{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3IIXDL4SP6M3VDIXNB7FAGXZ3G","short_pith_number":"pith:3IIXDL4S","canonical_record":{"source":{"id":"1503.07249","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-25T00:50:26Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7e91380096148817893e91edc4eaec40e91c71bdd993ec35b1f1dba203267602","abstract_canon_sha256":"616fc2e7662d49bf3207c65adc0f3ddfbcb62e4c78cef2817c147fb10798eeba"},"schema_version":"1.0"},"canonical_sha256":"da1171af927f99ba8d17687e501af9d9951eaa8c6cfc16d18391540f087fcb3b","source":{"kind":"arxiv","id":"1503.07249","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07249","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07249v4","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07249","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"3IIXDL4SP6M3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3IIXDL4SP6M3VDIX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3IIXDL4S","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3IIXDL4SP6M3VDIXNB7FAGXZ3G","target":"record","payload":{"canonical_record":{"source":{"id":"1503.07249","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-25T00:50:26Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7e91380096148817893e91edc4eaec40e91c71bdd993ec35b1f1dba203267602","abstract_canon_sha256":"616fc2e7662d49bf3207c65adc0f3ddfbcb62e4c78cef2817c147fb10798eeba"},"schema_version":"1.0"},"canonical_sha256":"da1171af927f99ba8d17687e501af9d9951eaa8c6cfc16d18391540f087fcb3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:08.589027Z","signature_b64":"VDeooTmN8sPlO6Z+snxLoSYLtWUx8pk9OFrBsKbJiWw7KdPYWA1kv6p/Bo4xloamoLJTBJxWnxiTCD685T0sAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da1171af927f99ba8d17687e501af9d9951eaa8c6cfc16d18391540f087fcb3b","last_reissued_at":"2026-05-18T01:23:08.588595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:08.588595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.07249","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":"2026-05-18T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"letCfZs/DEyeG4xZi6HwHgQ6IYRANlFqo540pHB+KQtImrYtf01aio4HxParYygFyfeXCpPU8JLO+nHvpFD4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:57:18.746916Z"},"content_sha256":"03497d3ddb610f778ff1d25a7f8b46ccea2141b441bd71676c10678c16157263","schema_version":"1.0","event_id":"sha256:03497d3ddb610f778ff1d25a7f8b46ccea2141b441bd71676c10678c16157263"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3IIXDL4SP6M3VDIXNB7FAGXZ3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An effective estimate for the Lebesgue measure of preimages of iterates of the Farey map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Byron Heersink","submitted_at":"2015-03-25T00:50:26Z","abstract_excerpt":"Using techniques from infinite ergodic theory, Kessebohmer and Stratmann determined the asymptotic behavior of the Lebesgue measure of sets of the form $F^{-n}[\\alpha,\\beta]$, where $[\\alpha,\\beta]\\subseteq(0,1]$ and $F$ is the Farey map. In this paper, we provide an effective version of this result, employing mostly basic properties of the transfer operator of the Farey map and an application of Freud's effective version of Karamata's Tauberian theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07249","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":"2026-05-18T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q8e6bLmqELEEtTHyNEZCLPfF4lUuqkI9K8ELAYQXp/Ap3eFNbOOT1sT1oe5FIQXmAxj3xBTNPGlfwpjKZhyJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:57:18.747258Z"},"content_sha256":"61cb259562f13e915c4998a04a20adaa079be8fc38b965cc2b0084c3de91695f","schema_version":"1.0","event_id":"sha256:61cb259562f13e915c4998a04a20adaa079be8fc38b965cc2b0084c3de91695f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3IIXDL4SP6M3VDIXNB7FAGXZ3G/bundle.json","state_url":"https://pith.science/pith/3IIXDL4SP6M3VDIXNB7FAGXZ3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3IIXDL4SP6M3VDIXNB7FAGXZ3G/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":"2026-06-02T05:57:18Z","links":{"resolver":"https://pith.science/pith/3IIXDL4SP6M3VDIXNB7FAGXZ3G","bundle":"https://pith.science/pith/3IIXDL4SP6M3VDIXNB7FAGXZ3G/bundle.json","state":"https://pith.science/pith/3IIXDL4SP6M3VDIXNB7FAGXZ3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3IIXDL4SP6M3VDIXNB7FAGXZ3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3IIXDL4SP6M3VDIXNB7FAGXZ3G","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":"616fc2e7662d49bf3207c65adc0f3ddfbcb62e4c78cef2817c147fb10798eeba","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-25T00:50:26Z","title_canon_sha256":"7e91380096148817893e91edc4eaec40e91c71bdd993ec35b1f1dba203267602"},"schema_version":"1.0","source":{"id":"1503.07249","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07249","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07249v4","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07249","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"3IIXDL4SP6M3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3IIXDL4SP6M3VDIX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3IIXDL4S","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:61cb259562f13e915c4998a04a20adaa079be8fc38b965cc2b0084c3de91695f","target":"graph","created_at":"2026-05-18T01:23:08Z","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":"Using techniques from infinite ergodic theory, Kessebohmer and Stratmann determined the asymptotic behavior of the Lebesgue measure of sets of the form $F^{-n}[\\alpha,\\beta]$, where $[\\alpha,\\beta]\\subseteq(0,1]$ and $F$ is the Farey map. In this paper, we provide an effective version of this result, employing mostly basic properties of the transfer operator of the Farey map and an application of Freud's effective version of Karamata's Tauberian theorem.","authors_text":"Byron Heersink","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-25T00:50:26Z","title":"An effective estimate for the Lebesgue measure of preimages of iterates of the Farey map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07249","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":"sha256:03497d3ddb610f778ff1d25a7f8b46ccea2141b441bd71676c10678c16157263","target":"record","created_at":"2026-05-18T01:23:08Z","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":"616fc2e7662d49bf3207c65adc0f3ddfbcb62e4c78cef2817c147fb10798eeba","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-25T00:50:26Z","title_canon_sha256":"7e91380096148817893e91edc4eaec40e91c71bdd993ec35b1f1dba203267602"},"schema_version":"1.0","source":{"id":"1503.07249","kind":"arxiv","version":4}},"canonical_sha256":"da1171af927f99ba8d17687e501af9d9951eaa8c6cfc16d18391540f087fcb3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da1171af927f99ba8d17687e501af9d9951eaa8c6cfc16d18391540f087fcb3b","first_computed_at":"2026-05-18T01:23:08.588595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:08.588595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VDeooTmN8sPlO6Z+snxLoSYLtWUx8pk9OFrBsKbJiWw7KdPYWA1kv6p/Bo4xloamoLJTBJxWnxiTCD685T0sAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:08.589027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07249","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03497d3ddb610f778ff1d25a7f8b46ccea2141b441bd71676c10678c16157263","sha256:61cb259562f13e915c4998a04a20adaa079be8fc38b965cc2b0084c3de91695f"],"state_sha256":"4fd9daed6a3f19866dacf07670848e2c70caf635a6df54296fcfde098697abcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TYij7vvmiCPyso9vosaOxfwztuZTgR+/eyzD3RJp1fh3nBV7905u+is1+RZKoFXQOeZA5b810m/8d4XWMwbCBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:57:18.749130Z","bundle_sha256":"08e4bd497f103c2052b3a7abc5e33b5993dcc1bb34b346ac0a1613060e3df895"}}