{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1992:SL73YFVZIHKPB2FRXEJC7JDEL5","short_pith_number":"pith:SL73YFVZ","canonical_record":{"source":{"id":"math/9209220","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1992-09-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"1d46b45e279e9792796298f41eeaf165ae288ad014948076b0b79cc1d14ff1d3","abstract_canon_sha256":"8dc7f98c80298d9fcc794000ad43c867915bfcc2c4e2e52fdf5c5e0c8c9635fe"},"schema_version":"1.0"},"canonical_sha256":"92ffbc16b941d4f0e8b1b9122fa4645f65c018e5a08706c8473192eaf35a4d99","source":{"kind":"arxiv","id":"math/9209220","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9209220","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9209220v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9209220","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"SL73YFVZIHKP","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"SL73YFVZIHKPB2FR","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"SL73YFVZ","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1992:SL73YFVZIHKPB2FRXEJC7JDEL5","target":"record","payload":{"canonical_record":{"source":{"id":"math/9209220","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1992-09-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"1d46b45e279e9792796298f41eeaf165ae288ad014948076b0b79cc1d14ff1d3","abstract_canon_sha256":"8dc7f98c80298d9fcc794000ad43c867915bfcc2c4e2e52fdf5c5e0c8c9635fe"},"schema_version":"1.0"},"canonical_sha256":"92ffbc16b941d4f0e8b1b9122fa4645f65c018e5a08706c8473192eaf35a4d99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:52.631998Z","signature_b64":"NrQhHwn5jFkKrkQbIjDdb/NQPA5rwQ4RKUTDlVx9lPndBnQvsCtEoVNA/czVPol/XjCE2sg62S2t1ggmwUk/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92ffbc16b941d4f0e8b1b9122fa4645f65c018e5a08706c8473192eaf35a4d99","last_reissued_at":"2026-05-18T01:05:52.631445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:52.631445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9209220","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":"2026-05-18T01:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y6aSGAcHbo7JHkqKTPUN8AYO4TUi2Uv9wAhOKmv2WN8vUS0cIuz2ZPpEvxs6zgIKZJqEpVRrB5xqYXrwc6LPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T18:13:55.803658Z"},"content_sha256":"96fa4a860912fa1a074dbd041d3ba2648a39c790e7a97e53b0f98bd99f64c6d1","schema_version":"1.0","event_id":"sha256:96fa4a860912fa1a074dbd041d3ba2648a39c790e7a97e53b0f98bd99f64c6d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1992:SL73YFVZIHKPB2FRXEJC7JDEL5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak disks of Denjoy minimal sets","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Philip Boyland","submitted_at":"1992-09-01T00:00:00Z","abstract_excerpt":"This paper investigates the existence of Denjoy minimal sets and, more generally, strictly ergodic sets in the dynamics of iterated homeomorphisms. It is shown that for the full two-shift, the collection of such invariant sets with the weak topology contains topological balls of all finite dimensions. One implication is an analogous result that holds for diffeomorphisms with transverse homoclinic points. It is also shown that the union of Denjoy minimal sets is dense in the two-shift and that the set of unique probability measures supported on these sets is weakly dense in the set of all shift"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9209220","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":"2026-05-18T01:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fNMiJWSSH6VK15XiClPVcW/bkMI0c/ZoV9BIK6lEKmTzIRqzA4G9nzwX/BY2jVlFQcOPa7AtxO9bPqAo2X4FAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T18:13:55.803987Z"},"content_sha256":"8bf587b196181fc702392bad11a97c570fd423a30210e2a026b71f2aecc58ba2","schema_version":"1.0","event_id":"sha256:8bf587b196181fc702392bad11a97c570fd423a30210e2a026b71f2aecc58ba2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SL73YFVZIHKPB2FRXEJC7JDEL5/bundle.json","state_url":"https://pith.science/pith/SL73YFVZIHKPB2FRXEJC7JDEL5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SL73YFVZIHKPB2FRXEJC7JDEL5/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":"2026-07-03T18:13:55Z","links":{"resolver":"https://pith.science/pith/SL73YFVZIHKPB2FRXEJC7JDEL5","bundle":"https://pith.science/pith/SL73YFVZIHKPB2FRXEJC7JDEL5/bundle.json","state":"https://pith.science/pith/SL73YFVZIHKPB2FRXEJC7JDEL5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SL73YFVZIHKPB2FRXEJC7JDEL5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:SL73YFVZIHKPB2FRXEJC7JDEL5","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":"8dc7f98c80298d9fcc794000ad43c867915bfcc2c4e2e52fdf5c5e0c8c9635fe","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1992-09-01T00:00:00Z","title_canon_sha256":"1d46b45e279e9792796298f41eeaf165ae288ad014948076b0b79cc1d14ff1d3"},"schema_version":"1.0","source":{"id":"math/9209220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9209220","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9209220v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9209220","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"SL73YFVZIHKP","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"SL73YFVZIHKPB2FR","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"SL73YFVZ","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:8bf587b196181fc702392bad11a97c570fd423a30210e2a026b71f2aecc58ba2","target":"graph","created_at":"2026-05-18T01:05:52Z","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":"This paper investigates the existence of Denjoy minimal sets and, more generally, strictly ergodic sets in the dynamics of iterated homeomorphisms. It is shown that for the full two-shift, the collection of such invariant sets with the weak topology contains topological balls of all finite dimensions. One implication is an analogous result that holds for diffeomorphisms with transverse homoclinic points. It is also shown that the union of Denjoy minimal sets is dense in the two-shift and that the set of unique probability measures supported on these sets is weakly dense in the set of all shift","authors_text":"Philip Boyland","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"1992-09-01T00:00:00Z","title":"Weak disks of Denjoy minimal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9209220","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":"sha256:96fa4a860912fa1a074dbd041d3ba2648a39c790e7a97e53b0f98bd99f64c6d1","target":"record","created_at":"2026-05-18T01:05:52Z","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":"8dc7f98c80298d9fcc794000ad43c867915bfcc2c4e2e52fdf5c5e0c8c9635fe","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1992-09-01T00:00:00Z","title_canon_sha256":"1d46b45e279e9792796298f41eeaf165ae288ad014948076b0b79cc1d14ff1d3"},"schema_version":"1.0","source":{"id":"math/9209220","kind":"arxiv","version":1}},"canonical_sha256":"92ffbc16b941d4f0e8b1b9122fa4645f65c018e5a08706c8473192eaf35a4d99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92ffbc16b941d4f0e8b1b9122fa4645f65c018e5a08706c8473192eaf35a4d99","first_computed_at":"2026-05-18T01:05:52.631445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:52.631445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NrQhHwn5jFkKrkQbIjDdb/NQPA5rwQ4RKUTDlVx9lPndBnQvsCtEoVNA/czVPol/XjCE2sg62S2t1ggmwUk/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:52.631998Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9209220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96fa4a860912fa1a074dbd041d3ba2648a39c790e7a97e53b0f98bd99f64c6d1","sha256:8bf587b196181fc702392bad11a97c570fd423a30210e2a026b71f2aecc58ba2"],"state_sha256":"06e386f1ba7b34055bef1defe3f132bda3f8ac67c22d4e4b7fd46cf8b1315508"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rBqua0eZ3W+p2yh7B/Yp0R7LoHmL+4StbSNvlJDISWOsa/qqTrPxRtes6MuCeB0/OKR3hMBwiEjqMXvb5utgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T18:13:55.805791Z","bundle_sha256":"0ea22aabc6c233efd7675093eb3ef436f2eaffe3db98a894965252e9b5ed210c"}}