ff8103d4bfb75c8a71cd6c5e33c833"],"state_sha256":"e84732aeb49c7d40ab2c633a593801062f7fcb481405b82ebacffe372f040f52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2qHZ219tuNVBCFuJjID0iq0XRgUEH695j5wlST8o2Z/CI420kdiZbwZBlbUsU4hAfuxlXmoUp3PbYCP3gl9yDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:44:20.269230Z","bundle_sha256":"bcea78d1809ea063e8db78c38aae3a2e9033ef4475a6442245e2fc34f20fa961"}}