{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CJOVWLWPBNKEHP66QYMS5JSXXD","short_pith_number":"pith:CJOVWLWP","canonical_record":{"source":{"id":"1701.04498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-17T00:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"6f3812543baac72818bf31eaa77f8b175db21c321e304388b447709620e6dd8c","abstract_canon_sha256":"44b722cf79d2fb5a67aeddccfec9f6f687b14760c8ab64b62162ba86d149200c"},"schema_version":"1.0"},"canonical_sha256":"125d5b2ecf0b5443bfde86192ea657b8e8e64ad8b8b4259565fdf9f9ba95a97d","source":{"kind":"arxiv","id":"1701.04498","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04498","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04498v1","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04498","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"CJOVWLWPBNKE","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CJOVWLWPBNKEHP66","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CJOVWLWP","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CJOVWLWPBNKEHP66QYMS5JSXXD","target":"record","payload":{"canonical_record":{"source":{"id":"1701.04498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-17T00:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"6f3812543baac72818bf31eaa77f8b175db21c321e304388b447709620e6dd8c","abstract_canon_sha256":"44b722cf79d2fb5a67aeddccfec9f6f687b14760c8ab64b62162ba86d149200c"},"schema_version":"1.0"},"canonical_sha256":"125d5b2ecf0b5443bfde86192ea657b8e8e64ad8b8b4259565fdf9f9ba95a97d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:43.539737Z","signature_b64":"oI6g7vKNNbpy+ZJmeL97IQej9rCfHoVBkvIyW2yhP3S3CHpVuVHY64J96L9oko2EYWaWrdF2f7RMRGLZ1TeWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"125d5b2ecf0b5443bfde86192ea657b8e8e64ad8b8b4259565fdf9f9ba95a97d","last_reissued_at":"2026-05-18T00:52:43.539108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:43.539108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.04498","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"atKr5AJ82cT31FrvTjFPg1W3TYvDk5Yx7zExgMk88xPB3LVWfXHOGbcJLKkFUG7ouau7LHUX3u3rB5KlKzxeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:40:44.877814Z"},"content_sha256":"f9938e49cc4b9366a83d0190bc4b08e256b9ee4e5d8ceb17e45562ddd7c88ad1","schema_version":"1.0","event_id":"sha256:f9938e49cc4b9366a83d0190bc4b08e256b9ee4e5d8ceb17e45562ddd7c88ad1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CJOVWLWPBNKEHP66QYMS5JSXXD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synchronization is full measure for all $\\alpha$-deformations of an infinite class of continued fraction transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Cor Kraaikamp, Kariane Calta, Thomas A. Schmidt","submitted_at":"2017-01-17T00:54:40Z","abstract_excerpt":"We study an infinite family of one-parameter deformations, so-called $\\alpha$-continued fractions, of interval maps associated to distinct triangle Fuchsian groups. In general for such one-parameter deformations, the function giving the entropy of the map indexed by $\\alpha$ varies in a way directly related to whether or not the orbits of the endpoints of the map synchronize. For two cases of one-parameter deformations associated to the classical case of the modular group $\\text{PSL}_2(\\mathbb Z)$, the set of $\\alpha$ for which synchronization occurs has been determined.\n  Here, we explicitly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04498","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":""},"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":"2026-05-18T00:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4RcALMvXG9fjU5BIqwOFLCT838wAftaWHn3Bo2RPgg6WGuwsAwVJpiFlMWXB+yW0o/7cvyYKmSket3aXIx9YCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:40:44.878239Z"},"content_sha256":"52cc0b8f6b4edf044ff709fbf9223c97e2503f2cdcc6e64d074860a6dc5cdc39","schema_version":"1.0","event_id":"sha256:52cc0b8f6b4edf044ff709fbf9223c97e2503f2cdcc6e64d074860a6dc5cdc39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJOVWLWPBNKEHP66QYMS5JSXXD/bundle.json","state_url":"https://pith.science/pith/CJOVWLWPBNKEHP66QYMS5JSXXD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJOVWLWPBNKEHP66QYMS5JSXXD/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":"2026-05-27T21:40:44Z","links":{"resolver":"https://pith.science/pith/CJOVWLWPBNKEHP66QYMS5JSXXD","bundle":"https://pith.science/pith/CJOVWLWPBNKEHP66QYMS5JSXXD/bundle.json","state":"https://pith.science/pith/CJOVWLWPBNKEHP66QYMS5JSXXD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJOVWLWPBNKEHP66QYMS5JSXXD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CJOVWLWPBNKEHP66QYMS5JSXXD","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":"44b722cf79d2fb5a67aeddccfec9f6f687b14760c8ab64b62162ba86d149200c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-17T00:54:40Z","title_canon_sha256":"6f3812543baac72818bf31eaa77f8b175db21c321e304388b447709620e6dd8c"},"schema_version":"1.0","source":{"id":"1701.04498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04498","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04498v1","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04498","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"CJOVWLWPBNKE","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CJOVWLWPBNKEHP66","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CJOVWLWP","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:52cc0b8f6b4edf044ff709fbf9223c97e2503f2cdcc6e64d074860a6dc5cdc39","target":"graph","created_at":"2026-05-18T00:52:43Z","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 study an infinite family of one-parameter deformations, so-called $\\alpha$-continued fractions, of interval maps associated to distinct triangle Fuchsian groups. In general for such one-parameter deformations, the function giving the entropy of the map indexed by $\\alpha$ varies in a way directly related to whether or not the orbits of the endpoints of the map synchronize. For two cases of one-parameter deformations associated to the classical case of the modular group $\\text{PSL}_2(\\mathbb Z)$, the set of $\\alpha$ for which synchronization occurs has been determined.\n  Here, we explicitly ","authors_text":"Cor Kraaikamp, Kariane Calta, Thomas A. Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-17T00:54:40Z","title":"Synchronization is full measure for all $\\alpha$-deformations of an infinite class of continued fraction transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04498","kind":"arxiv","version":1},"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:f9938e49cc4b9366a83d0190bc4b08e256b9ee4e5d8ceb17e45562ddd7c88ad1","target":"record","created_at":"2026-05-18T00:52:43Z","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":"44b722cf79d2fb5a67aeddccfec9f6f687b14760c8ab64b62162ba86d149200c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-17T00:54:40Z","title_canon_sha256":"6f3812543baac72818bf31eaa77f8b175db21c321e304388b447709620e6dd8c"},"schema_version":"1.0","source":{"id":"1701.04498","kind":"arxiv","version":1}},"canonical_sha256":"125d5b2ecf0b5443bfde86192ea657b8e8e64ad8b8b4259565fdf9f9ba95a97d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"125d5b2ecf0b5443bfde86192ea657b8e8e64ad8b8b4259565fdf9f9ba95a97d","first_computed_at":"2026-05-18T00:52:43.539108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:43.539108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oI6g7vKNNbpy+ZJmeL97IQej9rCfHoVBkvIyW2yhP3S3CHpVuVHY64J96L9oko2EYWaWrdF2f7RMRGLZ1TeWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:43.539737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9938e49cc4b9366a83d0190bc4b08e256b9ee4e5d8ceb17e45562ddd7c88ad1","sha256:52cc0b8f6b4edf044ff709fbf9223c97e2503f2cdcc6e64d074860a6dc5cdc39"],"state_sha256":"c731d251ba4932192a16d85a51e1a23964e5af3c4665f67da24fe1fdfdb29f9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vR/4mXSNA5MTKseEdLi8yPy2MGmXpXO9Fh7LlmwseWJywlunouVjAtr0EdmhucVOO6MZo40DkObKg0rHG+GDDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:40:44.881544Z","bundle_sha256":"f75de76e95f256d3a3d8b0fefd3ed421ab8396864551c5c7f428813f20636e78"}}