{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XXSPKAYTRAU2GRFRGODVGT2Q7F","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":"79a127ff37ae2164ad39f764f19c50b9635f31e62558713aaa243bb94619ce8c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-24T06:17:14Z","title_canon_sha256":"dd9e19c99f2446f548da0a193d38e2c272be5cdc3f4c65a57dc3357da0214a7f"},"schema_version":"1.0","source":{"id":"1812.09841","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09841","created_at":"2026-05-17T23:49:50Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09841v3","created_at":"2026-05-17T23:49:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09841","created_at":"2026-05-17T23:49:50Z"},{"alias_kind":"pith_short_12","alias_value":"XXSPKAYTRAU2","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"XXSPKAYTRAU2GRFR","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"XXSPKAYT","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:3420f85e1693f98eb2a8ce2a010cc6c72fdca07e200404eefd45c4c5849004b8","target":"graph","created_at":"2026-05-17T23:49:50Z","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":"Given a sequence of $s$-uniform hypergraphs $\\{H_n\\}_{n \\geq 1}$, denote by $T_p(H_n)$ the number of edges in the random induced hypergraph obtained by including every vertex in $H_n$ independently with probability $p \\in (0, 1)$. Recent advances in the large deviations of low complexity non-linear functions of independent Bernoulli variables can be used to show that tail probabilities of $T_p(H_n)$ are precisely approximated by the so-called 'mean-field' variational problem, under certain assumptions on the sequence $\\{H_n\\}_{n \\geq 1}$. In this paper, we study properties of this variational ","authors_text":"Bhaswar B. Bhattacharya, Somabha Mukherjee","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-24T06:17:14Z","title":"Replica Symmetry in Upper Tails of Mean-Field Hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09841","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":"sha256:141d3de618313b83b205feffaf670c48bb736c6def47b2fdf5fac76598422242","target":"record","created_at":"2026-05-17T23:49:50Z","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":"79a127ff37ae2164ad39f764f19c50b9635f31e62558713aaa243bb94619ce8c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-24T06:17:14Z","title_canon_sha256":"dd9e19c99f2446f548da0a193d38e2c272be5cdc3f4c65a57dc3357da0214a7f"},"schema_version":"1.0","source":{"id":"1812.09841","kind":"arxiv","version":3}},"canonical_sha256":"bde4f503138829a344b13387534f50f9599f85c8f393bd646468b3ccff302de1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bde4f503138829a344b13387534f50f9599f85c8f393bd646468b3ccff302de1","first_computed_at":"2026-05-17T23:49:50.376243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:50.376243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ptG6nsnYaQ0FQIfQIISrKuc0L/kY/VV0hWBS1gsUOp9SAwAfbV+bdWnmxeG11mrv6RQ3owUaeZU6nNIxg4k4Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:50.376808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09841","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:141d3de618313b83b205feffaf670c48bb736c6def47b2fdf5fac76598422242","sha256:3420f85e1693f98eb2a8ce2a010cc6c72fdca07e200404eefd45c4c5849004b8"],"state_sha256":"a2f14848841cb55fbb2ba2ebe7742d1069816e7defe1bcd1d3ad8715a3962eaa"}