{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DH2XL363OHQEGUOCHTZ4CESRER","short_pith_number":"pith:DH2XL363","canonical_record":{"source":{"id":"1105.1675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-09T14:13:56Z","cross_cats_sorted":[],"title_canon_sha256":"2c4b0a6fff5f98e1a8c61e570315109bb35a60e2da596d735b98f55829aeed91","abstract_canon_sha256":"9bd8662984fdc20cc7fe162ec68fca2fc9409918a126aae23a80b5c1a61f7860"},"schema_version":"1.0"},"canonical_sha256":"19f575efdb71e04351c23cf3c112512466610783eb9aec2cf67e124b7a678fdb","source":{"kind":"arxiv","id":"1105.1675","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1675","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1675v1","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1675","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"pith_short_12","alias_value":"DH2XL363OHQE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DH2XL363OHQEGUOC","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DH2XL363","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DH2XL363OHQEGUOCHTZ4CESRER","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-09T14:13:56Z","cross_cats_sorted":[],"title_canon_sha256":"2c4b0a6fff5f98e1a8c61e570315109bb35a60e2da596d735b98f55829aeed91","abstract_canon_sha256":"9bd8662984fdc20cc7fe162ec68fca2fc9409918a126aae23a80b5c1a61f7860"},"schema_version":"1.0"},"canonical_sha256":"19f575efdb71e04351c23cf3c112512466610783eb9aec2cf67e124b7a678fdb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:32.705248Z","signature_b64":"VZqZawTau4HXQeZVjJWEscLLml5FROek13rS7UimERuOTmja1UwTiuHghmpm+NkuMAzokRSQRSircQmQyiwPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19f575efdb71e04351c23cf3c112512466610783eb9aec2cf67e124b7a678fdb","last_reissued_at":"2026-05-18T04:22:32.704660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:32.704660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1675","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":"2026-05-18T04:22:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N98tl08oGb3nk9Vrie4fL9QX897OZ06dV/tFHQOqCC9eTy3qFNyuRZ7UNT3vbXni2Xohzfbugti3KP3rdSVzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:27:35.248576Z"},"content_sha256":"ebb264c5f14dcd69acacd10c93146e35da5d3b7f888aa7b9b37e2e1a3e3b54d3","schema_version":"1.0","event_id":"sha256:ebb264c5f14dcd69acacd10c93146e35da5d3b7f888aa7b9b37e2e1a3e3b54d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DH2XL363OHQEGUOCHTZ4CESRER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Poisson boundary of CAT(0) cube complex groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Amos Nevo, Michah Sageev","submitted_at":"2011-05-09T14:13:56Z","abstract_excerpt":"We consider a finite-dimensional, locally finite CAT(0) cube complex X admitting a co-compact properly discontinuous countable group of automorphisms G. We construct a natural compact metric space B(X) on which G acts by homeomorphisms, the action being minimal and strongly proximal. Furthermore, for any generating probability measure on G, B(X) admits a unique stationary measure, and when the measure has finite logarithmic moment, it constitutes a compact metric model of the Poisson boundary. We identify a dense G-delta subset of B(X) on which the action of G is Borel-amenable, and describe t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1675","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":"2026-05-18T04:22:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MBMX89AybYx1Q0Q6BKHIFrs8cRgLG8V8ww8yb69/UCd/MQPDyFF5pLUAk7pyTpG7LdThX8tv/74lmDOssJVMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:27:35.248905Z"},"content_sha256":"430f9726e6d6ac8b15a4d1955bef7782c607a43e237dd043b8d11fe4ef3ffe69","schema_version":"1.0","event_id":"sha256:430f9726e6d6ac8b15a4d1955bef7782c607a43e237dd043b8d11fe4ef3ffe69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DH2XL363OHQEGUOCHTZ4CESRER/bundle.json","state_url":"https://pith.science/pith/DH2XL363OHQEGUOCHTZ4CESRER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DH2XL363OHQEGUOCHTZ4CESRER/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":"2026-06-21T13:27:35Z","links":{"resolver":"https://pith.science/pith/DH2XL363OHQEGUOCHTZ4CESRER","bundle":"https://pith.science/pith/DH2XL363OHQEGUOCHTZ4CESRER/bundle.json","state":"https://pith.science/pith/DH2XL363OHQEGUOCHTZ4CESRER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DH2XL363OHQEGUOCHTZ4CESRER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DH2XL363OHQEGUOCHTZ4CESRER","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":"9bd8662984fdc20cc7fe162ec68fca2fc9409918a126aae23a80b5c1a61f7860","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-09T14:13:56Z","title_canon_sha256":"2c4b0a6fff5f98e1a8c61e570315109bb35a60e2da596d735b98f55829aeed91"},"schema_version":"1.0","source":{"id":"1105.1675","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1675","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1675v1","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1675","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"pith_short_12","alias_value":"DH2XL363OHQE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DH2XL363OHQEGUOC","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DH2XL363","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:430f9726e6d6ac8b15a4d1955bef7782c607a43e237dd043b8d11fe4ef3ffe69","target":"graph","created_at":"2026-05-18T04:22:32Z","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":"We consider a finite-dimensional, locally finite CAT(0) cube complex X admitting a co-compact properly discontinuous countable group of automorphisms G. We construct a natural compact metric space B(X) on which G acts by homeomorphisms, the action being minimal and strongly proximal. Furthermore, for any generating probability measure on G, B(X) admits a unique stationary measure, and when the measure has finite logarithmic moment, it constitutes a compact metric model of the Poisson boundary. We identify a dense G-delta subset of B(X) on which the action of G is Borel-amenable, and describe t","authors_text":"Amos Nevo, Michah Sageev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-09T14:13:56Z","title":"The Poisson boundary of CAT(0) cube complex groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1675","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:ebb264c5f14dcd69acacd10c93146e35da5d3b7f888aa7b9b37e2e1a3e3b54d3","target":"record","created_at":"2026-05-18T04:22:32Z","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":"9bd8662984fdc20cc7fe162ec68fca2fc9409918a126aae23a80b5c1a61f7860","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-09T14:13:56Z","title_canon_sha256":"2c4b0a6fff5f98e1a8c61e570315109bb35a60e2da596d735b98f55829aeed91"},"schema_version":"1.0","source":{"id":"1105.1675","kind":"arxiv","version":1}},"canonical_sha256":"19f575efdb71e04351c23cf3c112512466610783eb9aec2cf67e124b7a678fdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19f575efdb71e04351c23cf3c112512466610783eb9aec2cf67e124b7a678fdb","first_computed_at":"2026-05-18T04:22:32.704660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:32.704660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VZqZawTau4HXQeZVjJWEscLLml5FROek13rS7UimERuOTmja1UwTiuHghmpm+NkuMAzokRSQRSircQmQyiwPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:32.705248Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1675","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebb264c5f14dcd69acacd10c93146e35da5d3b7f888aa7b9b37e2e1a3e3b54d3","sha256:430f9726e6d6ac8b15a4d1955bef7782c607a43e237dd043b8d11fe4ef3ffe69"],"state_sha256":"a772f4dc16fcc9d76fa179d70a04812859349df1c90ba3f565d05cc3e8be29a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xfZkuIGCmGyRhYR9Ur/GN5rMj/ZdVqWcl+srKq3i3qQXOmIntYNW1Ug/c6Fr6jlw0Q53/qkMrF8wkC0lIyRADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T13:27:35.250944Z","bundle_sha256":"c3236d5ee71b3c1e7d20f1d2dafbb4f1b8f49d930f4e2fe960a400c7f8af8c61"}}