{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WR6HTKQPURAYDOM2C5LSRELWDH","short_pith_number":"pith:WR6HTKQP","canonical_record":{"source":{"id":"2606.03941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T17:30:16Z","cross_cats_sorted":[],"title_canon_sha256":"9d5199cf2e86ecabd34d56ba953270a147f03f3be133fb4978b06cc7864d2566","abstract_canon_sha256":"5d752078269b00ec06f0e12ae35876378566baf0d4a78d19d93ef3d3a6d3ef60"},"schema_version":"1.0"},"canonical_sha256":"b47c79aa0fa44181b99a175728917619e80f708abd6ad13a1850a944d2724dc0","source":{"kind":"arxiv","id":"2606.03941","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03941","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03941v1","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03941","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"WR6HTKQPURAY","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"WR6HTKQPURAYDOM2","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"WR6HTKQP","created_at":"2026-06-03T02:06:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WR6HTKQPURAYDOM2C5LSRELWDH","target":"record","payload":{"canonical_record":{"source":{"id":"2606.03941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T17:30:16Z","cross_cats_sorted":[],"title_canon_sha256":"9d5199cf2e86ecabd34d56ba953270a147f03f3be133fb4978b06cc7864d2566","abstract_canon_sha256":"5d752078269b00ec06f0e12ae35876378566baf0d4a78d19d93ef3d3a6d3ef60"},"schema_version":"1.0"},"canonical_sha256":"b47c79aa0fa44181b99a175728917619e80f708abd6ad13a1850a944d2724dc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T02:06:07.522304Z","signature_b64":"gEMaPfJx3i8LaID3AD9vR1PKxfhSuPXUZIci4/vNZ6PnyBQCtgU+3RCuKfdSZD/MbnN5CBwqlzN3AQyOwC1WDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b47c79aa0fa44181b99a175728917619e80f708abd6ad13a1850a944d2724dc0","last_reissued_at":"2026-06-03T02:06:07.521895Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T02:06:07.521895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.03941","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":"2026-06-03T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DwdOhwkwcS6eIbPbQ052oBw+smg/5M8HGa1OajBooyfkQKSr+SbVCsAE11ePnKRKmXhkfCSAPc2eJc3qsPmiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:25:27.832251Z"},"content_sha256":"7e2e3b0972e76a773bbacd83d0e48f240235be0614266bd77423c6650bf660be","schema_version":"1.0","event_id":"sha256:7e2e3b0972e76a773bbacd83d0e48f240235be0614266bd77423c6650bf660be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WR6HTKQPURAYDOM2C5LSRELWDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rate distortion dimension of Gibbs measures for functions depending on the first two coordinates on the full shift of Ahlfors regular spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kanji Inui, Mao Shinoda","submitted_at":"2026-06-02T17:30:16Z","abstract_excerpt":"The study on shift spaces in ergodic theory has been beyond the classical setting, but there is a room to discuss an extension of the Kolmogorov-Sinai entropy in the ergodic theoretical point of view.\n  On the other hand, the rate distortion dimension recently attracted attention in mean dimension theory because it behaves like the Kolmogorov-Sinai entropy on dynamical systems in the ``large\" spaces in which the usual entropies is in general infinite.\n  According to these background, we investigate the connection between the Gibbs measure on the product spaces and the variational principle bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03941","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/2606.03941/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":"2026-06-03T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yVoSekYVDzEtCZ8/mSKlTgi4B5klAjRQ7VmsBZqIKGLYTVgvI3Dh4Yp7opw+cP3K4REZTy+nU2wq1nOkbyWSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:25:27.832631Z"},"content_sha256":"ae0eaf396e859b43a7b4f8bb9908a8bfab4b29dc4b9a29857ee36e67f27b8c80","schema_version":"1.0","event_id":"sha256:ae0eaf396e859b43a7b4f8bb9908a8bfab4b29dc4b9a29857ee36e67f27b8c80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WR6HTKQPURAYDOM2C5LSRELWDH/bundle.json","state_url":"https://pith.science/pith/WR6HTKQPURAYDOM2C5LSRELWDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WR6HTKQPURAYDOM2C5LSRELWDH/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":"2026-06-27T20:25:27Z","links":{"resolver":"https://pith.science/pith/WR6HTKQPURAYDOM2C5LSRELWDH","bundle":"https://pith.science/pith/WR6HTKQPURAYDOM2C5LSRELWDH/bundle.json","state":"https://pith.science/pith/WR6HTKQPURAYDOM2C5LSRELWDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WR6HTKQPURAYDOM2C5LSRELWDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WR6HTKQPURAYDOM2C5LSRELWDH","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":"5d752078269b00ec06f0e12ae35876378566baf0d4a78d19d93ef3d3a6d3ef60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T17:30:16Z","title_canon_sha256":"9d5199cf2e86ecabd34d56ba953270a147f03f3be133fb4978b06cc7864d2566"},"schema_version":"1.0","source":{"id":"2606.03941","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03941","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03941v1","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03941","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"WR6HTKQPURAY","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"WR6HTKQPURAYDOM2","created_at":"2026-06-03T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"WR6HTKQP","created_at":"2026-06-03T02:06:07Z"}],"graph_snapshots":[{"event_id":"sha256:ae0eaf396e859b43a7b4f8bb9908a8bfab4b29dc4b9a29857ee36e67f27b8c80","target":"graph","created_at":"2026-06-03T02:06:07Z","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/2606.03941/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The study on shift spaces in ergodic theory has been beyond the classical setting, but there is a room to discuss an extension of the Kolmogorov-Sinai entropy in the ergodic theoretical point of view.\n  On the other hand, the rate distortion dimension recently attracted attention in mean dimension theory because it behaves like the Kolmogorov-Sinai entropy on dynamical systems in the ``large\" spaces in which the usual entropies is in general infinite.\n  According to these background, we investigate the connection between the Gibbs measure on the product spaces and the variational principle bas","authors_text":"Kanji Inui, Mao Shinoda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T17:30:16Z","title":"Rate distortion dimension of Gibbs measures for functions depending on the first two coordinates on the full shift of Ahlfors regular spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03941","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":"sha256:7e2e3b0972e76a773bbacd83d0e48f240235be0614266bd77423c6650bf660be","target":"record","created_at":"2026-06-03T02:06:07Z","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":"5d752078269b00ec06f0e12ae35876378566baf0d4a78d19d93ef3d3a6d3ef60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-02T17:30:16Z","title_canon_sha256":"9d5199cf2e86ecabd34d56ba953270a147f03f3be133fb4978b06cc7864d2566"},"schema_version":"1.0","source":{"id":"2606.03941","kind":"arxiv","version":1}},"canonical_sha256":"b47c79aa0fa44181b99a175728917619e80f708abd6ad13a1850a944d2724dc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b47c79aa0fa44181b99a175728917619e80f708abd6ad13a1850a944d2724dc0","first_computed_at":"2026-06-03T02:06:07.521895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T02:06:07.521895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gEMaPfJx3i8LaID3AD9vR1PKxfhSuPXUZIci4/vNZ6PnyBQCtgU+3RCuKfdSZD/MbnN5CBwqlzN3AQyOwC1WDw==","signature_status":"signed_v1","signed_at":"2026-06-03T02:06:07.522304Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.03941","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e2e3b0972e76a773bbacd83d0e48f240235be0614266bd77423c6650bf660be","sha256:ae0eaf396e859b43a7b4f8bb9908a8bfab4b29dc4b9a29857ee36e67f27b8c80"],"state_sha256":"c326351c8d74f0080bf401cf41c881765174276ca4dc8ed870baa0b14fee92e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yiiu9I4/bvUigq1T5sO5Rd190vz0LUehyShNiN68uSmdOJKtYlvfmE4FngSGbmO95G6p7Jw1GsMFcTiZE6FWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:25:27.834470Z","bundle_sha256":"1319c5cf65ec73b34403bbc792facac728ea61e229af7eed50da0b1b4b1a5f0c"}}