{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WT2ECM5TQWKD6V57N6JEEFUNQG","short_pith_number":"pith:WT2ECM5T","canonical_record":{"source":{"id":"1211.3019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-13T15:23:00Z","cross_cats_sorted":[],"title_canon_sha256":"c240795319f22afb8743295625af2083c17e563a51209e26c649694241b86be8","abstract_canon_sha256":"0a2c72b8ec2359081a2c027b0eb28f9aebfca6b15d5818500d2dbc98055458c2"},"schema_version":"1.0"},"canonical_sha256":"b4f44133b385943f57bf6f9242168d81ba37cf493aedc1dc64c7496356392abe","source":{"kind":"arxiv","id":"1211.3019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3019","created_at":"2026-05-18T03:40:52Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3019v1","created_at":"2026-05-18T03:40:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3019","created_at":"2026-05-18T03:40:52Z"},{"alias_kind":"pith_short_12","alias_value":"WT2ECM5TQWKD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WT2ECM5TQWKD6V57","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WT2ECM5T","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WT2ECM5TQWKD6V57N6JEEFUNQG","target":"record","payload":{"canonical_record":{"source":{"id":"1211.3019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-13T15:23:00Z","cross_cats_sorted":[],"title_canon_sha256":"c240795319f22afb8743295625af2083c17e563a51209e26c649694241b86be8","abstract_canon_sha256":"0a2c72b8ec2359081a2c027b0eb28f9aebfca6b15d5818500d2dbc98055458c2"},"schema_version":"1.0"},"canonical_sha256":"b4f44133b385943f57bf6f9242168d81ba37cf493aedc1dc64c7496356392abe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:52.061585Z","signature_b64":"cRYY1MlwDq4wDEX2+jqYHl38/pA0g3PMlTB4zRGbLc7/xEQZKDvhbPRDaTGy8YV4qJQfhpqKMfbGkGtexuysCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4f44133b385943f57bf6f9242168d81ba37cf493aedc1dc64c7496356392abe","last_reissued_at":"2026-05-18T03:40:52.060600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:52.060600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.3019","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":"2026-05-18T03:40:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mu3tNSmyxEs7W56vXAx+cc2qZE5/EQiCERSPBWDWiKcQnr8KPSpv0rwXlApryTF1jq9YAmIGDPdl5hLkm0pXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:10:29.131556Z"},"content_sha256":"4ebc12160f78844b15020a08cf66384e947b08caba8835d9c46ee1e678120de6","schema_version":"1.0","event_id":"sha256:4ebc12160f78844b15020a08cf66384e947b08caba8835d9c46ee1e678120de6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WT2ECM5TQWKD6V57N6JEEFUNQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and Hausdorff dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anke D. Pohl, Shirali Kadyrov","submitted_at":"2012-11-13T15:23:00Z","abstract_excerpt":"Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\\Gamma\\backslash G$, where $G$ is any connected semisimple Lie group of real rank 1 with finite center and $\\Gamma$ is any nonuniform lattice in $G$. We show that this bound is sharp and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3019","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":"2026-05-18T03:40:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o/XxT0BDpt7y5KANuJU08/CjxMijoLmDciVJk/cYQ3k+0a2B8VcvqD9E2IOqicipVShvB0vjSCWuIt3ZBdGXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:10:29.132183Z"},"content_sha256":"c3d2240a26afd506d575bf2711a184963ac36cf613c9c09c80a7c1f43ed1249e","schema_version":"1.0","event_id":"sha256:c3d2240a26afd506d575bf2711a184963ac36cf613c9c09c80a7c1f43ed1249e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WT2ECM5TQWKD6V57N6JEEFUNQG/bundle.json","state_url":"https://pith.science/pith/WT2ECM5TQWKD6V57N6JEEFUNQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WT2ECM5TQWKD6V57N6JEEFUNQG/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":"2026-05-30T05:10:29Z","links":{"resolver":"https://pith.science/pith/WT2ECM5TQWKD6V57N6JEEFUNQG","bundle":"https://pith.science/pith/WT2ECM5TQWKD6V57N6JEEFUNQG/bundle.json","state":"https://pith.science/pith/WT2ECM5TQWKD6V57N6JEEFUNQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WT2ECM5TQWKD6V57N6JEEFUNQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WT2ECM5TQWKD6V57N6JEEFUNQG","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":"0a2c72b8ec2359081a2c027b0eb28f9aebfca6b15d5818500d2dbc98055458c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-13T15:23:00Z","title_canon_sha256":"c240795319f22afb8743295625af2083c17e563a51209e26c649694241b86be8"},"schema_version":"1.0","source":{"id":"1211.3019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3019","created_at":"2026-05-18T03:40:52Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3019v1","created_at":"2026-05-18T03:40:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3019","created_at":"2026-05-18T03:40:52Z"},{"alias_kind":"pith_short_12","alias_value":"WT2ECM5TQWKD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WT2ECM5TQWKD6V57","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WT2ECM5T","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:c3d2240a26afd506d575bf2711a184963ac36cf613c9c09c80a7c1f43ed1249e","target":"graph","created_at":"2026-05-18T03:40:52Z","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":"Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\\Gamma\\backslash G$, where $G$ is any connected semisimple Lie group of real rank 1 with finite center and $\\Gamma$ is any nonuniform lattice in $G$. We show that this bound is sharp and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average.","authors_text":"Anke D. Pohl, Shirali Kadyrov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-13T15:23:00Z","title":"Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and Hausdorff dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3019","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":"sha256:4ebc12160f78844b15020a08cf66384e947b08caba8835d9c46ee1e678120de6","target":"record","created_at":"2026-05-18T03:40:52Z","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":"0a2c72b8ec2359081a2c027b0eb28f9aebfca6b15d5818500d2dbc98055458c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-13T15:23:00Z","title_canon_sha256":"c240795319f22afb8743295625af2083c17e563a51209e26c649694241b86be8"},"schema_version":"1.0","source":{"id":"1211.3019","kind":"arxiv","version":1}},"canonical_sha256":"b4f44133b385943f57bf6f9242168d81ba37cf493aedc1dc64c7496356392abe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4f44133b385943f57bf6f9242168d81ba37cf493aedc1dc64c7496356392abe","first_computed_at":"2026-05-18T03:40:52.060600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:52.060600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cRYY1MlwDq4wDEX2+jqYHl38/pA0g3PMlTB4zRGbLc7/xEQZKDvhbPRDaTGy8YV4qJQfhpqKMfbGkGtexuysCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:52.061585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ebc12160f78844b15020a08cf66384e947b08caba8835d9c46ee1e678120de6","sha256:c3d2240a26afd506d575bf2711a184963ac36cf613c9c09c80a7c1f43ed1249e"],"state_sha256":"698f2301dd199d404e7804cdc9072bbf349c3dedc5f516605d700661dfc6d8f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PchbVFeuF4icX+LBoPxxRagtA8xW6G+5PwZCuoUBGssBfPKjnkSwUBTyNc0jy3s/h22rf7vhAIlr+1JBPC/KDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:10:29.136379Z","bundle_sha256":"c58b4b8943aaea9e728683075b38b4997dd1b8aba2f3de5505a737d9f3413d4b"}}