{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PVUREQFTTJBBN7NL6YQ3UXRCWZ","short_pith_number":"pith:PVUREQFT","canonical_record":{"source":{"id":"1208.3819","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T10:12:47Z","cross_cats_sorted":[],"title_canon_sha256":"db8851d54c63b9df3741273c34199bb779e44b83f475beecd99714d30179e64e","abstract_canon_sha256":"35133cf969fc3732495047ff80907cdf79fd9411664978f7c8183430e27d1e8f"},"schema_version":"1.0"},"canonical_sha256":"7d691240b39a4216fdabf621ba5e22b6768919e6f03c15ce22e1f52eaf552eb0","source":{"kind":"arxiv","id":"1208.3819","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3819","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3819v3","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3819","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"pith_short_12","alias_value":"PVUREQFTTJBB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PVUREQFTTJBBN7NL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PVUREQFT","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PVUREQFTTJBBN7NL6YQ3UXRCWZ","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3819","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T10:12:47Z","cross_cats_sorted":[],"title_canon_sha256":"db8851d54c63b9df3741273c34199bb779e44b83f475beecd99714d30179e64e","abstract_canon_sha256":"35133cf969fc3732495047ff80907cdf79fd9411664978f7c8183430e27d1e8f"},"schema_version":"1.0"},"canonical_sha256":"7d691240b39a4216fdabf621ba5e22b6768919e6f03c15ce22e1f52eaf552eb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:17.295878Z","signature_b64":"hkhi+VOaFZ9VElABjZ3SR1yieNxkPVDKTV+9BKoTIslW8CyZQ1RZ4IqseXidwI3bAZ/G27u/j7mAp6K4h44GBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d691240b39a4216fdabf621ba5e22b6768919e6f03c15ce22e1f52eaf552eb0","last_reissued_at":"2026-05-18T03:31:17.295242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:17.295242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3819","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":"2026-05-18T03:31:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w/HWnJyblcB900XRgrTbYLbXlzy0cJIhmDs1LC4mbK2fJOReAe+Fe0hNrcfP4C1WQQHXfCOji1lrVWPsQwmjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:36:35.316630Z"},"content_sha256":"8d39b5afe05ffd13b9770fb1f22dfc04732197d80871995fce38819ad52d9d71","schema_version":"1.0","event_id":"sha256:8d39b5afe05ffd13b9770fb1f22dfc04732197d80871995fce38819ad52d9d71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PVUREQFTTJBBN7NL6YQ3UXRCWZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On minors of maximal determinant matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Judy-anne H. Osborn, Richard P. Brent","submitted_at":"2012-08-19T10:12:47Z","abstract_excerpt":"By an old result of Cohn (1965), a Hadamard matrix of order n has no proper Hadamard submatrices of order m > n/2. We generalise this result to maximal determinant submatrices of Hadamard matrices, and show that an interval of length asymptotically equal to n/2 is excluded from the allowable orders. We make a conjecture regarding a lower bound for sums of squares of minors of maximal determinant matrices, and give evidence in support of the conjecture. We give tables of the values taken by the minors of all maximal determinant matrices of orders up to and including 21 and make some observation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3819","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":""},"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":"2026-05-18T03:31:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xYtEO+z5WhlHfGLmw/vxLIZmjveD1qvKu/XOFFTskXGx9P0S5+x3G2V0p/xO7FTYR95PxaTcOg41hY1F0t+8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:36:35.317433Z"},"content_sha256":"e56c7b728f7f18103e3cfbcde04fb781c62e27782844ccddda7ea4a3d1d17c06","schema_version":"1.0","event_id":"sha256:e56c7b728f7f18103e3cfbcde04fb781c62e27782844ccddda7ea4a3d1d17c06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVUREQFTTJBBN7NL6YQ3UXRCWZ/bundle.json","state_url":"https://pith.science/pith/PVUREQFTTJBBN7NL6YQ3UXRCWZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVUREQFTTJBBN7NL6YQ3UXRCWZ/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":"2026-06-10T04:36:35Z","links":{"resolver":"https://pith.science/pith/PVUREQFTTJBBN7NL6YQ3UXRCWZ","bundle":"https://pith.science/pith/PVUREQFTTJBBN7NL6YQ3UXRCWZ/bundle.json","state":"https://pith.science/pith/PVUREQFTTJBBN7NL6YQ3UXRCWZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVUREQFTTJBBN7NL6YQ3UXRCWZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PVUREQFTTJBBN7NL6YQ3UXRCWZ","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":"35133cf969fc3732495047ff80907cdf79fd9411664978f7c8183430e27d1e8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T10:12:47Z","title_canon_sha256":"db8851d54c63b9df3741273c34199bb779e44b83f475beecd99714d30179e64e"},"schema_version":"1.0","source":{"id":"1208.3819","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3819","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3819v3","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3819","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"pith_short_12","alias_value":"PVUREQFTTJBB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PVUREQFTTJBBN7NL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PVUREQFT","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:e56c7b728f7f18103e3cfbcde04fb781c62e27782844ccddda7ea4a3d1d17c06","target":"graph","created_at":"2026-05-18T03:31:17Z","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":"By an old result of Cohn (1965), a Hadamard matrix of order n has no proper Hadamard submatrices of order m > n/2. We generalise this result to maximal determinant submatrices of Hadamard matrices, and show that an interval of length asymptotically equal to n/2 is excluded from the allowable orders. We make a conjecture regarding a lower bound for sums of squares of minors of maximal determinant matrices, and give evidence in support of the conjecture. We give tables of the values taken by the minors of all maximal determinant matrices of orders up to and including 21 and make some observation","authors_text":"Judy-anne H. Osborn, Richard P. Brent","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T10:12:47Z","title":"On minors of maximal determinant matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3819","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":"sha256:8d39b5afe05ffd13b9770fb1f22dfc04732197d80871995fce38819ad52d9d71","target":"record","created_at":"2026-05-18T03:31:17Z","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":"35133cf969fc3732495047ff80907cdf79fd9411664978f7c8183430e27d1e8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T10:12:47Z","title_canon_sha256":"db8851d54c63b9df3741273c34199bb779e44b83f475beecd99714d30179e64e"},"schema_version":"1.0","source":{"id":"1208.3819","kind":"arxiv","version":3}},"canonical_sha256":"7d691240b39a4216fdabf621ba5e22b6768919e6f03c15ce22e1f52eaf552eb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d691240b39a4216fdabf621ba5e22b6768919e6f03c15ce22e1f52eaf552eb0","first_computed_at":"2026-05-18T03:31:17.295242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:17.295242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hkhi+VOaFZ9VElABjZ3SR1yieNxkPVDKTV+9BKoTIslW8CyZQ1RZ4IqseXidwI3bAZ/G27u/j7mAp6K4h44GBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:17.295878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3819","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d39b5afe05ffd13b9770fb1f22dfc04732197d80871995fce38819ad52d9d71","sha256:e56c7b728f7f18103e3cfbcde04fb781c62e27782844ccddda7ea4a3d1d17c06"],"state_sha256":"8fe7ac96b95c583b18bc12930ba719fcbae5e626b868d437fc3c456c84de136b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DJmVmKqUDq+ZHTcLVOP9QJ78NnJKLzNMe5cGfreN0jnyLg4KPJ+DRMDB3Q9V2zNzQajPiYMH8BvCqPxhi4fbBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T04:36:35.321195Z","bundle_sha256":"bb40c384bfaedfafc604fbb260bb62b0a11cc3c2621b0c71b3361f93cdb7c427"}}