{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NJ2CASLL6MGB4V7N4RE3XQ25JB","short_pith_number":"pith:NJ2CASLL","canonical_record":{"source":{"id":"1603.03018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-09T20:09:39Z","cross_cats_sorted":[],"title_canon_sha256":"d19d38764c9ec9c4a31721ceb244cf3d157e574fc7d0a9ac0deb324ef20f4627","abstract_canon_sha256":"47dd6718a04ec59cdd4510d1494ac9ca84cd98205cd825fbcfd845034c81b35b"},"schema_version":"1.0"},"canonical_sha256":"6a7420496bf30c1e57ede449bbc35d48737aa1f2b17b0936c51703c518e68712","source":{"kind":"arxiv","id":"1603.03018","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03018","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03018v1","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03018","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"pith_short_12","alias_value":"NJ2CASLL6MGB","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJ2CASLL6MGB4V7N","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJ2CASLL","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NJ2CASLL6MGB4V7N4RE3XQ25JB","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-09T20:09:39Z","cross_cats_sorted":[],"title_canon_sha256":"d19d38764c9ec9c4a31721ceb244cf3d157e574fc7d0a9ac0deb324ef20f4627","abstract_canon_sha256":"47dd6718a04ec59cdd4510d1494ac9ca84cd98205cd825fbcfd845034c81b35b"},"schema_version":"1.0"},"canonical_sha256":"6a7420496bf30c1e57ede449bbc35d48737aa1f2b17b0936c51703c518e68712","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:19.350042Z","signature_b64":"2sleCxXV7MBpgpjguf0qM11g6uzpM5jStH/4jw7VZ/Qjeq6T+qoPnRHpv3ATU/wj7oQfuz2KiqSQvu9rNPUfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a7420496bf30c1e57ede449bbc35d48737aa1f2b17b0936c51703c518e68712","last_reissued_at":"2026-05-18T01:19:19.349643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:19.349643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03018","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":"2026-05-18T01:19:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NgWZa9rVdU11XGQMFaJBXYyJJGQp+ByHoDtkwfItDHDu+XQdhNDCO+lhhE5JEKsumZKZEDV32lAzItTqNqBQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:04:05.435295Z"},"content_sha256":"e8bc997b273cf832fd92bfa940cad4988a6b2552c9ac24ba661ef69cb3f1acdc","schema_version":"1.0","event_id":"sha256:e8bc997b273cf832fd92bfa940cad4988a6b2552c9ac24ba661ef69cb3f1acdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NJ2CASLL6MGB4V7N4RE3XQ25JB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faces of simplices of invariant measures for actions of amenable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bartosz Frej, Dawid Huczek","submitted_at":"2016-03-09T20:09:39Z","abstract_excerpt":"We prove that every face in the simplex of invariant measures on a zero-dimensional dynamical system with free action of an amenable group $G$ can be modeled as the entire simplex of invariant measures on some other zero-dimensional dynamical system with free action of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03018","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":"2026-05-18T01:19:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cRM7AZBGDYYxuBGIzE1Xoq4PlLnKo2HJm6X+9NHUVrxMs9a/3gtZiexEzxtsAj9QhuOkIpAw2q1VZasmlIzTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:04:05.436017Z"},"content_sha256":"75c795658ffb7fe339752f44dad0a6b23f09fe53045bc9afa883dc2179ff1dcd","schema_version":"1.0","event_id":"sha256:75c795658ffb7fe339752f44dad0a6b23f09fe53045bc9afa883dc2179ff1dcd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJ2CASLL6MGB4V7N4RE3XQ25JB/bundle.json","state_url":"https://pith.science/pith/NJ2CASLL6MGB4V7N4RE3XQ25JB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJ2CASLL6MGB4V7N4RE3XQ25JB/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":"2026-05-31T16:04:05Z","links":{"resolver":"https://pith.science/pith/NJ2CASLL6MGB4V7N4RE3XQ25JB","bundle":"https://pith.science/pith/NJ2CASLL6MGB4V7N4RE3XQ25JB/bundle.json","state":"https://pith.science/pith/NJ2CASLL6MGB4V7N4RE3XQ25JB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJ2CASLL6MGB4V7N4RE3XQ25JB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NJ2CASLL6MGB4V7N4RE3XQ25JB","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":"47dd6718a04ec59cdd4510d1494ac9ca84cd98205cd825fbcfd845034c81b35b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-09T20:09:39Z","title_canon_sha256":"d19d38764c9ec9c4a31721ceb244cf3d157e574fc7d0a9ac0deb324ef20f4627"},"schema_version":"1.0","source":{"id":"1603.03018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03018","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03018v1","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03018","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"pith_short_12","alias_value":"NJ2CASLL6MGB","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJ2CASLL6MGB4V7N","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJ2CASLL","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:75c795658ffb7fe339752f44dad0a6b23f09fe53045bc9afa883dc2179ff1dcd","target":"graph","created_at":"2026-05-18T01:19:19Z","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 prove that every face in the simplex of invariant measures on a zero-dimensional dynamical system with free action of an amenable group $G$ can be modeled as the entire simplex of invariant measures on some other zero-dimensional dynamical system with free action of $G$.","authors_text":"Bartosz Frej, Dawid Huczek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-09T20:09:39Z","title":"Faces of simplices of invariant measures for actions of amenable groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03018","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:e8bc997b273cf832fd92bfa940cad4988a6b2552c9ac24ba661ef69cb3f1acdc","target":"record","created_at":"2026-05-18T01:19:19Z","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":"47dd6718a04ec59cdd4510d1494ac9ca84cd98205cd825fbcfd845034c81b35b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-09T20:09:39Z","title_canon_sha256":"d19d38764c9ec9c4a31721ceb244cf3d157e574fc7d0a9ac0deb324ef20f4627"},"schema_version":"1.0","source":{"id":"1603.03018","kind":"arxiv","version":1}},"canonical_sha256":"6a7420496bf30c1e57ede449bbc35d48737aa1f2b17b0936c51703c518e68712","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a7420496bf30c1e57ede449bbc35d48737aa1f2b17b0936c51703c518e68712","first_computed_at":"2026-05-18T01:19:19.349643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:19.349643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2sleCxXV7MBpgpjguf0qM11g6uzpM5jStH/4jw7VZ/Qjeq6T+qoPnRHpv3ATU/wj7oQfuz2KiqSQvu9rNPUfDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:19.350042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8bc997b273cf832fd92bfa940cad4988a6b2552c9ac24ba661ef69cb3f1acdc","sha256:75c795658ffb7fe339752f44dad0a6b23f09fe53045bc9afa883dc2179ff1dcd"],"state_sha256":"4bd961866afec7f9f68455f59d7ec786229c3491ff3417a07c8d5b90e9cd1867"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z3I1zDLZHaNbSNOw6AF/GpFlkDJk30AYy63uXvLMd77N2sJnQa2Qp57iSjCNOz2cjsOh/9Izu4TAP2UcqzHjDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:04:05.440544Z","bundle_sha256":"e715e6330ca3d7cd3f3366972350611f6871d4c5dafad34dff7fb635b90674ef"}}