{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LX2FC2ORBLHYVVMTQGW6NNLIRR","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":"d291bd47db8e1ebb21bb675e6c67cbab4cf1b62b9761f692860ce7bfca3e2a91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2023-10-21T15:40:32Z","title_canon_sha256":"ed247717bd0098c3c43bbe65ee337eed40ef8c0e20d3c1934829410862584fcf"},"schema_version":"1.0","source":{"id":"2310.14043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.14043","created_at":"2026-06-23T02:13:12Z"},{"alias_kind":"arxiv_version","alias_value":"2310.14043v1","created_at":"2026-06-23T02:13:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.14043","created_at":"2026-06-23T02:13:12Z"},{"alias_kind":"pith_short_12","alias_value":"LX2FC2ORBLHY","created_at":"2026-06-23T02:13:12Z"},{"alias_kind":"pith_short_16","alias_value":"LX2FC2ORBLHYVVMT","created_at":"2026-06-23T02:13:12Z"},{"alias_kind":"pith_short_8","alias_value":"LX2FC2OR","created_at":"2026-06-23T02:13:12Z"}],"graph_snapshots":[{"event_id":"sha256:c6421082f923472fe85e13a5196b40d7ba2f9ecfa853d695c39773dfad546d96","target":"graph","created_at":"2026-06-23T02:13:12Z","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/2310.14043/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the first of this series of two articles, we studied some geometrical aspects of the Birkhoff polytope, the compact convex set of all $n \\times n$ doubly stochastic matrices, namely the Chebyshev center, and the Chebyshev radius of the Birkhoff polytope associated with metrics induced by the operator norms from $\\ell_n^p$ to $\\ell_n^p$ for $1 \\leq p \\leq \\infty$. In the present paper, we take another look at those very questions, but for a different family of matrix norms, namely the Schatten $p$-norms, for $1 \\leq p < \\infty$. While studying these properties, the intrinsic connection to th","authors_text":"Fr\\'ed\\'eric Morneau-Gu\\'erin, Javad Mashreghi, Ludovick Bouthat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2023-10-21T15:40:32Z","title":"On the Geometry of the Birkhoff Polytope. II. The Schatten $p$-norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.14043","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":"sha256:5fbc59e710d44ec5f718ae1fe313ee219815e298ee58e64f696df29ec495df7f","target":"record","created_at":"2026-06-23T02:13:12Z","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":"d291bd47db8e1ebb21bb675e6c67cbab4cf1b62b9761f692860ce7bfca3e2a91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2023-10-21T15:40:32Z","title_canon_sha256":"ed247717bd0098c3c43bbe65ee337eed40ef8c0e20d3c1934829410862584fcf"},"schema_version":"1.0","source":{"id":"2310.14043","kind":"arxiv","version":1}},"canonical_sha256":"5df45169d10acf8ad59381ade6b5688c7a3876b959875ec58500093cf62f6ee5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5df45169d10acf8ad59381ade6b5688c7a3876b959875ec58500093cf62f6ee5","first_computed_at":"2026-06-23T02:13:12.087226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:12.087226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6EK5+MujrloGpITEGSUT4ia28yA3Xjg16rTnKErqlvDLoHJxjRSgzzlD4hS6NhcFCaHyued2Cn2M95JbsHPnDA==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:12.087620Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.14043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fbc59e710d44ec5f718ae1fe313ee219815e298ee58e64f696df29ec495df7f","sha256:c6421082f923472fe85e13a5196b40d7ba2f9ecfa853d695c39773dfad546d96"],"state_sha256":"554417c58374221c3b2a317f3fcba17e03aa7396fc91bb8188536bf8813038ee"}