{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:BQ43W773P4FBBV3INYU5IYNXSR","short_pith_number":"pith:BQ43W773","canonical_record":{"source":{"id":"2305.08330","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-05-15T03:44:27Z","cross_cats_sorted":[],"title_canon_sha256":"7757103130045155a0c1285d6efb6bee66fb67b36dcfcaa6d5feafdf1eb7c533","abstract_canon_sha256":"10f2447f507762471a41caf7c4ed66ea45bce50153344bdf5f9dba2907f559f1"},"schema_version":"1.0"},"canonical_sha256":"0c39bb7ffb7f0a10d7686e29d461b7945adb5722755fd017637b33349515fec2","source":{"kind":"arxiv","id":"2305.08330","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.08330","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"arxiv_version","alias_value":"2305.08330v5","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.08330","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"pith_short_12","alias_value":"BQ43W773P4FB","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"pith_short_16","alias_value":"BQ43W773P4FBBV3I","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"pith_short_8","alias_value":"BQ43W773","created_at":"2026-07-05T09:02:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:BQ43W773P4FBBV3INYU5IYNXSR","target":"record","payload":{"canonical_record":{"source":{"id":"2305.08330","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-05-15T03:44:27Z","cross_cats_sorted":[],"title_canon_sha256":"7757103130045155a0c1285d6efb6bee66fb67b36dcfcaa6d5feafdf1eb7c533","abstract_canon_sha256":"10f2447f507762471a41caf7c4ed66ea45bce50153344bdf5f9dba2907f559f1"},"schema_version":"1.0"},"canonical_sha256":"0c39bb7ffb7f0a10d7686e29d461b7945adb5722755fd017637b33349515fec2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:02:53.681968Z","signature_b64":"iGjXCLguBZCOYRQlsGhgNcuY0vsN1Aiui27Gbswyk2N15lxYJtwHssxx9dhRj2Do+E1XmdLVk4vqXgaNeVEoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c39bb7ffb7f0a10d7686e29d461b7945adb5722755fd017637b33349515fec2","last_reissued_at":"2026-07-05T09:02:53.681491Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:02:53.681491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.08330","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:02:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+qfVy/VRNojbXpwoXsGk7aXUXy6R/nYc+kaIU/te7q80nZFZCFydpjsqrypHzsFmv+2OeoCdj3Nbtt6DUNTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:55:12.251259Z"},"content_sha256":"a3b3ad0045945ec0d392d0f976176cbe127b3aed4ac0e918dd2a97a0fe0cdf23","schema_version":"1.0","event_id":"sha256:a3b3ad0045945ec0d392d0f976176cbe127b3aed4ac0e918dd2a97a0fe0cdf23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:BQ43W773P4FBBV3INYU5IYNXSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper metric mean dimensions with potential of $\\epsilon$-stable sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ercai Chen, Rui Yang, Xiaoyao Zhou","submitted_at":"2023-05-15T03:44:27Z","abstract_excerpt":"It is well-known that $\\epsilon$-stable sets have a deep connection with the topological entropy of dynamical systems. In the present paper, we investigate the relationships of three types of upper metric mean dimensions with potential between \\emph{the blocks of $\\epsilon$-stable sets, $\\epsilon$-stable sets, the dispersion of preimages of $\\epsilon$-stable sets} and the whole phase space. Besides, some chaotic phenomenons are revealed in infinite entropy systems.\n  As an application of main results, we show tail entropy, preimage neighborhood entropy and topological entropy have the same met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08330","kind":"arxiv","version":5},"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/2305.08330/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":"2026-07-05T09:02:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VHjymL0cula5p1pa5IfAXobtltXpzQtMrOrtWfMzBSl59zETi2ujg+fD6f64GZIaj5aYQKm990rG9w80DZeFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:55:12.251777Z"},"content_sha256":"08b0df96035f1032e2ecd4d41331c0a1ce4af320729a6c50f41631b9afd60c96","schema_version":"1.0","event_id":"sha256:08b0df96035f1032e2ecd4d41331c0a1ce4af320729a6c50f41631b9afd60c96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQ43W773P4FBBV3INYU5IYNXSR/bundle.json","state_url":"https://pith.science/pith/BQ43W773P4FBBV3INYU5IYNXSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQ43W773P4FBBV3INYU5IYNXSR/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":"2026-08-12T22:55:12Z","links":{"resolver":"https://pith.science/pith/BQ43W773P4FBBV3INYU5IYNXSR","bundle":"https://pith.science/pith/BQ43W773P4FBBV3INYU5IYNXSR/bundle.json","state":"https://pith.science/pith/BQ43W773P4FBBV3INYU5IYNXSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQ43W773P4FBBV3INYU5IYNXSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BQ43W773P4FBBV3INYU5IYNXSR","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":"10f2447f507762471a41caf7c4ed66ea45bce50153344bdf5f9dba2907f559f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-05-15T03:44:27Z","title_canon_sha256":"7757103130045155a0c1285d6efb6bee66fb67b36dcfcaa6d5feafdf1eb7c533"},"schema_version":"1.0","source":{"id":"2305.08330","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.08330","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"arxiv_version","alias_value":"2305.08330v5","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.08330","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"pith_short_12","alias_value":"BQ43W773P4FB","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"pith_short_16","alias_value":"BQ43W773P4FBBV3I","created_at":"2026-07-05T09:02:53Z"},{"alias_kind":"pith_short_8","alias_value":"BQ43W773","created_at":"2026-07-05T09:02:53Z"}],"graph_snapshots":[{"event_id":"sha256:08b0df96035f1032e2ecd4d41331c0a1ce4af320729a6c50f41631b9afd60c96","target":"graph","created_at":"2026-07-05T09:02:53Z","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/2305.08330/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is well-known that $\\epsilon$-stable sets have a deep connection with the topological entropy of dynamical systems. In the present paper, we investigate the relationships of three types of upper metric mean dimensions with potential between \\emph{the blocks of $\\epsilon$-stable sets, $\\epsilon$-stable sets, the dispersion of preimages of $\\epsilon$-stable sets} and the whole phase space. Besides, some chaotic phenomenons are revealed in infinite entropy systems.\n  As an application of main results, we show tail entropy, preimage neighborhood entropy and topological entropy have the same met","authors_text":"Ercai Chen, Rui Yang, Xiaoyao Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-05-15T03:44:27Z","title":"Upper metric mean dimensions with potential of $\\epsilon$-stable sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08330","kind":"arxiv","version":5},"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:a3b3ad0045945ec0d392d0f976176cbe127b3aed4ac0e918dd2a97a0fe0cdf23","target":"record","created_at":"2026-07-05T09:02:53Z","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":"10f2447f507762471a41caf7c4ed66ea45bce50153344bdf5f9dba2907f559f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-05-15T03:44:27Z","title_canon_sha256":"7757103130045155a0c1285d6efb6bee66fb67b36dcfcaa6d5feafdf1eb7c533"},"schema_version":"1.0","source":{"id":"2305.08330","kind":"arxiv","version":5}},"canonical_sha256":"0c39bb7ffb7f0a10d7686e29d461b7945adb5722755fd017637b33349515fec2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c39bb7ffb7f0a10d7686e29d461b7945adb5722755fd017637b33349515fec2","first_computed_at":"2026-07-05T09:02:53.681491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:02:53.681491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iGjXCLguBZCOYRQlsGhgNcuY0vsN1Aiui27Gbswyk2N15lxYJtwHssxx9dhRj2Do+E1XmdLVk4vqXgaNeVEoCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:02:53.681968Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.08330","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3b3ad0045945ec0d392d0f976176cbe127b3aed4ac0e918dd2a97a0fe0cdf23","sha256:08b0df96035f1032e2ecd4d41331c0a1ce4af320729a6c50f41631b9afd60c96"],"state_sha256":"f0d32d06f1e34c0c59daace6bf514a6f0766f92ea839aec173962f27def1d3cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6OoZDsVnytypUmm6TMbNUFJJTTJ7NeMItjfTklPoVD3LvgoMQ28NK6E4SP1qOFEGVKk7a3SIQVkzgjLf0UGDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:55:12.259046Z","bundle_sha256":"a0c26c43e0faef4f1b3d4d47b5d5970c568c0dfaef7828346c973929e560fe9a"}}