{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZHPN6JOOKDXHMXNVPOWT6V52XH","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":"42734eca3e09753764ee6d1e16093c492103dd950dad26fff9075e105004c745","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-20T11:28:34Z","title_canon_sha256":"a774da70c4ccdcda446a48a452e9ccfd70282ea4caebb97f002193094064bbdb"},"schema_version":"1.0","source":{"id":"1908.07277","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07277","created_at":"2026-07-05T05:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07277v2","created_at":"2026-07-05T05:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07277","created_at":"2026-07-05T05:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZHPN6JOOKDXH","created_at":"2026-07-05T05:08:24Z"},{"alias_kind":"pith_short_16","alias_value":"ZHPN6JOOKDXHMXNV","created_at":"2026-07-05T05:08:24Z"},{"alias_kind":"pith_short_8","alias_value":"ZHPN6JOO","created_at":"2026-07-05T05:08:24Z"}],"graph_snapshots":[{"event_id":"sha256:0162eac1e9a2b2a6cb10e2a0d1f78eeb8028e1b61ed4066a3fd8e4264dcef37d","target":"graph","created_at":"2026-07-05T05:08:24Z","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/1908.07277/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that permutations with few inversions exhibit a local-global dichotomy in the following sense. Suppose ${\\boldsymbol\\sigma}$ is a permutation chosen uniformly at random from the set of all permutations of $[n]$ with exactly $m=m(n)\\ll n^2$ inversions. If $i<j$ are chosen uniformly at random from $[n]$, then ${\\boldsymbol\\sigma}(i)<{\\boldsymbol\\sigma}(j)$ asymptotically almost surely. However, if $i$ and $j$ are chosen so that $j-i\\ll m/n$, and $m \\ll n^2/\\log^2 n$, then $\\lim_{n\\to\\infty}\\mathbb{P}\\big[{\\boldsymbol\\sigma}(i)<{\\boldsymbol\\sigma}(j)\\big]=\\frac{1}{2}$. Moreover, if $k=k(","authors_text":"David Bevan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-20T11:28:34Z","title":"Permutations with few inversions are locally uniform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07277","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":"sha256:22b6c0835734475a3a884bae162d41bf6c9a4e2ab54a9bdd32f549d9eb3b310a","target":"record","created_at":"2026-07-05T05:08:24Z","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":"42734eca3e09753764ee6d1e16093c492103dd950dad26fff9075e105004c745","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-20T11:28:34Z","title_canon_sha256":"a774da70c4ccdcda446a48a452e9ccfd70282ea4caebb97f002193094064bbdb"},"schema_version":"1.0","source":{"id":"1908.07277","kind":"arxiv","version":2}},"canonical_sha256":"c9dedf25ce50ee765db57bad3f57bab9cc44a9b3c96c5df50ef7f7b79bf7e4da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9dedf25ce50ee765db57bad3f57bab9cc44a9b3c96c5df50ef7f7b79bf7e4da","first_computed_at":"2026-07-05T05:08:24.046560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:08:24.046560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vaqyA+nv+kJwdngGwOxjIVsfJmo5LNWVQU86GhZ1YQZKid21ceaLQdlW4kcjHB8pK3jOU6MF50eTyOVU09IABg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:08:24.046994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07277","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22b6c0835734475a3a884bae162d41bf6c9a4e2ab54a9bdd32f549d9eb3b310a","sha256:0162eac1e9a2b2a6cb10e2a0d1f78eeb8028e1b61ed4066a3fd8e4264dcef37d"],"state_sha256":"cf909540a0c02d620d414a56b9229049d36c12d55873819313e49529e0856aba"}