{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QNIJQAGPR4NXBLRSKQADTNJHXN","short_pith_number":"pith:QNIJQAGP","canonical_record":{"source":{"id":"1712.02481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T03:35:10Z","cross_cats_sorted":[],"title_canon_sha256":"ba6dfc318e9a56ed9af6a52f21f1e400c77ed62c0e1b7809c8faafd8479779f3","abstract_canon_sha256":"4238d98ba70b422f12535bae65121002c0d1141cdc7e215fd7e722de3d4b7695"},"schema_version":"1.0"},"canonical_sha256":"83509800cf8f1b70ae32540039b527bb58e7a7cbe1c12a6f9fb37fe8bd64a799","source":{"kind":"arxiv","id":"1712.02481","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02481","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02481v1","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02481","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"QNIJQAGPR4NX","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QNIJQAGPR4NXBLRS","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QNIJQAGP","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QNIJQAGPR4NXBLRSKQADTNJHXN","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T03:35:10Z","cross_cats_sorted":[],"title_canon_sha256":"ba6dfc318e9a56ed9af6a52f21f1e400c77ed62c0e1b7809c8faafd8479779f3","abstract_canon_sha256":"4238d98ba70b422f12535bae65121002c0d1141cdc7e215fd7e722de3d4b7695"},"schema_version":"1.0"},"canonical_sha256":"83509800cf8f1b70ae32540039b527bb58e7a7cbe1c12a6f9fb37fe8bd64a799","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:33.926036Z","signature_b64":"I9KH6cxXeRumxzyW+bYy05gfNmytItuLQ1w5ci4FTlfibC/CSUQ3FPiXeSjfiV1aIF5B6Xux7rnDWluUrmxwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83509800cf8f1b70ae32540039b527bb58e7a7cbe1c12a6f9fb37fe8bd64a799","last_reissued_at":"2026-05-18T00:28:33.925345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:33.925345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02481","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":"2026-05-18T00:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ina+qAMrx/izUwPaPEYLFnuin6E7euct59E3Ibv4PMKr/A/N6RgRqjqPvUa9COJTMGrTalOUTc6E3tW3EJ2kCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:27:40.051872Z"},"content_sha256":"33fa2e77c022338ae50292aaf9ef9397a0640656cd24b44082f54674f1f34840","schema_version":"1.0","event_id":"sha256:33fa2e77c022338ae50292aaf9ef9397a0640656cd24b44082f54674f1f34840"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QNIJQAGPR4NXBLRSKQADTNJHXN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On topological genericity of the mode-locking phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Zhiyuan Zhang","submitted_at":"2017-12-07T03:35:10Z","abstract_excerpt":"We study the circle homeomorphisms extensions over a strictly ergodic homeomorphism. Under a very mild restriction, we show that the fibered rotation number is locally constant on an open and dense subset. In the complement of this set, we found a dense subset in which every map is conjugate to a direct product. Our result provides a generalisation of Avila-Bochi-Damanik's result on ${\\rm SL}(2,\\mathbb{R})-$cocycles, and Jager-Wang-Zhou's result on quasi-periodically forced maps, to a broader setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02481","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":"2026-05-18T00:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HF/Gj8m6ZGBEz5gftiau57g/eA8FEIDOiPf0//qEDspev0SQVtR5kS5NEomtP6oKUoIJ2p5BinUapJg5tvW4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:27:40.052207Z"},"content_sha256":"71fe2c095478eea2f949b07074bb7929f12d80b92b10dcc3d19e08adc26b22d2","schema_version":"1.0","event_id":"sha256:71fe2c095478eea2f949b07074bb7929f12d80b92b10dcc3d19e08adc26b22d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNIJQAGPR4NXBLRSKQADTNJHXN/bundle.json","state_url":"https://pith.science/pith/QNIJQAGPR4NXBLRSKQADTNJHXN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNIJQAGPR4NXBLRSKQADTNJHXN/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":"2026-06-07T10:27:40Z","links":{"resolver":"https://pith.science/pith/QNIJQAGPR4NXBLRSKQADTNJHXN","bundle":"https://pith.science/pith/QNIJQAGPR4NXBLRSKQADTNJHXN/bundle.json","state":"https://pith.science/pith/QNIJQAGPR4NXBLRSKQADTNJHXN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNIJQAGPR4NXBLRSKQADTNJHXN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QNIJQAGPR4NXBLRSKQADTNJHXN","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":"4238d98ba70b422f12535bae65121002c0d1141cdc7e215fd7e722de3d4b7695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T03:35:10Z","title_canon_sha256":"ba6dfc318e9a56ed9af6a52f21f1e400c77ed62c0e1b7809c8faafd8479779f3"},"schema_version":"1.0","source":{"id":"1712.02481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02481","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02481v1","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02481","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"QNIJQAGPR4NX","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QNIJQAGPR4NXBLRS","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QNIJQAGP","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:71fe2c095478eea2f949b07074bb7929f12d80b92b10dcc3d19e08adc26b22d2","target":"graph","created_at":"2026-05-18T00:28:33Z","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 the circle homeomorphisms extensions over a strictly ergodic homeomorphism. Under a very mild restriction, we show that the fibered rotation number is locally constant on an open and dense subset. In the complement of this set, we found a dense subset in which every map is conjugate to a direct product. Our result provides a generalisation of Avila-Bochi-Damanik's result on ${\\rm SL}(2,\\mathbb{R})-$cocycles, and Jager-Wang-Zhou's result on quasi-periodically forced maps, to a broader setting.","authors_text":"Zhiyuan Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T03:35:10Z","title":"On topological genericity of the mode-locking phenomenon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02481","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":"sha256:33fa2e77c022338ae50292aaf9ef9397a0640656cd24b44082f54674f1f34840","target":"record","created_at":"2026-05-18T00:28:33Z","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":"4238d98ba70b422f12535bae65121002c0d1141cdc7e215fd7e722de3d4b7695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T03:35:10Z","title_canon_sha256":"ba6dfc318e9a56ed9af6a52f21f1e400c77ed62c0e1b7809c8faafd8479779f3"},"schema_version":"1.0","source":{"id":"1712.02481","kind":"arxiv","version":1}},"canonical_sha256":"83509800cf8f1b70ae32540039b527bb58e7a7cbe1c12a6f9fb37fe8bd64a799","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83509800cf8f1b70ae32540039b527bb58e7a7cbe1c12a6f9fb37fe8bd64a799","first_computed_at":"2026-05-18T00:28:33.925345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:33.925345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I9KH6cxXeRumxzyW+bYy05gfNmytItuLQ1w5ci4FTlfibC/CSUQ3FPiXeSjfiV1aIF5B6Xux7rnDWluUrmxwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:33.926036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33fa2e77c022338ae50292aaf9ef9397a0640656cd24b44082f54674f1f34840","sha256:71fe2c095478eea2f949b07074bb7929f12d80b92b10dcc3d19e08adc26b22d2"],"state_sha256":"e88f0009e72b604a56aafb429bf8eac075c0475d632220722676363c21d9ef3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZB5sL9lfVadVMdxyVBYi0SiJAkz858qKFGN3Ye3Ew4kI4nUBODlOjZjwm5io7NZ1n6ZjvanPGwSzO8aNK/NDAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:27:40.054250Z","bundle_sha256":"8920a3e838a971a0fd41220f2a6dde0cd40eab6b0287129aef8d6d03aa316510"}}