{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3DITVMKGW4FV23VU4PYST7WWVP","short_pith_number":"pith:3DITVMKG","schema_version":"1.0","canonical_sha256":"d8d13ab146b70b5d6eb4e3f129fed6abc662590408e4efe2ee980e3135a4b372","source":{"kind":"arxiv","id":"2501.03474","version":1},"attestation_state":"computed","paper":{"title":"Benjamini-Schramm limits of high genus translation surfaces: research announcement","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.GT","authors_text":"Hunter Vallejos, Kasra Rafi, Lewis Bowen","submitted_at":"2025-01-07T02:31:28Z","abstract_excerpt":"We prove that the sequence of Masur-Smillie-Veech (MSV) distributed random translation surfaces, with area equal to genus, Benjamini-Schramm converges as genus tends to infinity. This means that for any fixed radius $r>0$, if $X_g$ is an MSV-distributed random translation surface with area $g$ and genus $g$, and $o$ is a uniformly random point in $X_g$, then the radius-$r$ neighborhood of $o$ in $X_g$, as a pointed measured metric space, converges in distribution to the radius $r$ neighborhood of the root in a Poisson translation plane, which is a random pointed surface we introduce here. Alon"},"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":"2501.03474","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-01-07T02:31:28Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"1764a978e055be3eedbdc8a2f4ff8e08a1d2e895ce2e77ba1f20b180ec419407","abstract_canon_sha256":"1d416b93f5a2e7eee70a215cd7cfaeeb7a83494e6042a7b636bf40e9f55c0df3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:55.347752Z","signature_b64":"ud9AZyayuCZDTwQ6Ensjm8tZzbsbi/iWJocYxqr8aIm4BG4OQr1CFwjtyNuQMI2axHC+c+UWtsMscAEin5VXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8d13ab146b70b5d6eb4e3f129fed6abc662590408e4efe2ee980e3135a4b372","last_reissued_at":"2026-07-05T09:57:55.347256Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:55.347256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Benjamini-Schramm limits of high genus translation surfaces: research announcement","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.GT","authors_text":"Hunter Vallejos, Kasra Rafi, Lewis Bowen","submitted_at":"2025-01-07T02:31:28Z","abstract_excerpt":"We prove that the sequence of Masur-Smillie-Veech (MSV) distributed random translation surfaces, with area equal to genus, Benjamini-Schramm converges as genus tends to infinity. This means that for any fixed radius $r>0$, if $X_g$ is an MSV-distributed random translation surface with area $g$ and genus $g$, and $o$ is a uniformly random point in $X_g$, then the radius-$r$ neighborhood of $o$ in $X_g$, as a pointed measured metric space, converges in distribution to the radius $r$ neighborhood of the root in a Poisson translation plane, which is a random pointed surface we introduce here. Alon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03474","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.03474/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2501.03474","created_at":"2026-07-05T09:57:55.347304+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.03474v1","created_at":"2026-07-05T09:57:55.347304+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03474","created_at":"2026-07-05T09:57:55.347304+00:00"},{"alias_kind":"pith_short_12","alias_value":"3DITVMKGW4FV","created_at":"2026-07-05T09:57:55.347304+00:00"},{"alias_kind":"pith_short_16","alias_value":"3DITVMKGW4FV23VU","created_at":"2026-07-05T09:57:55.347304+00:00"},{"alias_kind":"pith_short_8","alias_value":"3DITVMKG","created_at":"2026-07-05T09:57:55.347304+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06331","citing_title":"Bass notes of random hyperbolic surfaces of large genus","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3DITVMKGW4FV23VU4PYST7WWVP","json":"https://pith.science/pith/3DITVMKGW4FV23VU4PYST7WWVP.json","graph_json":"https://pith.science/api/pith-number/3DITVMKGW4FV23VU4PYST7WWVP/graph.json","events_json":"https://pith.science/api/pith-number/3DITVMKGW4FV23VU4PYST7WWVP/events.json","paper":"https://pith.science/paper/3DITVMKG"},"agent_actions":{"view_html":"https://pith.science/pith/3DITVMKGW4FV23VU4PYST7WWVP","download_json":"https://pith.science/pith/3DITVMKGW4FV23VU4PYST7WWVP.json","view_paper":"https://pith.science/paper/3DITVMKG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.03474&json=true","fetch_graph":"https://pith.science/api/pith-number/3DITVMKGW4FV23VU4PYST7WWVP/graph.json","fetch_events":"https://pith.science/api/pith-number/3DITVMKGW4FV23VU4PYST7WWVP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3DITVMKGW4FV23VU4PYST7WWVP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3DITVMKGW4FV23VU4PYST7WWVP/action/storage_attestation","attest_author":"https://pith.science/pith/3DITVMKGW4FV23VU4PYST7WWVP/action/author_attestation","sign_citation":"https://pith.science/pith/3DITVMKGW4FV23VU4PYST7WWVP/action/citation_signature","submit_replication":"https://pith.science/pith/3DITVMKGW4FV23VU4PYST7WWVP/action/replication_record"}},"created_at":"2026-07-05T09:57:55.347304+00:00","updated_at":"2026-07-05T09:57:55.347304+00:00"}