{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LBQGVMJZZ5GGOHIEZED5FDPCVX","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":"17349cd3d2d707920a73fd55a212eb1819bb29f7fceeb26bd78f3fbec4986f52","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-19T04:52:28Z","title_canon_sha256":"855bc9ffa210eedee4db92d5c1f639b14bd70f0adfc26f0ac6cbc8b1aaaf8d79"},"schema_version":"1.0","source":{"id":"1209.4148","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4148","created_at":"2026-05-18T02:50:52Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4148v2","created_at":"2026-05-18T02:50:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4148","created_at":"2026-05-18T02:50:52Z"},{"alias_kind":"pith_short_12","alias_value":"LBQGVMJZZ5GG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LBQGVMJZZ5GGOHIE","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LBQGVMJZ","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:bf756327308d69e066b903c2fc58e3795200e341129bd1fb15de3e78a2545b39","target":"graph","created_at":"2026-05-18T02:50:52Z","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 establish the result of the title.\n  In combinatorial terms this has the implication that for sufficiently small eps > 0, for all n, any marking of an eps fraction of the vertices of the n-dimensional hypercube necessarily leaves a vertex x such that marked vertices are a minority of every sphere centered at x.","authors_text":"Alexandra Kolla, Aram W. Harrow, Leonard J. Schulman","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-19T04:52:28Z","title":"Dimension-free L2 maximal inequality for spherical means in the hypercube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4148","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":"sha256:0db2edead38b135524c4ed385b1d82c1a4cfb93eff3390d3d163f97a349de3a9","target":"record","created_at":"2026-05-18T02:50:52Z","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":"17349cd3d2d707920a73fd55a212eb1819bb29f7fceeb26bd78f3fbec4986f52","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-19T04:52:28Z","title_canon_sha256":"855bc9ffa210eedee4db92d5c1f639b14bd70f0adfc26f0ac6cbc8b1aaaf8d79"},"schema_version":"1.0","source":{"id":"1209.4148","kind":"arxiv","version":2}},"canonical_sha256":"58606ab139cf4c671d04c907d28de2adf713eed15c151f1a55e8a48d754711c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58606ab139cf4c671d04c907d28de2adf713eed15c151f1a55e8a48d754711c9","first_computed_at":"2026-05-18T02:50:52.047107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:52.047107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4vnSp0w02jw9yP/nHEOO3LGfFWHVstIfQPPgS7U+FLvPgLVuWDvhttvuA0sSB4YG8JEPn576Qg4IZyvHJGbkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:52.047640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4148","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0db2edead38b135524c4ed385b1d82c1a4cfb93eff3390d3d163f97a349de3a9","sha256:bf756327308d69e066b903c2fc58e3795200e341129bd1fb15de3e78a2545b39"],"state_sha256":"5b0d360462aa50f543e117e58896342131d2e89608166bda8a9ff081556a62ab"}