{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QQQMDPIQWZWJPIBLS2BBFXNA66","short_pith_number":"pith:QQQMDPIQ","canonical_record":{"source":{"id":"1907.02728","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-05T08:44:39Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"073e7866649f908313c18a9fbe1cda1ce2185bd701c3bb6d9633a10e25a5a621","abstract_canon_sha256":"b16b10452c22b9c223f6952537e891c93f4e388c86b0f38d18b6f9dffbadfea4"},"schema_version":"1.0"},"canonical_sha256":"8420c1bd10b66c97a02b968212dda0f7afca21626bb022fc6fc8244131eb56a1","source":{"kind":"arxiv","id":"1907.02728","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02728","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02728v1","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02728","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"QQQMDPIQWZWJ","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"pith_short_16","alias_value":"QQQMDPIQWZWJPIBL","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"pith_short_8","alias_value":"QQQMDPIQ","created_at":"2026-07-05T00:22:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QQQMDPIQWZWJPIBLS2BBFXNA66","target":"record","payload":{"canonical_record":{"source":{"id":"1907.02728","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-05T08:44:39Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"073e7866649f908313c18a9fbe1cda1ce2185bd701c3bb6d9633a10e25a5a621","abstract_canon_sha256":"b16b10452c22b9c223f6952537e891c93f4e388c86b0f38d18b6f9dffbadfea4"},"schema_version":"1.0"},"canonical_sha256":"8420c1bd10b66c97a02b968212dda0f7afca21626bb022fc6fc8244131eb56a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:22:40.452609Z","signature_b64":"5wjUfoYomv2URBASgHO9sPyoow7fklptoJSXu7Fzxu3y3FGXPa8l7KZk7iB+tH2+4jLk5Nd2ndQrABpniP/UAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8420c1bd10b66c97a02b968212dda0f7afca21626bb022fc6fc8244131eb56a1","last_reissued_at":"2026-07-05T00:22:40.452087Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:22:40.452087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.02728","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":"2026-07-05T00:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nUcjgRrEGVOGO7McYHRpZOJB7OgyeQKBzHhfWoSvJImWW6/51WwWvM9OxaOMXaj5H1mQdQ5epeugH7q2lmfYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T13:23:57.992464Z"},"content_sha256":"66ae61d232d311687ba25a8b7fcc45cb67f8c6aff51e04db8d7152e3d9165ec4","schema_version":"1.0","event_id":"sha256:66ae61d232d311687ba25a8b7fcc45cb67f8c6aff51e04db8d7152e3d9165ec4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QQQMDPIQWZWJPIBLS2BBFXNA66","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subspaces intersecting in at most a point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Sascha Kurz","submitted_at":"2019-07-05T08:44:39Z","abstract_excerpt":"We improve on the lower bound of the maximum number of planes in $\\operatorname{PG}(8,q)\\cong\\F_q^{9}$ pairwise intersecting in at most a point. In terms of constant dimension codes this leads to $A_q(9,4;3)\\ge q^{12}+ 2q^8+2q^7+q^6+2q^5+2q^4-2q^2-2q+1$. This result is obtained via a more general construction strategy, which also yields other improvements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02728","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.02728/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":"2026-07-05T00:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQvNsV8Hyay/m7R7NXGfCyg9kIx5m0EUng3gDwMnmkJCBkD7k9+jqi5LKk/xA/oR83nVkeV6V1OUn8yZjelhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T13:23:57.993132Z"},"content_sha256":"0eb0844311d7111fe53586ed5ecda5c3046e3308449a5a5f0fdd1fdda889463b","schema_version":"1.0","event_id":"sha256:0eb0844311d7111fe53586ed5ecda5c3046e3308449a5a5f0fdd1fdda889463b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QQQMDPIQWZWJPIBLS2BBFXNA66/bundle.json","state_url":"https://pith.science/pith/QQQMDPIQWZWJPIBLS2BBFXNA66/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QQQMDPIQWZWJPIBLS2BBFXNA66/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":"2026-08-11T13:23:57Z","links":{"resolver":"https://pith.science/pith/QQQMDPIQWZWJPIBLS2BBFXNA66","bundle":"https://pith.science/pith/QQQMDPIQWZWJPIBLS2BBFXNA66/bundle.json","state":"https://pith.science/pith/QQQMDPIQWZWJPIBLS2BBFXNA66/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QQQMDPIQWZWJPIBLS2BBFXNA66/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QQQMDPIQWZWJPIBLS2BBFXNA66","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":"b16b10452c22b9c223f6952537e891c93f4e388c86b0f38d18b6f9dffbadfea4","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-05T08:44:39Z","title_canon_sha256":"073e7866649f908313c18a9fbe1cda1ce2185bd701c3bb6d9633a10e25a5a621"},"schema_version":"1.0","source":{"id":"1907.02728","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02728","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02728v1","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02728","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"QQQMDPIQWZWJ","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"pith_short_16","alias_value":"QQQMDPIQWZWJPIBL","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"pith_short_8","alias_value":"QQQMDPIQ","created_at":"2026-07-05T00:22:40Z"}],"graph_snapshots":[{"event_id":"sha256:0eb0844311d7111fe53586ed5ecda5c3046e3308449a5a5f0fdd1fdda889463b","target":"graph","created_at":"2026-07-05T00:22:40Z","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/1907.02728/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We improve on the lower bound of the maximum number of planes in $\\operatorname{PG}(8,q)\\cong\\F_q^{9}$ pairwise intersecting in at most a point. In terms of constant dimension codes this leads to $A_q(9,4;3)\\ge q^{12}+ 2q^8+2q^7+q^6+2q^5+2q^4-2q^2-2q+1$. This result is obtained via a more general construction strategy, which also yields other improvements.","authors_text":"Sascha Kurz","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-05T08:44:39Z","title":"Subspaces intersecting in at most a point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02728","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":"sha256:66ae61d232d311687ba25a8b7fcc45cb67f8c6aff51e04db8d7152e3d9165ec4","target":"record","created_at":"2026-07-05T00:22:40Z","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":"b16b10452c22b9c223f6952537e891c93f4e388c86b0f38d18b6f9dffbadfea4","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-05T08:44:39Z","title_canon_sha256":"073e7866649f908313c18a9fbe1cda1ce2185bd701c3bb6d9633a10e25a5a621"},"schema_version":"1.0","source":{"id":"1907.02728","kind":"arxiv","version":1}},"canonical_sha256":"8420c1bd10b66c97a02b968212dda0f7afca21626bb022fc6fc8244131eb56a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8420c1bd10b66c97a02b968212dda0f7afca21626bb022fc6fc8244131eb56a1","first_computed_at":"2026-07-05T00:22:40.452087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:22:40.452087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5wjUfoYomv2URBASgHO9sPyoow7fklptoJSXu7Fzxu3y3FGXPa8l7KZk7iB+tH2+4jLk5Nd2ndQrABpniP/UAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:22:40.452609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02728","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66ae61d232d311687ba25a8b7fcc45cb67f8c6aff51e04db8d7152e3d9165ec4","sha256:0eb0844311d7111fe53586ed5ecda5c3046e3308449a5a5f0fdd1fdda889463b"],"state_sha256":"22c5503ea18cf882c6464d2e74ff1c71b8994f056adc3b5a1fb23b098211a159"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O1+Bxkg1y4qtS51a2RGDlYVnjcQ2c/LlcU9XIuAibSBNYv1qTOV8WYbwKJx+aBHv/Z5hEFUYziBZB3DlK21RDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T13:23:57.998236Z","bundle_sha256":"5f4acd6c4dfb76936e9a396e5552d20531cd6ca3743d586c2315a28debfa088e"}}