{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XU5M36MRR5QLIIGCMW3UHUPKHF","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":"bef788573b62ceb59dc37b00d2760beb1a1c88d3ec3f2c0489c39a52ae333b21","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-07T18:01:23Z","title_canon_sha256":"ea5a79ef45ef8fee90ebadca18092555f7a630e9e8b3700dee1f344b847e1fd3"},"schema_version":"1.0","source":{"id":"1504.01689","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01689","created_at":"2026-05-18T01:20:17Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01689v3","created_at":"2026-05-18T01:20:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01689","created_at":"2026-05-18T01:20:17Z"},{"alias_kind":"pith_short_12","alias_value":"XU5M36MRR5QL","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XU5M36MRR5QLIIGC","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XU5M36MR","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:808528ff2f111676205505587a820a2eb3f5bb27aafa861da7337ad8b5ab568f","target":"graph","created_at":"2026-05-18T01:20:17Z","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 prove an invariance principle for functions on a slice of the Boolean cube, which is the set of all vectors {0,1}^n with Hamming weight k. Our invariance principle shows that a low-degree, low-influence function has similar distributions on the slice, on the entire Boolean cube, and on Gaussian space.\n  Our proof relies on a combination of ideas from analysis and probability, algebra and combinatorics.\n  Our result imply a version of majority is stablest for functions on the slice, a version of Bourgain's tail bound, and a version of the Kindler-Safra theorem. As a corollary of the Kindler-","authors_text":"Elchanan Mossel, Guy Kindler, Karl Wimmer, Yuval Filmus","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-07T18:01:23Z","title":"Invariance principle on the slice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01689","kind":"arxiv","version":3},"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":"sha256:71029f43749b560b1990f4004a547ed4d1314dbf44f3edfe1b4f2990eb173238","target":"record","created_at":"2026-05-18T01:20:17Z","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":"bef788573b62ceb59dc37b00d2760beb1a1c88d3ec3f2c0489c39a52ae333b21","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-07T18:01:23Z","title_canon_sha256":"ea5a79ef45ef8fee90ebadca18092555f7a630e9e8b3700dee1f344b847e1fd3"},"schema_version":"1.0","source":{"id":"1504.01689","kind":"arxiv","version":3}},"canonical_sha256":"bd3acdf9918f60b420c265b743d1ea3955fd3d60effa65b036566e1207c0fbcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd3acdf9918f60b420c265b743d1ea3955fd3d60effa65b036566e1207c0fbcf","first_computed_at":"2026-05-18T01:20:17.256263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:17.256263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BX+1fnB1brhFcDelwVdTXK6Hn84F3tVazTEpHLChw3fq9kD0uYhsO6LSIUZKREnRPNCGo7YDkrypqskaR1L6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:17.256937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01689","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71029f43749b560b1990f4004a547ed4d1314dbf44f3edfe1b4f2990eb173238","sha256:808528ff2f111676205505587a820a2eb3f5bb27aafa861da7337ad8b5ab568f"],"state_sha256":"01df4632bbfd97abe36bf8dc65b0995681bb1d616f53a0d38cb8803014e86afd"}