{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VSRGCX2RGQP4VKFUXWT6CQASZP","short_pith_number":"pith:VSRGCX2R","canonical_record":{"source":{"id":"1304.8127","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-30T19:29:35Z","cross_cats_sorted":[],"title_canon_sha256":"0c8a0321e0d531c36aada4d6399aff08cc4177f1e3c11ce8ca9afc1426c8e3c0","abstract_canon_sha256":"969f512cca8451a1d3012b1a5de177eb504008f5935ae6274f99bdf58875088b"},"schema_version":"1.0"},"canonical_sha256":"aca2615f51341fcaa8b4bda7e14012cbc1419027f73bc2144f1fa0f76f93d721","source":{"kind":"arxiv","id":"1304.8127","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.8127","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.8127v2","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.8127","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"pith_short_12","alias_value":"VSRGCX2RGQP4","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VSRGCX2RGQP4VKFU","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VSRGCX2R","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VSRGCX2RGQP4VKFUXWT6CQASZP","target":"record","payload":{"canonical_record":{"source":{"id":"1304.8127","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-30T19:29:35Z","cross_cats_sorted":[],"title_canon_sha256":"0c8a0321e0d531c36aada4d6399aff08cc4177f1e3c11ce8ca9afc1426c8e3c0","abstract_canon_sha256":"969f512cca8451a1d3012b1a5de177eb504008f5935ae6274f99bdf58875088b"},"schema_version":"1.0"},"canonical_sha256":"aca2615f51341fcaa8b4bda7e14012cbc1419027f73bc2144f1fa0f76f93d721","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:17.242566Z","signature_b64":"Kr/4Qap2CFxz6LqaWyaSR2ZcyXk4ZIPjn9lrUlPXpjew0nTjcGrEl8EXIS2afwiRJrefcKyr21v3TnJPr8X8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aca2615f51341fcaa8b4bda7e14012cbc1419027f73bc2144f1fa0f76f93d721","last_reissued_at":"2026-05-18T02:41:17.242119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:17.242119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.8127","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qnBPTan923xIVzX1UBI4R30Z0knmWmqD+4Sf+K0LjrQAncu2m7tC0q8EWXCwnfFBMHnmwY7dVJ5sGODrNeODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T07:58:46.103707Z"},"content_sha256":"2208804f2070d5162307d34683d9fc183b41e7c79f98d3d93848e8ee7ee722c8","schema_version":"1.0","event_id":"sha256:2208804f2070d5162307d34683d9fc183b41e7c79f98d3d93848e8ee7ee722c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VSRGCX2RGQP4VKFUXWT6CQASZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological mixing for some residual sets of interval exchange transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jon Chaika, Jon Fickenscher","submitted_at":"2013-04-30T19:29:35Z","abstract_excerpt":"We show that a residual set of non-degenerate IETs on more than 3 letters is topologically mixing. This shows that there exists a uniquely ergodic topologically mixing IET. This is then applied to show that some billiard flows in a fixed direction in an L-shaped polygon are topologically mixing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8127","kind":"arxiv","version":2},"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":"2026-05-18T02:41:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Og/CCcYMm3NRYOEC10FD/EyDYtwpEZqyv06GYur0+2dcfFXl9lkBB1Lbyt0FQiD170opsVrWGPLnO9gnHaQ/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T07:58:46.104389Z"},"content_sha256":"a5295183332054fa392e70ee3ed25d55b3795119848244970c8aca642394e438","schema_version":"1.0","event_id":"sha256:a5295183332054fa392e70ee3ed25d55b3795119848244970c8aca642394e438"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSRGCX2RGQP4VKFUXWT6CQASZP/bundle.json","state_url":"https://pith.science/pith/VSRGCX2RGQP4VKFUXWT6CQASZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSRGCX2RGQP4VKFUXWT6CQASZP/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":"2026-05-22T07:58:46Z","links":{"resolver":"https://pith.science/pith/VSRGCX2RGQP4VKFUXWT6CQASZP","bundle":"https://pith.science/pith/VSRGCX2RGQP4VKFUXWT6CQASZP/bundle.json","state":"https://pith.science/pith/VSRGCX2RGQP4VKFUXWT6CQASZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSRGCX2RGQP4VKFUXWT6CQASZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VSRGCX2RGQP4VKFUXWT6CQASZP","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":"969f512cca8451a1d3012b1a5de177eb504008f5935ae6274f99bdf58875088b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-30T19:29:35Z","title_canon_sha256":"0c8a0321e0d531c36aada4d6399aff08cc4177f1e3c11ce8ca9afc1426c8e3c0"},"schema_version":"1.0","source":{"id":"1304.8127","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.8127","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.8127v2","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.8127","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"pith_short_12","alias_value":"VSRGCX2RGQP4","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VSRGCX2RGQP4VKFU","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VSRGCX2R","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:a5295183332054fa392e70ee3ed25d55b3795119848244970c8aca642394e438","target":"graph","created_at":"2026-05-18T02:41:17Z","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 show that a residual set of non-degenerate IETs on more than 3 letters is topologically mixing. This shows that there exists a uniquely ergodic topologically mixing IET. This is then applied to show that some billiard flows in a fixed direction in an L-shaped polygon are topologically mixing.","authors_text":"Jon Chaika, Jon Fickenscher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-30T19:29:35Z","title":"Topological mixing for some residual sets of interval exchange transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8127","kind":"arxiv","version":2},"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":"sha256:2208804f2070d5162307d34683d9fc183b41e7c79f98d3d93848e8ee7ee722c8","target":"record","created_at":"2026-05-18T02:41:17Z","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":"969f512cca8451a1d3012b1a5de177eb504008f5935ae6274f99bdf58875088b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-30T19:29:35Z","title_canon_sha256":"0c8a0321e0d531c36aada4d6399aff08cc4177f1e3c11ce8ca9afc1426c8e3c0"},"schema_version":"1.0","source":{"id":"1304.8127","kind":"arxiv","version":2}},"canonical_sha256":"aca2615f51341fcaa8b4bda7e14012cbc1419027f73bc2144f1fa0f76f93d721","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aca2615f51341fcaa8b4bda7e14012cbc1419027f73bc2144f1fa0f76f93d721","first_computed_at":"2026-05-18T02:41:17.242119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:17.242119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kr/4Qap2CFxz6LqaWyaSR2ZcyXk4ZIPjn9lrUlPXpjew0nTjcGrEl8EXIS2afwiRJrefcKyr21v3TnJPr8X8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:17.242566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.8127","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2208804f2070d5162307d34683d9fc183b41e7c79f98d3d93848e8ee7ee722c8","sha256:a5295183332054fa392e70ee3ed25d55b3795119848244970c8aca642394e438"],"state_sha256":"00ba746a2354bfa2955d4dd962906636f4f872a2167052a5f7bec4e29d5e15f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PX7Pgd1T59b8dPoZnM7zNO0abFAXxDJ+VzFeA0xq0cL5yFxlizVScAZEbuVPQLR4RnOZAs+8W/RvGK/Ni0h6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T07:58:46.108389Z","bundle_sha256":"3d932f4235770652206be02b13a91143357d3708ee7033a1745f8aa97b5dc2ef"}}