{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7FCV4OSIKHBX2EEJ3DG7EQ25JM","short_pith_number":"pith:7FCV4OSI","canonical_record":{"source":{"id":"1401.4148","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T19:58:30Z","cross_cats_sorted":["math.GT","math.NT"],"title_canon_sha256":"5993e0967119ec89193559ac04c17597e45cabfd5eb8d22d632c536f2f9c4d08","abstract_canon_sha256":"5da807ccad0c33eedd0342697c4c39be72459a8576aa6fac09ae9feb80dcf045"},"schema_version":"1.0"},"canonical_sha256":"f9455e3a4851c37d1089d8cdf2435d4b32b0af748f413ed95542e4b715fef30c","source":{"kind":"arxiv","id":"1401.4148","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4148","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4148v4","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4148","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"7FCV4OSIKHBX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7FCV4OSIKHBX2EEJ","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7FCV4OSI","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7FCV4OSIKHBX2EEJ3DG7EQ25JM","target":"record","payload":{"canonical_record":{"source":{"id":"1401.4148","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T19:58:30Z","cross_cats_sorted":["math.GT","math.NT"],"title_canon_sha256":"5993e0967119ec89193559ac04c17597e45cabfd5eb8d22d632c536f2f9c4d08","abstract_canon_sha256":"5da807ccad0c33eedd0342697c4c39be72459a8576aa6fac09ae9feb80dcf045"},"schema_version":"1.0"},"canonical_sha256":"f9455e3a4851c37d1089d8cdf2435d4b32b0af748f413ed95542e4b715fef30c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:59.075028Z","signature_b64":"XU48ISiUBFNIePmtCLq2ayl+ZLfD94AYXE4zpCPGr2UvdPIeNvFq4qvUBwaY/1qOAR9nh6fcavhpCfZwxvk1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9455e3a4851c37d1089d8cdf2435d4b32b0af748f413ed95542e4b715fef30c","last_reissued_at":"2026-05-18T01:14:59.074530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:59.074530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.4148","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szNa4czfNQ6a2FM0dUdmPTYkZDUDnb+aSijqE5sMlPLqU/40wePBo1PmXgAQC6h6yCbpyVIKxfBdE99MeR0tAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:43:33.815275Z"},"content_sha256":"6491afdea8afce6c72fa6ba2cfa08a45229b2111729a910714bc271fcbd32dce","schema_version":"1.0","event_id":"sha256:6491afdea8afce6c72fa6ba2cfa08a45229b2111729a910714bc271fcbd32dce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7FCV4OSIKHBX2EEJ3DG7EQ25JM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodic Theory and Diophantine approximation for translation surfaces and linear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.NT"],"primary_cat":"math.DS","authors_text":"Andrew Parrish, Jayadev Athreya, Jimmy Tseng","submitted_at":"2014-01-16T19:58:30Z","abstract_excerpt":"We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together with an approximation argument, also give an alternative proof of a weak version of a classical theorem in multi-dimensional Diophantine approximation due to W. Schmidt \\cite{SchmidtMetrical, SchmidtMetrical2}. The approximation argument allows us to deduce the Birkhoff genericity of almost all lattices in a certain submanifold of the space of unimodular lattic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4148","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T1Jw+8aZCt4+p2zJYVXyi1OMRoteMmmgG71xiJgIMQVyfoizw+z1lmF1yc8j/gHdfIDU+3rpVNp19n3H5beLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:43:33.815959Z"},"content_sha256":"cf68f2c494bb7a70fd436c66cf703efee538a2c9778c286b9caf84d6ada37669","schema_version":"1.0","event_id":"sha256:cf68f2c494bb7a70fd436c66cf703efee538a2c9778c286b9caf84d6ada37669"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FCV4OSIKHBX2EEJ3DG7EQ25JM/bundle.json","state_url":"https://pith.science/pith/7FCV4OSIKHBX2EEJ3DG7EQ25JM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FCV4OSIKHBX2EEJ3DG7EQ25JM/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":"2026-06-04T03:43:33Z","links":{"resolver":"https://pith.science/pith/7FCV4OSIKHBX2EEJ3DG7EQ25JM","bundle":"https://pith.science/pith/7FCV4OSIKHBX2EEJ3DG7EQ25JM/bundle.json","state":"https://pith.science/pith/7FCV4OSIKHBX2EEJ3DG7EQ25JM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FCV4OSIKHBX2EEJ3DG7EQ25JM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7FCV4OSIKHBX2EEJ3DG7EQ25JM","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":"5da807ccad0c33eedd0342697c4c39be72459a8576aa6fac09ae9feb80dcf045","cross_cats_sorted":["math.GT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T19:58:30Z","title_canon_sha256":"5993e0967119ec89193559ac04c17597e45cabfd5eb8d22d632c536f2f9c4d08"},"schema_version":"1.0","source":{"id":"1401.4148","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4148","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4148v4","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4148","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"7FCV4OSIKHBX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7FCV4OSIKHBX2EEJ","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7FCV4OSI","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:cf68f2c494bb7a70fd436c66cf703efee538a2c9778c286b9caf84d6ada37669","target":"graph","created_at":"2026-05-18T01:14:59Z","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"},"paper":{"abstract_excerpt":"We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together with an approximation argument, also give an alternative proof of a weak version of a classical theorem in multi-dimensional Diophantine approximation due to W. Schmidt \\cite{SchmidtMetrical, SchmidtMetrical2}. The approximation argument allows us to deduce the Birkhoff genericity of almost all lattices in a certain submanifold of the space of unimodular lattic","authors_text":"Andrew Parrish, Jayadev Athreya, Jimmy Tseng","cross_cats":["math.GT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T19:58:30Z","title":"Ergodic Theory and Diophantine approximation for translation surfaces and linear forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4148","kind":"arxiv","version":4},"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":"sha256:6491afdea8afce6c72fa6ba2cfa08a45229b2111729a910714bc271fcbd32dce","target":"record","created_at":"2026-05-18T01:14:59Z","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":"5da807ccad0c33eedd0342697c4c39be72459a8576aa6fac09ae9feb80dcf045","cross_cats_sorted":["math.GT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-16T19:58:30Z","title_canon_sha256":"5993e0967119ec89193559ac04c17597e45cabfd5eb8d22d632c536f2f9c4d08"},"schema_version":"1.0","source":{"id":"1401.4148","kind":"arxiv","version":4}},"canonical_sha256":"f9455e3a4851c37d1089d8cdf2435d4b32b0af748f413ed95542e4b715fef30c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9455e3a4851c37d1089d8cdf2435d4b32b0af748f413ed95542e4b715fef30c","first_computed_at":"2026-05-18T01:14:59.074530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:59.074530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XU48ISiUBFNIePmtCLq2ayl+ZLfD94AYXE4zpCPGr2UvdPIeNvFq4qvUBwaY/1qOAR9nh6fcavhpCfZwxvk1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:59.075028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4148","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6491afdea8afce6c72fa6ba2cfa08a45229b2111729a910714bc271fcbd32dce","sha256:cf68f2c494bb7a70fd436c66cf703efee538a2c9778c286b9caf84d6ada37669"],"state_sha256":"7c976f3fca74cb92eebb2b709ed19712e00c1a6101263cb06fa9e2e111452692"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QpgdLZGRdQq7tD17NXc3uyUM9A3TJY6eOWD9CCoBVKKzhx0tS6hwJN7AapNpJh2MFeIVg//pYIsgpnB92SohDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:43:33.819806Z","bundle_sha256":"4cd3ea138f296f9f2910ba731a525305a6d006d7af36149f48da70407c856118"}}