{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:6TV5KW4ZPCMRBBVEPGI53RW6HB","short_pith_number":"pith:6TV5KW4Z","canonical_record":{"source":{"id":"0910.2566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-14T09:33:47Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"caaa21c268bf8c2112530a52776d44ca13beaf21e062e877e9379fcc21703a83","abstract_canon_sha256":"c15842f0a5633f028d4d46f0721d8a54ccf3f73d628ede0d049c222cc818c8d7"},"schema_version":"1.0"},"canonical_sha256":"f4ebd55b9978991086a47991ddc6de3866e201733f1155c3c0a71d0d3c9de145","source":{"kind":"arxiv","id":"0910.2566","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2566","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2566v2","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2566","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"6TV5KW4ZPCMR","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6TV5KW4ZPCMRBBVE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6TV5KW4Z","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:6TV5KW4ZPCMRBBVEPGI53RW6HB","target":"record","payload":{"canonical_record":{"source":{"id":"0910.2566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-14T09:33:47Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"caaa21c268bf8c2112530a52776d44ca13beaf21e062e877e9379fcc21703a83","abstract_canon_sha256":"c15842f0a5633f028d4d46f0721d8a54ccf3f73d628ede0d049c222cc818c8d7"},"schema_version":"1.0"},"canonical_sha256":"f4ebd55b9978991086a47991ddc6de3866e201733f1155c3c0a71d0d3c9de145","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:37.057197Z","signature_b64":"+CqLIwwQ0CSxNLKetwoyP9tjd/qLbfDh7vwCIZ9jYUCQCvVhV6CaJlre5k8GtlBUyQxB38ivrF1kDT1Qlt/kDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4ebd55b9978991086a47991ddc6de3866e201733f1155c3c0a71d0d3c9de145","last_reissued_at":"2026-05-18T03:40:37.056285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:37.056285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.2566","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oQUOOVYA37nYyldLarqrmXvx3cm59hmMBKyKhE2UWZoITSXXMuU7i2YKbZY8yWI1wEwxH8CPQBKWBNfoVLGFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:23:41.938877Z"},"content_sha256":"67e8eb1220efaeedff3549952be2618d56cfbc49a16c81c951da1ba1b6ffaccd","schema_version":"1.0","event_id":"sha256:67e8eb1220efaeedff3549952be2618d56cfbc49a16c81c951da1ba1b6ffaccd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:6TV5KW4ZPCMRBBVEPGI53RW6HB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero Krengel Entropy does not kill Poisson Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"\\'Elise Janvresse (LMRS), Thierry de la Rue (LMRS)","submitted_at":"2009-10-14T09:33:47Z","abstract_excerpt":"We prove that the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measure-preserving transformation with zero Krengel entropy (the induced transformation on a set of measure 1 is the Von Neumann-Kakutani odometer), but whose associated Poisson suspension has positive entropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2566","kind":"arxiv","version":2},"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":"2026-05-18T03:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MaqYdXAkGCXkr2gtkdtXzwpNi/ByLqGJnX2DHICBiY/SykXcDcFhgsLyAC/zYPSzUZDATnJJKRQmab3oC5BZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:23:41.939599Z"},"content_sha256":"5fe445d4596f80c897dfccfdd53bce1de270030567f43072938f3c37b3cff9f8","schema_version":"1.0","event_id":"sha256:5fe445d4596f80c897dfccfdd53bce1de270030567f43072938f3c37b3cff9f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TV5KW4ZPCMRBBVEPGI53RW6HB/bundle.json","state_url":"https://pith.science/pith/6TV5KW4ZPCMRBBVEPGI53RW6HB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TV5KW4ZPCMRBBVEPGI53RW6HB/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":"2026-06-06T14:23:41Z","links":{"resolver":"https://pith.science/pith/6TV5KW4ZPCMRBBVEPGI53RW6HB","bundle":"https://pith.science/pith/6TV5KW4ZPCMRBBVEPGI53RW6HB/bundle.json","state":"https://pith.science/pith/6TV5KW4ZPCMRBBVEPGI53RW6HB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TV5KW4ZPCMRBBVEPGI53RW6HB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6TV5KW4ZPCMRBBVEPGI53RW6HB","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":"c15842f0a5633f028d4d46f0721d8a54ccf3f73d628ede0d049c222cc818c8d7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-14T09:33:47Z","title_canon_sha256":"caaa21c268bf8c2112530a52776d44ca13beaf21e062e877e9379fcc21703a83"},"schema_version":"1.0","source":{"id":"0910.2566","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2566","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2566v2","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2566","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"6TV5KW4ZPCMR","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6TV5KW4ZPCMRBBVE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6TV5KW4Z","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:5fe445d4596f80c897dfccfdd53bce1de270030567f43072938f3c37b3cff9f8","target":"graph","created_at":"2026-05-18T03:40:37Z","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 the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measure-preserving transformation with zero Krengel entropy (the induced transformation on a set of measure 1 is the Von Neumann-Kakutani odometer), but whose associated Poisson suspension has positive entropy.","authors_text":"\\'Elise Janvresse (LMRS), Thierry de la Rue (LMRS)","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-14T09:33:47Z","title":"Zero Krengel Entropy does not kill Poisson Entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2566","kind":"arxiv","version":2},"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":"sha256:67e8eb1220efaeedff3549952be2618d56cfbc49a16c81c951da1ba1b6ffaccd","target":"record","created_at":"2026-05-18T03:40:37Z","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":"c15842f0a5633f028d4d46f0721d8a54ccf3f73d628ede0d049c222cc818c8d7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-14T09:33:47Z","title_canon_sha256":"caaa21c268bf8c2112530a52776d44ca13beaf21e062e877e9379fcc21703a83"},"schema_version":"1.0","source":{"id":"0910.2566","kind":"arxiv","version":2}},"canonical_sha256":"f4ebd55b9978991086a47991ddc6de3866e201733f1155c3c0a71d0d3c9de145","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4ebd55b9978991086a47991ddc6de3866e201733f1155c3c0a71d0d3c9de145","first_computed_at":"2026-05-18T03:40:37.056285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:37.056285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+CqLIwwQ0CSxNLKetwoyP9tjd/qLbfDh7vwCIZ9jYUCQCvVhV6CaJlre5k8GtlBUyQxB38ivrF1kDT1Qlt/kDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:37.057197Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2566","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67e8eb1220efaeedff3549952be2618d56cfbc49a16c81c951da1ba1b6ffaccd","sha256:5fe445d4596f80c897dfccfdd53bce1de270030567f43072938f3c37b3cff9f8"],"state_sha256":"037903dc45b42955f6a9097950ef645dc3f80b20fa77635fd224a1c3bc62ba19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"87T8vSGrCfwspBbcgXCUGjYNMB5oaCvGGUw2+8R27RY11zi68Y2voaXRC0ae3rk49hAwTE+BqMainA0pphoqCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:23:41.943083Z","bundle_sha256":"48f69fe8f88ff5a42657003449919ddff5df3723def37003ffd2a63a245f5d98"}}