{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:WGJ3DUOGS7WKY2RMK45K7IXYBE","short_pith_number":"pith:WGJ3DUOG","canonical_record":{"source":{"id":"2406.10674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-15T15:46:19Z","cross_cats_sorted":[],"title_canon_sha256":"b1f77ed42564b419ee362fc50bbc17c613c41b7c9c6b65fdadf77bacf2f504c8","abstract_canon_sha256":"34b40096e6b4bff1983a8de5f382c4df0cc31f3289e05755824944d8d8c2adbf"},"schema_version":"1.0"},"canonical_sha256":"b193b1d1c697ecac6a2c573aafa2f80912582664bbaf314a854eb9ec2709367a","source":{"kind":"arxiv","id":"2406.10674","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.10674","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"2406.10674v1","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.10674","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"WGJ3DUOGS7WK","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"pith_short_16","alias_value":"WGJ3DUOGS7WKY2RM","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"pith_short_8","alias_value":"WGJ3DUOG","created_at":"2026-07-05T08:32:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:WGJ3DUOGS7WKY2RMK45K7IXYBE","target":"record","payload":{"canonical_record":{"source":{"id":"2406.10674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-15T15:46:19Z","cross_cats_sorted":[],"title_canon_sha256":"b1f77ed42564b419ee362fc50bbc17c613c41b7c9c6b65fdadf77bacf2f504c8","abstract_canon_sha256":"34b40096e6b4bff1983a8de5f382c4df0cc31f3289e05755824944d8d8c2adbf"},"schema_version":"1.0"},"canonical_sha256":"b193b1d1c697ecac6a2c573aafa2f80912582664bbaf314a854eb9ec2709367a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:32:20.148251Z","signature_b64":"qtIaPOxxg/1TkKe/18QkpZLHYzwSROaNAJykpyFsl3FHSoCn0prsyaqnxxczZwhaX+Bsx60gg2EPwG2XChacAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b193b1d1c697ecac6a2c573aafa2f80912582664bbaf314a854eb9ec2709367a","last_reissued_at":"2026-07-05T08:32:20.147794Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:32:20.147794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.10674","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":"2026-07-05T08:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qOOZ1YHhvAE+YraAvoeLs+eubim/gqdcwlth99QDHWRipbazxdERSSxkmOZrs1J53unyRI6iE5Sw9fpy3wtJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-18T11:50:47.402480Z"},"content_sha256":"51c9391c22fd2cad4b6c09411ba4e8476a71d51d8327abdece95fea19ae6d0c3","schema_version":"1.0","event_id":"sha256:51c9391c22fd2cad4b6c09411ba4e8476a71d51d8327abdece95fea19ae6d0c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:WGJ3DUOGS7WKY2RMK45K7IXYBE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The structure of periodic point free distal homeomorphisms on the annulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Enhui Shi, Hui Xu, Ziqi Yu","submitted_at":"2024-06-15T15:46:19Z","abstract_excerpt":"Let $A$ be an annulus in the plane $\\mathbb R^2$ and $g:A\\rightarrow A$ be a boundary components preserving homeomorphism which is distal and has no periodic points. Then there is a continuous decomposition of $A$ into $g$-invariant circles such that all the restrictions of $g$ on them share a common irrational rotation number and all these circles are linearly ordered by the inclusion relation on the sets of bounded components of their complements in $\\mathbb R^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.10674","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.10674/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cKgSDbi0M/rCBStPFd1xR6CqWKDIktmVjR+nh7s2Mt96ISL1L1aT5br0S8vXUelIM1iZlEPgzsp4Zb4JLioQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-18T11:50:47.402851Z"},"content_sha256":"2359152431afaf5492bcb574d44413958c7cf5254f6d84ec60cc4bfb02540798","schema_version":"1.0","event_id":"sha256:2359152431afaf5492bcb574d44413958c7cf5254f6d84ec60cc4bfb02540798"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WGJ3DUOGS7WKY2RMK45K7IXYBE/bundle.json","state_url":"https://pith.science/pith/WGJ3DUOGS7WKY2RMK45K7IXYBE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WGJ3DUOGS7WKY2RMK45K7IXYBE/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":"2026-07-18T11:50:47Z","links":{"resolver":"https://pith.science/pith/WGJ3DUOGS7WKY2RMK45K7IXYBE","bundle":"https://pith.science/pith/WGJ3DUOGS7WKY2RMK45K7IXYBE/bundle.json","state":"https://pith.science/pith/WGJ3DUOGS7WKY2RMK45K7IXYBE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WGJ3DUOGS7WKY2RMK45K7IXYBE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WGJ3DUOGS7WKY2RMK45K7IXYBE","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":"34b40096e6b4bff1983a8de5f382c4df0cc31f3289e05755824944d8d8c2adbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-15T15:46:19Z","title_canon_sha256":"b1f77ed42564b419ee362fc50bbc17c613c41b7c9c6b65fdadf77bacf2f504c8"},"schema_version":"1.0","source":{"id":"2406.10674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.10674","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"2406.10674v1","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.10674","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"WGJ3DUOGS7WK","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"pith_short_16","alias_value":"WGJ3DUOGS7WKY2RM","created_at":"2026-07-05T08:32:20Z"},{"alias_kind":"pith_short_8","alias_value":"WGJ3DUOG","created_at":"2026-07-05T08:32:20Z"}],"graph_snapshots":[{"event_id":"sha256:2359152431afaf5492bcb574d44413958c7cf5254f6d84ec60cc4bfb02540798","target":"graph","created_at":"2026-07-05T08:32:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.10674/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $A$ be an annulus in the plane $\\mathbb R^2$ and $g:A\\rightarrow A$ be a boundary components preserving homeomorphism which is distal and has no periodic points. Then there is a continuous decomposition of $A$ into $g$-invariant circles such that all the restrictions of $g$ on them share a common irrational rotation number and all these circles are linearly ordered by the inclusion relation on the sets of bounded components of their complements in $\\mathbb R^2$.","authors_text":"Enhui Shi, Hui Xu, Ziqi Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-15T15:46:19Z","title":"The structure of periodic point free distal homeomorphisms on the annulus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.10674","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":"sha256:51c9391c22fd2cad4b6c09411ba4e8476a71d51d8327abdece95fea19ae6d0c3","target":"record","created_at":"2026-07-05T08:32:20Z","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":"34b40096e6b4bff1983a8de5f382c4df0cc31f3289e05755824944d8d8c2adbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-15T15:46:19Z","title_canon_sha256":"b1f77ed42564b419ee362fc50bbc17c613c41b7c9c6b65fdadf77bacf2f504c8"},"schema_version":"1.0","source":{"id":"2406.10674","kind":"arxiv","version":1}},"canonical_sha256":"b193b1d1c697ecac6a2c573aafa2f80912582664bbaf314a854eb9ec2709367a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b193b1d1c697ecac6a2c573aafa2f80912582664bbaf314a854eb9ec2709367a","first_computed_at":"2026-07-05T08:32:20.147794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:32:20.147794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qtIaPOxxg/1TkKe/18QkpZLHYzwSROaNAJykpyFsl3FHSoCn0prsyaqnxxczZwhaX+Bsx60gg2EPwG2XChacAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:32:20.148251Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.10674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51c9391c22fd2cad4b6c09411ba4e8476a71d51d8327abdece95fea19ae6d0c3","sha256:2359152431afaf5492bcb574d44413958c7cf5254f6d84ec60cc4bfb02540798"],"state_sha256":"1e31abdc7e16d597fa40ef424e3f5fe476b19bb7806e1c5de9b72b81512feaa6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ax+WL/55TVXBBHHfwYtdbjTEsCDKPA1j51To9GOlrpaTKHX9rR5hRRg+DuLLAoAYV9dMu7gfeXcHveixGszfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-18T11:50:47.405328Z","bundle_sha256":"140c1ef83a460ae0069f8a8c5a646f2b8a442bf1a475638900d9e5adf2121753"}}