{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:HDNZKSZ2NN2S2DFDU476EDFLUM","short_pith_number":"pith:HDNZKSZ2","canonical_record":{"source":{"id":"2110.07708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-14T20:57:17Z","cross_cats_sorted":["math.DS","math.GR","math.RT"],"title_canon_sha256":"6022af06db6d7424a9e56280ef2d18d31e733148cfa23b643ada0a369e8d6f9c","abstract_canon_sha256":"cb4863f142943c66a88be8589c594547926be56bbeb0c3088ef4e47dcf66f93e"},"schema_version":"1.0"},"canonical_sha256":"38db954b3a6b752d0ca3a73fe20caba33de9239b38b980ce54d9aae1780152ff","source":{"kind":"arxiv","id":"2110.07708","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.07708","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"2110.07708v1","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.07708","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"HDNZKSZ2NN2S","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"pith_short_16","alias_value":"HDNZKSZ2NN2S2DFD","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"pith_short_8","alias_value":"HDNZKSZ2","created_at":"2026-07-05T11:37:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:HDNZKSZ2NN2S2DFDU476EDFLUM","target":"record","payload":{"canonical_record":{"source":{"id":"2110.07708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-14T20:57:17Z","cross_cats_sorted":["math.DS","math.GR","math.RT"],"title_canon_sha256":"6022af06db6d7424a9e56280ef2d18d31e733148cfa23b643ada0a369e8d6f9c","abstract_canon_sha256":"cb4863f142943c66a88be8589c594547926be56bbeb0c3088ef4e47dcf66f93e"},"schema_version":"1.0"},"canonical_sha256":"38db954b3a6b752d0ca3a73fe20caba33de9239b38b980ce54d9aae1780152ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:37:58.356520Z","signature_b64":"lFUbuoIiHQtbnI+0YwGfyDL+VHYWl0flfs0NWKK0Sk4bcglvm5kFtfPqQp22FlirCUPxTHLq6mDf1c+EcHmlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38db954b3a6b752d0ca3a73fe20caba33de9239b38b980ce54d9aae1780152ff","last_reissued_at":"2026-07-05T11:37:58.355996Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:37:58.355996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.07708","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":"2026-07-05T11:37:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5umD0Qnr4xNGENCfaGmwAVTKQH156jzsq/NYyVWy/XWzdITM6gtwLxQT3atb0vl87x/Pwt4nPWKUPzlFw+dKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:05:49.453805Z"},"content_sha256":"a44c37f59500bba2ee860f66a591b92e90a0c9bdaae2c2d4c0692edc6c5cfd24","schema_version":"1.0","event_id":"sha256:a44c37f59500bba2ee860f66a591b92e90a0c9bdaae2c2d4c0692edc6c5cfd24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:HDNZKSZ2NN2S2DFDU476EDFLUM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative ergodic theory of higher rank lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR","math.RT"],"primary_cat":"math.OA","authors_text":"Cyril Houdayer","submitted_at":"2021-10-14T20:57:17Z","abstract_excerpt":"We survey recent results regarding the study of dynamical properties of the space of positive definite functions and characters of higher rank lattices. These results have several applications to ergodic theory, topological dynamics, unitary representation theory and operator algebras. The key novelty in our work is a dynamical dichotomy theorem for equivariant faithful normal unital completely positive maps between noncommutative von Neumann algebras and the space of bounded measurable functions defined on the Poisson boundary of semisimple Lie groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.07708","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/2110.07708/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":"2026-07-05T11:37:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z4x3jf4Ecmba8dete2Si8XviDY0WFKi1QrJiYX1IzRVmvhYTxwLFtd99S3bUibaLupGVTTGBf7t1QEUJ6Wx9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:05:49.454187Z"},"content_sha256":"434d7d6966e3054b6c0628fb9afd752e70df1f8b045d6819fd69a3c7660cec76","schema_version":"1.0","event_id":"sha256:434d7d6966e3054b6c0628fb9afd752e70df1f8b045d6819fd69a3c7660cec76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HDNZKSZ2NN2S2DFDU476EDFLUM/bundle.json","state_url":"https://pith.science/pith/HDNZKSZ2NN2S2DFDU476EDFLUM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HDNZKSZ2NN2S2DFDU476EDFLUM/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":"2026-07-06T14:05:49Z","links":{"resolver":"https://pith.science/pith/HDNZKSZ2NN2S2DFDU476EDFLUM","bundle":"https://pith.science/pith/HDNZKSZ2NN2S2DFDU476EDFLUM/bundle.json","state":"https://pith.science/pith/HDNZKSZ2NN2S2DFDU476EDFLUM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HDNZKSZ2NN2S2DFDU476EDFLUM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HDNZKSZ2NN2S2DFDU476EDFLUM","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":"cb4863f142943c66a88be8589c594547926be56bbeb0c3088ef4e47dcf66f93e","cross_cats_sorted":["math.DS","math.GR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-14T20:57:17Z","title_canon_sha256":"6022af06db6d7424a9e56280ef2d18d31e733148cfa23b643ada0a369e8d6f9c"},"schema_version":"1.0","source":{"id":"2110.07708","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.07708","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"2110.07708v1","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.07708","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"HDNZKSZ2NN2S","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"pith_short_16","alias_value":"HDNZKSZ2NN2S2DFD","created_at":"2026-07-05T11:37:58Z"},{"alias_kind":"pith_short_8","alias_value":"HDNZKSZ2","created_at":"2026-07-05T11:37:58Z"}],"graph_snapshots":[{"event_id":"sha256:434d7d6966e3054b6c0628fb9afd752e70df1f8b045d6819fd69a3c7660cec76","target":"graph","created_at":"2026-07-05T11:37:58Z","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/2110.07708/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We survey recent results regarding the study of dynamical properties of the space of positive definite functions and characters of higher rank lattices. These results have several applications to ergodic theory, topological dynamics, unitary representation theory and operator algebras. The key novelty in our work is a dynamical dichotomy theorem for equivariant faithful normal unital completely positive maps between noncommutative von Neumann algebras and the space of bounded measurable functions defined on the Poisson boundary of semisimple Lie groups.","authors_text":"Cyril Houdayer","cross_cats":["math.DS","math.GR","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-14T20:57:17Z","title":"Noncommutative ergodic theory of higher rank lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.07708","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:a44c37f59500bba2ee860f66a591b92e90a0c9bdaae2c2d4c0692edc6c5cfd24","target":"record","created_at":"2026-07-05T11:37:58Z","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":"cb4863f142943c66a88be8589c594547926be56bbeb0c3088ef4e47dcf66f93e","cross_cats_sorted":["math.DS","math.GR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-14T20:57:17Z","title_canon_sha256":"6022af06db6d7424a9e56280ef2d18d31e733148cfa23b643ada0a369e8d6f9c"},"schema_version":"1.0","source":{"id":"2110.07708","kind":"arxiv","version":1}},"canonical_sha256":"38db954b3a6b752d0ca3a73fe20caba33de9239b38b980ce54d9aae1780152ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38db954b3a6b752d0ca3a73fe20caba33de9239b38b980ce54d9aae1780152ff","first_computed_at":"2026-07-05T11:37:58.355996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:37:58.355996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lFUbuoIiHQtbnI+0YwGfyDL+VHYWl0flfs0NWKK0Sk4bcglvm5kFtfPqQp22FlirCUPxTHLq6mDf1c+EcHmlCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:37:58.356520Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.07708","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a44c37f59500bba2ee860f66a591b92e90a0c9bdaae2c2d4c0692edc6c5cfd24","sha256:434d7d6966e3054b6c0628fb9afd752e70df1f8b045d6819fd69a3c7660cec76"],"state_sha256":"aecc69a960f9935befeee57ed52f51494b4120ae21cbb1ae1fd9646282c3d7ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LfRsYlyhPVTeTXaxlVwwnDwzwT9GD/9IqUJuYRFi06aa6KjqbQ5lvLEp/4hfRMo9AiyVj8pE5eFZYlMue7SfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T14:05:49.456185Z","bundle_sha256":"f17dffa09ad192ac68fbd7f7ff48d69c7a77688dba645f5e0ea0bf3727728237"}}