{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VQ5OGGAH4KNUUVTHS4OE34FSAE","short_pith_number":"pith:VQ5OGGAH","canonical_record":{"source":{"id":"2505.21195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-27T13:43:06Z","cross_cats_sorted":[],"title_canon_sha256":"77c91db375c51a2f5250efcbd3b8ff3c4dadaff47d79ec228daab896cc3e8f85","abstract_canon_sha256":"8fc4831f9a948c0f828914e446f3928bffac2b15815fc43519499c3ff1e2df8f"},"schema_version":"1.0"},"canonical_sha256":"ac3ae31807e29b4a5667971c4df0b20123873b901862f75940fbab489cf7e24d","source":{"kind":"arxiv","id":"2505.21195","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21195","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21195v1","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21195","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"pith_short_12","alias_value":"VQ5OGGAH4KNU","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"pith_short_16","alias_value":"VQ5OGGAH4KNUUVTH","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"pith_short_8","alias_value":"VQ5OGGAH","created_at":"2026-07-05T11:10:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VQ5OGGAH4KNUUVTHS4OE34FSAE","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-27T13:43:06Z","cross_cats_sorted":[],"title_canon_sha256":"77c91db375c51a2f5250efcbd3b8ff3c4dadaff47d79ec228daab896cc3e8f85","abstract_canon_sha256":"8fc4831f9a948c0f828914e446f3928bffac2b15815fc43519499c3ff1e2df8f"},"schema_version":"1.0"},"canonical_sha256":"ac3ae31807e29b4a5667971c4df0b20123873b901862f75940fbab489cf7e24d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:38.581281Z","signature_b64":"MJDvkRWuXKcatbWhVyvaGIiU2dppGMVNbGCq3dLZdkYD0EcvyTOSD+BOh2gx9Yy8vq/zNyusWlZuw8IUWQFYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac3ae31807e29b4a5667971c4df0b20123873b901862f75940fbab489cf7e24d","last_reissued_at":"2026-07-05T11:10:38.580671Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:38.580671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21195","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":"2026-07-05T11:10:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KX6U/1EgY9yIb4u9AkXiXzaLtUWSzRLFHBd5pxryn+nGCLjexAbsbBF95B3pbdiY3ZCouPVjE4iIRyhh1wtNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:19:00.419422Z"},"content_sha256":"7a78754cfd48ae1667e51fbb1b382abf279aa74f70558daee815f57e03eea44e","schema_version":"1.0","event_id":"sha256:7a78754cfd48ae1667e51fbb1b382abf279aa74f70558daee815f57e03eea44e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VQ5OGGAH4KNUUVTHS4OE34FSAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction and limit theorems for supCAR fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andriy Olenko, Illia Donhauzer, Nikolai Leonenko","submitted_at":"2025-05-27T13:43:06Z","abstract_excerpt":"The paper introduces a new class of random fields, supCAR fields, which are constructed as superpositions of continuous autoregressive random fields. These supCAR fields possess infinitely divisible marginal distributions. Their second-order properties are characterised by a novel family of covariance functions which can exhibit short- and long-range spatial dependencies. First, the existence of such fields is examined. Then, functional limit theorems for supCAR fields are derived under general assumptions. Four limiting scenarios that depend on the marginals of the underlying autoregressive f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21195","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.21195/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:10:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tFq0lZIDbGoG0gZJAHOpsR0Rvu1RZgglxt21ha2He8kjfRxlenoqzzvpbA6jaCFxiZ9iTknZjjsze6mdpWo5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:19:00.419948Z"},"content_sha256":"7e0d5a339e6ad8994a5d76e6afd06b5c1531f034bd4f759b6d882f122f365b14","schema_version":"1.0","event_id":"sha256:7e0d5a339e6ad8994a5d76e6afd06b5c1531f034bd4f759b6d882f122f365b14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQ5OGGAH4KNUUVTHS4OE34FSAE/bundle.json","state_url":"https://pith.science/pith/VQ5OGGAH4KNUUVTHS4OE34FSAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQ5OGGAH4KNUUVTHS4OE34FSAE/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":"2026-08-08T16:19:00Z","links":{"resolver":"https://pith.science/pith/VQ5OGGAH4KNUUVTHS4OE34FSAE","bundle":"https://pith.science/pith/VQ5OGGAH4KNUUVTHS4OE34FSAE/bundle.json","state":"https://pith.science/pith/VQ5OGGAH4KNUUVTHS4OE34FSAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQ5OGGAH4KNUUVTHS4OE34FSAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VQ5OGGAH4KNUUVTHS4OE34FSAE","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":"8fc4831f9a948c0f828914e446f3928bffac2b15815fc43519499c3ff1e2df8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-27T13:43:06Z","title_canon_sha256":"77c91db375c51a2f5250efcbd3b8ff3c4dadaff47d79ec228daab896cc3e8f85"},"schema_version":"1.0","source":{"id":"2505.21195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21195","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21195v1","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21195","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"pith_short_12","alias_value":"VQ5OGGAH4KNU","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"pith_short_16","alias_value":"VQ5OGGAH4KNUUVTH","created_at":"2026-07-05T11:10:38Z"},{"alias_kind":"pith_short_8","alias_value":"VQ5OGGAH","created_at":"2026-07-05T11:10:38Z"}],"graph_snapshots":[{"event_id":"sha256:7e0d5a339e6ad8994a5d76e6afd06b5c1531f034bd4f759b6d882f122f365b14","target":"graph","created_at":"2026-07-05T11:10:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.21195/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The paper introduces a new class of random fields, supCAR fields, which are constructed as superpositions of continuous autoregressive random fields. These supCAR fields possess infinitely divisible marginal distributions. Their second-order properties are characterised by a novel family of covariance functions which can exhibit short- and long-range spatial dependencies. First, the existence of such fields is examined. Then, functional limit theorems for supCAR fields are derived under general assumptions. Four limiting scenarios that depend on the marginals of the underlying autoregressive f","authors_text":"Andriy Olenko, Illia Donhauzer, Nikolai Leonenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-27T13:43:06Z","title":"Construction and limit theorems for supCAR fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21195","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":"sha256:7a78754cfd48ae1667e51fbb1b382abf279aa74f70558daee815f57e03eea44e","target":"record","created_at":"2026-07-05T11:10:38Z","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":"8fc4831f9a948c0f828914e446f3928bffac2b15815fc43519499c3ff1e2df8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-27T13:43:06Z","title_canon_sha256":"77c91db375c51a2f5250efcbd3b8ff3c4dadaff47d79ec228daab896cc3e8f85"},"schema_version":"1.0","source":{"id":"2505.21195","kind":"arxiv","version":1}},"canonical_sha256":"ac3ae31807e29b4a5667971c4df0b20123873b901862f75940fbab489cf7e24d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac3ae31807e29b4a5667971c4df0b20123873b901862f75940fbab489cf7e24d","first_computed_at":"2026-07-05T11:10:38.580671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:38.580671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MJDvkRWuXKcatbWhVyvaGIiU2dppGMVNbGCq3dLZdkYD0EcvyTOSD+BOh2gx9Yy8vq/zNyusWlZuw8IUWQFYBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:38.581281Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a78754cfd48ae1667e51fbb1b382abf279aa74f70558daee815f57e03eea44e","sha256:7e0d5a339e6ad8994a5d76e6afd06b5c1531f034bd4f759b6d882f122f365b14"],"state_sha256":"f525530c97f4294a1c159e82e8f625315c4098d78d02b97ee6ef950289c56e20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x6QxXRcsefhtxrD9hCylQbM8enVnHYVhi2ngHelKxi4ZvypRgsMJ9+hW79OrmC/ae0D581b0OFpegRCGu/LtAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:19:00.423786Z","bundle_sha256":"6fa738a8e937ff7c114e5797879b9f5b7b5e71d79eddf37effd1558c2c5d8469"}}