{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SFLFOSCQ4VZKGUUHUZHAB4GXUB","short_pith_number":"pith:SFLFOSCQ","canonical_record":{"source":{"id":"1601.02275","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-10T23:00:05Z","cross_cats_sorted":["math.DS","math.RT"],"title_canon_sha256":"42341f1827c15c2b0aaa1eb0ffc7767f5bc11d3e08b926187aea7d5de1084f31","abstract_canon_sha256":"90bea26320dfa78b5fd22bd8151db6bbd48748da5dc1d9b9d880edecf7e83175"},"schema_version":"1.0"},"canonical_sha256":"9156574850e572a35287a64e00f0d7a0767f093b349519d1ec015577165b5062","source":{"kind":"arxiv","id":"1601.02275","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02275","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02275v1","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02275","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"pith_short_12","alias_value":"SFLFOSCQ4VZK","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SFLFOSCQ4VZKGUUH","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SFLFOSCQ","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SFLFOSCQ4VZKGUUHUZHAB4GXUB","target":"record","payload":{"canonical_record":{"source":{"id":"1601.02275","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-10T23:00:05Z","cross_cats_sorted":["math.DS","math.RT"],"title_canon_sha256":"42341f1827c15c2b0aaa1eb0ffc7767f5bc11d3e08b926187aea7d5de1084f31","abstract_canon_sha256":"90bea26320dfa78b5fd22bd8151db6bbd48748da5dc1d9b9d880edecf7e83175"},"schema_version":"1.0"},"canonical_sha256":"9156574850e572a35287a64e00f0d7a0767f093b349519d1ec015577165b5062","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:06.813490Z","signature_b64":"xAkHmeSuQM+mgF6cNYlwXnXmZg+Gw82F5vw5a8C15/oGaL+5XqWdmYGq/fwSatduSYv5Z0GXKQxB9WY8cmlmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9156574850e572a35287a64e00f0d7a0767f093b349519d1ec015577165b5062","last_reissued_at":"2026-05-18T01:23:06.812971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:06.812971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.02275","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":"2026-05-18T01:23:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a8ZyJKrjuPqws1aMwyzuxhErtAcp+vocnwlEgSdLGd89fy3HWNXpOtBMkFNwcz27LgnjXKoPP9WIoMZuunmICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:28:01.144533Z"},"content_sha256":"1ca1d93196ca6f3228602053b1b88669d8f75ceef59f8728d78d454aa3d6c2a7","schema_version":"1.0","event_id":"sha256:1ca1d93196ca6f3228602053b1b88669d8f75ceef59f8728d78d454aa3d6c2a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SFLFOSCQ4VZKGUUHUZHAB4GXUB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equidistribution, ergodicity and irreducibility associated with Gibbs measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.RT"],"primary_cat":"math.GR","authors_text":"Adrien Boyer, Dustin Mayeda","submitted_at":"2016-01-10T23:00:05Z","abstract_excerpt":"We generalize an equidistribution theorem \\`a la Bader-Muchnik for operator-valued measures constructed from a family of boundary representations associated with Gibbs measures in the context of convex cocompact discrete group of isometries of a simply connected connected Riemannian manifold with pinched negative curvature. We combine a functional analytic tool, namely the property RD of hyperbolic groups, together with a dynamical tool: an equidistribution theorem of Paulin, Pollicott and Schapira inspired by a result of Roblin. In particular, we deduce irreducibility of these new classes of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02275","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":"2026-05-18T01:23:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+fQhEPhXrJQmu2/RH9uPewHsr060zHkyOYACCQEmeW8mLsIy0u35CAzqxFmp4vu4/shtAT1KMpFKw280hTqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:28:01.144877Z"},"content_sha256":"6c74b93a6bf2541d541fd6ca10bb771d6487c73c2f1cd42d17694361074f7518","schema_version":"1.0","event_id":"sha256:6c74b93a6bf2541d541fd6ca10bb771d6487c73c2f1cd42d17694361074f7518"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFLFOSCQ4VZKGUUHUZHAB4GXUB/bundle.json","state_url":"https://pith.science/pith/SFLFOSCQ4VZKGUUHUZHAB4GXUB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFLFOSCQ4VZKGUUHUZHAB4GXUB/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":"2026-06-22T18:28:01Z","links":{"resolver":"https://pith.science/pith/SFLFOSCQ4VZKGUUHUZHAB4GXUB","bundle":"https://pith.science/pith/SFLFOSCQ4VZKGUUHUZHAB4GXUB/bundle.json","state":"https://pith.science/pith/SFLFOSCQ4VZKGUUHUZHAB4GXUB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFLFOSCQ4VZKGUUHUZHAB4GXUB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SFLFOSCQ4VZKGUUHUZHAB4GXUB","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":"90bea26320dfa78b5fd22bd8151db6bbd48748da5dc1d9b9d880edecf7e83175","cross_cats_sorted":["math.DS","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-10T23:00:05Z","title_canon_sha256":"42341f1827c15c2b0aaa1eb0ffc7767f5bc11d3e08b926187aea7d5de1084f31"},"schema_version":"1.0","source":{"id":"1601.02275","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02275","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02275v1","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02275","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"pith_short_12","alias_value":"SFLFOSCQ4VZK","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SFLFOSCQ4VZKGUUH","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SFLFOSCQ","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:6c74b93a6bf2541d541fd6ca10bb771d6487c73c2f1cd42d17694361074f7518","target":"graph","created_at":"2026-05-18T01:23:06Z","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 generalize an equidistribution theorem \\`a la Bader-Muchnik for operator-valued measures constructed from a family of boundary representations associated with Gibbs measures in the context of convex cocompact discrete group of isometries of a simply connected connected Riemannian manifold with pinched negative curvature. We combine a functional analytic tool, namely the property RD of hyperbolic groups, together with a dynamical tool: an equidistribution theorem of Paulin, Pollicott and Schapira inspired by a result of Roblin. In particular, we deduce irreducibility of these new classes of ","authors_text":"Adrien Boyer, Dustin Mayeda","cross_cats":["math.DS","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-10T23:00:05Z","title":"Equidistribution, ergodicity and irreducibility associated with Gibbs measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02275","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":"sha256:1ca1d93196ca6f3228602053b1b88669d8f75ceef59f8728d78d454aa3d6c2a7","target":"record","created_at":"2026-05-18T01:23:06Z","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":"90bea26320dfa78b5fd22bd8151db6bbd48748da5dc1d9b9d880edecf7e83175","cross_cats_sorted":["math.DS","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-10T23:00:05Z","title_canon_sha256":"42341f1827c15c2b0aaa1eb0ffc7767f5bc11d3e08b926187aea7d5de1084f31"},"schema_version":"1.0","source":{"id":"1601.02275","kind":"arxiv","version":1}},"canonical_sha256":"9156574850e572a35287a64e00f0d7a0767f093b349519d1ec015577165b5062","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9156574850e572a35287a64e00f0d7a0767f093b349519d1ec015577165b5062","first_computed_at":"2026-05-18T01:23:06.812971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:06.812971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xAkHmeSuQM+mgF6cNYlwXnXmZg+Gw82F5vw5a8C15/oGaL+5XqWdmYGq/fwSatduSYv5Z0GXKQxB9WY8cmlmCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:06.813490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02275","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ca1d93196ca6f3228602053b1b88669d8f75ceef59f8728d78d454aa3d6c2a7","sha256:6c74b93a6bf2541d541fd6ca10bb771d6487c73c2f1cd42d17694361074f7518"],"state_sha256":"6b0f6a72bc2e14a7ba959639014920fa5cbd0fbb3aecb365452cc980ea1bfadc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BMfNnQa/azLwbNX10dbd4NlLp/lb265sLJ/s9Y6tpJJPwPLDwLx0ZN7hVBaNAdkzgMo5EpzRbw5E5aKHvtj4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:28:01.147091Z","bundle_sha256":"27d474f701b8eeaf541a3555c5ce53412af604c1e95bdbabfbedbc9e2f63d5a5"}}