{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HQNJCTPXXCUZXPB7ZTOK6KAH6N","short_pith_number":"pith:HQNJCTPX","schema_version":"1.0","canonical_sha256":"3c1a914df7b8a99bbc3fccdcaf2807f341ca0276e98a41ca1ac992121429144d","source":{"kind":"arxiv","id":"1611.07545","version":2},"attestation_state":"computed","paper":{"title":"Largest projections for random walks and shortest curves in random mapping tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.GT","authors_text":"Alessandro Sisto, Samuel J. Taylor","submitted_at":"2016-11-22T21:35:50Z","abstract_excerpt":"We show that the largest subsurface projection distance between a marking and its image under the nth step of a random walk grows logarithmically in n, with probability approaching 1 as n tends to infinity. Our setup is general and also applies to (relatively) hyperbolic groups and to $\\mathrm{Out}(F_n)$. We then use this result to prove Rivin's conjecture that for a random walk $(w_n)$ on the mapping class group, the shortest geodesic in the hyperbolic mapping torus $M_{w_n}$ has length on the order of $1/ \\log^2(n)$."},"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":"1611.07545","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-11-22T21:35:50Z","cross_cats_sorted":["math.GR","math.PR"],"title_canon_sha256":"f30a7a0d410f673661f7732d6c41e61a30f969ec8e23c2132fc05dc2f597ada9","abstract_canon_sha256":"b33845f7367171b47fb9cd21494c41f850adefb4730c38041dc656e807233d1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:39.213851Z","signature_b64":"LWUV9ylRZSCd33/01mrHnjwWxP77vZJYpZuJ9K/dLLMz2w8eAHDmtgLNlt8weYmsX/7LJ0ysq30z0+9ROtd1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c1a914df7b8a99bbc3fccdcaf2807f341ca0276e98a41ca1ac992121429144d","last_reissued_at":"2026-05-18T00:42:39.213187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:39.213187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Largest projections for random walks and shortest curves in random mapping tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.GT","authors_text":"Alessandro Sisto, Samuel J. Taylor","submitted_at":"2016-11-22T21:35:50Z","abstract_excerpt":"We show that the largest subsurface projection distance between a marking and its image under the nth step of a random walk grows logarithmically in n, with probability approaching 1 as n tends to infinity. Our setup is general and also applies to (relatively) hyperbolic groups and to $\\mathrm{Out}(F_n)$. We then use this result to prove Rivin's conjecture that for a random walk $(w_n)$ on the mapping class group, the shortest geodesic in the hyperbolic mapping torus $M_{w_n}$ has length on the order of $1/ \\log^2(n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07545","kind":"arxiv","version":2},"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":"1611.07545","created_at":"2026-05-18T00:42:39.213324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.07545v2","created_at":"2026-05-18T00:42:39.213324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07545","created_at":"2026-05-18T00:42:39.213324+00:00"},{"alias_kind":"pith_short_12","alias_value":"HQNJCTPXXCUZ","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HQNJCTPXXCUZXPB7","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HQNJCTPX","created_at":"2026-05-18T12:30:19.053100+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/HQNJCTPXXCUZXPB7ZTOK6KAH6N","json":"https://pith.science/pith/HQNJCTPXXCUZXPB7ZTOK6KAH6N.json","graph_json":"https://pith.science/api/pith-number/HQNJCTPXXCUZXPB7ZTOK6KAH6N/graph.json","events_json":"https://pith.science/api/pith-number/HQNJCTPXXCUZXPB7ZTOK6KAH6N/events.json","paper":"https://pith.science/paper/HQNJCTPX"},"agent_actions":{"view_html":"https://pith.science/pith/HQNJCTPXXCUZXPB7ZTOK6KAH6N","download_json":"https://pith.science/pith/HQNJCTPXXCUZXPB7ZTOK6KAH6N.json","view_paper":"https://pith.science/paper/HQNJCTPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.07545&json=true","fetch_graph":"https://pith.science/api/pith-number/HQNJCTPXXCUZXPB7ZTOK6KAH6N/graph.json","fetch_events":"https://pith.science/api/pith-number/HQNJCTPXXCUZXPB7ZTOK6KAH6N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HQNJCTPXXCUZXPB7ZTOK6KAH6N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HQNJCTPXXCUZXPB7ZTOK6KAH6N/action/storage_attestation","attest_author":"https://pith.science/pith/HQNJCTPXXCUZXPB7ZTOK6KAH6N/action/author_attestation","sign_citation":"https://pith.science/pith/HQNJCTPXXCUZXPB7ZTOK6KAH6N/action/citation_signature","submit_replication":"https://pith.science/pith/HQNJCTPXXCUZXPB7ZTOK6KAH6N/action/replication_record"}},"created_at":"2026-05-18T00:42:39.213324+00:00","updated_at":"2026-05-18T00:42:39.213324+00:00"}