{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:3KVTQ4LJ6CUTWISVFGB55GE2JT","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":"8c7a73b94a4435901e980894d10d65cf8b732ad2296ef0d95b1fc02299a24b83","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2021-04-17T08:39:57Z","title_canon_sha256":"0e2b8a5cc131462db00b86744a26a3d8eac7ae0376379cf68eed527f695e3170"},"schema_version":"1.0","source":{"id":"2104.08484","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.08484","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"2104.08484v1","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.08484","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"3KVTQ4LJ6CUT","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"pith_short_16","alias_value":"3KVTQ4LJ6CUTWISV","created_at":"2026-07-05T06:39:28Z"},{"alias_kind":"pith_short_8","alias_value":"3KVTQ4LJ","created_at":"2026-07-05T06:39:28Z"}],"graph_snapshots":[{"event_id":"sha256:533928d506d186e5de57c357e92e75c03c70e0623196c356e4b9840c63836eae","target":"graph","created_at":"2026-07-05T06:39:28Z","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/2104.08484/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a $d$-dimensional closed ball $B$ whose center coincides with that of the hypercube $[0,1]^d$. Pick the radius of $B$ in such a way that the vertices of the hypercube are outside of $B$ and the midpoints of its edges in the interior of $B$. It is known that, when $d\\geq3$, the $(d-1)$-dimensional volume of $H\\cap[0,1]^d$, where $H$ is a hyperplane of $\\mathbb{R}^d$ tangent to $B$, is largest possible if and only if $H$ is orthogonal to a diagonal of the hypercube. It is shown here that the same holds when $d\\geq5$ but the interior of $B$ is only required to contain the centers of the ","authors_text":"Lionel Pournin","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2021-04-17T08:39:57Z","title":"Shallow sections of the hypercube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.08484","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":"sha256:7382a653d58cdecec5f9244c31753fca7b1230e4d207991daa4b7c312a663d80","target":"record","created_at":"2026-07-05T06:39:28Z","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":"8c7a73b94a4435901e980894d10d65cf8b732ad2296ef0d95b1fc02299a24b83","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2021-04-17T08:39:57Z","title_canon_sha256":"0e2b8a5cc131462db00b86744a26a3d8eac7ae0376379cf68eed527f695e3170"},"schema_version":"1.0","source":{"id":"2104.08484","kind":"arxiv","version":1}},"canonical_sha256":"daab387169f0a93b22552983de989a4cdc0fa9a0cc38d27e0f41024c7b0f4131","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daab387169f0a93b22552983de989a4cdc0fa9a0cc38d27e0f41024c7b0f4131","first_computed_at":"2026-07-05T06:39:28.525077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:39:28.525077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yrBoUHdZ5sp93k4UU/ZNyzYupQiu6q5hw3Y2y911R/Qj9b5femTu9BfSWeRvQTLMQp+eUNSCfybbCAVndbOvBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:39:28.525534Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.08484","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7382a653d58cdecec5f9244c31753fca7b1230e4d207991daa4b7c312a663d80","sha256:533928d506d186e5de57c357e92e75c03c70e0623196c356e4b9840c63836eae"],"state_sha256":"866b612a244f70dababd2f49d9dfe6c5063087022f3f75421cba52d49948db22"}