{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4T3EX2XT72TP6ZMUSVZFGLP4LD","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":"66db137af40fcf33f165351bed0108df626dfcb672de8667cb663aad30ddb1a1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-04-25T05:20:40Z","title_canon_sha256":"8a6a44cca29a0cd42188c960c219ff7920162d6ed9d16fc0d4df417bc4a7022d"},"schema_version":"1.0","source":{"id":"1904.11159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11159","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11159v2","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11159","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"4T3EX2XT72TP","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"pith_short_16","alias_value":"4T3EX2XT72TP6ZMU","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"pith_short_8","alias_value":"4T3EX2XT","created_at":"2026-07-05T02:02:50Z"}],"graph_snapshots":[{"event_id":"sha256:36bf388a996ff7ffab747360b442750cd6845894b3d571fec2fe73915854b18e","target":"graph","created_at":"2026-07-05T02:02:50Z","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/1904.11159/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we use the linear programming approach to find new upper bounds for the moments of isotropic measures. These bounds are then utilized for finding lower packing bounds and energy bounds for projective codes. We also show that the obtained energy bounds are sharp for several infinite families of codes.","authors_text":"Alexey Glazyrin","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-04-25T05:20:40Z","title":"Moments of isotropic measures and optimal projective codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11159","kind":"arxiv","version":2},"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":"sha256:411d23f8ad9632fe93fbf5d14078335013102d8cb95a06f2ff1a3aba6686ab7c","target":"record","created_at":"2026-07-05T02:02:50Z","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":"66db137af40fcf33f165351bed0108df626dfcb672de8667cb663aad30ddb1a1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-04-25T05:20:40Z","title_canon_sha256":"8a6a44cca29a0cd42188c960c219ff7920162d6ed9d16fc0d4df417bc4a7022d"},"schema_version":"1.0","source":{"id":"1904.11159","kind":"arxiv","version":2}},"canonical_sha256":"e4f64beaf3fea6ff65949572532dfc58e574ae9df23058961cec1ea0abe46845","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4f64beaf3fea6ff65949572532dfc58e574ae9df23058961cec1ea0abe46845","first_computed_at":"2026-07-05T02:02:50.211348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:02:50.211348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EQPuZKe1qEH0tcFJ7G9skcbWPi01e/leC52p721Xy/WDC11pF5AGOyv+ly6ZSXP+n/twN/zixSIcD+oUY9GECw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:02:50.211910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.11159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:411d23f8ad9632fe93fbf5d14078335013102d8cb95a06f2ff1a3aba6686ab7c","sha256:36bf388a996ff7ffab747360b442750cd6845894b3d571fec2fe73915854b18e"],"state_sha256":"80ccfc19679493f21011acdebcabe62f0129213f2f2afcc16fa484f77f47bcfb"}