{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:V7BLWNFPL3VUZ4SFRFSBJR4CI4","short_pith_number":"pith:V7BLWNFP","canonical_record":{"source":{"id":"1111.6574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T20:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"6bd58d7c93cddc5939bf7e10d6a0b024676e875b143ef80631e62864c490cba0","abstract_canon_sha256":"67187d70c0314825d1cf303732a2e2226daea8204445b9945eb4c309a05ce784"},"schema_version":"1.0"},"canonical_sha256":"afc2bb34af5eeb4cf245896414c782470972316a0d329f87a3322215203d0075","source":{"kind":"arxiv","id":"1111.6574","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6574","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6574v2","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6574","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"pith_short_12","alias_value":"V7BLWNFPL3VU","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V7BLWNFPL3VUZ4SF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V7BLWNFP","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:V7BLWNFPL3VUZ4SFRFSBJR4CI4","target":"record","payload":{"canonical_record":{"source":{"id":"1111.6574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T20:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"6bd58d7c93cddc5939bf7e10d6a0b024676e875b143ef80631e62864c490cba0","abstract_canon_sha256":"67187d70c0314825d1cf303732a2e2226daea8204445b9945eb4c309a05ce784"},"schema_version":"1.0"},"canonical_sha256":"afc2bb34af5eeb4cf245896414c782470972316a0d329f87a3322215203d0075","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:08.069801Z","signature_b64":"dmP6FSLB1ndOlmiUyMsUi9HfkJ+9zts0lP9y+30GsraFCTr5vPhLoJNSgz85Q14dpwFJInVHMnGNXR0T82olBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afc2bb34af5eeb4cf245896414c782470972316a0d329f87a3322215203d0075","last_reissued_at":"2026-05-18T03:32:08.069130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:08.069130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.6574","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":"2026-05-18T03:32:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"okqyDB55xlo1eEKSOc2YAVAll5aJuF7RKe77SLxflf+UTjyQkU5AzDaSPaeGOFjTXXVbSpyH8KI/PAU8r/aiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T18:38:28.201913Z"},"content_sha256":"208034ad3515280444246078865493f1919d0cbf5dd7c46f7ee19220f9e02ccc","schema_version":"1.0","event_id":"sha256:208034ad3515280444246078865493f1919d0cbf5dd7c46f7ee19220f9e02ccc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:V7BLWNFPL3VUZ4SFRFSBJR4CI4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimensions of attractors in pinched skew products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"M. Gr\\\"oger, T. J\\\"ager","submitted_at":"2011-11-28T20:33:57Z","abstract_excerpt":"We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6574","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":"2026-05-18T03:32:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n1S66CYL0YCYGghNE7Q+NQ0WqaL0jEIHZrvDzdtiBPKhlDZ2fcVy82m7ZaSj87E8DQs+VMt9SZDCa1jKXur9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T18:38:28.202298Z"},"content_sha256":"47b6c3673278dbef3d89d53782d071a36a4ed9863b25d97d759fdc7667c67b76","schema_version":"1.0","event_id":"sha256:47b6c3673278dbef3d89d53782d071a36a4ed9863b25d97d759fdc7667c67b76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7BLWNFPL3VUZ4SFRFSBJR4CI4/bundle.json","state_url":"https://pith.science/pith/V7BLWNFPL3VUZ4SFRFSBJR4CI4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7BLWNFPL3VUZ4SFRFSBJR4CI4/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":"2026-06-29T18:38:28Z","links":{"resolver":"https://pith.science/pith/V7BLWNFPL3VUZ4SFRFSBJR4CI4","bundle":"https://pith.science/pith/V7BLWNFPL3VUZ4SFRFSBJR4CI4/bundle.json","state":"https://pith.science/pith/V7BLWNFPL3VUZ4SFRFSBJR4CI4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7BLWNFPL3VUZ4SFRFSBJR4CI4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V7BLWNFPL3VUZ4SFRFSBJR4CI4","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":"67187d70c0314825d1cf303732a2e2226daea8204445b9945eb4c309a05ce784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T20:33:57Z","title_canon_sha256":"6bd58d7c93cddc5939bf7e10d6a0b024676e875b143ef80631e62864c490cba0"},"schema_version":"1.0","source":{"id":"1111.6574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6574","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6574v2","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6574","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"pith_short_12","alias_value":"V7BLWNFPL3VU","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V7BLWNFPL3VUZ4SF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V7BLWNFP","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:47b6c3673278dbef3d89d53782d071a36a4ed9863b25d97d759fdc7667c67b76","target":"graph","created_at":"2026-05-18T03:32:08Z","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 dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989.","authors_text":"M. Gr\\\"oger, T. J\\\"ager","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T20:33:57Z","title":"Dimensions of attractors in pinched skew products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6574","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":"sha256:208034ad3515280444246078865493f1919d0cbf5dd7c46f7ee19220f9e02ccc","target":"record","created_at":"2026-05-18T03:32:08Z","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":"67187d70c0314825d1cf303732a2e2226daea8204445b9945eb4c309a05ce784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T20:33:57Z","title_canon_sha256":"6bd58d7c93cddc5939bf7e10d6a0b024676e875b143ef80631e62864c490cba0"},"schema_version":"1.0","source":{"id":"1111.6574","kind":"arxiv","version":2}},"canonical_sha256":"afc2bb34af5eeb4cf245896414c782470972316a0d329f87a3322215203d0075","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afc2bb34af5eeb4cf245896414c782470972316a0d329f87a3322215203d0075","first_computed_at":"2026-05-18T03:32:08.069130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:08.069130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dmP6FSLB1ndOlmiUyMsUi9HfkJ+9zts0lP9y+30GsraFCTr5vPhLoJNSgz85Q14dpwFJInVHMnGNXR0T82olBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:08.069801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:208034ad3515280444246078865493f1919d0cbf5dd7c46f7ee19220f9e02ccc","sha256:47b6c3673278dbef3d89d53782d071a36a4ed9863b25d97d759fdc7667c67b76"],"state_sha256":"5e11a2c9fa5cf9ee368c06b7efb188113333598f21eda3cd3c0f0713e88c1f8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C1GvFiP2aIxMhyaDSDnk2dGyOVhVbQN2PFHWt5ApthsjQpF2AhHeHIhU1nmhQ2++nqCvfhXiqa13C4l3flGcBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T18:38:28.204168Z","bundle_sha256":"ed64816aa898cf718b0cc118a8f200a9707989e054a9ce11371b6ab3f41bbb81"}}