{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z7622655UCASK6JA4G6AJOH3RJ","short_pith_number":"pith:Z7622655","canonical_record":{"source":{"id":"1504.03887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-15T12:36:18Z","cross_cats_sorted":[],"title_canon_sha256":"8183bd2d933f87898bb1b462f77a277efd82e269f5317a275225f95cc86287cb","abstract_canon_sha256":"09bdb0291f63ec6063ca6a24c4fe3467fb80fc786e6657e25e7166382b23765d"},"schema_version":"1.0"},"canonical_sha256":"cffdad7bbda081257920e1bc04b8fb8a65a4479645fb5dd3e7526d71a3141f19","source":{"kind":"arxiv","id":"1504.03887","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03887","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03887v1","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03887","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"Z7622655UCAS","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z7622655UCASK6JA","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z7622655","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z7622655UCASK6JA4G6AJOH3RJ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.03887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-15T12:36:18Z","cross_cats_sorted":[],"title_canon_sha256":"8183bd2d933f87898bb1b462f77a277efd82e269f5317a275225f95cc86287cb","abstract_canon_sha256":"09bdb0291f63ec6063ca6a24c4fe3467fb80fc786e6657e25e7166382b23765d"},"schema_version":"1.0"},"canonical_sha256":"cffdad7bbda081257920e1bc04b8fb8a65a4479645fb5dd3e7526d71a3141f19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:41.782940Z","signature_b64":"x+jUECF77h/MzvC1P7DnpWbPf2IQ4nnEB4gBzodr9q38IxOzJgQPl8olL5bzkvZ6jTzJ0p/UOcxh8NQ0vXznAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cffdad7bbda081257920e1bc04b8fb8a65a4479645fb5dd3e7526d71a3141f19","last_reissued_at":"2026-05-18T02:18:41.782243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:41.782243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.03887","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":"2026-05-18T02:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CYbdpISgLK6Q5oTfbKjrkPk5MxfaqW6uBCuVElB7zO99RdeHh2D7QSSJzZKom7wSWovoy6JX3NlInKJAx/9+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:15:29.422526Z"},"content_sha256":"eccf3ef24916a6a14670f5588ce6218bcb31b4c2c6395fbfa10bcca2de123a86","schema_version":"1.0","event_id":"sha256:eccf3ef24916a6a14670f5588ce6218bcb31b4c2c6395fbfa10bcca2de123a86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z7622655UCASK6JA4G6AJOH3RJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abundance of mode-locking for quasiperiodically forced circle maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jing Wang, Tobias J\\\"ager","submitted_at":"2015-04-15T12:36:18Z","abstract_excerpt":"We study the phenomenon of mode-locking in the context of quasiperiodically forced non-linear circle maps. As a main result, we show that under certain C1-open condition on the geometry of twist parameter families of such systems, the closure of the union of modelocking plateaus has positive measure. In particular, this implies the existence of infinitely many mode-locking plateaus (open Arnold tongues). The proof builds on multiscale analysis and parameter exclusion methods in the spirit of Benedicks and Carleson, which were previously developed for quasiperiodic SL(2,R)-cocycles by Young and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03887","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":"2026-05-18T02:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w0SYlR59Ib1H3a814Sy9ZB63yGnq9iUhjihMVPJEnz2qZrfXmZsI6yZS+ROzEiWb4nHCSgSGaOxI8e5IdDI3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:15:29.423118Z"},"content_sha256":"53b7d0e398d588eeee8d8d1f417bf3d2b8f6de2bb9d27301c2fc1b9ab405ba0d","schema_version":"1.0","event_id":"sha256:53b7d0e398d588eeee8d8d1f417bf3d2b8f6de2bb9d27301c2fc1b9ab405ba0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7622655UCASK6JA4G6AJOH3RJ/bundle.json","state_url":"https://pith.science/pith/Z7622655UCASK6JA4G6AJOH3RJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7622655UCASK6JA4G6AJOH3RJ/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":"2026-06-07T02:15:29Z","links":{"resolver":"https://pith.science/pith/Z7622655UCASK6JA4G6AJOH3RJ","bundle":"https://pith.science/pith/Z7622655UCASK6JA4G6AJOH3RJ/bundle.json","state":"https://pith.science/pith/Z7622655UCASK6JA4G6AJOH3RJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7622655UCASK6JA4G6AJOH3RJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z7622655UCASK6JA4G6AJOH3RJ","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":"09bdb0291f63ec6063ca6a24c4fe3467fb80fc786e6657e25e7166382b23765d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-15T12:36:18Z","title_canon_sha256":"8183bd2d933f87898bb1b462f77a277efd82e269f5317a275225f95cc86287cb"},"schema_version":"1.0","source":{"id":"1504.03887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03887","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03887v1","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03887","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"Z7622655UCAS","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z7622655UCASK6JA","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z7622655","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:53b7d0e398d588eeee8d8d1f417bf3d2b8f6de2bb9d27301c2fc1b9ab405ba0d","target":"graph","created_at":"2026-05-18T02:18:41Z","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 phenomenon of mode-locking in the context of quasiperiodically forced non-linear circle maps. As a main result, we show that under certain C1-open condition on the geometry of twist parameter families of such systems, the closure of the union of modelocking plateaus has positive measure. In particular, this implies the existence of infinitely many mode-locking plateaus (open Arnold tongues). The proof builds on multiscale analysis and parameter exclusion methods in the spirit of Benedicks and Carleson, which were previously developed for quasiperiodic SL(2,R)-cocycles by Young and","authors_text":"Jing Wang, Tobias J\\\"ager","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-15T12:36:18Z","title":"Abundance of mode-locking for quasiperiodically forced circle maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03887","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:eccf3ef24916a6a14670f5588ce6218bcb31b4c2c6395fbfa10bcca2de123a86","target":"record","created_at":"2026-05-18T02:18:41Z","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":"09bdb0291f63ec6063ca6a24c4fe3467fb80fc786e6657e25e7166382b23765d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-15T12:36:18Z","title_canon_sha256":"8183bd2d933f87898bb1b462f77a277efd82e269f5317a275225f95cc86287cb"},"schema_version":"1.0","source":{"id":"1504.03887","kind":"arxiv","version":1}},"canonical_sha256":"cffdad7bbda081257920e1bc04b8fb8a65a4479645fb5dd3e7526d71a3141f19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cffdad7bbda081257920e1bc04b8fb8a65a4479645fb5dd3e7526d71a3141f19","first_computed_at":"2026-05-18T02:18:41.782243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:41.782243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x+jUECF77h/MzvC1P7DnpWbPf2IQ4nnEB4gBzodr9q38IxOzJgQPl8olL5bzkvZ6jTzJ0p/UOcxh8NQ0vXznAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:41.782940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eccf3ef24916a6a14670f5588ce6218bcb31b4c2c6395fbfa10bcca2de123a86","sha256:53b7d0e398d588eeee8d8d1f417bf3d2b8f6de2bb9d27301c2fc1b9ab405ba0d"],"state_sha256":"00b9401a2c280b55e3f83379ec2e0afa0c62e1c0996a4e980027a9a1b60fe616"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JB7YXhjoXT+PLIQhVy9Ld2v7LuGYlDS+UeCqvy9T1xuXkusTjIN4qLh+fuKLlcR4PyJ8FE7jXBEmuapEwYp7DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:15:29.426110Z","bundle_sha256":"8e6e5a32f6e52c85eb56b2fba4ab732549e37c47290b4fed287a8f23e41c5784"}}