{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:3PS6I3HNU3H6IMJWCKTA7DC6LI","short_pith_number":"pith:3PS6I3HN","canonical_record":{"source":{"id":"2301.09457","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-01-23T14:30:22Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"628052e01dd9234e4a2e76f83e8c0ae3109e803c8fd0cd2fe286ce606cf77f93","abstract_canon_sha256":"af464837f0070098094e1c6fd58554363340f88cdb4ee74627bbb45bdd5cf942"},"schema_version":"1.0"},"canonical_sha256":"dbe5e46ceda6cfe4313612a60f8c5e5a17cebe89242de2ac813e930849221ee8","source":{"kind":"arxiv","id":"2301.09457","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.09457","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"arxiv_version","alias_value":"2301.09457v3","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.09457","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"pith_short_12","alias_value":"3PS6I3HNU3H6","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"pith_short_16","alias_value":"3PS6I3HNU3H6IMJW","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"pith_short_8","alias_value":"3PS6I3HN","created_at":"2026-07-05T08:17:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:3PS6I3HNU3H6IMJWCKTA7DC6LI","target":"record","payload":{"canonical_record":{"source":{"id":"2301.09457","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-01-23T14:30:22Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"628052e01dd9234e4a2e76f83e8c0ae3109e803c8fd0cd2fe286ce606cf77f93","abstract_canon_sha256":"af464837f0070098094e1c6fd58554363340f88cdb4ee74627bbb45bdd5cf942"},"schema_version":"1.0"},"canonical_sha256":"dbe5e46ceda6cfe4313612a60f8c5e5a17cebe89242de2ac813e930849221ee8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:08.928008Z","signature_b64":"zY+KgT8mkC78i8sFl0DRJiY4BEJyepWbLjxYX0B5loHMbwZZvXMcy1kaQSJ3NQnBOc5UF6lDkfoKIYqJYPfMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbe5e46ceda6cfe4313612a60f8c5e5a17cebe89242de2ac813e930849221ee8","last_reissued_at":"2026-07-05T08:17:08.927525Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:08.927525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.09457","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:17:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZP0RQnvSJWGpFbL1yAwSSCPCpe+Y3oKGOGwsISvZl0Wew3ojTXASmOovan//zT28mbNhhL3Z2glluVHZHgCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:55:22.014594Z"},"content_sha256":"52dacadc50deb7536b6a5135f057d6647409c7b3d1a9b8d0763baf5c0c2db379","schema_version":"1.0","event_id":"sha256:52dacadc50deb7536b6a5135f057d6647409c7b3d1a9b8d0763baf5c0c2db379"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:3PS6I3HNU3H6IMJWCKTA7DC6LI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blocking sets, minimal codes and trifferent codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Aditya Potukuchi, Anurag Bishnoi, Dion Gijswijt, Jozefien D'haeseleer","submitted_at":"2023-01-23T14:30:22Z","abstract_excerpt":"We prove new upper bounds on the smallest size of affine blocking sets, that is, sets of points in a finite affine space that intersect every affine subspace of a fixed codimension. We show an equivalence between affine blocking sets with respect to codimension-$2$ subspaces that are generated by taking a union of lines through the origin, and strong blocking sets in the corresponding projective space, which in turn are equivalent to minimal codes. Using this equivalence, we improve the current best upper bounds on the smallest size of a strong blocking set in finite projective spaces over fie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.09457","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.09457/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:17:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SGvMP2nEyn6lXMeBySGKU8kGIbDWYD9gA++EF3ca1OhrFRp+Fy/TYV6rLg6tcqhMBYvgXjXkExGWlF34ijytAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:55:22.015225Z"},"content_sha256":"de9efcad0a4b6cac0660f8baaa84b8c522d7a4090de10c7a44575237f7f5733a","schema_version":"1.0","event_id":"sha256:de9efcad0a4b6cac0660f8baaa84b8c522d7a4090de10c7a44575237f7f5733a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3PS6I3HNU3H6IMJWCKTA7DC6LI/bundle.json","state_url":"https://pith.science/pith/3PS6I3HNU3H6IMJWCKTA7DC6LI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3PS6I3HNU3H6IMJWCKTA7DC6LI/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":"2026-08-03T18:55:22Z","links":{"resolver":"https://pith.science/pith/3PS6I3HNU3H6IMJWCKTA7DC6LI","bundle":"https://pith.science/pith/3PS6I3HNU3H6IMJWCKTA7DC6LI/bundle.json","state":"https://pith.science/pith/3PS6I3HNU3H6IMJWCKTA7DC6LI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3PS6I3HNU3H6IMJWCKTA7DC6LI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3PS6I3HNU3H6IMJWCKTA7DC6LI","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":"af464837f0070098094e1c6fd58554363340f88cdb4ee74627bbb45bdd5cf942","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-01-23T14:30:22Z","title_canon_sha256":"628052e01dd9234e4a2e76f83e8c0ae3109e803c8fd0cd2fe286ce606cf77f93"},"schema_version":"1.0","source":{"id":"2301.09457","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.09457","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"arxiv_version","alias_value":"2301.09457v3","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.09457","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"pith_short_12","alias_value":"3PS6I3HNU3H6","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"pith_short_16","alias_value":"3PS6I3HNU3H6IMJW","created_at":"2026-07-05T08:17:08Z"},{"alias_kind":"pith_short_8","alias_value":"3PS6I3HN","created_at":"2026-07-05T08:17:08Z"}],"graph_snapshots":[{"event_id":"sha256:de9efcad0a4b6cac0660f8baaa84b8c522d7a4090de10c7a44575237f7f5733a","target":"graph","created_at":"2026-07-05T08:17:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2301.09457/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove new upper bounds on the smallest size of affine blocking sets, that is, sets of points in a finite affine space that intersect every affine subspace of a fixed codimension. We show an equivalence between affine blocking sets with respect to codimension-$2$ subspaces that are generated by taking a union of lines through the origin, and strong blocking sets in the corresponding projective space, which in turn are equivalent to minimal codes. Using this equivalence, we improve the current best upper bounds on the smallest size of a strong blocking set in finite projective spaces over fie","authors_text":"Aditya Potukuchi, Anurag Bishnoi, Dion Gijswijt, Jozefien D'haeseleer","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-01-23T14:30:22Z","title":"Blocking sets, minimal codes and trifferent codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.09457","kind":"arxiv","version":3},"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":"sha256:52dacadc50deb7536b6a5135f057d6647409c7b3d1a9b8d0763baf5c0c2db379","target":"record","created_at":"2026-07-05T08:17:08Z","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":"af464837f0070098094e1c6fd58554363340f88cdb4ee74627bbb45bdd5cf942","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-01-23T14:30:22Z","title_canon_sha256":"628052e01dd9234e4a2e76f83e8c0ae3109e803c8fd0cd2fe286ce606cf77f93"},"schema_version":"1.0","source":{"id":"2301.09457","kind":"arxiv","version":3}},"canonical_sha256":"dbe5e46ceda6cfe4313612a60f8c5e5a17cebe89242de2ac813e930849221ee8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbe5e46ceda6cfe4313612a60f8c5e5a17cebe89242de2ac813e930849221ee8","first_computed_at":"2026-07-05T08:17:08.927525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:17:08.927525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zY+KgT8mkC78i8sFl0DRJiY4BEJyepWbLjxYX0B5loHMbwZZvXMcy1kaQSJ3NQnBOc5UF6lDkfoKIYqJYPfMCA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:17:08.928008Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.09457","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52dacadc50deb7536b6a5135f057d6647409c7b3d1a9b8d0763baf5c0c2db379","sha256:de9efcad0a4b6cac0660f8baaa84b8c522d7a4090de10c7a44575237f7f5733a"],"state_sha256":"f32f493e673a77b43d2b189fb1ee87a9e383a74c5cf8ffc618f0ed7d8f7f61da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nw8xujcs0tZ7jwwrJjbets2n/11HD6fC6osqk1DBSBZZmCtoeNBZoHUlZMvgIbGTv4VqUjEsGhDdm2QFI2VgDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T18:55:22.018903Z","bundle_sha256":"824f40caec80bb512d6ecd1322b4e4121f21e6d01c8de28b4fab486d59218d55"}}