{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5DONGLU7PHBHTDELKJF3BGJL5G","short_pith_number":"pith:5DONGLU7","schema_version":"1.0","canonical_sha256":"e8dcd32e9f79c2798c8b524bb0992be9bf87344bb85ae93c0a1fb99fd9dca4c5","source":{"kind":"arxiv","id":"2603.17091","version":3},"attestation_state":"computed","paper":{"title":"On quantization and the classical variational principle for the metric mean dimension","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gustavo Pessil, Maria Carvalho","submitted_at":"2026-03-17T19:25:09Z","abstract_excerpt":"This paper investigates the relationship between quantization of measures and metric mean dimension of topological dynamical systems. We introduce the concept of mean quantization dimension for invariant probability measures and establish a classical variational principle: the metric mean dimension of a dynamical system is equal to the maximum mean quantization dimension among all invariant measures. This approach effectively characterizes the complexity of systems with infinite entropy by identifying a measure that captures information across all scales; and yields a fundamental property that"},"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":"2603.17091","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-03-17T19:25:09Z","cross_cats_sorted":[],"title_canon_sha256":"912114a55b591019f53d66112f20d8cc1dadd5f98e2453e7ab304c71b3307c61","abstract_canon_sha256":"f9261d81492558b396793e2934e2fac6e0ab698ea0874d11308b6d1ad4afc149"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T02:05:01.191242Z","signature_b64":"80DYeIKlDzsEsRTaTYBrKn7MB9xCie18cynHUk+QvI+LPwytsveRcpnLB6wtYJxQYsULT8+tVVi7Vx9hOfjLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8dcd32e9f79c2798c8b524bb0992be9bf87344bb85ae93c0a1fb99fd9dca4c5","last_reissued_at":"2026-05-21T02:05:01.190542Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T02:05:01.190542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On quantization and the classical variational principle for the metric mean dimension","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gustavo Pessil, Maria Carvalho","submitted_at":"2026-03-17T19:25:09Z","abstract_excerpt":"This paper investigates the relationship between quantization of measures and metric mean dimension of topological dynamical systems. We introduce the concept of mean quantization dimension for invariant probability measures and establish a classical variational principle: the metric mean dimension of a dynamical system is equal to the maximum mean quantization dimension among all invariant measures. This approach effectively characterizes the complexity of systems with infinite entropy by identifying a measure that captures information across all scales; and yields a fundamental property that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.17091","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.17091/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2603.17091","created_at":"2026-05-21T02:05:01.190628+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.17091v3","created_at":"2026-05-21T02:05:01.190628+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.17091","created_at":"2026-05-21T02:05:01.190628+00:00"},{"alias_kind":"pith_short_12","alias_value":"5DONGLU7PHBH","created_at":"2026-05-21T02:05:01.190628+00:00"},{"alias_kind":"pith_short_16","alias_value":"5DONGLU7PHBHTDEL","created_at":"2026-05-21T02:05:01.190628+00:00"},{"alias_kind":"pith_short_8","alias_value":"5DONGLU7","created_at":"2026-05-21T02:05:01.190628+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/5DONGLU7PHBHTDELKJF3BGJL5G","json":"https://pith.science/pith/5DONGLU7PHBHTDELKJF3BGJL5G.json","graph_json":"https://pith.science/api/pith-number/5DONGLU7PHBHTDELKJF3BGJL5G/graph.json","events_json":"https://pith.science/api/pith-number/5DONGLU7PHBHTDELKJF3BGJL5G/events.json","paper":"https://pith.science/paper/5DONGLU7"},"agent_actions":{"view_html":"https://pith.science/pith/5DONGLU7PHBHTDELKJF3BGJL5G","download_json":"https://pith.science/pith/5DONGLU7PHBHTDELKJF3BGJL5G.json","view_paper":"https://pith.science/paper/5DONGLU7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.17091&json=true","fetch_graph":"https://pith.science/api/pith-number/5DONGLU7PHBHTDELKJF3BGJL5G/graph.json","fetch_events":"https://pith.science/api/pith-number/5DONGLU7PHBHTDELKJF3BGJL5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5DONGLU7PHBHTDELKJF3BGJL5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5DONGLU7PHBHTDELKJF3BGJL5G/action/storage_attestation","attest_author":"https://pith.science/pith/5DONGLU7PHBHTDELKJF3BGJL5G/action/author_attestation","sign_citation":"https://pith.science/pith/5DONGLU7PHBHTDELKJF3BGJL5G/action/citation_signature","submit_replication":"https://pith.science/pith/5DONGLU7PHBHTDELKJF3BGJL5G/action/replication_record"}},"created_at":"2026-05-21T02:05:01.190628+00:00","updated_at":"2026-05-21T02:05:01.190628+00:00"}