{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5ACCX2IZ5Q5FBZYO76RGXDLNQX","short_pith_number":"pith:5ACCX2IZ","canonical_record":{"source":{"id":"1212.5305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-21T00:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"9dfea3975b28dc3dccd6612ef8398f392cdaa608716f22abf38c6d5899fabe29","abstract_canon_sha256":"9cec5993a20001374d660455f00401301cfaf03d2d9d543da6ef104ecf1cf2fc"},"schema_version":"1.0"},"canonical_sha256":"e8042be919ec3a50e70effa26b8d6d85c6805f50576ed5889dcd610420e7e52c","source":{"kind":"arxiv","id":"1212.5305","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5305","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5305v2","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5305","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"5ACCX2IZ5Q5F","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5ACCX2IZ5Q5FBZYO","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5ACCX2IZ","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5ACCX2IZ5Q5FBZYO76RGXDLNQX","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-21T00:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"9dfea3975b28dc3dccd6612ef8398f392cdaa608716f22abf38c6d5899fabe29","abstract_canon_sha256":"9cec5993a20001374d660455f00401301cfaf03d2d9d543da6ef104ecf1cf2fc"},"schema_version":"1.0"},"canonical_sha256":"e8042be919ec3a50e70effa26b8d6d85c6805f50576ed5889dcd610420e7e52c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:34.187499Z","signature_b64":"C91vcQJPXCoyznN+n321pvY2GMN1fmOTdCqh14gdIEGjzcaga1z2ZZe5VY8rqQfDaBKVjpsXbl+6YH74KIYkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8042be919ec3a50e70effa26b8d6d85c6805f50576ed5889dcd610420e7e52c","last_reissued_at":"2026-05-18T03:27:34.186974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:34.186974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5305","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":"2026-05-18T03:27:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbzgJu9I5ut1fsg6nSUds6BhBBSah/XQ5j2k3Y/rS1GkWfYRRJWdrWXGMoM+r0EzKtA3BVmpLSC8KSqWM57DAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T23:29:14.114490Z"},"content_sha256":"16389c83af3462084b28713849ced35138ed9795632b5ac08f342b6a5036cf8e","schema_version":"1.0","event_id":"sha256:16389c83af3462084b28713849ced35138ed9795632b5ac08f342b6a5036cf8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5ACCX2IZ5Q5FBZYO76RGXDLNQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distance sets of two subsets of vector spaces over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Doowon Koh, Hae-Sang Sun","submitted_at":"2012-12-21T00:07:22Z","abstract_excerpt":"We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of the two subsets. As a result, we improve upon the results by Rainer Dietmann. In the case that one of the subsets is a product set, we obtain further improvement on the estimate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5305","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":"2026-05-18T03:27:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6F786EJ8xTa2rf4UOXPYC1DbKcw9Mb+p2U5/G2MF2HMfnLb7BG5KsqtlZ7o16uH7W1Q/MCK0d3PS2mr5dHvADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T23:29:14.114830Z"},"content_sha256":"75b6bb47827ac19d6ff341d8293ac55d1fcc9d72abbf7aa313a2b85f7a52411f","schema_version":"1.0","event_id":"sha256:75b6bb47827ac19d6ff341d8293ac55d1fcc9d72abbf7aa313a2b85f7a52411f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ACCX2IZ5Q5FBZYO76RGXDLNQX/bundle.json","state_url":"https://pith.science/pith/5ACCX2IZ5Q5FBZYO76RGXDLNQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ACCX2IZ5Q5FBZYO76RGXDLNQX/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":"2026-07-02T23:29:14Z","links":{"resolver":"https://pith.science/pith/5ACCX2IZ5Q5FBZYO76RGXDLNQX","bundle":"https://pith.science/pith/5ACCX2IZ5Q5FBZYO76RGXDLNQX/bundle.json","state":"https://pith.science/pith/5ACCX2IZ5Q5FBZYO76RGXDLNQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ACCX2IZ5Q5FBZYO76RGXDLNQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5ACCX2IZ5Q5FBZYO76RGXDLNQX","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":"9cec5993a20001374d660455f00401301cfaf03d2d9d543da6ef104ecf1cf2fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-21T00:07:22Z","title_canon_sha256":"9dfea3975b28dc3dccd6612ef8398f392cdaa608716f22abf38c6d5899fabe29"},"schema_version":"1.0","source":{"id":"1212.5305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5305","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5305v2","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5305","created_at":"2026-05-18T03:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"5ACCX2IZ5Q5F","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5ACCX2IZ5Q5FBZYO","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5ACCX2IZ","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:75b6bb47827ac19d6ff341d8293ac55d1fcc9d72abbf7aa313a2b85f7a52411f","target":"graph","created_at":"2026-05-18T03:27:34Z","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 investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of the two subsets. As a result, we improve upon the results by Rainer Dietmann. In the case that one of the subsets is a product set, we obtain further improvement on the estimate.","authors_text":"Doowon Koh, Hae-Sang Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-21T00:07:22Z","title":"Distance sets of two subsets of vector spaces over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5305","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":"sha256:16389c83af3462084b28713849ced35138ed9795632b5ac08f342b6a5036cf8e","target":"record","created_at":"2026-05-18T03:27:34Z","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":"9cec5993a20001374d660455f00401301cfaf03d2d9d543da6ef104ecf1cf2fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-21T00:07:22Z","title_canon_sha256":"9dfea3975b28dc3dccd6612ef8398f392cdaa608716f22abf38c6d5899fabe29"},"schema_version":"1.0","source":{"id":"1212.5305","kind":"arxiv","version":2}},"canonical_sha256":"e8042be919ec3a50e70effa26b8d6d85c6805f50576ed5889dcd610420e7e52c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8042be919ec3a50e70effa26b8d6d85c6805f50576ed5889dcd610420e7e52c","first_computed_at":"2026-05-18T03:27:34.186974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:34.186974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C91vcQJPXCoyznN+n321pvY2GMN1fmOTdCqh14gdIEGjzcaga1z2ZZe5VY8rqQfDaBKVjpsXbl+6YH74KIYkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:34.187499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16389c83af3462084b28713849ced35138ed9795632b5ac08f342b6a5036cf8e","sha256:75b6bb47827ac19d6ff341d8293ac55d1fcc9d72abbf7aa313a2b85f7a52411f"],"state_sha256":"f7a9fdb42125812172b784ae0d280aa56a71d345d6b23af4dc25d6a6508bedf3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qyPP51WrsWXT6XFzXGgVhoesqkXgqY+DR/QK5HzbFp2XGF8Q5mifNpQigXzIa/ZWgHcHExbj25tPnvNQ7v50AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T23:29:14.116843Z","bundle_sha256":"5cb2ee225e6c016eb2d0bb85d9de4f18d4599b1b75caed557338ecbf906ef6e5"}}