{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VREXMW3PIM5JAJKIKIXT5NZX6G","short_pith_number":"pith:VREXMW3P","canonical_record":{"source":{"id":"0910.2694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-10-14T19:29:27Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"96c7334614d6a6f4301dd97d6ec99f62031b28de3ce3fb176b3911084fc101bc","abstract_canon_sha256":"4c62895a77692264fc316cd502b499a33a9df434ae0872766ee5f10116c71023"},"schema_version":"1.0"},"canonical_sha256":"ac49765b6f433a902548522f3eb737f1a91670e75b7f95a726620b9371d527e9","source":{"kind":"arxiv","id":"0910.2694","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2694","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2694v2","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2694","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"VREXMW3PIM5J","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VREXMW3PIM5JAJKI","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VREXMW3P","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VREXMW3PIM5JAJKIKIXT5NZX6G","target":"record","payload":{"canonical_record":{"source":{"id":"0910.2694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-10-14T19:29:27Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"96c7334614d6a6f4301dd97d6ec99f62031b28de3ce3fb176b3911084fc101bc","abstract_canon_sha256":"4c62895a77692264fc316cd502b499a33a9df434ae0872766ee5f10116c71023"},"schema_version":"1.0"},"canonical_sha256":"ac49765b6f433a902548522f3eb737f1a91670e75b7f95a726620b9371d527e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:36.380974Z","signature_b64":"dBKTWhGROvYBfdExvToDKebGRQnvS8S2uOC8gbWGyAaPi1S2cZiKUbRERa5U7WLk/65A++dn/2O1Hple9t9/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac49765b6f433a902548522f3eb737f1a91670e75b7f95a726620b9371d527e9","last_reissued_at":"2026-05-18T04:24:36.380472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:36.380472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.2694","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":"2026-05-18T04:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BRl9UgqrwizLErrzHseyMAXZu7izqmsqrYwIetVktbFQDdN34ae2QuR6jqE5eqTAPwjb11s1fH6hDtyLpWkuAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:25:15.526634Z"},"content_sha256":"67595ded779d2641f4393f04bed954a58432a46073d2fea72966c241d73e00a5","schema_version":"1.0","event_id":"sha256:67595ded779d2641f4393f04bed954a58432a46073d2fea72966c241d73e00a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VREXMW3PIM5JAJKIKIXT5NZX6G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shrinking targets for IETs: Extending a theorem of Kurzweil","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Jon Chaika","submitted_at":"2009-10-14T19:29:27Z","abstract_excerpt":"This paper proves shrinking target results for IETs. Let {a_1\\geq a_2 \\geq...} be a sequence of positive real numbers with divergent sum. Then for almost every IET T, the limsup of B(T^ix,a_i) has full Lebesgue measure (where B(z, e) is the open ball around z of radius e). Related results are established including the analogous result for geodesic flows on a translation surface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2694","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"un2br71Tq2lvHlhw2vD0agRX1V7tX/jGqxBZs6aBgv66vYCU6qgp4k6tCiHDkcih0O7CCLcqdGzGHbsMTAdEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:25:15.527307Z"},"content_sha256":"dee8732dc3f52035c1ee4a39e7a680ec11036927889cf3b204d630adc2e1168a","schema_version":"1.0","event_id":"sha256:dee8732dc3f52035c1ee4a39e7a680ec11036927889cf3b204d630adc2e1168a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VREXMW3PIM5JAJKIKIXT5NZX6G/bundle.json","state_url":"https://pith.science/pith/VREXMW3PIM5JAJKIKIXT5NZX6G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VREXMW3PIM5JAJKIKIXT5NZX6G/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":"2026-05-22T14:25:15Z","links":{"resolver":"https://pith.science/pith/VREXMW3PIM5JAJKIKIXT5NZX6G","bundle":"https://pith.science/pith/VREXMW3PIM5JAJKIKIXT5NZX6G/bundle.json","state":"https://pith.science/pith/VREXMW3PIM5JAJKIKIXT5NZX6G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VREXMW3PIM5JAJKIKIXT5NZX6G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VREXMW3PIM5JAJKIKIXT5NZX6G","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":"4c62895a77692264fc316cd502b499a33a9df434ae0872766ee5f10116c71023","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-10-14T19:29:27Z","title_canon_sha256":"96c7334614d6a6f4301dd97d6ec99f62031b28de3ce3fb176b3911084fc101bc"},"schema_version":"1.0","source":{"id":"0910.2694","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2694","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2694v2","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2694","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"VREXMW3PIM5J","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VREXMW3PIM5JAJKI","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VREXMW3P","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:dee8732dc3f52035c1ee4a39e7a680ec11036927889cf3b204d630adc2e1168a","target":"graph","created_at":"2026-05-18T04:24:36Z","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":"This paper proves shrinking target results for IETs. Let {a_1\\geq a_2 \\geq...} be a sequence of positive real numbers with divergent sum. Then for almost every IET T, the limsup of B(T^ix,a_i) has full Lebesgue measure (where B(z, e) is the open ball around z of radius e). Related results are established including the analogous result for geodesic flows on a translation surface.","authors_text":"Jon Chaika","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-10-14T19:29:27Z","title":"Shrinking targets for IETs: Extending a theorem of Kurzweil"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2694","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":"sha256:67595ded779d2641f4393f04bed954a58432a46073d2fea72966c241d73e00a5","target":"record","created_at":"2026-05-18T04:24:36Z","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":"4c62895a77692264fc316cd502b499a33a9df434ae0872766ee5f10116c71023","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-10-14T19:29:27Z","title_canon_sha256":"96c7334614d6a6f4301dd97d6ec99f62031b28de3ce3fb176b3911084fc101bc"},"schema_version":"1.0","source":{"id":"0910.2694","kind":"arxiv","version":2}},"canonical_sha256":"ac49765b6f433a902548522f3eb737f1a91670e75b7f95a726620b9371d527e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac49765b6f433a902548522f3eb737f1a91670e75b7f95a726620b9371d527e9","first_computed_at":"2026-05-18T04:24:36.380472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:36.380472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dBKTWhGROvYBfdExvToDKebGRQnvS8S2uOC8gbWGyAaPi1S2cZiKUbRERa5U7WLk/65A++dn/2O1Hple9t9/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:36.380974Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2694","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67595ded779d2641f4393f04bed954a58432a46073d2fea72966c241d73e00a5","sha256:dee8732dc3f52035c1ee4a39e7a680ec11036927889cf3b204d630adc2e1168a"],"state_sha256":"aa121d31cc466463e1db04d22fd564de94f14b77123a03cf071a513440cf3eaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FbTX8hmFYU2s1FGuSn6KzCWCFZWsPLV881s26Y+3tw8HklWWX0MFyBsyow6tpzeVOHkd6g0dsFbM7b3kWQfvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T14:25:15.530954Z","bundle_sha256":"7a912db4da9db5b3598ee8e032136f6d7cf5a1dc2d140f70287e4a16ff2d0bfc"}}