{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4GWHZTOPIUNUHSIPHQP3IX26GI","short_pith_number":"pith:4GWHZTOP","canonical_record":{"source":{"id":"1809.02461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-09-07T13:26:59Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"16bc755389a5e267e47812ee0b441b5042f47794810a88c66105e597b340cfee","abstract_canon_sha256":"3e5c152e3efef53bd8bb346dbf08b62e8f729a54a4413cc2331323a4041cc02f"},"schema_version":"1.0"},"canonical_sha256":"e1ac7ccdcf451b43c90f3c1fb45f5e32275ab967922f512d33ec94c9377f8eb1","source":{"kind":"arxiv","id":"1809.02461","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02461","created_at":"2026-05-18T00:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02461v1","created_at":"2026-05-18T00:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02461","created_at":"2026-05-18T00:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"4GWHZTOPIUNU","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4GWHZTOPIUNUHSIP","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4GWHZTOP","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4GWHZTOPIUNUHSIPHQP3IX26GI","target":"record","payload":{"canonical_record":{"source":{"id":"1809.02461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-09-07T13:26:59Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"16bc755389a5e267e47812ee0b441b5042f47794810a88c66105e597b340cfee","abstract_canon_sha256":"3e5c152e3efef53bd8bb346dbf08b62e8f729a54a4413cc2331323a4041cc02f"},"schema_version":"1.0"},"canonical_sha256":"e1ac7ccdcf451b43c90f3c1fb45f5e32275ab967922f512d33ec94c9377f8eb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:17.038116Z","signature_b64":"m2/d9l6IEnhUzrXReeN25X2ObXCuULQOLIOU6hUhCzCsKA9bLIhpg9HP2unVk5HHvFP1ZsRiolbveaDQkbQgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1ac7ccdcf451b43c90f3c1fb45f5e32275ab967922f512d33ec94c9377f8eb1","last_reissued_at":"2026-05-18T00:06:17.037568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:17.037568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.02461","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":"2026-05-18T00:06:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6tCs3df6KdRW/xVCffzIw6Ti9GEDqpGDDyTO8+GB3XUXW8qt60WKy45gk9JlIMdZOPrlVReZGI+Tny0+TO+bAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:14:11.388252Z"},"content_sha256":"4ad5938c9124288396073b2d62fabe58c8dc7c3e883e2dcf9c01494b0c166bb9","schema_version":"1.0","event_id":"sha256:4ad5938c9124288396073b2d62fabe58c8dc7c3e883e2dcf9c01494b0c166bb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4GWHZTOPIUNUHSIPHQP3IX26GI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-invariant measures for generalized approximately proper equivalence relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.OA","authors_text":"R. Bissacot, R. Exel, R. Frausino, T. Raszeja","submitted_at":"2018-09-07T13:26:59Z","abstract_excerpt":"We introduce a generalization of the notion of approximately proper equivalence relations studied by Renault and with it we build an \\'etale groupoid. Choosing a suitable set of continuous functions to play the role of a potential, we construct a cocycle in that groupoid and discuss the corresponding Radon-Nikodym problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02461","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":"2026-05-18T00:06:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQwrM9DxT5DNKQLywp18BsfoImQ+Tp4fT70Q8J6ANtIEieIxbEyRKqNVFWiTFEd7BweW2Ec3g1JJeMgMMbqhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:14:11.388790Z"},"content_sha256":"0705188e137f374ee37f91d585531ead610bbc8cf9b348d5c0759baf0cf2c640","schema_version":"1.0","event_id":"sha256:0705188e137f374ee37f91d585531ead610bbc8cf9b348d5c0759baf0cf2c640"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4GWHZTOPIUNUHSIPHQP3IX26GI/bundle.json","state_url":"https://pith.science/pith/4GWHZTOPIUNUHSIPHQP3IX26GI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4GWHZTOPIUNUHSIPHQP3IX26GI/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":"2026-05-27T11:14:11Z","links":{"resolver":"https://pith.science/pith/4GWHZTOPIUNUHSIPHQP3IX26GI","bundle":"https://pith.science/pith/4GWHZTOPIUNUHSIPHQP3IX26GI/bundle.json","state":"https://pith.science/pith/4GWHZTOPIUNUHSIPHQP3IX26GI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4GWHZTOPIUNUHSIPHQP3IX26GI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4GWHZTOPIUNUHSIPHQP3IX26GI","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":"3e5c152e3efef53bd8bb346dbf08b62e8f729a54a4413cc2331323a4041cc02f","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-09-07T13:26:59Z","title_canon_sha256":"16bc755389a5e267e47812ee0b441b5042f47794810a88c66105e597b340cfee"},"schema_version":"1.0","source":{"id":"1809.02461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02461","created_at":"2026-05-18T00:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02461v1","created_at":"2026-05-18T00:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02461","created_at":"2026-05-18T00:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"4GWHZTOPIUNU","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4GWHZTOPIUNUHSIP","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4GWHZTOP","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:0705188e137f374ee37f91d585531ead610bbc8cf9b348d5c0759baf0cf2c640","target":"graph","created_at":"2026-05-18T00:06:17Z","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 introduce a generalization of the notion of approximately proper equivalence relations studied by Renault and with it we build an \\'etale groupoid. Choosing a suitable set of continuous functions to play the role of a potential, we construct a cocycle in that groupoid and discuss the corresponding Radon-Nikodym problem.","authors_text":"R. Bissacot, R. Exel, R. Frausino, T. Raszeja","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-09-07T13:26:59Z","title":"Quasi-invariant measures for generalized approximately proper equivalence relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02461","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":"sha256:4ad5938c9124288396073b2d62fabe58c8dc7c3e883e2dcf9c01494b0c166bb9","target":"record","created_at":"2026-05-18T00:06:17Z","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":"3e5c152e3efef53bd8bb346dbf08b62e8f729a54a4413cc2331323a4041cc02f","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-09-07T13:26:59Z","title_canon_sha256":"16bc755389a5e267e47812ee0b441b5042f47794810a88c66105e597b340cfee"},"schema_version":"1.0","source":{"id":"1809.02461","kind":"arxiv","version":1}},"canonical_sha256":"e1ac7ccdcf451b43c90f3c1fb45f5e32275ab967922f512d33ec94c9377f8eb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1ac7ccdcf451b43c90f3c1fb45f5e32275ab967922f512d33ec94c9377f8eb1","first_computed_at":"2026-05-18T00:06:17.037568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:17.037568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m2/d9l6IEnhUzrXReeN25X2ObXCuULQOLIOU6hUhCzCsKA9bLIhpg9HP2unVk5HHvFP1ZsRiolbveaDQkbQgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:17.038116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ad5938c9124288396073b2d62fabe58c8dc7c3e883e2dcf9c01494b0c166bb9","sha256:0705188e137f374ee37f91d585531ead610bbc8cf9b348d5c0759baf0cf2c640"],"state_sha256":"56d3b95475439a8efcd99735eafbbe17af03f3a99f52e28e3ecfcbc99d3bf207"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"27JyIOQS6X9Ru9TReFnqQlZRcS3E62B2VVPxDSqemOCT74blHZtsE1WO9Hrwlar5M+rB2JTEQC+BMaaqsCaIDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:14:11.392183Z","bundle_sha256":"8f2cb71c0b9c16f7c2d437b9a2ede5e132bf1ce54ebdcfa9b9532c05ceb39a90"}}