{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XAEASTGSV6Q36OG3FM6C4R7O63","short_pith_number":"pith:XAEASTGS","canonical_record":{"source":{"id":"1110.3777","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-17T19:43:53Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"b76589eaa8b014a93550f084191ca5a18fa190df0bf1c2619f2949c04381447a","abstract_canon_sha256":"23c4f2908dca02933e731aa1b6dac5b3f20e04a50c6965408529c08e5beb11b4"},"schema_version":"1.0"},"canonical_sha256":"b808094cd2afa1bf38db2b3c2e47eef6d85dbf97bd30f1ab7aec9c1ae739ac09","source":{"kind":"arxiv","id":"1110.3777","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3777","created_at":"2026-05-18T03:00:14Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3777v4","created_at":"2026-05-18T03:00:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3777","created_at":"2026-05-18T03:00:14Z"},{"alias_kind":"pith_short_12","alias_value":"XAEASTGSV6Q3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XAEASTGSV6Q36OG3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XAEASTGS","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XAEASTGSV6Q36OG3FM6C4R7O63","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3777","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-17T19:43:53Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"b76589eaa8b014a93550f084191ca5a18fa190df0bf1c2619f2949c04381447a","abstract_canon_sha256":"23c4f2908dca02933e731aa1b6dac5b3f20e04a50c6965408529c08e5beb11b4"},"schema_version":"1.0"},"canonical_sha256":"b808094cd2afa1bf38db2b3c2e47eef6d85dbf97bd30f1ab7aec9c1ae739ac09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:14.984926Z","signature_b64":"0JEPWUbBJFcQegeg4VEKq3KWr/tZ+vZGhbrkQTPs+wqgoNipYygBj3LpCbesAs3akWnf0XsOHQfRZnzc9gmDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b808094cd2afa1bf38db2b3c2e47eef6d85dbf97bd30f1ab7aec9c1ae739ac09","last_reissued_at":"2026-05-18T03:00:14.984236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:14.984236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3777","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:00:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RcQTbk9t+sB+tvrNeC3kbRPrKYP4oymJUlOC2AXD9sWpUwD1PZCrzUSRdu5rwtRJGOe1dG3QB4OR8KuPC4c1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:26:02.735199Z"},"content_sha256":"8effbeb2121895c981cdddd2bf96ae029680b1aa7bf59fd9f4b76de5fa53a2a5","schema_version":"1.0","event_id":"sha256:8effbeb2121895c981cdddd2bf96ae029680b1aa7bf59fd9f4b76de5fa53a2a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XAEASTGSV6Q36OG3FM6C4R7O63","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gaussian semiparametric estimates on the unit sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Claudio Durastanti, Domenico Marinucci, Xiaohong Lan","submitted_at":"2011-10-17T19:43:53Z","abstract_excerpt":"We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate maximum likelihood estimator and we investigate its asympotic weak consistency and Gaussianity, in both parametric and semiparametric cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3777","kind":"arxiv","version":4},"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":"2026-05-18T03:00:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZ3DBLLAAkPxzCrfQYrpDMueMyGwG76hWC340d+9s1YN6pyBJtM76eLBWw3bk75gJ2ENC/ii1PHGyixTp7+UCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:26:02.735560Z"},"content_sha256":"65a74cc6d2d938b6914695b9f727066891745647ab50e4926a115230151a8f0e","schema_version":"1.0","event_id":"sha256:65a74cc6d2d938b6914695b9f727066891745647ab50e4926a115230151a8f0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAEASTGSV6Q36OG3FM6C4R7O63/bundle.json","state_url":"https://pith.science/pith/XAEASTGSV6Q36OG3FM6C4R7O63/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAEASTGSV6Q36OG3FM6C4R7O63/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":"2026-05-30T14:26:02Z","links":{"resolver":"https://pith.science/pith/XAEASTGSV6Q36OG3FM6C4R7O63","bundle":"https://pith.science/pith/XAEASTGSV6Q36OG3FM6C4R7O63/bundle.json","state":"https://pith.science/pith/XAEASTGSV6Q36OG3FM6C4R7O63/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAEASTGSV6Q36OG3FM6C4R7O63/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XAEASTGSV6Q36OG3FM6C4R7O63","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":"23c4f2908dca02933e731aa1b6dac5b3f20e04a50c6965408529c08e5beb11b4","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-17T19:43:53Z","title_canon_sha256":"b76589eaa8b014a93550f084191ca5a18fa190df0bf1c2619f2949c04381447a"},"schema_version":"1.0","source":{"id":"1110.3777","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3777","created_at":"2026-05-18T03:00:14Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3777v4","created_at":"2026-05-18T03:00:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3777","created_at":"2026-05-18T03:00:14Z"},{"alias_kind":"pith_short_12","alias_value":"XAEASTGSV6Q3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XAEASTGSV6Q36OG3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XAEASTGS","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:65a74cc6d2d938b6914695b9f727066891745647ab50e4926a115230151a8f0e","target":"graph","created_at":"2026-05-18T03:00:14Z","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":"We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate maximum likelihood estimator and we investigate its asympotic weak consistency and Gaussianity, in both parametric and semiparametric cases.","authors_text":"Claudio Durastanti, Domenico Marinucci, Xiaohong Lan","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-17T19:43:53Z","title":"Gaussian semiparametric estimates on the unit sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3777","kind":"arxiv","version":4},"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":"sha256:8effbeb2121895c981cdddd2bf96ae029680b1aa7bf59fd9f4b76de5fa53a2a5","target":"record","created_at":"2026-05-18T03:00:14Z","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":"23c4f2908dca02933e731aa1b6dac5b3f20e04a50c6965408529c08e5beb11b4","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-17T19:43:53Z","title_canon_sha256":"b76589eaa8b014a93550f084191ca5a18fa190df0bf1c2619f2949c04381447a"},"schema_version":"1.0","source":{"id":"1110.3777","kind":"arxiv","version":4}},"canonical_sha256":"b808094cd2afa1bf38db2b3c2e47eef6d85dbf97bd30f1ab7aec9c1ae739ac09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b808094cd2afa1bf38db2b3c2e47eef6d85dbf97bd30f1ab7aec9c1ae739ac09","first_computed_at":"2026-05-18T03:00:14.984236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:14.984236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0JEPWUbBJFcQegeg4VEKq3KWr/tZ+vZGhbrkQTPs+wqgoNipYygBj3LpCbesAs3akWnf0XsOHQfRZnzc9gmDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:14.984926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3777","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8effbeb2121895c981cdddd2bf96ae029680b1aa7bf59fd9f4b76de5fa53a2a5","sha256:65a74cc6d2d938b6914695b9f727066891745647ab50e4926a115230151a8f0e"],"state_sha256":"f0c322d126631974240a3b2490c6809f14a7c1e46e76f853f4c80f6d4fc0e721"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r/cfCqBvam7Fb1wmKiTiq/3BG1D44rKRf47dmXb3tUu46khsCTnu3UdDxaCayDaKnO9FAMZMo3f0ZEV/Po47Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:26:02.737786Z","bundle_sha256":"9cac9efe5624adf79b19214435edcce0d5f07426b3b564919a4079d476904c26"}}