{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NKPPRWAA3UFGVZC3KN4KMQJ5GN","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":"a6882478dffd04236877519f22b176ab10df31c61686c08dfefbb8165f8b81b4","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-08-21T11:14:05Z","title_canon_sha256":"6d1b7d1ecbe32fe839bf32721eaa63dbd3d9bd01d94165915e702b8f82c5c441"},"schema_version":"1.0","source":{"id":"2308.10635","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.10635","created_at":"2026-07-05T10:06:01Z"},{"alias_kind":"arxiv_version","alias_value":"2308.10635v2","created_at":"2026-07-05T10:06:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.10635","created_at":"2026-07-05T10:06:01Z"},{"alias_kind":"pith_short_12","alias_value":"NKPPRWAA3UFG","created_at":"2026-07-05T10:06:01Z"},{"alias_kind":"pith_short_16","alias_value":"NKPPRWAA3UFGVZC3","created_at":"2026-07-05T10:06:01Z"},{"alias_kind":"pith_short_8","alias_value":"NKPPRWAA","created_at":"2026-07-05T10:06:01Z"}],"graph_snapshots":[{"event_id":"sha256:a0b8aa6faebf6a4901d5ff18e0cad0275d1e6816b80deb739a4ae6cfe08101dc","target":"graph","created_at":"2026-07-05T10:06:01Z","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/2308.10635/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this note is to study the asymptotic volume of intersections of unit balls associated with two norms in $\\mathbb{R}^n$ as their dimension $n$ tends to infinity. A general framework is provided and then specialized to the following cases. For classical $\\ell_p^n$-balls the focus lies on the case $p=\\infty$, which has previously not been studied in the literature. As far as Schatten $p$-balls are considered, we concentrate on the cases $p=2$ and $p=\\infty$. In both situations we uncover an unconventional limiting behavior.","authors_text":"Christoph Th\\\"ale, Mathias Sonnleitner","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-08-21T11:14:05Z","title":"A note on critical intersections of classical and Schatten $p$-balls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.10635","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:a7a7c13fb8fa7acfb86b2f1c003c6683a0b20f1a1f98938381ba52e82adbe3f1","target":"record","created_at":"2026-07-05T10:06:01Z","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":"a6882478dffd04236877519f22b176ab10df31c61686c08dfefbb8165f8b81b4","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-08-21T11:14:05Z","title_canon_sha256":"6d1b7d1ecbe32fe839bf32721eaa63dbd3d9bd01d94165915e702b8f82c5c441"},"schema_version":"1.0","source":{"id":"2308.10635","kind":"arxiv","version":2}},"canonical_sha256":"6a9ef8d800dd0a6ae45b5378a6413d334193691ed7faa3b8158c0f027c291c73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a9ef8d800dd0a6ae45b5378a6413d334193691ed7faa3b8158c0f027c291c73","first_computed_at":"2026-07-05T10:06:01.467437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:06:01.467437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3hmedWU5D45id6SLl97IV1OkucvZFdlSexK3HH8e/WhbYFoefFbRzaKM+t8AoU1UyUtYRzWKHO2ClYy2RUIWCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:06:01.467938Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.10635","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7a7c13fb8fa7acfb86b2f1c003c6683a0b20f1a1f98938381ba52e82adbe3f1","sha256:a0b8aa6faebf6a4901d5ff18e0cad0275d1e6816b80deb739a4ae6cfe08101dc"],"state_sha256":"60306cbe6b2f91c89ea43287fc061d35b187cdbb0de1405275afa24538a2a989"}