{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZNBPRMN3R3QVDUP2UHHL5GUALK","short_pith_number":"pith:ZNBPRMN3","canonical_record":{"source":{"id":"1906.07323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-18T00:50:17Z","cross_cats_sorted":[],"title_canon_sha256":"35e6e1e2cad317f4cb6fd6d4a1b1aa9feea6c864c706109ee0e470c9dba51afb","abstract_canon_sha256":"d5fa39fbf5e195e5e8815c41d50ad40ee4d4dd9597593c7aea72d7f77137a281"},"schema_version":"1.0"},"canonical_sha256":"cb42f8b1bb8ee151d1faa1cebe9a805ab177a0592d69f9f5602b62b3e51faa31","source":{"kind":"arxiv","id":"1906.07323","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.07323","created_at":"2026-05-17T23:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"1906.07323v1","created_at":"2026-05-17T23:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07323","created_at":"2026-05-17T23:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZNBPRMN3R3QV","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZNBPRMN3R3QVDUP2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZNBPRMN3","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZNBPRMN3R3QVDUP2UHHL5GUALK","target":"record","payload":{"canonical_record":{"source":{"id":"1906.07323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-18T00:50:17Z","cross_cats_sorted":[],"title_canon_sha256":"35e6e1e2cad317f4cb6fd6d4a1b1aa9feea6c864c706109ee0e470c9dba51afb","abstract_canon_sha256":"d5fa39fbf5e195e5e8815c41d50ad40ee4d4dd9597593c7aea72d7f77137a281"},"schema_version":"1.0"},"canonical_sha256":"cb42f8b1bb8ee151d1faa1cebe9a805ab177a0592d69f9f5602b62b3e51faa31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:08.205044Z","signature_b64":"4hGEmTkg/dlxzOhKYVJTXvXh3ppdjti5ElD1UyZEfGEweA7eriUMTvYS43j87PAqx0lfonQU6Rr3abhUolV+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb42f8b1bb8ee151d1faa1cebe9a805ab177a0592d69f9f5602b62b3e51faa31","last_reissued_at":"2026-05-17T23:43:08.204503Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:08.204503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.07323","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":"2026-05-17T23:43:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+DzlRf9drGHL17Ij3bfTIQJ3xmjR8AwhxDvTE7Tb5vlrAoMJ4JNURd6GoMi6uwNHtWNOxo66htIfX7OwLWpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:11:29.239510Z"},"content_sha256":"f28dc684aaca2a22203dea0a7a087da2a0d63d4e550297946ad0de33e8ae2378","schema_version":"1.0","event_id":"sha256:f28dc684aaca2a22203dea0a7a087da2a0d63d4e550297946ad0de33e8ae2378"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZNBPRMN3R3QVDUP2UHHL5GUALK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension Estimates for Non-conformal Repellers and Continuity of Sub-additive Topological Pressure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yakov Pesin, Yongluo Cao, Yun Zhao","submitted_at":"2019-06-18T00:50:17Z","abstract_excerpt":"Given a non-conformal repeller $\\Lambda$ of a $C^{1+\\gamma}$ map, we study the Hausdorff dimension of the repeller and continuity of the sub-additive topological pressure for the sub-additive singular valued potentials. Such a potential always possesses an equilibrium state. We then use a substantially modified version of Katok's approximating argument, to construct a compact invariant set on which the corresponding dynamical quantities (such as Lyapunov exponents and metric entropy) are close to that of the equilibrium measure. This allows us to establish continuity of the sub-additive topolo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07323","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":""},"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":"2026-05-17T23:43:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iqbKlfJQL8k/55IZKwD/N8Sr9wH/RI6l5dlvsNFF7Bos+zdHr56zKNwJ/Qr8v+IyJSHlgLIXLzkl+3z83nLBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:11:29.239870Z"},"content_sha256":"a304b586a8891e95a14348a13fc26ce04c78ae955fe1957c8839f52129be857c","schema_version":"1.0","event_id":"sha256:a304b586a8891e95a14348a13fc26ce04c78ae955fe1957c8839f52129be857c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZNBPRMN3R3QVDUP2UHHL5GUALK/bundle.json","state_url":"https://pith.science/pith/ZNBPRMN3R3QVDUP2UHHL5GUALK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZNBPRMN3R3QVDUP2UHHL5GUALK/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":"2026-05-31T00:11:29Z","links":{"resolver":"https://pith.science/pith/ZNBPRMN3R3QVDUP2UHHL5GUALK","bundle":"https://pith.science/pith/ZNBPRMN3R3QVDUP2UHHL5GUALK/bundle.json","state":"https://pith.science/pith/ZNBPRMN3R3QVDUP2UHHL5GUALK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZNBPRMN3R3QVDUP2UHHL5GUALK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZNBPRMN3R3QVDUP2UHHL5GUALK","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":"d5fa39fbf5e195e5e8815c41d50ad40ee4d4dd9597593c7aea72d7f77137a281","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-18T00:50:17Z","title_canon_sha256":"35e6e1e2cad317f4cb6fd6d4a1b1aa9feea6c864c706109ee0e470c9dba51afb"},"schema_version":"1.0","source":{"id":"1906.07323","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.07323","created_at":"2026-05-17T23:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"1906.07323v1","created_at":"2026-05-17T23:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07323","created_at":"2026-05-17T23:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZNBPRMN3R3QV","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZNBPRMN3R3QVDUP2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZNBPRMN3","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:a304b586a8891e95a14348a13fc26ce04c78ae955fe1957c8839f52129be857c","target":"graph","created_at":"2026-05-17T23:43:08Z","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"},"paper":{"abstract_excerpt":"Given a non-conformal repeller $\\Lambda$ of a $C^{1+\\gamma}$ map, we study the Hausdorff dimension of the repeller and continuity of the sub-additive topological pressure for the sub-additive singular valued potentials. Such a potential always possesses an equilibrium state. We then use a substantially modified version of Katok's approximating argument, to construct a compact invariant set on which the corresponding dynamical quantities (such as Lyapunov exponents and metric entropy) are close to that of the equilibrium measure. This allows us to establish continuity of the sub-additive topolo","authors_text":"Yakov Pesin, Yongluo Cao, Yun Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-18T00:50:17Z","title":"Dimension Estimates for Non-conformal Repellers and Continuity of Sub-additive Topological Pressure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07323","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:f28dc684aaca2a22203dea0a7a087da2a0d63d4e550297946ad0de33e8ae2378","target":"record","created_at":"2026-05-17T23:43:08Z","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":"d5fa39fbf5e195e5e8815c41d50ad40ee4d4dd9597593c7aea72d7f77137a281","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-18T00:50:17Z","title_canon_sha256":"35e6e1e2cad317f4cb6fd6d4a1b1aa9feea6c864c706109ee0e470c9dba51afb"},"schema_version":"1.0","source":{"id":"1906.07323","kind":"arxiv","version":1}},"canonical_sha256":"cb42f8b1bb8ee151d1faa1cebe9a805ab177a0592d69f9f5602b62b3e51faa31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb42f8b1bb8ee151d1faa1cebe9a805ab177a0592d69f9f5602b62b3e51faa31","first_computed_at":"2026-05-17T23:43:08.204503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:08.204503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4hGEmTkg/dlxzOhKYVJTXvXh3ppdjti5ElD1UyZEfGEweA7eriUMTvYS43j87PAqx0lfonQU6Rr3abhUolV+BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:08.205044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.07323","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f28dc684aaca2a22203dea0a7a087da2a0d63d4e550297946ad0de33e8ae2378","sha256:a304b586a8891e95a14348a13fc26ce04c78ae955fe1957c8839f52129be857c"],"state_sha256":"6c2425f4e832ff6643574c9230a02a2114165d76d99d709588f3b5dbc0b99833"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UACkIGc4J3pZjlP3SUF0uQljhompjoi6Krg0k8QFTNGTbEiYJqpiO6sDDkLDZTqUTyfMhjp61k5yF1XEx/zKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:11:29.243326Z","bundle_sha256":"a7d1154a236cb3a75d4c5f3b784e9e213363ec0d4009b89742afbf38da59ab38"}}