{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:55UBELPDC4NJKJ2REQOE4YLSY4","short_pith_number":"pith:55UBELPD","schema_version":"1.0","canonical_sha256":"ef68122de3171a952751241c4e6172c71a9bc2cb82090d30dddf88858f030838","source":{"kind":"arxiv","id":"2503.13091","version":1},"attestation_state":"computed","paper":{"title":"Counting statistics for geodesics on flat surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.PR"],"primary_cat":"math.DS","authors_text":"Mark Pollicott, Stephen Cantrell","submitted_at":"2025-03-17T11:58:10Z","abstract_excerpt":"We study counting limit laws that compare length functions on infinite graphs. We then apply these results to flat surfaces to obtain a statistical comparison between the geometric length and the number of singularities visited by geodesic paths."},"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":"2503.13091","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-03-17T11:58:10Z","cross_cats_sorted":["math.GT","math.PR"],"title_canon_sha256":"a19b3b3779e11ac5e15873559ffb65b6cc85b6342b18a0648562f5a5414cb2f5","abstract_canon_sha256":"09e2a8510e8965a8c30089cb1e4e0535edc4044351ce3d4a66cb802fae4ef558"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:32:52.923461Z","signature_b64":"keyCYx+mGWBgaBSq8mVKoYmg6rGufGz2zpGCKShtRtaCmj94mxcwpfBOpdlOg2Zkd42DnuSzNxLFe1OXbCPJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef68122de3171a952751241c4e6172c71a9bc2cb82090d30dddf88858f030838","last_reissued_at":"2026-07-05T10:32:52.922841Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:32:52.922841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting statistics for geodesics on flat surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.PR"],"primary_cat":"math.DS","authors_text":"Mark Pollicott, Stephen Cantrell","submitted_at":"2025-03-17T11:58:10Z","abstract_excerpt":"We study counting limit laws that compare length functions on infinite graphs. We then apply these results to flat surfaces to obtain a statistical comparison between the geometric length and the number of singularities visited by geodesic paths."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.13091","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/2503.13091/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":"2503.13091","created_at":"2026-07-05T10:32:52.922911+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.13091v1","created_at":"2026-07-05T10:32:52.922911+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.13091","created_at":"2026-07-05T10:32:52.922911+00:00"},{"alias_kind":"pith_short_12","alias_value":"55UBELPDC4NJ","created_at":"2026-07-05T10:32:52.922911+00:00"},{"alias_kind":"pith_short_16","alias_value":"55UBELPDC4NJKJ2R","created_at":"2026-07-05T10:32:52.922911+00:00"},{"alias_kind":"pith_short_8","alias_value":"55UBELPD","created_at":"2026-07-05T10:32:52.922911+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/55UBELPDC4NJKJ2REQOE4YLSY4","json":"https://pith.science/pith/55UBELPDC4NJKJ2REQOE4YLSY4.json","graph_json":"https://pith.science/api/pith-number/55UBELPDC4NJKJ2REQOE4YLSY4/graph.json","events_json":"https://pith.science/api/pith-number/55UBELPDC4NJKJ2REQOE4YLSY4/events.json","paper":"https://pith.science/paper/55UBELPD"},"agent_actions":{"view_html":"https://pith.science/pith/55UBELPDC4NJKJ2REQOE4YLSY4","download_json":"https://pith.science/pith/55UBELPDC4NJKJ2REQOE4YLSY4.json","view_paper":"https://pith.science/paper/55UBELPD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.13091&json=true","fetch_graph":"https://pith.science/api/pith-number/55UBELPDC4NJKJ2REQOE4YLSY4/graph.json","fetch_events":"https://pith.science/api/pith-number/55UBELPDC4NJKJ2REQOE4YLSY4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/55UBELPDC4NJKJ2REQOE4YLSY4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/55UBELPDC4NJKJ2REQOE4YLSY4/action/storage_attestation","attest_author":"https://pith.science/pith/55UBELPDC4NJKJ2REQOE4YLSY4/action/author_attestation","sign_citation":"https://pith.science/pith/55UBELPDC4NJKJ2REQOE4YLSY4/action/citation_signature","submit_replication":"https://pith.science/pith/55UBELPDC4NJKJ2REQOE4YLSY4/action/replication_record"}},"created_at":"2026-07-05T10:32:52.922911+00:00","updated_at":"2026-07-05T10:32:52.922911+00:00"}