{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:RTEI3R7XYGWHWKZDTBP4N6FVFN","short_pith_number":"pith:RTEI3R7X","schema_version":"1.0","canonical_sha256":"8cc88dc7f7c1ac7b2b23985fc6f8b52b49da896f7fc8e5ccacd5fa8211ea88cd","source":{"kind":"arxiv","id":"1611.01860","version":1},"attestation_state":"computed","paper":{"title":"Spherically Symmetric Random Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Alexander Gnedin, Vadim Gorin","submitted_at":"2016-11-06T23:57:48Z","abstract_excerpt":"We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group $S_n$ and are consistent as $n$ varies. The extreme infinitely spherically symmetric permutation-valued processes are identified for the Hamming, Kendall-tau and Caley metrics. The proofs in all three cases are based on a unified approach through stochastic monotonicity."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.01860","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-06T23:57:48Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"dc53bd2967bc36e4e2ac4ca4c33dc9b3fee1e1cc12bfb5f3d74d4fd74a0bb304","abstract_canon_sha256":"bc8899c79bbb5fb2524fd9d460d79519a5a55b18a68da2300bca91f4dfc4a788"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:04.307354Z","signature_b64":"Zd+mtNE6rBYS+c3dAQeai+4Otu0nr6bNNNPUC4nCwEN+ZasMkRi/U/O06coHNaue0poegUTl3cKNuBzSkNVtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cc88dc7f7c1ac7b2b23985fc6f8b52b49da896f7fc8e5ccacd5fa8211ea88cd","last_reissued_at":"2026-05-18T01:00:04.306620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:04.306620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spherically Symmetric Random Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Alexander Gnedin, Vadim Gorin","submitted_at":"2016-11-06T23:57:48Z","abstract_excerpt":"We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group $S_n$ and are consistent as $n$ varies. The extreme infinitely spherically symmetric permutation-valued processes are identified for the Hamming, Kendall-tau and Caley metrics. The proofs in all three cases are based on a unified approach through stochastic monotonicity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01860","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.01860","created_at":"2026-05-18T01:00:04.306742+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.01860v1","created_at":"2026-05-18T01:00:04.306742+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01860","created_at":"2026-05-18T01:00:04.306742+00:00"},{"alias_kind":"pith_short_12","alias_value":"RTEI3R7XYGWH","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"RTEI3R7XYGWHWKZD","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"RTEI3R7X","created_at":"2026-05-18T12:30:41.710351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RTEI3R7XYGWHWKZDTBP4N6FVFN","json":"https://pith.science/pith/RTEI3R7XYGWHWKZDTBP4N6FVFN.json","graph_json":"https://pith.science/api/pith-number/RTEI3R7XYGWHWKZDTBP4N6FVFN/graph.json","events_json":"https://pith.science/api/pith-number/RTEI3R7XYGWHWKZDTBP4N6FVFN/events.json","paper":"https://pith.science/paper/RTEI3R7X"},"agent_actions":{"view_html":"https://pith.science/pith/RTEI3R7XYGWHWKZDTBP4N6FVFN","download_json":"https://pith.science/pith/RTEI3R7XYGWHWKZDTBP4N6FVFN.json","view_paper":"https://pith.science/paper/RTEI3R7X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.01860&json=true","fetch_graph":"https://pith.science/api/pith-number/RTEI3R7XYGWHWKZDTBP4N6FVFN/graph.json","fetch_events":"https://pith.science/api/pith-number/RTEI3R7XYGWHWKZDTBP4N6FVFN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RTEI3R7XYGWHWKZDTBP4N6FVFN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RTEI3R7XYGWHWKZDTBP4N6FVFN/action/storage_attestation","attest_author":"https://pith.science/pith/RTEI3R7XYGWHWKZDTBP4N6FVFN/action/author_attestation","sign_citation":"https://pith.science/pith/RTEI3R7XYGWHWKZDTBP4N6FVFN/action/citation_signature","submit_replication":"https://pith.science/pith/RTEI3R7XYGWHWKZDTBP4N6FVFN/action/replication_record"}},"created_at":"2026-05-18T01:00:04.306742+00:00","updated_at":"2026-05-18T01:00:04.306742+00:00"}