{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:R4J6ZOAYVLIJEBQDQDHFMDM7CG","short_pith_number":"pith:R4J6ZOAY","canonical_record":{"source":{"id":"1006.5730","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-06-29T21:01:02Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"989e22cccb8681def4826496a9e18cfa0dbbd907a99d4d1e5d1b41a11ba7d0be","abstract_canon_sha256":"09a942e0b6989f37e9348a910747097e8343a63c934f0951fdbb2f9fe9c332e1"},"schema_version":"1.0"},"canonical_sha256":"8f13ecb818aad092060380ce560d9f119718dbe8d355eba6f735732f74d2ebe0","source":{"kind":"arxiv","id":"1006.5730","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5730","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5730v3","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5730","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"R4J6ZOAYVLIJ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"R4J6ZOAYVLIJEBQD","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"R4J6ZOAY","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:R4J6ZOAYVLIJEBQDQDHFMDM7CG","target":"record","payload":{"canonical_record":{"source":{"id":"1006.5730","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-06-29T21:01:02Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"989e22cccb8681def4826496a9e18cfa0dbbd907a99d4d1e5d1b41a11ba7d0be","abstract_canon_sha256":"09a942e0b6989f37e9348a910747097e8343a63c934f0951fdbb2f9fe9c332e1"},"schema_version":"1.0"},"canonical_sha256":"8f13ecb818aad092060380ce560d9f119718dbe8d355eba6f735732f74d2ebe0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:39.875567Z","signature_b64":"3SKKwWn7mRF69MzPEQba3y2WyE8aJlVDSsUJw9WiDHVdvtzYQnKlhQOK+xYjZPW+JVDbBKNrW18WwXDp7HZYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f13ecb818aad092060380ce560d9f119718dbe8d355eba6f735732f74d2ebe0","last_reissued_at":"2026-05-18T02:54:39.875172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:39.875172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.5730","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":"2026-05-18T02:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrEHXgjrzRsgBz0gjT1Ympcix7+R/Im6FU0FXxPD7p47FUb/fnbVKKFDi6zDXL78G1IrMT4/mW0vJKj+zaffDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:23:52.480755Z"},"content_sha256":"d5d863dfa86cc5815cb9f40d75c540a355636c4232e9f179c08d43a41d333b9b","schema_version":"1.0","event_id":"sha256:d5d863dfa86cc5815cb9f40d75c540a355636c4232e9f179c08d43a41d333b9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:R4J6ZOAYVLIJEBQDQDHFMDM7CG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the variances of a spatial unit root model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"S\\'andor Baran","submitted_at":"2010-06-29T21:01:02Z","abstract_excerpt":"The asymptotic properties of the variances of the spatial autoregressive model $X_{k,\\ell}=\\alpha X_{k-1,\\ell}+\\beta X_{k,\\ell-1}+\\gamma X_{k-1,\\ell-1}+\\epsilon_{k,\\ell}$ are investigated in the unit root case, that is when the parameters are on the boundary of domain of stability that forms a tetrahedron in $[-1,1]^3$. The limit of the variance of $n^{-\\varrho}X_{[ns],[nt]}$ is determined, where on the interior of the faces of the domain of stability $\\varrho=1/4$, on the edges $\\varrho =1/2$, while on the vertices $\\varrho =1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5730","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":"2026-05-18T02:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TckFBKDZpIsXptVXx9GESi8XH98KuiEK8poGV7PeaZeEP5DkEQEjzLuejouIiF+RWnToSMQXQyjQzmtNLqSfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:23:52.481102Z"},"content_sha256":"af8bbb55fdcc59551a6e6fabf26d7f60d6de4b3186fcf3076204e7e16ca2a3c4","schema_version":"1.0","event_id":"sha256:af8bbb55fdcc59551a6e6fabf26d7f60d6de4b3186fcf3076204e7e16ca2a3c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4J6ZOAYVLIJEBQDQDHFMDM7CG/bundle.json","state_url":"https://pith.science/pith/R4J6ZOAYVLIJEBQDQDHFMDM7CG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4J6ZOAYVLIJEBQDQDHFMDM7CG/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":"2026-06-22T14:23:52Z","links":{"resolver":"https://pith.science/pith/R4J6ZOAYVLIJEBQDQDHFMDM7CG","bundle":"https://pith.science/pith/R4J6ZOAYVLIJEBQDQDHFMDM7CG/bundle.json","state":"https://pith.science/pith/R4J6ZOAYVLIJEBQDQDHFMDM7CG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4J6ZOAYVLIJEBQDQDHFMDM7CG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:R4J6ZOAYVLIJEBQDQDHFMDM7CG","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":"09a942e0b6989f37e9348a910747097e8343a63c934f0951fdbb2f9fe9c332e1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-06-29T21:01:02Z","title_canon_sha256":"989e22cccb8681def4826496a9e18cfa0dbbd907a99d4d1e5d1b41a11ba7d0be"},"schema_version":"1.0","source":{"id":"1006.5730","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5730","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5730v3","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5730","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"R4J6ZOAYVLIJ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"R4J6ZOAYVLIJEBQD","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"R4J6ZOAY","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:af8bbb55fdcc59551a6e6fabf26d7f60d6de4b3186fcf3076204e7e16ca2a3c4","target":"graph","created_at":"2026-05-18T02:54:39Z","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 asymptotic properties of the variances of the spatial autoregressive model $X_{k,\\ell}=\\alpha X_{k-1,\\ell}+\\beta X_{k,\\ell-1}+\\gamma X_{k-1,\\ell-1}+\\epsilon_{k,\\ell}$ are investigated in the unit root case, that is when the parameters are on the boundary of domain of stability that forms a tetrahedron in $[-1,1]^3$. The limit of the variance of $n^{-\\varrho}X_{[ns],[nt]}$ is determined, where on the interior of the faces of the domain of stability $\\varrho=1/4$, on the edges $\\varrho =1/2$, while on the vertices $\\varrho =1$.","authors_text":"S\\'andor Baran","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-06-29T21:01:02Z","title":"On the variances of a spatial unit root model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5730","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:d5d863dfa86cc5815cb9f40d75c540a355636c4232e9f179c08d43a41d333b9b","target":"record","created_at":"2026-05-18T02:54:39Z","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":"09a942e0b6989f37e9348a910747097e8343a63c934f0951fdbb2f9fe9c332e1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-06-29T21:01:02Z","title_canon_sha256":"989e22cccb8681def4826496a9e18cfa0dbbd907a99d4d1e5d1b41a11ba7d0be"},"schema_version":"1.0","source":{"id":"1006.5730","kind":"arxiv","version":3}},"canonical_sha256":"8f13ecb818aad092060380ce560d9f119718dbe8d355eba6f735732f74d2ebe0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f13ecb818aad092060380ce560d9f119718dbe8d355eba6f735732f74d2ebe0","first_computed_at":"2026-05-18T02:54:39.875172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:39.875172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3SKKwWn7mRF69MzPEQba3y2WyE8aJlVDSsUJw9WiDHVdvtzYQnKlhQOK+xYjZPW+JVDbBKNrW18WwXDp7HZYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:39.875567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5730","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5d863dfa86cc5815cb9f40d75c540a355636c4232e9f179c08d43a41d333b9b","sha256:af8bbb55fdcc59551a6e6fabf26d7f60d6de4b3186fcf3076204e7e16ca2a3c4"],"state_sha256":"cd3c95ed116ef7a032afba8e39ab4056f36bed24b8dc029b6f10c42f9eff23a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8FqJ0HJTVbzBgO7mk8Zo0wwgNo7SC9y1q3OzWUcjNLY7P+FwAeh6MUz82W+8bQ/v0zwATdQtnwF+TTVlCObjCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:23:52.483039Z","bundle_sha256":"8f260eb5bf767ae2f552accb2d5935657559076752d62380011c7254d82358eb"}}