{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CXO5SBVT2VVM72NUC5PAZ4SU5X","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":"30d2711783bbdaddbdb942a4436fd6f13551d1fea7fb1a13f4100c77a7bac163","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2026-08-06T13:58:29Z","title_canon_sha256":"b5db218204c86e829124651eddc3e305f25c1422765eb99e0a8d00303ed08f02"},"schema_version":"1.0","source":{"id":"2608.06051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06051","created_at":"2026-08-07T01:39:45Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06051v1","created_at":"2026-08-07T01:39:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06051","created_at":"2026-08-07T01:39:45Z"},{"alias_kind":"pith_short_12","alias_value":"CXO5SBVT2VVM","created_at":"2026-08-07T01:39:45Z"},{"alias_kind":"pith_short_16","alias_value":"CXO5SBVT2VVM72NU","created_at":"2026-08-07T01:39:45Z"},{"alias_kind":"pith_short_8","alias_value":"CXO5SBVT","created_at":"2026-08-07T01:39:45Z"}],"graph_snapshots":[{"event_id":"sha256:0fc60cb45506f6d966a54442659881264115f9dc8d248af55c5c362ed0843752","target":"graph","created_at":"2026-08-07T01:39:45Z","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/2608.06051/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For various definitions of fractal dimension that are finitely stable, including upper box dimension, upper intermediate dimensions and Assouad spectra, we show that, given a compact subset $E$ of a metric space, typically $R^n$, there is a convergent sequence of points contained in $E$ of the same dimension as $E$ itself. Moreover, under certain conditions it is possible for a sequence to witness the dimension of $E$ for many definitions of dimension simultaneously, for example in a self-affine set $E$ there is a single convergent sequence that has the same Assouad spectrum or intermediate di","authors_text":"Kenneth Falconer, Yuyang Liu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2026-08-06T13:58:29Z","title":"The sequence property for fractal dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06051","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":"sha256:25e52342df086a09345fef69f597ef1a3ef20cc766606f4ef1665263379088d8","target":"record","created_at":"2026-08-07T01:39:45Z","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":"30d2711783bbdaddbdb942a4436fd6f13551d1fea7fb1a13f4100c77a7bac163","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2026-08-06T13:58:29Z","title_canon_sha256":"b5db218204c86e829124651eddc3e305f25c1422765eb99e0a8d00303ed08f02"},"schema_version":"1.0","source":{"id":"2608.06051","kind":"arxiv","version":1}},"canonical_sha256":"15ddd906b3d56acfe9b4175e0cf254edc3e9d03b03ce039cb0fae921050d6c12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15ddd906b3d56acfe9b4175e0cf254edc3e9d03b03ce039cb0fae921050d6c12","first_computed_at":"2026-08-07T01:39:45.418291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T01:39:45.418291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JJy6PKS+Bn3XqUOABQXHjkDZUWYBpey8BrzdydcSTYOy/tf1pTOSl0DF6ADp7n6ASl6F+VjbtSnglnDeXTx2Dw==","signature_status":"signed_v1","signed_at":"2026-08-07T01:39:45.419937Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25e52342df086a09345fef69f597ef1a3ef20cc766606f4ef1665263379088d8","sha256:0fc60cb45506f6d966a54442659881264115f9dc8d248af55c5c362ed0843752"],"state_sha256":"b06d96f75c170375669bf00ad3c8a05c09960159c19649e0400118fbe8342dab"}