{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HR3RRE7S24W5Q2PDKHY2YJ67AW","short_pith_number":"pith:HR3RRE7S","canonical_record":{"source":{"id":"2505.10458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-15T16:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"ff425a7519dcf0fb018bec8eae07eddc7f63550e03cf1b40ce6735d56dde96b4","abstract_canon_sha256":"1f32e2ec6d3cd9a769035900cf60dcfdbd182fb4a567c73345d4b8a260c4f915"},"schema_version":"1.0"},"canonical_sha256":"3c771893f2d72dd869e351f1ac27df05b64f01aa65655f9f0ac8e8db5ea6dc6e","source":{"kind":"arxiv","id":"2505.10458","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.10458","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"2505.10458v1","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.10458","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"HR3RRE7S24W5","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"pith_short_16","alias_value":"HR3RRE7S24W5Q2PD","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"pith_short_8","alias_value":"HR3RRE7S","created_at":"2026-07-05T11:03:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HR3RRE7S24W5Q2PDKHY2YJ67AW","target":"record","payload":{"canonical_record":{"source":{"id":"2505.10458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-15T16:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"ff425a7519dcf0fb018bec8eae07eddc7f63550e03cf1b40ce6735d56dde96b4","abstract_canon_sha256":"1f32e2ec6d3cd9a769035900cf60dcfdbd182fb4a567c73345d4b8a260c4f915"},"schema_version":"1.0"},"canonical_sha256":"3c771893f2d72dd869e351f1ac27df05b64f01aa65655f9f0ac8e8db5ea6dc6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:03:38.572410Z","signature_b64":"upZ7FC6p/LNTdxCSeyfXcG8K/LzT69VuwYtSRqUJLbjgO9aJZFg1H24Lc/7wcWB1SQ10wJZe7r08xELy4ZbFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c771893f2d72dd869e351f1ac27df05b64f01aa65655f9f0ac8e8db5ea6dc6e","last_reissued_at":"2026-07-05T11:03:38.571912Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:03:38.571912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.10458","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":"2026-07-05T11:03:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n8HUfg6e+nRNViXemVVz3VI3n5OWcrKnMeZbqCW7JX8RRMByVmnPvb5sNY6irRzxF1/WsO5kMZIJ0FVnT64vBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:41:00.506857Z"},"content_sha256":"76a168454f506352fc5a66baec5df5faf9c21d89a474bbdc641ec627e5bdd6a9","schema_version":"1.0","event_id":"sha256:76a168454f506352fc5a66baec5df5faf9c21d89a474bbdc641ec627e5bdd6a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HR3RRE7S24W5Q2PDKHY2YJ67AW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smooth surface systems may contain smooth curves which have no measure of maximal entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guohua Zhang, Xulei Wang","submitted_at":"2025-05-15T16:15:17Z","abstract_excerpt":"In this paper, we study Borel probability measures of maximal entropy for analytic subsets in a dynamical system. It is well known that higher smoothness of the map over smooth space plays important role in the study of invariant measures of maximal entropy. A famous theorem of Newhouse states that smooth diffeomorphisms on compact manifolds without boundary have invariant measures of maximal entropy. However, we show that the situation becomes completely different when we study measures of maximal entropy for analytic subsets. Namely, we construct a smooth surface system which contains a smoo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10458","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/2505.10458/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":"2026-07-05T11:03:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d6cVQ+ycOpuq3kVZ3f5oK+9i179SkBmaSAGCLXagTpGjRLuKRQb7HDqzkjrWoaKopHwFNpThqlvgT/8nXT52CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:41:00.508045Z"},"content_sha256":"31d8278d10e36f1a1583cd51829b47e5f9e05e40e60bf0f2dcf0d2922aa64bef","schema_version":"1.0","event_id":"sha256:31d8278d10e36f1a1583cd51829b47e5f9e05e40e60bf0f2dcf0d2922aa64bef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HR3RRE7S24W5Q2PDKHY2YJ67AW/bundle.json","state_url":"https://pith.science/pith/HR3RRE7S24W5Q2PDKHY2YJ67AW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HR3RRE7S24W5Q2PDKHY2YJ67AW/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":"2026-08-13T21:41:00Z","links":{"resolver":"https://pith.science/pith/HR3RRE7S24W5Q2PDKHY2YJ67AW","bundle":"https://pith.science/pith/HR3RRE7S24W5Q2PDKHY2YJ67AW/bundle.json","state":"https://pith.science/pith/HR3RRE7S24W5Q2PDKHY2YJ67AW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HR3RRE7S24W5Q2PDKHY2YJ67AW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HR3RRE7S24W5Q2PDKHY2YJ67AW","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":"1f32e2ec6d3cd9a769035900cf60dcfdbd182fb4a567c73345d4b8a260c4f915","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-15T16:15:17Z","title_canon_sha256":"ff425a7519dcf0fb018bec8eae07eddc7f63550e03cf1b40ce6735d56dde96b4"},"schema_version":"1.0","source":{"id":"2505.10458","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.10458","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"2505.10458v1","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.10458","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"HR3RRE7S24W5","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"pith_short_16","alias_value":"HR3RRE7S24W5Q2PD","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"pith_short_8","alias_value":"HR3RRE7S","created_at":"2026-07-05T11:03:38Z"}],"graph_snapshots":[{"event_id":"sha256:31d8278d10e36f1a1583cd51829b47e5f9e05e40e60bf0f2dcf0d2922aa64bef","target":"graph","created_at":"2026-07-05T11:03:38Z","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/2505.10458/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study Borel probability measures of maximal entropy for analytic subsets in a dynamical system. It is well known that higher smoothness of the map over smooth space plays important role in the study of invariant measures of maximal entropy. A famous theorem of Newhouse states that smooth diffeomorphisms on compact manifolds without boundary have invariant measures of maximal entropy. However, we show that the situation becomes completely different when we study measures of maximal entropy for analytic subsets. Namely, we construct a smooth surface system which contains a smoo","authors_text":"Guohua Zhang, Xulei Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-15T16:15:17Z","title":"Smooth surface systems may contain smooth curves which have no measure of maximal entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10458","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":"sha256:76a168454f506352fc5a66baec5df5faf9c21d89a474bbdc641ec627e5bdd6a9","target":"record","created_at":"2026-07-05T11:03:38Z","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":"1f32e2ec6d3cd9a769035900cf60dcfdbd182fb4a567c73345d4b8a260c4f915","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-15T16:15:17Z","title_canon_sha256":"ff425a7519dcf0fb018bec8eae07eddc7f63550e03cf1b40ce6735d56dde96b4"},"schema_version":"1.0","source":{"id":"2505.10458","kind":"arxiv","version":1}},"canonical_sha256":"3c771893f2d72dd869e351f1ac27df05b64f01aa65655f9f0ac8e8db5ea6dc6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c771893f2d72dd869e351f1ac27df05b64f01aa65655f9f0ac8e8db5ea6dc6e","first_computed_at":"2026-07-05T11:03:38.571912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:03:38.571912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"upZ7FC6p/LNTdxCSeyfXcG8K/LzT69VuwYtSRqUJLbjgO9aJZFg1H24Lc/7wcWB1SQ10wJZe7r08xELy4ZbFBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:03:38.572410Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.10458","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76a168454f506352fc5a66baec5df5faf9c21d89a474bbdc641ec627e5bdd6a9","sha256:31d8278d10e36f1a1583cd51829b47e5f9e05e40e60bf0f2dcf0d2922aa64bef"],"state_sha256":"40e1d7fc259c80568b1f909939faecff791d3e9857fe636a93a46130361f71a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q+IInVfZN/c5Vu8mHxbfXrQnEUaJSz80BIJ+kwHdyimFtZNFiznRqnncj4gavUrU2Dqdm6+DEea8S0UXs1swDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T21:41:00.520055Z","bundle_sha256":"38fd04fa30b39a81d48155b887604937c336faf5c79340e01ac980fb4fdbfaaf"}}