{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:UFKTNYBQNLHR6S4K2LUIU67CZY","short_pith_number":"pith:UFKTNYBQ","canonical_record":{"source":{"id":"cs/0512025","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2005-12-06T04:36:39Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"64005ce1b3e85f9058c6844ca3d2afadf0fd08e6f38ae33b8bd00f93ab9a63fe","abstract_canon_sha256":"d598fa3b3cbf4694b8db173c1a84c0d0981abee2fa0ce5c6c50012277b1b19f0"},"schema_version":"1.0"},"canonical_sha256":"a15536e0306acf1f4b8ad2e88a7be2ce0f357f1faf477a32ee4934a41e2c5b59","source":{"kind":"arxiv","id":"cs/0512025","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0512025","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0512025v2","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0512025","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"UFKTNYBQNLHR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"UFKTNYBQNLHR6S4K","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"UFKTNYBQ","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:UFKTNYBQNLHR6S4K2LUIU67CZY","target":"record","payload":{"canonical_record":{"source":{"id":"cs/0512025","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2005-12-06T04:36:39Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"64005ce1b3e85f9058c6844ca3d2afadf0fd08e6f38ae33b8bd00f93ab9a63fe","abstract_canon_sha256":"d598fa3b3cbf4694b8db173c1a84c0d0981abee2fa0ce5c6c50012277b1b19f0"},"schema_version":"1.0"},"canonical_sha256":"a15536e0306acf1f4b8ad2e88a7be2ce0f357f1faf477a32ee4934a41e2c5b59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:22.319481Z","signature_b64":"WVdEeGyTJPjLOGt5cxmaIL86r2iGKGxbOn2w7HTPMz0WhUo+mqUvC7bZp9wDQk4lMJ2foLb1mbjccBw8lwKzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a15536e0306acf1f4b8ad2e88a7be2ce0f357f1faf477a32ee4934a41e2c5b59","last_reissued_at":"2026-05-17T23:46:22.318855Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:22.318855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cs/0512025","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":"2026-05-17T23:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Or0BiHmfr4wiRVcIhOxyD2hJxTWcCcxgmScuBXVXUz6BHQkL/vWCDYAaA3EtCwqBKOxi3dZrrXVlyqLeSkFWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:25:30.748290Z"},"content_sha256":"fe88914c3cc6cbf42676c370f1d5319665a1312643f28a16f89fc7a99cb4c59a","schema_version":"1.0","event_id":"sha256:fe88914c3cc6cbf42676c370f1d5319665a1312643f28a16f89fc7a99cb4c59a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:UFKTNYBQNLHR6S4K2LUIU67CZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral approach to linear programming bounds on codes","license":"","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Alexander Barg, Dmitry Nogin","submitted_at":"2005-12-06T04:36:39Z","abstract_excerpt":"We give new proofs of asymptotic upper bounds of coding theory obtained within the frame of Delsarte's linear programming method. The proofs rely on the analysis of eigenvectors of some finite-dimensional operators related to orthogonal polynomials. The examples of the method considered in the paper include binary codes, binary constant-weight codes, spherical codes, and codes in the projective spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0512025","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":"2026-05-17T23:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQgI8WB9ggTIancOtbgZYBVddddbrvB5dZX90xu8Zf0xpl0JtAs/I7J73p8758qYJhUbpXiwxgqNssWQNEQvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:25:30.749183Z"},"content_sha256":"86afcf60ed41fe9d5ae8932ed1f9c9b55a515a60116c852fcb86417f9136e4a2","schema_version":"1.0","event_id":"sha256:86afcf60ed41fe9d5ae8932ed1f9c9b55a515a60116c852fcb86417f9136e4a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UFKTNYBQNLHR6S4K2LUIU67CZY/bundle.json","state_url":"https://pith.science/pith/UFKTNYBQNLHR6S4K2LUIU67CZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UFKTNYBQNLHR6S4K2LUIU67CZY/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":"2026-06-07T15:25:30Z","links":{"resolver":"https://pith.science/pith/UFKTNYBQNLHR6S4K2LUIU67CZY","bundle":"https://pith.science/pith/UFKTNYBQNLHR6S4K2LUIU67CZY/bundle.json","state":"https://pith.science/pith/UFKTNYBQNLHR6S4K2LUIU67CZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UFKTNYBQNLHR6S4K2LUIU67CZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:UFKTNYBQNLHR6S4K2LUIU67CZY","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":"d598fa3b3cbf4694b8db173c1a84c0d0981abee2fa0ce5c6c50012277b1b19f0","cross_cats_sorted":["math.CO","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2005-12-06T04:36:39Z","title_canon_sha256":"64005ce1b3e85f9058c6844ca3d2afadf0fd08e6f38ae33b8bd00f93ab9a63fe"},"schema_version":"1.0","source":{"id":"cs/0512025","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0512025","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0512025v2","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0512025","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"UFKTNYBQNLHR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"UFKTNYBQNLHR6S4K","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"UFKTNYBQ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:86afcf60ed41fe9d5ae8932ed1f9c9b55a515a60116c852fcb86417f9136e4a2","target":"graph","created_at":"2026-05-17T23:46:22Z","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 give new proofs of asymptotic upper bounds of coding theory obtained within the frame of Delsarte's linear programming method. The proofs rely on the analysis of eigenvectors of some finite-dimensional operators related to orthogonal polynomials. The examples of the method considered in the paper include binary codes, binary constant-weight codes, spherical codes, and codes in the projective spaces.","authors_text":"Alexander Barg, Dmitry Nogin","cross_cats":["math.CO","math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2005-12-06T04:36:39Z","title":"Spectral approach to linear programming bounds on codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0512025","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:fe88914c3cc6cbf42676c370f1d5319665a1312643f28a16f89fc7a99cb4c59a","target":"record","created_at":"2026-05-17T23:46:22Z","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":"d598fa3b3cbf4694b8db173c1a84c0d0981abee2fa0ce5c6c50012277b1b19f0","cross_cats_sorted":["math.CO","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2005-12-06T04:36:39Z","title_canon_sha256":"64005ce1b3e85f9058c6844ca3d2afadf0fd08e6f38ae33b8bd00f93ab9a63fe"},"schema_version":"1.0","source":{"id":"cs/0512025","kind":"arxiv","version":2}},"canonical_sha256":"a15536e0306acf1f4b8ad2e88a7be2ce0f357f1faf477a32ee4934a41e2c5b59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a15536e0306acf1f4b8ad2e88a7be2ce0f357f1faf477a32ee4934a41e2c5b59","first_computed_at":"2026-05-17T23:46:22.318855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:22.318855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WVdEeGyTJPjLOGt5cxmaIL86r2iGKGxbOn2w7HTPMz0WhUo+mqUvC7bZp9wDQk4lMJ2foLb1mbjccBw8lwKzBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:22.319481Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0512025","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe88914c3cc6cbf42676c370f1d5319665a1312643f28a16f89fc7a99cb4c59a","sha256:86afcf60ed41fe9d5ae8932ed1f9c9b55a515a60116c852fcb86417f9136e4a2"],"state_sha256":"fae82b389cd39a0321eb6ddae2237625b8fceffc733f607400417e534dba7c69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SJ0WU4OPqh/8CaMy7w9MhIVC6h6Dxtd9DQQJqKtnOMnNKvtpBuha7R7XSu4r70wcYBW/ARw9XTNqlChGmYEEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T15:25:30.755452Z","bundle_sha256":"743bd3681e97d88d5ed39af5aedfb18fa7126668ae39ff4ff944cc9de009385c"}}