{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IJ7G52XEHUYWI2C5AN4DT5S5ZG","short_pith_number":"pith:IJ7G52XE","canonical_record":{"source":{"id":"1803.10129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-27T15:20:35Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"1e5cefa2533cb0060ca392723fd0264394d73b8b440f79005889ed191cb06af3","abstract_canon_sha256":"217de28e638f21edeb0df2f6ed7f42ed90e67c44cc8dcf9bd4ed29340f26f349"},"schema_version":"1.0"},"canonical_sha256":"427e6eeae43d3164685d037839f65dc99658500b336f5cf1af2a2b720ab393b6","source":{"kind":"arxiv","id":"1803.10129","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10129","created_at":"2026-05-18T00:20:00Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10129v1","created_at":"2026-05-18T00:20:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10129","created_at":"2026-05-18T00:20:00Z"},{"alias_kind":"pith_short_12","alias_value":"IJ7G52XEHUYW","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IJ7G52XEHUYWI2C5","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IJ7G52XE","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IJ7G52XEHUYWI2C5AN4DT5S5ZG","target":"record","payload":{"canonical_record":{"source":{"id":"1803.10129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-27T15:20:35Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"1e5cefa2533cb0060ca392723fd0264394d73b8b440f79005889ed191cb06af3","abstract_canon_sha256":"217de28e638f21edeb0df2f6ed7f42ed90e67c44cc8dcf9bd4ed29340f26f349"},"schema_version":"1.0"},"canonical_sha256":"427e6eeae43d3164685d037839f65dc99658500b336f5cf1af2a2b720ab393b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:00.355112Z","signature_b64":"rGcHAaB4nJHeW19mnR/KPMX8kz0e9y8CbYR/S49uSE23L7+Xhs3D0REvkUvJHLtOMfQL1nvcTYhK8cF51cruDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"427e6eeae43d3164685d037839f65dc99658500b336f5cf1af2a2b720ab393b6","last_reissued_at":"2026-05-18T00:20:00.354434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:00.354434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.10129","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":"2026-05-18T00:20:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CWOrmg05mxXwY48J/304n4gTU6CkWr3uqFKj3A6M/ca0ux8SdhoYM4u/zUbE7EUPSIYUEXj3CxX76VMceGa0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:34:05.352258Z"},"content_sha256":"39988b0f635b78315870a9a85e6adb63466308a1172e8fb93dddfa68af5cf275","schema_version":"1.0","event_id":"sha256:39988b0f635b78315870a9a85e6adb63466308a1172e8fb93dddfa68af5cf275"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IJ7G52XEHUYWI2C5AN4DT5S5ZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Teichm\\\"uller dynamics, dilation tori and piecewise affine circle homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"Selim Ghazouani","submitted_at":"2018-03-27T15:20:35Z","abstract_excerpt":"We study the coarse geometry of the moduli space of dilation tori with two singularities and the dynamical properties of the action of the Teichmuller flow on this moduli space. This leads to a proof that the vertical foliation of a dilation torus is almost always Morse-Smale. As a corollary, we get that the generic piecewise affine circle homeomorphism with two break points -with respect to the Lebesgue measure- is Morse-Smale."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10129","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":"2026-05-18T00:20:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FfOkdxnJ62dDMQAxAOoQWRNgUmVibbDjWImG0NsJu20Iu/z/cwKUmUcImlseAns27BikAA3TLO6T/lxRO0shDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:34:05.352869Z"},"content_sha256":"c2f061e1324f0b5b0d280bcd7c0524f5f3d1cc1719639771a4d8a17508cf3d7c","schema_version":"1.0","event_id":"sha256:c2f061e1324f0b5b0d280bcd7c0524f5f3d1cc1719639771a4d8a17508cf3d7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJ7G52XEHUYWI2C5AN4DT5S5ZG/bundle.json","state_url":"https://pith.science/pith/IJ7G52XEHUYWI2C5AN4DT5S5ZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJ7G52XEHUYWI2C5AN4DT5S5ZG/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":"2026-06-04T20:34:05Z","links":{"resolver":"https://pith.science/pith/IJ7G52XEHUYWI2C5AN4DT5S5ZG","bundle":"https://pith.science/pith/IJ7G52XEHUYWI2C5AN4DT5S5ZG/bundle.json","state":"https://pith.science/pith/IJ7G52XEHUYWI2C5AN4DT5S5ZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJ7G52XEHUYWI2C5AN4DT5S5ZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IJ7G52XEHUYWI2C5AN4DT5S5ZG","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":"217de28e638f21edeb0df2f6ed7f42ed90e67c44cc8dcf9bd4ed29340f26f349","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-27T15:20:35Z","title_canon_sha256":"1e5cefa2533cb0060ca392723fd0264394d73b8b440f79005889ed191cb06af3"},"schema_version":"1.0","source":{"id":"1803.10129","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10129","created_at":"2026-05-18T00:20:00Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10129v1","created_at":"2026-05-18T00:20:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10129","created_at":"2026-05-18T00:20:00Z"},{"alias_kind":"pith_short_12","alias_value":"IJ7G52XEHUYW","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IJ7G52XEHUYWI2C5","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IJ7G52XE","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:c2f061e1324f0b5b0d280bcd7c0524f5f3d1cc1719639771a4d8a17508cf3d7c","target":"graph","created_at":"2026-05-18T00:20:00Z","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 coarse geometry of the moduli space of dilation tori with two singularities and the dynamical properties of the action of the Teichmuller flow on this moduli space. This leads to a proof that the vertical foliation of a dilation torus is almost always Morse-Smale. As a corollary, we get that the generic piecewise affine circle homeomorphism with two break points -with respect to the Lebesgue measure- is Morse-Smale.","authors_text":"Selim Ghazouani","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-27T15:20:35Z","title":"Teichm\\\"uller dynamics, dilation tori and piecewise affine circle homeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10129","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":"sha256:39988b0f635b78315870a9a85e6adb63466308a1172e8fb93dddfa68af5cf275","target":"record","created_at":"2026-05-18T00:20:00Z","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":"217de28e638f21edeb0df2f6ed7f42ed90e67c44cc8dcf9bd4ed29340f26f349","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-27T15:20:35Z","title_canon_sha256":"1e5cefa2533cb0060ca392723fd0264394d73b8b440f79005889ed191cb06af3"},"schema_version":"1.0","source":{"id":"1803.10129","kind":"arxiv","version":1}},"canonical_sha256":"427e6eeae43d3164685d037839f65dc99658500b336f5cf1af2a2b720ab393b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"427e6eeae43d3164685d037839f65dc99658500b336f5cf1af2a2b720ab393b6","first_computed_at":"2026-05-18T00:20:00.354434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:00.354434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rGcHAaB4nJHeW19mnR/KPMX8kz0e9y8CbYR/S49uSE23L7+Xhs3D0REvkUvJHLtOMfQL1nvcTYhK8cF51cruDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:00.355112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10129","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39988b0f635b78315870a9a85e6adb63466308a1172e8fb93dddfa68af5cf275","sha256:c2f061e1324f0b5b0d280bcd7c0524f5f3d1cc1719639771a4d8a17508cf3d7c"],"state_sha256":"2733df1e9a89473ce6e11d99d0baaf55fa5dc14cbd50ffedac1f79343e99e1ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btBx0AaAhREJi0ptVmxd05eY01vI96w+kNuRHYA70KcW38dYnCuBxRZ0jIs+vGK/hMNI9C2ihCNtUJoE+863Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:34:05.356091Z","bundle_sha256":"cf09f29605242f453c7f985628606c6f8b23cf6270e3b50e5aba590e660a813e"}}