{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:ITT7BEVTWZQMGD4ZLHR67WD7SU","short_pith_number":"pith:ITT7BEVT","canonical_record":{"source":{"id":"2308.04023","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-08-08T03:37:55Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"14e1ce8736533465db9d6222e09d41cd4d96c8c6114640d05d692b2788731e55","abstract_canon_sha256":"b8f25eff19cbc29988f71500c3ddbfc6702ad87b95dd0c01ff702e050990dbd8"},"schema_version":"1.0"},"canonical_sha256":"44e7f092b3b660c30f9959e3efd87f952dd463b050ca935e3db91b6cb6b2b812","source":{"kind":"arxiv","id":"2308.04023","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.04023","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"2308.04023v4","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.04023","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"ITT7BEVTWZQM","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"pith_short_16","alias_value":"ITT7BEVTWZQMGD4Z","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"pith_short_8","alias_value":"ITT7BEVT","created_at":"2026-07-05T10:41:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:ITT7BEVTWZQMGD4ZLHR67WD7SU","target":"record","payload":{"canonical_record":{"source":{"id":"2308.04023","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-08-08T03:37:55Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"14e1ce8736533465db9d6222e09d41cd4d96c8c6114640d05d692b2788731e55","abstract_canon_sha256":"b8f25eff19cbc29988f71500c3ddbfc6702ad87b95dd0c01ff702e050990dbd8"},"schema_version":"1.0"},"canonical_sha256":"44e7f092b3b660c30f9959e3efd87f952dd463b050ca935e3db91b6cb6b2b812","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:41:10.231522Z","signature_b64":"R+hEnhXHvteMrrXSw6TMUHtEW1XQdyj6y5OVFgmAsoqD1WBcGuFJIMA7VEAnxAsdxEccdQbk80UIqYZc36a8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44e7f092b3b660c30f9959e3efd87f952dd463b050ca935e3db91b6cb6b2b812","last_reissued_at":"2026-07-05T10:41:10.231050Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:41:10.231050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.04023","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HWRF7udLsRqhFPFiQn2BLAZJ5UXPk0AvoAXsO2zCCTLhGHm/orCplx9QqlgpUby9VHREfF9kguxszVdRYJlECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T18:17:53.841812Z"},"content_sha256":"059c3bf85ffb229a192d4dc7f21d884dc2a4d265d465e3f0b299d4eb2283c2e6","schema_version":"1.0","event_id":"sha256:059c3bf85ffb229a192d4dc7f21d884dc2a4d265d465e3f0b299d4eb2283c2e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:ITT7BEVTWZQMGD4ZLHR67WD7SU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Patterson-Sullivan measures for relatively Anosov groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Andrew Zimmer, Richard Canary, Tengren Zhang","submitted_at":"2023-08-08T03:37:55Z","abstract_excerpt":"We establish existence, uniqueness and ergodicity results for Patterson-Sullivan measures for relatively Anosov groups. As applications we obtain an entropy gap theorem and a strict concavity result for entropies associated to linear functionals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04023","kind":"arxiv","version":4},"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/2308.04023/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":"2026-07-05T10:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSyXK41h3aQ4IAP3ucf+8A80z0j7UdWvLJekOGnSUIiesapmVIZPVuBSHcIP9txC0XGQu+3gRgkyuJdGTrmfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T18:17:53.842454Z"},"content_sha256":"d134eb4f89a9db3637860124d8fa08314c77d03ca1c19ccf4b1c552a84efd59c","schema_version":"1.0","event_id":"sha256:d134eb4f89a9db3637860124d8fa08314c77d03ca1c19ccf4b1c552a84efd59c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITT7BEVTWZQMGD4ZLHR67WD7SU/bundle.json","state_url":"https://pith.science/pith/ITT7BEVTWZQMGD4ZLHR67WD7SU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITT7BEVTWZQMGD4ZLHR67WD7SU/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":"2026-08-10T18:17:53Z","links":{"resolver":"https://pith.science/pith/ITT7BEVTWZQMGD4ZLHR67WD7SU","bundle":"https://pith.science/pith/ITT7BEVTWZQMGD4ZLHR67WD7SU/bundle.json","state":"https://pith.science/pith/ITT7BEVTWZQMGD4ZLHR67WD7SU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITT7BEVTWZQMGD4ZLHR67WD7SU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ITT7BEVTWZQMGD4ZLHR67WD7SU","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":"b8f25eff19cbc29988f71500c3ddbfc6702ad87b95dd0c01ff702e050990dbd8","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-08-08T03:37:55Z","title_canon_sha256":"14e1ce8736533465db9d6222e09d41cd4d96c8c6114640d05d692b2788731e55"},"schema_version":"1.0","source":{"id":"2308.04023","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.04023","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"2308.04023v4","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.04023","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"ITT7BEVTWZQM","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"pith_short_16","alias_value":"ITT7BEVTWZQMGD4Z","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"pith_short_8","alias_value":"ITT7BEVT","created_at":"2026-07-05T10:41:10Z"}],"graph_snapshots":[{"event_id":"sha256:d134eb4f89a9db3637860124d8fa08314c77d03ca1c19ccf4b1c552a84efd59c","target":"graph","created_at":"2026-07-05T10:41:10Z","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/2308.04023/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish existence, uniqueness and ergodicity results for Patterson-Sullivan measures for relatively Anosov groups. As applications we obtain an entropy gap theorem and a strict concavity result for entropies associated to linear functionals.","authors_text":"Andrew Zimmer, Richard Canary, Tengren Zhang","cross_cats":["math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-08-08T03:37:55Z","title":"Patterson-Sullivan measures for relatively Anosov groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04023","kind":"arxiv","version":4},"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":"sha256:059c3bf85ffb229a192d4dc7f21d884dc2a4d265d465e3f0b299d4eb2283c2e6","target":"record","created_at":"2026-07-05T10:41:10Z","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":"b8f25eff19cbc29988f71500c3ddbfc6702ad87b95dd0c01ff702e050990dbd8","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-08-08T03:37:55Z","title_canon_sha256":"14e1ce8736533465db9d6222e09d41cd4d96c8c6114640d05d692b2788731e55"},"schema_version":"1.0","source":{"id":"2308.04023","kind":"arxiv","version":4}},"canonical_sha256":"44e7f092b3b660c30f9959e3efd87f952dd463b050ca935e3db91b6cb6b2b812","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44e7f092b3b660c30f9959e3efd87f952dd463b050ca935e3db91b6cb6b2b812","first_computed_at":"2026-07-05T10:41:10.231050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:10.231050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R+hEnhXHvteMrrXSw6TMUHtEW1XQdyj6y5OVFgmAsoqD1WBcGuFJIMA7VEAnxAsdxEccdQbk80UIqYZc36a8CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:10.231522Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.04023","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:059c3bf85ffb229a192d4dc7f21d884dc2a4d265d465e3f0b299d4eb2283c2e6","sha256:d134eb4f89a9db3637860124d8fa08314c77d03ca1c19ccf4b1c552a84efd59c"],"state_sha256":"410c6208e0ce3e742a8e820d80f5dcfd5daccc894168ab57539dddf4bf121a5c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T8pWqabSC3otE9VR+Vg3NkbsGqr7d1nTaUKao3e9dbSm05Ya6XR8j8vWh4Ja5ihXhT43p3JJwAtRCOXYFqv9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T18:17:53.846923Z","bundle_sha256":"6fc31c4297603a23577e7fea78df9971ad4f20c36d0ad006a52bc2f2754b9c31"}}