{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:P2UOTEXYYKUTATE5KYKCF2PTCI","short_pith_number":"pith:P2UOTEXY","schema_version":"1.0","canonical_sha256":"7ea8e992f8c2a9304c9d561422e9f312342eedc8740899621e77993590ef2011","source":{"kind":"arxiv","id":"1609.07360","version":2},"attestation_state":"computed","paper":{"title":"Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Antti K\\\"aenm\\\"aki, Ian D. Morris","submitted_at":"2016-09-23T13:36:13Z","abstract_excerpt":"A fundamental problem in the dimension theory of self-affine sets is the construction of high-dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction of such high-dimensional measures is to investigate measures of maximal Lyapunov dimension; these measures can be alternatively interpreted as equilibrium states of the singular value function introduced by Falconer. Whilst the existence of these equilibrium states has been well-known for some years their structure has remained elusive, particularly in dimensions higher t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.07360","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-23T13:36:13Z","cross_cats_sorted":[],"title_canon_sha256":"c38aaa7bf30c199df6f260df2dc356c3623c89f2a6acee5a5c49c510f039edd4","abstract_canon_sha256":"6093303cbbd8ef17d38ef2f23a6d2e7cc1e433079493e5add2bcacca96b71636"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:38.053505Z","signature_b64":"52N2ZripOpKZEOnUYoc719SrGPSnEEr6LTFlFKh6zQHtWUVmPFisAG/pyuCOtj2l4r6Xp2MN2u7/8pZ2gBC0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ea8e992f8c2a9304c9d561422e9f312342eedc8740899621e77993590ef2011","last_reissued_at":"2026-05-18T00:15:38.053007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:38.053007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Antti K\\\"aenm\\\"aki, Ian D. Morris","submitted_at":"2016-09-23T13:36:13Z","abstract_excerpt":"A fundamental problem in the dimension theory of self-affine sets is the construction of high-dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction of such high-dimensional measures is to investigate measures of maximal Lyapunov dimension; these measures can be alternatively interpreted as equilibrium states of the singular value function introduced by Falconer. Whilst the existence of these equilibrium states has been well-known for some years their structure has remained elusive, particularly in dimensions higher t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07360","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.07360","created_at":"2026-05-18T00:15:38.053070+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07360v2","created_at":"2026-05-18T00:15:38.053070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07360","created_at":"2026-05-18T00:15:38.053070+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2UOTEXYYKUT","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2UOTEXYYKUTATE5","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2UOTEXY","created_at":"2026-05-18T12:30:36.002864+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P2UOTEXYYKUTATE5KYKCF2PTCI","json":"https://pith.science/pith/P2UOTEXYYKUTATE5KYKCF2PTCI.json","graph_json":"https://pith.science/api/pith-number/P2UOTEXYYKUTATE5KYKCF2PTCI/graph.json","events_json":"https://pith.science/api/pith-number/P2UOTEXYYKUTATE5KYKCF2PTCI/events.json","paper":"https://pith.science/paper/P2UOTEXY"},"agent_actions":{"view_html":"https://pith.science/pith/P2UOTEXYYKUTATE5KYKCF2PTCI","download_json":"https://pith.science/pith/P2UOTEXYYKUTATE5KYKCF2PTCI.json","view_paper":"https://pith.science/paper/P2UOTEXY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07360&json=true","fetch_graph":"https://pith.science/api/pith-number/P2UOTEXYYKUTATE5KYKCF2PTCI/graph.json","fetch_events":"https://pith.science/api/pith-number/P2UOTEXYYKUTATE5KYKCF2PTCI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2UOTEXYYKUTATE5KYKCF2PTCI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2UOTEXYYKUTATE5KYKCF2PTCI/action/storage_attestation","attest_author":"https://pith.science/pith/P2UOTEXYYKUTATE5KYKCF2PTCI/action/author_attestation","sign_citation":"https://pith.science/pith/P2UOTEXYYKUTATE5KYKCF2PTCI/action/citation_signature","submit_replication":"https://pith.science/pith/P2UOTEXYYKUTATE5KYKCF2PTCI/action/replication_record"}},"created_at":"2026-05-18T00:15:38.053070+00:00","updated_at":"2026-05-18T00:15:38.053070+00:00"}