{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HFLTTR77JVV2PZB4MS4KTMNEB5","short_pith_number":"pith:HFLTTR77","canonical_record":{"source":{"id":"1201.4765","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-23T16:56:42Z","cross_cats_sorted":[],"title_canon_sha256":"12a0ec1386132215c3c502dea47e17485a3514bb7dfb7fb035373c297b28dc1b","abstract_canon_sha256":"201b2eb02863e2e2306a3742b06350797b64505435a4412dc3964deef74066a1"},"schema_version":"1.0"},"canonical_sha256":"395739c7ff4d6ba7e43c64b8a9b1a40f70bcfccae33712a176f44fcace1d4fc0","source":{"kind":"arxiv","id":"1201.4765","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4765","created_at":"2026-05-18T03:08:14Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4765v3","created_at":"2026-05-18T03:08:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4765","created_at":"2026-05-18T03:08:14Z"},{"alias_kind":"pith_short_12","alias_value":"HFLTTR77JVV2","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HFLTTR77JVV2PZB4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HFLTTR77","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HFLTTR77JVV2PZB4MS4KTMNEB5","target":"record","payload":{"canonical_record":{"source":{"id":"1201.4765","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-23T16:56:42Z","cross_cats_sorted":[],"title_canon_sha256":"12a0ec1386132215c3c502dea47e17485a3514bb7dfb7fb035373c297b28dc1b","abstract_canon_sha256":"201b2eb02863e2e2306a3742b06350797b64505435a4412dc3964deef74066a1"},"schema_version":"1.0"},"canonical_sha256":"395739c7ff4d6ba7e43c64b8a9b1a40f70bcfccae33712a176f44fcace1d4fc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:14.717398Z","signature_b64":"9e6k7W/EAfCGmU6UQp+338VWLKcbbjXmrleZDpi0c36lDduDFoCAjygq/0s626yFy6kCQ4DqhCuWDkFjfJa0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"395739c7ff4d6ba7e43c64b8a9b1a40f70bcfccae33712a176f44fcace1d4fc0","last_reissued_at":"2026-05-18T03:08:14.716910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:14.716910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.4765","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":"2026-05-18T03:08:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pBSX/qMC2eEvbHMPgqbM/DwguCzM3jJEzDoLg1dG/KT7UDlBfbfhc8zdvpLt3QA9EGymny0K22lU/ZoBSgVCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:58:01.020656Z"},"content_sha256":"c16ef858bf347addb5a98cbb9cb8ff659c3d52ad49bcd5bf9b7aaaba60395650","schema_version":"1.0","event_id":"sha256:c16ef858bf347addb5a98cbb9cb8ff659c3d52ad49bcd5bf9b7aaaba60395650"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HFLTTR77JVV2PZB4MS4KTMNEB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationarity of multivariate particle systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ilya Molchanov, Kaspar Stucki","submitted_at":"2012-01-23T16:56:42Z","abstract_excerpt":"A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in R^d and in some cases provide a full characterisation of the stationarity property. In particular, a full characterisation of stationary multivariate Brown-Resnick processes is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4765","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":"2026-05-18T03:08:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nhqoJTrVRiCfFAdqTZmLltmwDuRCoWqs/9omDX1kF5W0boUNFF6k9LN4hM3xvbt4dTGWTnBAGqURdJ2XpWCiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:58:01.021373Z"},"content_sha256":"c1de69b793e3a0990d51edcd59bcef8e32f7b1ada9413f3f5a8916ea199eb578","schema_version":"1.0","event_id":"sha256:c1de69b793e3a0990d51edcd59bcef8e32f7b1ada9413f3f5a8916ea199eb578"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HFLTTR77JVV2PZB4MS4KTMNEB5/bundle.json","state_url":"https://pith.science/pith/HFLTTR77JVV2PZB4MS4KTMNEB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HFLTTR77JVV2PZB4MS4KTMNEB5/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":"2026-05-30T03:58:01Z","links":{"resolver":"https://pith.science/pith/HFLTTR77JVV2PZB4MS4KTMNEB5","bundle":"https://pith.science/pith/HFLTTR77JVV2PZB4MS4KTMNEB5/bundle.json","state":"https://pith.science/pith/HFLTTR77JVV2PZB4MS4KTMNEB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HFLTTR77JVV2PZB4MS4KTMNEB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HFLTTR77JVV2PZB4MS4KTMNEB5","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":"201b2eb02863e2e2306a3742b06350797b64505435a4412dc3964deef74066a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-23T16:56:42Z","title_canon_sha256":"12a0ec1386132215c3c502dea47e17485a3514bb7dfb7fb035373c297b28dc1b"},"schema_version":"1.0","source":{"id":"1201.4765","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4765","created_at":"2026-05-18T03:08:14Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4765v3","created_at":"2026-05-18T03:08:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4765","created_at":"2026-05-18T03:08:14Z"},{"alias_kind":"pith_short_12","alias_value":"HFLTTR77JVV2","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HFLTTR77JVV2PZB4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HFLTTR77","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:c1de69b793e3a0990d51edcd59bcef8e32f7b1ada9413f3f5a8916ea199eb578","target":"graph","created_at":"2026-05-18T03:08:14Z","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":"A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in R^d and in some cases provide a full characterisation of the stationarity property. In particular, a full characterisation of stationary multivariate Brown-Resnick processes is given.","authors_text":"Ilya Molchanov, Kaspar Stucki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-23T16:56:42Z","title":"Stationarity of multivariate particle systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4765","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:c16ef858bf347addb5a98cbb9cb8ff659c3d52ad49bcd5bf9b7aaaba60395650","target":"record","created_at":"2026-05-18T03:08:14Z","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":"201b2eb02863e2e2306a3742b06350797b64505435a4412dc3964deef74066a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-23T16:56:42Z","title_canon_sha256":"12a0ec1386132215c3c502dea47e17485a3514bb7dfb7fb035373c297b28dc1b"},"schema_version":"1.0","source":{"id":"1201.4765","kind":"arxiv","version":3}},"canonical_sha256":"395739c7ff4d6ba7e43c64b8a9b1a40f70bcfccae33712a176f44fcace1d4fc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"395739c7ff4d6ba7e43c64b8a9b1a40f70bcfccae33712a176f44fcace1d4fc0","first_computed_at":"2026-05-18T03:08:14.716910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:14.716910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9e6k7W/EAfCGmU6UQp+338VWLKcbbjXmrleZDpi0c36lDduDFoCAjygq/0s626yFy6kCQ4DqhCuWDkFjfJa0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:14.717398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4765","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c16ef858bf347addb5a98cbb9cb8ff659c3d52ad49bcd5bf9b7aaaba60395650","sha256:c1de69b793e3a0990d51edcd59bcef8e32f7b1ada9413f3f5a8916ea199eb578"],"state_sha256":"639db0759164aced60b753c90e3db6ae1b884383daac42bea2a5601aecbaef88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5AoeMCA2ISJS6tcsi/2NmleMvzhysuSbWkdFBm5/iwQxxZCsKVDa1yI8zpnKfgWy9EEKGbO7dvpxn3SfN9KxAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:58:01.026255Z","bundle_sha256":"6f26618930f2fb0f6cb16e67233c7252ba8ba7f8c1811c908782e417773225c4"}}