{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HUZHCATE3UH5PDM5IXHPVBX2JM","short_pith_number":"pith:HUZHCATE","canonical_record":{"source":{"id":"1705.00182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-29T12:57:59Z","cross_cats_sorted":[],"title_canon_sha256":"15d7ef558b5018cf4ee7a80a62fbd84b262cc961af6ad0e924b9a852982f2a7e","abstract_canon_sha256":"f1ecf585506df21ba3c3b8140f5ca9a3f884ab9bd0374f77dc41af4b6a585a7c"},"schema_version":"1.0"},"canonical_sha256":"3d32710264dd0fd78d9d45cefa86fa4b1d7cc27d0542f30ca94c46e0d285d080","source":{"kind":"arxiv","id":"1705.00182","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00182","created_at":"2026-05-18T00:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00182v1","created_at":"2026-05-18T00:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00182","created_at":"2026-05-18T00:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"HUZHCATE3UH5","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HUZHCATE3UH5PDM5","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HUZHCATE","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HUZHCATE3UH5PDM5IXHPVBX2JM","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-29T12:57:59Z","cross_cats_sorted":[],"title_canon_sha256":"15d7ef558b5018cf4ee7a80a62fbd84b262cc961af6ad0e924b9a852982f2a7e","abstract_canon_sha256":"f1ecf585506df21ba3c3b8140f5ca9a3f884ab9bd0374f77dc41af4b6a585a7c"},"schema_version":"1.0"},"canonical_sha256":"3d32710264dd0fd78d9d45cefa86fa4b1d7cc27d0542f30ca94c46e0d285d080","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:21.251208Z","signature_b64":"kh7qEJrKWuJX7JVHxA6oR8NdivJj+NbmQ7z3QO7ScoDcAmw+j68vOjAp7v9QaW4vgQ5fulD+d4uZonpiDLmqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d32710264dd0fd78d9d45cefa86fa4b1d7cc27d0542f30ca94c46e0d285d080","last_reissued_at":"2026-05-18T00:45:21.250563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:21.250563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00182","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":"2026-05-18T00:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SXQxofVmoOAGCz7e796Eoo1vazg0zZaFMDcwTU+q8GDGWg6yUnEuB5+sijJbDhGQdni9bMGN0OskkZAypRgyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T14:13:42.019804Z"},"content_sha256":"7f05f4ed2d355e22e464b6a2db5addac34ebdaeadde03199b30df7cd53925da9","schema_version":"1.0","event_id":"sha256:7f05f4ed2d355e22e464b6a2db5addac34ebdaeadde03199b30df7cd53925da9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HUZHCATE3UH5PDM5IXHPVBX2JM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lamperti type theorems for random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Vygantas Paulauskas, Youri Davydov","submitted_at":"2017-04-29T12:57:59Z","abstract_excerpt":"In the paper we consider Lamperti type theorems for random fields. Together with known results we present some new results on ${\\mathbb R}^m$-valued self-similar fields $\\{{\\bf X} ({\\bf t}), \\ {\\bf t} \\in {\\mathbb R}^d \\}$, their domains of attraction and the so-called Lamperti transformations, expressing the relation between self-similarity and stationarity. Also we investigate regularly and slowly varying functions of several variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00182","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":"2026-05-18T00:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u6y4L6y8sLQyypouCW97ZVkQrwyrGaM8OU2Xejg5jDIy7Dht1pcYZARIxsXANCAhyOEoq8c/5IBP9G+/QkvVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T14:13:42.020146Z"},"content_sha256":"68c915091cc53918bfaab53b620195652012ba629d5ed8548c45e26e817ef0ff","schema_version":"1.0","event_id":"sha256:68c915091cc53918bfaab53b620195652012ba629d5ed8548c45e26e817ef0ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HUZHCATE3UH5PDM5IXHPVBX2JM/bundle.json","state_url":"https://pith.science/pith/HUZHCATE3UH5PDM5IXHPVBX2JM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HUZHCATE3UH5PDM5IXHPVBX2JM/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":"2026-07-03T14:13:42Z","links":{"resolver":"https://pith.science/pith/HUZHCATE3UH5PDM5IXHPVBX2JM","bundle":"https://pith.science/pith/HUZHCATE3UH5PDM5IXHPVBX2JM/bundle.json","state":"https://pith.science/pith/HUZHCATE3UH5PDM5IXHPVBX2JM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HUZHCATE3UH5PDM5IXHPVBX2JM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HUZHCATE3UH5PDM5IXHPVBX2JM","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":"f1ecf585506df21ba3c3b8140f5ca9a3f884ab9bd0374f77dc41af4b6a585a7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-29T12:57:59Z","title_canon_sha256":"15d7ef558b5018cf4ee7a80a62fbd84b262cc961af6ad0e924b9a852982f2a7e"},"schema_version":"1.0","source":{"id":"1705.00182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00182","created_at":"2026-05-18T00:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00182v1","created_at":"2026-05-18T00:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00182","created_at":"2026-05-18T00:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"HUZHCATE3UH5","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HUZHCATE3UH5PDM5","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HUZHCATE","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:68c915091cc53918bfaab53b620195652012ba629d5ed8548c45e26e817ef0ff","target":"graph","created_at":"2026-05-18T00:45:21Z","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":"In the paper we consider Lamperti type theorems for random fields. Together with known results we present some new results on ${\\mathbb R}^m$-valued self-similar fields $\\{{\\bf X} ({\\bf t}), \\ {\\bf t} \\in {\\mathbb R}^d \\}$, their domains of attraction and the so-called Lamperti transformations, expressing the relation between self-similarity and stationarity. Also we investigate regularly and slowly varying functions of several variables.","authors_text":"Vygantas Paulauskas, Youri Davydov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-29T12:57:59Z","title":"Lamperti type theorems for random fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00182","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":"sha256:7f05f4ed2d355e22e464b6a2db5addac34ebdaeadde03199b30df7cd53925da9","target":"record","created_at":"2026-05-18T00:45:21Z","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":"f1ecf585506df21ba3c3b8140f5ca9a3f884ab9bd0374f77dc41af4b6a585a7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-29T12:57:59Z","title_canon_sha256":"15d7ef558b5018cf4ee7a80a62fbd84b262cc961af6ad0e924b9a852982f2a7e"},"schema_version":"1.0","source":{"id":"1705.00182","kind":"arxiv","version":1}},"canonical_sha256":"3d32710264dd0fd78d9d45cefa86fa4b1d7cc27d0542f30ca94c46e0d285d080","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d32710264dd0fd78d9d45cefa86fa4b1d7cc27d0542f30ca94c46e0d285d080","first_computed_at":"2026-05-18T00:45:21.250563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:21.250563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kh7qEJrKWuJX7JVHxA6oR8NdivJj+NbmQ7z3QO7ScoDcAmw+j68vOjAp7v9QaW4vgQ5fulD+d4uZonpiDLmqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:21.251208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f05f4ed2d355e22e464b6a2db5addac34ebdaeadde03199b30df7cd53925da9","sha256:68c915091cc53918bfaab53b620195652012ba629d5ed8548c45e26e817ef0ff"],"state_sha256":"6265bd77d1f4bfda1d9b563f6f16b7b8e9abb765f89e9b563b7696d0a27c4d10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3yKGOpWVpYXT6snMt+oaCceN5w1pwWhLlMVnc2JW631ytRQkFG71pmoBPppVrDber8fQpPwff4pIAetAIKb0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T14:13:42.022277Z","bundle_sha256":"79f03a5a3970bf5fac8ae3351cd9ae6403a7949a22241a3b02ad81a357f13029"}}