{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4BKXVIUF6K6ZDAESSGFV5AZ4D3","short_pith_number":"pith:4BKXVIUF","canonical_record":{"source":{"id":"1710.07511","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-20T12:47:30Z","cross_cats_sorted":["math.FA","math.OA","math.PR"],"title_canon_sha256":"6815fccc572eb9cd23438d497de420824114788e7158edeec66ed86a17afa19a","abstract_canon_sha256":"80bd22f707b4c4864e17c58cdf7d7d875f6225a8814fca547a47ea56d8202567"},"schema_version":"1.0"},"canonical_sha256":"e0557aa285f2bd918092918b5e833c1ee05bc97b143584afa939699a1b3d7065","source":{"kind":"arxiv","id":"1710.07511","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07511","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07511v3","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07511","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"4BKXVIUF6K6Z","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4BKXVIUF6K6ZDAES","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4BKXVIUF","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4BKXVIUF6K6ZDAESSGFV5AZ4D3","target":"record","payload":{"canonical_record":{"source":{"id":"1710.07511","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-20T12:47:30Z","cross_cats_sorted":["math.FA","math.OA","math.PR"],"title_canon_sha256":"6815fccc572eb9cd23438d497de420824114788e7158edeec66ed86a17afa19a","abstract_canon_sha256":"80bd22f707b4c4864e17c58cdf7d7d875f6225a8814fca547a47ea56d8202567"},"schema_version":"1.0"},"canonical_sha256":"e0557aa285f2bd918092918b5e833c1ee05bc97b143584afa939699a1b3d7065","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:36.106996Z","signature_b64":"AphtMQPQh7r5hm+EJXwhuDO/AVKlC+nyUHZFD3m2TsiUJB/UMzrVraWslupJq6ACxrpI+lJYxvHDBTRctHSlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0557aa285f2bd918092918b5e833c1ee05bc97b143584afa939699a1b3d7065","last_reissued_at":"2026-05-18T00:02:36.106437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:36.106437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.07511","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hi4mkkICEJVJmgHWzFrGb8CqL4Vj25nWf46rPRHHlzTB3bv+6yZI7Mcgm4cvRnkibb5xpAxWNJ8G0oXqoga5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:05:46.222556Z"},"content_sha256":"3d8147e15989f7e2e84389605073361a2b1269607cb3ea5dec71ba00fe900416","schema_version":"1.0","event_id":"sha256:3d8147e15989f7e2e84389605073361a2b1269607cb3ea5dec71ba00fe900416"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4BKXVIUF6K6ZDAESSGFV5AZ4D3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuous groupoids on the symbolic space, quasi-invariant probabilities for Haar systems and the Haar-Ruelle operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OA","math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Elismar R. Oliveira","submitted_at":"2017-10-20T12:47:30Z","abstract_excerpt":"We consider groupoids on $\\{1,2,..,d\\}^\\mathbb{N}$, cocycles and the counting measure as transverse function. We generalize results relating quasi-invariant probabilities with eigenprobabilities for the dual of the Ruelle operator. We assume a mild compatibility of the groupoid with the symbolic structure. We present a generalization of the Ruelle operator - the Haar-Ruelle operator - taking into account the Haar structure. We consider continuous and also H\\\"older cocycles. IFS with weights appears in our reasoning in the H\\\"older case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07511","kind":"arxiv","version":3},"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":"2026-05-18T00:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wZx+PhrnpT7OVF82cjyQLXB3hy909InHzV/acSmJxh4rni9ufb5HqqeZEIzmBp9oFFYGYExPHggSU8MMyvIuAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:05:46.222898Z"},"content_sha256":"3e3bd9bf390492f2d3d7ee082b822dc1f95ff1e7db4ab90f2bc8b08172ff48e7","schema_version":"1.0","event_id":"sha256:3e3bd9bf390492f2d3d7ee082b822dc1f95ff1e7db4ab90f2bc8b08172ff48e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BKXVIUF6K6ZDAESSGFV5AZ4D3/bundle.json","state_url":"https://pith.science/pith/4BKXVIUF6K6ZDAESSGFV5AZ4D3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BKXVIUF6K6ZDAESSGFV5AZ4D3/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":"2026-06-20T18:05:46Z","links":{"resolver":"https://pith.science/pith/4BKXVIUF6K6ZDAESSGFV5AZ4D3","bundle":"https://pith.science/pith/4BKXVIUF6K6ZDAESSGFV5AZ4D3/bundle.json","state":"https://pith.science/pith/4BKXVIUF6K6ZDAESSGFV5AZ4D3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BKXVIUF6K6ZDAESSGFV5AZ4D3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4BKXVIUF6K6ZDAESSGFV5AZ4D3","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":"80bd22f707b4c4864e17c58cdf7d7d875f6225a8814fca547a47ea56d8202567","cross_cats_sorted":["math.FA","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-20T12:47:30Z","title_canon_sha256":"6815fccc572eb9cd23438d497de420824114788e7158edeec66ed86a17afa19a"},"schema_version":"1.0","source":{"id":"1710.07511","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07511","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07511v3","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07511","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"4BKXVIUF6K6Z","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4BKXVIUF6K6ZDAES","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4BKXVIUF","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:3e3bd9bf390492f2d3d7ee082b822dc1f95ff1e7db4ab90f2bc8b08172ff48e7","target":"graph","created_at":"2026-05-18T00:02:36Z","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 groupoids on $\\{1,2,..,d\\}^\\mathbb{N}$, cocycles and the counting measure as transverse function. We generalize results relating quasi-invariant probabilities with eigenprobabilities for the dual of the Ruelle operator. We assume a mild compatibility of the groupoid with the symbolic structure. We present a generalization of the Ruelle operator - the Haar-Ruelle operator - taking into account the Haar structure. We consider continuous and also H\\\"older cocycles. IFS with weights appears in our reasoning in the H\\\"older case.","authors_text":"Artur O. Lopes, Elismar R. Oliveira","cross_cats":["math.FA","math.OA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-20T12:47:30Z","title":"Continuous groupoids on the symbolic space, quasi-invariant probabilities for Haar systems and the Haar-Ruelle operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07511","kind":"arxiv","version":3},"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":"sha256:3d8147e15989f7e2e84389605073361a2b1269607cb3ea5dec71ba00fe900416","target":"record","created_at":"2026-05-18T00:02:36Z","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":"80bd22f707b4c4864e17c58cdf7d7d875f6225a8814fca547a47ea56d8202567","cross_cats_sorted":["math.FA","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-20T12:47:30Z","title_canon_sha256":"6815fccc572eb9cd23438d497de420824114788e7158edeec66ed86a17afa19a"},"schema_version":"1.0","source":{"id":"1710.07511","kind":"arxiv","version":3}},"canonical_sha256":"e0557aa285f2bd918092918b5e833c1ee05bc97b143584afa939699a1b3d7065","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0557aa285f2bd918092918b5e833c1ee05bc97b143584afa939699a1b3d7065","first_computed_at":"2026-05-18T00:02:36.106437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:36.106437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AphtMQPQh7r5hm+EJXwhuDO/AVKlC+nyUHZFD3m2TsiUJB/UMzrVraWslupJq6ACxrpI+lJYxvHDBTRctHSlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:36.106996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.07511","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d8147e15989f7e2e84389605073361a2b1269607cb3ea5dec71ba00fe900416","sha256:3e3bd9bf390492f2d3d7ee082b822dc1f95ff1e7db4ab90f2bc8b08172ff48e7"],"state_sha256":"b6b6f83c3497d4f4f9f79bf65b6876e473b6388adf23262f1dd873e7e3714f10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bB7LYREeagZsKXT2xRZRE7TvOgCD3Tpz0+JcMzWdykXnwqdKti3C2y5Tm38Elpe/XzWwlbLtVJPkcN4rchlpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T18:05:46.224713Z","bundle_sha256":"15c7b042e3365a78fd4c6ad50d7d94f6a4fafed81e23d7db06379b11a8fe420a"}}