{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:EWY3VQZ2QQULZINS2QBHCBBCE6","short_pith_number":"pith:EWY3VQZ2","canonical_record":{"source":{"id":"2412.08727","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-11T19:00:10Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"0debc84b6f2949a8ce8643a228fdd52fa3fae875bc36fe361f948a568e021eaa","abstract_canon_sha256":"551a3e55806622f7b4bdebf01ba0eaf73e61ff27c2c62e23a031a31d8cb8d0da"},"schema_version":"1.0"},"canonical_sha256":"25b1bac33a8428bca1b2d4027104222796e7d1233c7f3246eb5d6b6e4551369f","source":{"kind":"arxiv","id":"2412.08727","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.08727","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"arxiv_version","alias_value":"2412.08727v2","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.08727","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"pith_short_12","alias_value":"EWY3VQZ2QQUL","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"pith_short_16","alias_value":"EWY3VQZ2QQULZINS","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"pith_short_8","alias_value":"EWY3VQZ2","created_at":"2026-07-05T12:07:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:EWY3VQZ2QQULZINS2QBHCBBCE6","target":"record","payload":{"canonical_record":{"source":{"id":"2412.08727","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-11T19:00:10Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"0debc84b6f2949a8ce8643a228fdd52fa3fae875bc36fe361f948a568e021eaa","abstract_canon_sha256":"551a3e55806622f7b4bdebf01ba0eaf73e61ff27c2c62e23a031a31d8cb8d0da"},"schema_version":"1.0"},"canonical_sha256":"25b1bac33a8428bca1b2d4027104222796e7d1233c7f3246eb5d6b6e4551369f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:07:02.164485Z","signature_b64":"B8tijxmSkPblDu67KFCBoBfuFVn+djXpyzgSBn/NBCKdXbaSUSHgg+X36bBMjXkttJvupVQoDA/B9R3wnp7pDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25b1bac33a8428bca1b2d4027104222796e7d1233c7f3246eb5d6b6e4551369f","last_reissued_at":"2026-07-05T12:07:02.164004Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:07:02.164004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.08727","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:07:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JIoqthDRLPEwPqdH3W3KOsLJiCJsZv+MUF4Rkus2vgiHhmQChG7eSxSHNYjCSNyObIzu+bf/W/FJU1f+w4efBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:20:22.787856Z"},"content_sha256":"ad1ccda7e73180c87997928ec6c509bb329d9634c03829636d7379d8a4a46d98","schema_version":"1.0","event_id":"sha256:ad1ccda7e73180c87997928ec6c509bb329d9634c03829636d7379d8a4a46d98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:EWY3VQZ2QQULZINS2QBHCBBCE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lengths of saddle connections on random translation surfaces of large genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.GT","authors_text":"Anja Randecker, Howard Masur, Kasra Rafi","submitted_at":"2024-12-11T19:00:10Z","abstract_excerpt":"We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus $g$ tending to infinity, the number of saddle connections with lengths in a given interval $[\\frac{a}{g}, \\frac{b}{g}]$ converges in distribution to a Poisson distributed random variable. Furthermore, the numbers of saddle connections associated to disjoint intervals of lengths are independent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.08727","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.08727/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:07:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b2dHFU3N39HcsuupTN3p2sWHvCq9mrAOwNo5OUxh8TapCIv3VCEj2r9owNlCQyaOKQaIs1/GgUr8EoHLzlRDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:20:22.788341Z"},"content_sha256":"4f5943c231990f847500294aa9abe388fa9d1eef25a820608c99dde7a8cecc71","schema_version":"1.0","event_id":"sha256:4f5943c231990f847500294aa9abe388fa9d1eef25a820608c99dde7a8cecc71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EWY3VQZ2QQULZINS2QBHCBBCE6/bundle.json","state_url":"https://pith.science/pith/EWY3VQZ2QQULZINS2QBHCBBCE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EWY3VQZ2QQULZINS2QBHCBBCE6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T14:20:22Z","links":{"resolver":"https://pith.science/pith/EWY3VQZ2QQULZINS2QBHCBBCE6","bundle":"https://pith.science/pith/EWY3VQZ2QQULZINS2QBHCBBCE6/bundle.json","state":"https://pith.science/pith/EWY3VQZ2QQULZINS2QBHCBBCE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EWY3VQZ2QQULZINS2QBHCBBCE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EWY3VQZ2QQULZINS2QBHCBBCE6","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":"551a3e55806622f7b4bdebf01ba0eaf73e61ff27c2c62e23a031a31d8cb8d0da","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-11T19:00:10Z","title_canon_sha256":"0debc84b6f2949a8ce8643a228fdd52fa3fae875bc36fe361f948a568e021eaa"},"schema_version":"1.0","source":{"id":"2412.08727","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.08727","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"arxiv_version","alias_value":"2412.08727v2","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.08727","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"pith_short_12","alias_value":"EWY3VQZ2QQUL","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"pith_short_16","alias_value":"EWY3VQZ2QQULZINS","created_at":"2026-07-05T12:07:02Z"},{"alias_kind":"pith_short_8","alias_value":"EWY3VQZ2","created_at":"2026-07-05T12:07:02Z"}],"graph_snapshots":[{"event_id":"sha256:4f5943c231990f847500294aa9abe388fa9d1eef25a820608c99dde7a8cecc71","target":"graph","created_at":"2026-07-05T12:07:02Z","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/2412.08727/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus $g$ tending to infinity, the number of saddle connections with lengths in a given interval $[\\frac{a}{g}, \\frac{b}{g}]$ converges in distribution to a Poisson distributed random variable. Furthermore, the numbers of saddle connections associated to disjoint intervals of lengths are independent.","authors_text":"Anja Randecker, Howard Masur, Kasra Rafi","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-11T19:00:10Z","title":"Lengths of saddle connections on random translation surfaces of large genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.08727","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:ad1ccda7e73180c87997928ec6c509bb329d9634c03829636d7379d8a4a46d98","target":"record","created_at":"2026-07-05T12:07:02Z","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":"551a3e55806622f7b4bdebf01ba0eaf73e61ff27c2c62e23a031a31d8cb8d0da","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-11T19:00:10Z","title_canon_sha256":"0debc84b6f2949a8ce8643a228fdd52fa3fae875bc36fe361f948a568e021eaa"},"schema_version":"1.0","source":{"id":"2412.08727","kind":"arxiv","version":2}},"canonical_sha256":"25b1bac33a8428bca1b2d4027104222796e7d1233c7f3246eb5d6b6e4551369f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25b1bac33a8428bca1b2d4027104222796e7d1233c7f3246eb5d6b6e4551369f","first_computed_at":"2026-07-05T12:07:02.164004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:07:02.164004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B8tijxmSkPblDu67KFCBoBfuFVn+djXpyzgSBn/NBCKdXbaSUSHgg+X36bBMjXkttJvupVQoDA/B9R3wnp7pDw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:07:02.164485Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.08727","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad1ccda7e73180c87997928ec6c509bb329d9634c03829636d7379d8a4a46d98","sha256:4f5943c231990f847500294aa9abe388fa9d1eef25a820608c99dde7a8cecc71"],"state_sha256":"6b1b55bff29e83f72eab2248c1fc7257ab5b16475540ecfe1bc3f95243eb4fc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mb2mIfsX+xleTncXjpqF3/heq0LMjHZl7S30aQKkr8w9yGVxRgGeIQv3Gn3ZVchUc+x+q3pAW+yuZC9vLbu2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T14:20:22.791613Z","bundle_sha256":"3e18203a7eb7072c2dc55287b94c5e12d778734962b6049d070796b6b206fcc6"}}