{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YXOOINXYEMXGNHB64NFKU3NPM4","short_pith_number":"pith:YXOOINXY","canonical_record":{"source":{"id":"1109.6283","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-28T18:16:13Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"06af94da2c499c6f881c3b0a9c2ce46fe8b70f7e914b928259ee586b0b538809","abstract_canon_sha256":"ba5436bcc978d2f8111a1df819753a13c8ef0a1fa584d23a36f3a905ba5c8e18"},"schema_version":"1.0"},"canonical_sha256":"c5dce436f8232e669c3ee34aaa6daf672865db16df97f07a83090eca54a3a80e","source":{"kind":"arxiv","id":"1109.6283","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6283","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6283v1","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6283","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"YXOOINXYEMXG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YXOOINXYEMXGNHB6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YXOOINXY","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YXOOINXYEMXGNHB64NFKU3NPM4","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6283","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-28T18:16:13Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"06af94da2c499c6f881c3b0a9c2ce46fe8b70f7e914b928259ee586b0b538809","abstract_canon_sha256":"ba5436bcc978d2f8111a1df819753a13c8ef0a1fa584d23a36f3a905ba5c8e18"},"schema_version":"1.0"},"canonical_sha256":"c5dce436f8232e669c3ee34aaa6daf672865db16df97f07a83090eca54a3a80e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:09.402512Z","signature_b64":"x8doTFh8pPTxnDyzbJZ5Qut1iD3b7+k01YBXgtHo9z1douXXbO7UD/iNQiHJOGKAcZbsxao9W755D503VjpKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5dce436f8232e669c3ee34aaa6daf672865db16df97f07a83090eca54a3a80e","last_reissued_at":"2026-05-18T04:12:09.402019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:09.402019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6283","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":"2026-05-18T04:12:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/F/Hh19/Kx8OnccX5H0wg7HB0hxjscDdVRuY48Wss3xUQOqxTCP2O0+gKdTn9PIj+xu1EP2kaXpUMfSv2o7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:48:36.245467Z"},"content_sha256":"5fd9cd41dcf164f3a7ddd94c454355bf97eff0cd75c445af8b67cf4fb05c5030","schema_version":"1.0","event_id":"sha256:5fd9cd41dcf164f3a7ddd94c454355bf97eff0cd75c445af8b67cf4fb05c5030"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YXOOINXYEMXGNHB64NFKU3NPM4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster point processes on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Alexei Daletskii, Leonid Bogachev","submitted_at":"2011-09-28T18:16:13Z","abstract_excerpt":"The probability distribution $\\mu_{cl}$ of a general cluster point process in a Riemannian manifold $X$ (with independent random clusters attached to points of a configuration with distribution $\\mu$) is studied via the projection of an auxiliary measure $\\hat{\\mu}$ in the space of configurations $\\hat{\\gamma}=\\{(x,\\bar{y})\\}\\subset X\\times\\mathfrak{X}$, where $x\\in X$ indicates a cluster \"centre\" and $\\bar{y}\\in\\mathfrak{X}:=\\bigsqcup_{n} X^n$ represents a corresponding cluster relative to $x$. We show that the measure $\\mu_{cl}$ is quasi-invariant with respect to the group $Diff_{0}(X)$ of c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6283","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":"2026-05-18T04:12:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SEYZyvSTd+QNNPdWfIeOkMhJmZX8HnhTu2vMwFnIPbOwWl5eMXX1Mea0T5clMEvOg1TZOpOQl0lIN3hG1ZCsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:48:36.246437Z"},"content_sha256":"c8c75c382eeaa0c9672201e916c664e4832722b34efe6be65944107e59435450","schema_version":"1.0","event_id":"sha256:c8c75c382eeaa0c9672201e916c664e4832722b34efe6be65944107e59435450"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXOOINXYEMXGNHB64NFKU3NPM4/bundle.json","state_url":"https://pith.science/pith/YXOOINXYEMXGNHB64NFKU3NPM4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXOOINXYEMXGNHB64NFKU3NPM4/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":"2026-05-31T19:48:36Z","links":{"resolver":"https://pith.science/pith/YXOOINXYEMXGNHB64NFKU3NPM4","bundle":"https://pith.science/pith/YXOOINXYEMXGNHB64NFKU3NPM4/bundle.json","state":"https://pith.science/pith/YXOOINXYEMXGNHB64NFKU3NPM4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXOOINXYEMXGNHB64NFKU3NPM4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YXOOINXYEMXGNHB64NFKU3NPM4","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":"ba5436bcc978d2f8111a1df819753a13c8ef0a1fa584d23a36f3a905ba5c8e18","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-28T18:16:13Z","title_canon_sha256":"06af94da2c499c6f881c3b0a9c2ce46fe8b70f7e914b928259ee586b0b538809"},"schema_version":"1.0","source":{"id":"1109.6283","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6283","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6283v1","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6283","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"YXOOINXYEMXG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YXOOINXYEMXGNHB6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YXOOINXY","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:c8c75c382eeaa0c9672201e916c664e4832722b34efe6be65944107e59435450","target":"graph","created_at":"2026-05-18T04:12:09Z","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":"The probability distribution $\\mu_{cl}$ of a general cluster point process in a Riemannian manifold $X$ (with independent random clusters attached to points of a configuration with distribution $\\mu$) is studied via the projection of an auxiliary measure $\\hat{\\mu}$ in the space of configurations $\\hat{\\gamma}=\\{(x,\\bar{y})\\}\\subset X\\times\\mathfrak{X}$, where $x\\in X$ indicates a cluster \"centre\" and $\\bar{y}\\in\\mathfrak{X}:=\\bigsqcup_{n} X^n$ represents a corresponding cluster relative to $x$. We show that the measure $\\mu_{cl}$ is quasi-invariant with respect to the group $Diff_{0}(X)$ of c","authors_text":"Alexei Daletskii, Leonid Bogachev","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-28T18:16:13Z","title":"Cluster point processes on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6283","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":"sha256:5fd9cd41dcf164f3a7ddd94c454355bf97eff0cd75c445af8b67cf4fb05c5030","target":"record","created_at":"2026-05-18T04:12:09Z","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":"ba5436bcc978d2f8111a1df819753a13c8ef0a1fa584d23a36f3a905ba5c8e18","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-28T18:16:13Z","title_canon_sha256":"06af94da2c499c6f881c3b0a9c2ce46fe8b70f7e914b928259ee586b0b538809"},"schema_version":"1.0","source":{"id":"1109.6283","kind":"arxiv","version":1}},"canonical_sha256":"c5dce436f8232e669c3ee34aaa6daf672865db16df97f07a83090eca54a3a80e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5dce436f8232e669c3ee34aaa6daf672865db16df97f07a83090eca54a3a80e","first_computed_at":"2026-05-18T04:12:09.402019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:09.402019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x8doTFh8pPTxnDyzbJZ5Qut1iD3b7+k01YBXgtHo9z1douXXbO7UD/iNQiHJOGKAcZbsxao9W755D503VjpKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:09.402512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6283","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fd9cd41dcf164f3a7ddd94c454355bf97eff0cd75c445af8b67cf4fb05c5030","sha256:c8c75c382eeaa0c9672201e916c664e4832722b34efe6be65944107e59435450"],"state_sha256":"b0ae24e376bacc674bb618cd2003e0d36076f6caa7a7b8becf40d2e1e012aecd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V07J9Z+izmtmSPR3zxeHXewhWDm3B5BxEj3CV93faiWsqBONQ3A92bKX2jXB10y4TfpTvX/K1qiMBrG963LcCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:48:36.250269Z","bundle_sha256":"e7686d3640b212bdaa13c9aaaf2401893216dce082063033c6812053b4da6d1a"}}