{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:KC545NXUUHHG3ETKIAPRFWHMAJ","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":"c55545165b7e0806fc51df5347e492af9b4606c546de69eecf24b1fd1ed3e4fa","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.FA","submitted_at":"2001-02-19T13:51:31Z","title_canon_sha256":"1af9bd91dad58eaacd4632a6323a549d4c4bd73c09619eba6cc04c34705a93da"},"schema_version":"1.0","source":{"id":"math/0102146","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0102146","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0102146v2","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0102146","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"KC545NXUUHHG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"KC545NXUUHHG3ETK","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"KC545NXU","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:00d139b59b1b87bd984d57fe7be4366865eb449e4413acbfe1d065e35cb1f346","target":"graph","created_at":"2026-05-18T00:37:49Z","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":"We characterize the 1-unconditional subsequences of the canonical basis (e_rc) of elementary matrices in the Schatten-von-Neumann class S^p . The set I of couples (r,c) must be the set of edges of a bipartite graph without cycles of even length 4<=l<=p if p is an even integer, and without cycles at all if p is a positive real number that is not an even integer. In the latter case, I is even a Varopoulos set of V-interpolation of constant 1. We also study the metric unconditional approximation property for the space S^p_I spanned by (e_rc)_{(r,c)\\in I} in S^p .","authors_text":"Stefan Neuwirth","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2001-02-19T13:51:31Z","title":"Cycles and 1-unconditional matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0102146","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":"sha256:561c985c75594ab7f4c91e0fafdbd823e39dc0fb0b251f7b35e4968310903a70","target":"record","created_at":"2026-05-18T00:37:49Z","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":"c55545165b7e0806fc51df5347e492af9b4606c546de69eecf24b1fd1ed3e4fa","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.FA","submitted_at":"2001-02-19T13:51:31Z","title_canon_sha256":"1af9bd91dad58eaacd4632a6323a549d4c4bd73c09619eba6cc04c34705a93da"},"schema_version":"1.0","source":{"id":"math/0102146","kind":"arxiv","version":2}},"canonical_sha256":"50bbceb6f4a1ce6d926a401f12d8ec0260532f5825f3f40093f24e11b5223c5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50bbceb6f4a1ce6d926a401f12d8ec0260532f5825f3f40093f24e11b5223c5b","first_computed_at":"2026-05-18T00:37:49.258994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:49.258994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NkDbzJxmFFiBoLKKbzaGMcIH2tyH1P6fW/FpzYpGoWa8YWuXq0MgjSIwQjMnRe9pzdnMlptBP5+GDFHp01RmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:49.259610Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0102146","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:561c985c75594ab7f4c91e0fafdbd823e39dc0fb0b251f7b35e4968310903a70","sha256:00d139b59b1b87bd984d57fe7be4366865eb449e4413acbfe1d065e35cb1f346"],"state_sha256":"5f3b0891a18cb47b1624950f648fb9618414e93fa1c23346f0ddbca71c454845"}