{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:G6Z7E67RHFJ76COTYNWT2AFN7X","short_pith_number":"pith:G6Z7E67R","canonical_record":{"source":{"id":"1710.02512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-06T17:43:54Z","cross_cats_sorted":[],"title_canon_sha256":"4ba12c644864e4df38890a7f06d7b6bdda0816551253e8bcd7c4deaadf7dad55","abstract_canon_sha256":"787fbc34b512b02b21e2e78a8e58576e508d96cdde5ca80ed1b754467e62ee66"},"schema_version":"1.0"},"canonical_sha256":"37b3f27bf13953ff09d3c36d3d00adfdcd5c532d81f4143b72717daa6f4755bd","source":{"kind":"arxiv","id":"1710.02512","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02512","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02512v1","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02512","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"pith_short_12","alias_value":"G6Z7E67RHFJ7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G6Z7E67RHFJ76COT","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G6Z7E67R","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:G6Z7E67RHFJ76COTYNWT2AFN7X","target":"record","payload":{"canonical_record":{"source":{"id":"1710.02512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-06T17:43:54Z","cross_cats_sorted":[],"title_canon_sha256":"4ba12c644864e4df38890a7f06d7b6bdda0816551253e8bcd7c4deaadf7dad55","abstract_canon_sha256":"787fbc34b512b02b21e2e78a8e58576e508d96cdde5ca80ed1b754467e62ee66"},"schema_version":"1.0"},"canonical_sha256":"37b3f27bf13953ff09d3c36d3d00adfdcd5c532d81f4143b72717daa6f4755bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:33.259741Z","signature_b64":"5MXT8QKpqMsCQRUtqGeF35ag7/phIvrlXDnYmDgcIuVlLVSTYdxSMzHy8p04Xtsr7ywoQO1zXK0XIBWDl9VKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37b3f27bf13953ff09d3c36d3d00adfdcd5c532d81f4143b72717daa6f4755bd","last_reissued_at":"2026-05-18T00:33:33.259186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:33.259186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.02512","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":"2026-05-18T00:33:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZDhHnuvbDF1Q99LlMK7dIxxY2srXoDY0/otL2CGaVWj1FspZ2iHf/rQCDUSFh88IjB13ctr25TpvYEWvBwzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:56:29.158505Z"},"content_sha256":"4e96cfe46d2181d9adbe962ab81b9d5ee6f7776ca96e3e2945ce3b6640cb686b","schema_version":"1.0","event_id":"sha256:4e96cfe46d2181d9adbe962ab81b9d5ee6f7776ca96e3e2945ce3b6640cb686b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:G6Z7E67RHFJ76COTYNWT2AFN7X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On k-caps in PG(n, q), with q even and n \\geq 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joseph A. Thas","submitted_at":"2017-10-06T17:43:54Z","abstract_excerpt":"Let $m_2(n, q), n \\geq 3$, be the maximum size of k for which there exists a complete k-cap in PG(n, q). In this paper the known bounds for $m_2(n, q), n \\geq 4$, q even and $q \\geq 2048$, will be considerably improved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02512","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":"2026-05-18T00:33:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZUv/kq57iR87TchxQ8UWWEgCFt2/Mk+vRXZNGmDJ7XBqu/XlIHzBLNXlZ6AelPiTNHwm/XWI7ARe+iZPQ63yAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:56:29.159349Z"},"content_sha256":"ef42bbac02333239fb79af77552544ee9491bc1b2c8cd966893c1f075379d987","schema_version":"1.0","event_id":"sha256:ef42bbac02333239fb79af77552544ee9491bc1b2c8cd966893c1f075379d987"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G6Z7E67RHFJ76COTYNWT2AFN7X/bundle.json","state_url":"https://pith.science/pith/G6Z7E67RHFJ76COTYNWT2AFN7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G6Z7E67RHFJ76COTYNWT2AFN7X/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":"2026-05-30T23:56:29Z","links":{"resolver":"https://pith.science/pith/G6Z7E67RHFJ76COTYNWT2AFN7X","bundle":"https://pith.science/pith/G6Z7E67RHFJ76COTYNWT2AFN7X/bundle.json","state":"https://pith.science/pith/G6Z7E67RHFJ76COTYNWT2AFN7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G6Z7E67RHFJ76COTYNWT2AFN7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G6Z7E67RHFJ76COTYNWT2AFN7X","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":"787fbc34b512b02b21e2e78a8e58576e508d96cdde5ca80ed1b754467e62ee66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-06T17:43:54Z","title_canon_sha256":"4ba12c644864e4df38890a7f06d7b6bdda0816551253e8bcd7c4deaadf7dad55"},"schema_version":"1.0","source":{"id":"1710.02512","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02512","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02512v1","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02512","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"pith_short_12","alias_value":"G6Z7E67RHFJ7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G6Z7E67RHFJ76COT","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G6Z7E67R","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:ef42bbac02333239fb79af77552544ee9491bc1b2c8cd966893c1f075379d987","target":"graph","created_at":"2026-05-18T00:33:33Z","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":"Let $m_2(n, q), n \\geq 3$, be the maximum size of k for which there exists a complete k-cap in PG(n, q). In this paper the known bounds for $m_2(n, q), n \\geq 4$, q even and $q \\geq 2048$, will be considerably improved.","authors_text":"Joseph A. Thas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-06T17:43:54Z","title":"On k-caps in PG(n, q), with q even and n \\geq 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02512","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":"sha256:4e96cfe46d2181d9adbe962ab81b9d5ee6f7776ca96e3e2945ce3b6640cb686b","target":"record","created_at":"2026-05-18T00:33:33Z","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":"787fbc34b512b02b21e2e78a8e58576e508d96cdde5ca80ed1b754467e62ee66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-06T17:43:54Z","title_canon_sha256":"4ba12c644864e4df38890a7f06d7b6bdda0816551253e8bcd7c4deaadf7dad55"},"schema_version":"1.0","source":{"id":"1710.02512","kind":"arxiv","version":1}},"canonical_sha256":"37b3f27bf13953ff09d3c36d3d00adfdcd5c532d81f4143b72717daa6f4755bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37b3f27bf13953ff09d3c36d3d00adfdcd5c532d81f4143b72717daa6f4755bd","first_computed_at":"2026-05-18T00:33:33.259186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:33.259186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5MXT8QKpqMsCQRUtqGeF35ag7/phIvrlXDnYmDgcIuVlLVSTYdxSMzHy8p04Xtsr7ywoQO1zXK0XIBWDl9VKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:33.259741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.02512","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e96cfe46d2181d9adbe962ab81b9d5ee6f7776ca96e3e2945ce3b6640cb686b","sha256:ef42bbac02333239fb79af77552544ee9491bc1b2c8cd966893c1f075379d987"],"state_sha256":"b56302fe368c9d16012d9c109fca07a8baaae9e72a7435f1ce7e68d5e719c434"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cxHG7EbIGa3zCpefXAZ5Ztb/onCP2qQKVviVG23zj64gRZXGnXh+Qep9uXwqMNjjD+dR7o3bUObdpzPtoDtVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:56:29.163943Z","bundle_sha256":"aa77f79b4928ffdef5d297cf79e333e9bb8b7859bdd7f36d0cebb00a6dc46fd7"}}