{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5OT2QXOQ4UZLUDJVCOZ2C6OF2L","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":"49e0a4210b757f917c47b26fa8b429018d482e694d2e324f979f72c111a58787","cross_cats_sorted":["math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-01T09:29:19Z","title_canon_sha256":"9818b000907b06a2a3c6ef1d93d465bc7dfd1985d19932d8fec4ea9c7428dc19"},"schema_version":"1.0","source":{"id":"1006.0093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.0093","created_at":"2026-05-18T04:29:44Z"},{"alias_kind":"arxiv_version","alias_value":"1006.0093v1","created_at":"2026-05-18T04:29:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0093","created_at":"2026-05-18T04:29:44Z"},{"alias_kind":"pith_short_12","alias_value":"5OT2QXOQ4UZL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5OT2QXOQ4UZLUDJV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5OT2QXOQ","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:b0ff27baaa29ee2d2ded6467b42f04ad199387caab33e25b476402ece10818cb","target":"graph","created_at":"2026-05-18T04:29:44Z","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":"A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and on Grobner bases. A third algorithmic approach is presented: the non-existence of more than three mutually unbiased bases in composite dimensions can be decided by a global optimization method known as semidefinite programming. The method is used to confirm that the spectral matrix cannot be part of a complete set of seven mutually unbiased bases in dimension","authors_text":"Stefan Weigert, Stephen Brierley","cross_cats":["math-ph","math.MP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-01T09:29:19Z","title":"Mutually Unbiased Bases and Semi-definite Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0093","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":"sha256:38e065f5b6ed5f7df2978aaff153cf5cdb57bd9a40b8e51d70de658f983a10fb","target":"record","created_at":"2026-05-18T04:29:44Z","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":"49e0a4210b757f917c47b26fa8b429018d482e694d2e324f979f72c111a58787","cross_cats_sorted":["math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-01T09:29:19Z","title_canon_sha256":"9818b000907b06a2a3c6ef1d93d465bc7dfd1985d19932d8fec4ea9c7428dc19"},"schema_version":"1.0","source":{"id":"1006.0093","kind":"arxiv","version":1}},"canonical_sha256":"eba7a85dd0e532ba0d3513b3a179c5d2ed4762a34a8be8a35ab6a28b296c3d7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eba7a85dd0e532ba0d3513b3a179c5d2ed4762a34a8be8a35ab6a28b296c3d7e","first_computed_at":"2026-05-18T04:29:44.573945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:44.573945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YJIl+hHJAA1QxR8Z6s84fUIifEV1O/C8SSnaU7/qRbNZBPB3FGKCmDd5oRLHUOP0ymgSDoP9HMyeRSfq1kEbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:44.574508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.0093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38e065f5b6ed5f7df2978aaff153cf5cdb57bd9a40b8e51d70de658f983a10fb","sha256:b0ff27baaa29ee2d2ded6467b42f04ad199387caab33e25b476402ece10818cb"],"state_sha256":"5414cae3410ea89ee2d7d3c8f0eab2a09d2d9d6f00827469ab3f34d66e7825cf"}