{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SMRLZD7OHMI2GCIHX6NKOQH46B","short_pith_number":"pith:SMRLZD7O","canonical_record":{"source":{"id":"2503.06851","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-03-10T02:23:16Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"4aa382b4ebd2b235937fb5e78cfa22d2c9927c4041b07c527e06d10074158525","abstract_canon_sha256":"51cb5b230b97eab1550ad11449bac21f9d12540b54309fbc771ddef6c71eab33"},"schema_version":"1.0"},"canonical_sha256":"9322bc8fee3b11a30907bf9aa740fcf07365c3064367ec9a77c5711c52a55ae4","source":{"kind":"arxiv","id":"2503.06851","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.06851","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"2503.06851v1","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.06851","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"SMRLZD7OHMI2","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"pith_short_16","alias_value":"SMRLZD7OHMI2GCIH","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"pith_short_8","alias_value":"SMRLZD7O","created_at":"2026-07-05T10:27:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SMRLZD7OHMI2GCIHX6NKOQH46B","target":"record","payload":{"canonical_record":{"source":{"id":"2503.06851","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-03-10T02:23:16Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"4aa382b4ebd2b235937fb5e78cfa22d2c9927c4041b07c527e06d10074158525","abstract_canon_sha256":"51cb5b230b97eab1550ad11449bac21f9d12540b54309fbc771ddef6c71eab33"},"schema_version":"1.0"},"canonical_sha256":"9322bc8fee3b11a30907bf9aa740fcf07365c3064367ec9a77c5711c52a55ae4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:27:44.287817Z","signature_b64":"PsZLAzS5A09conl0SLn+Y365rML0IjsVEKhEJSSC6y6HUqXdFQwLtBaZWErd3rCvPz4Ujl7q+rr7f7ZgFrYbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9322bc8fee3b11a30907bf9aa740fcf07365c3064367ec9a77c5711c52a55ae4","last_reissued_at":"2026-07-05T10:27:44.287331Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:27:44.287331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.06851","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":"2026-07-05T10:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lp6uPRUjVP0/j25OWOvwq0y0Eq6bHAjRPtzu6XBB9xTGzxOaQj65kKEL9nv0URxt9avhXwfG3tJE+jDnHw/8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:25:26.629987Z"},"content_sha256":"d8c4940f31eb87c143f5f0d319681801b2cc5928f4c75a3f707b5f4b888f8d3d","schema_version":"1.0","event_id":"sha256:d8c4940f31eb87c143f5f0d319681801b2cc5928f4c75a3f707b5f4b888f8d3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SMRLZD7OHMI2GCIHX6NKOQH46B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rate distortion dimension and ergodic decomposition for $\\mathbb{R}^d$-actions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.DS","authors_text":"Masaki Tsukamoto","submitted_at":"2025-03-10T02:23:16Z","abstract_excerpt":"Rate distortion dimension describes the theoretical limit of lossy data compression methods as the distortion bound goes to zero. It was originally introduced in the context of information theory, and recently it was discovered that it has an intimate connection to Gromov's theory of mean dimension of dynamical systems. This paper studies the behavior of rate distortion dimension of $\\mathbb{R}^d$-actions under ergodic decomposition. Our main theorems provide natural convexity and concavity of upper and lower rate distortion dimensions under convex combination of invariant probability measures"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06851","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.06851/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iazz4yMcpM1wkAgBZNXWlxaK5nOSqNP8yTnZd2QFj5+BcP7srt7Fgx53Lye8iPDIuYYa65rO2iMKv9rMKwBMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:25:26.630812Z"},"content_sha256":"6c3176a895e6c6c3e2da8e2ef45ddf72806e05e9fa5ef1f36687be86230e3ec6","schema_version":"1.0","event_id":"sha256:6c3176a895e6c6c3e2da8e2ef45ddf72806e05e9fa5ef1f36687be86230e3ec6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMRLZD7OHMI2GCIHX6NKOQH46B/bundle.json","state_url":"https://pith.science/pith/SMRLZD7OHMI2GCIHX6NKOQH46B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMRLZD7OHMI2GCIHX6NKOQH46B/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":"2026-08-13T17:25:26Z","links":{"resolver":"https://pith.science/pith/SMRLZD7OHMI2GCIHX6NKOQH46B","bundle":"https://pith.science/pith/SMRLZD7OHMI2GCIHX6NKOQH46B/bundle.json","state":"https://pith.science/pith/SMRLZD7OHMI2GCIHX6NKOQH46B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMRLZD7OHMI2GCIHX6NKOQH46B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SMRLZD7OHMI2GCIHX6NKOQH46B","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":"51cb5b230b97eab1550ad11449bac21f9d12540b54309fbc771ddef6c71eab33","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-03-10T02:23:16Z","title_canon_sha256":"4aa382b4ebd2b235937fb5e78cfa22d2c9927c4041b07c527e06d10074158525"},"schema_version":"1.0","source":{"id":"2503.06851","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.06851","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"2503.06851v1","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.06851","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"SMRLZD7OHMI2","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"pith_short_16","alias_value":"SMRLZD7OHMI2GCIH","created_at":"2026-07-05T10:27:44Z"},{"alias_kind":"pith_short_8","alias_value":"SMRLZD7O","created_at":"2026-07-05T10:27:44Z"}],"graph_snapshots":[{"event_id":"sha256:6c3176a895e6c6c3e2da8e2ef45ddf72806e05e9fa5ef1f36687be86230e3ec6","target":"graph","created_at":"2026-07-05T10:27:44Z","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/2503.06851/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Rate distortion dimension describes the theoretical limit of lossy data compression methods as the distortion bound goes to zero. It was originally introduced in the context of information theory, and recently it was discovered that it has an intimate connection to Gromov's theory of mean dimension of dynamical systems. This paper studies the behavior of rate distortion dimension of $\\mathbb{R}^d$-actions under ergodic decomposition. Our main theorems provide natural convexity and concavity of upper and lower rate distortion dimensions under convex combination of invariant probability measures","authors_text":"Masaki Tsukamoto","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-03-10T02:23:16Z","title":"Rate distortion dimension and ergodic decomposition for $\\mathbb{R}^d$-actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06851","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:d8c4940f31eb87c143f5f0d319681801b2cc5928f4c75a3f707b5f4b888f8d3d","target":"record","created_at":"2026-07-05T10:27:44Z","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":"51cb5b230b97eab1550ad11449bac21f9d12540b54309fbc771ddef6c71eab33","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-03-10T02:23:16Z","title_canon_sha256":"4aa382b4ebd2b235937fb5e78cfa22d2c9927c4041b07c527e06d10074158525"},"schema_version":"1.0","source":{"id":"2503.06851","kind":"arxiv","version":1}},"canonical_sha256":"9322bc8fee3b11a30907bf9aa740fcf07365c3064367ec9a77c5711c52a55ae4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9322bc8fee3b11a30907bf9aa740fcf07365c3064367ec9a77c5711c52a55ae4","first_computed_at":"2026-07-05T10:27:44.287331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:27:44.287331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PsZLAzS5A09conl0SLn+Y365rML0IjsVEKhEJSSC6y6HUqXdFQwLtBaZWErd3rCvPz4Ujl7q+rr7f7ZgFrYbCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:27:44.287817Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.06851","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8c4940f31eb87c143f5f0d319681801b2cc5928f4c75a3f707b5f4b888f8d3d","sha256:6c3176a895e6c6c3e2da8e2ef45ddf72806e05e9fa5ef1f36687be86230e3ec6"],"state_sha256":"730fa9cbba4b3b27cb820d4da3d88a7c950f2446dbe0f75ce65102b19e5fccf0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2wFElBLfW80b7qQ+CIOsRUcRRgc4nIv2ScQ957GsrPeE8BM538GocXHMDz7KjUMsx+6MSTGAzphRduEsHCAqDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:25:26.640138Z","bundle_sha256":"c8f9a97d74c028df39d569242f7c5a24e7b9e3a99e2347be7ead2c8a51e077a4"}}