{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CH2N6XPM2KCLVMLL4VJSEFP7OZ","short_pith_number":"pith:CH2N6XPM","schema_version":"1.0","canonical_sha256":"11f4df5decd284bab16be5532215ff7665189de114eb301e14994a13d799d524","source":{"kind":"arxiv","id":"1205.6280","version":2},"attestation_state":"computed","paper":{"title":"Time dependent random fields on spherical non-homogeneous surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erkan Nane, Mirko D'Ovidio","submitted_at":"2012-05-29T07:13:11Z","abstract_excerpt":"We introduce a class of isotropic time dependent random fields on the non-homogeneous sphere represented by a time-changed spherical Brownian motion of order \\nu \\in (0,1] with which some anisotrophies can be captured in Cosmology. This process is a time-changed rotational diffusion (TRD) or the stochastic solution to the equation involving the spherical Laplace operator and a time-fractional derivative of order \\nu. TRD is a diffusion on the non-homogeneous sphere and therefore, the spherical coordinates given by TRD represent the coordinates of a non-homogeneous sphere by means of which an i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.6280","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-29T07:13:11Z","cross_cats_sorted":[],"title_canon_sha256":"fc706e76d25f489e5b2291ae3f4a051f608f6a0dbf352bd458f61aea3eb199b3","abstract_canon_sha256":"aadf173481596e8aa6f58f87cf23e8bcbe45cb9cfc3c7d79da19ba64acc723a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:02.348402Z","signature_b64":"tPjKu5v9uk2YjK7OxhNUpu6GFVaqot7t9W0gJPfVzPf4qkDeY4ucaPntaSzxutiwSzD1wmP/3CHxNHo0VK23AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11f4df5decd284bab16be5532215ff7665189de114eb301e14994a13d799d524","last_reissued_at":"2026-05-18T03:44:02.347661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:02.347661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Time dependent random fields on spherical non-homogeneous surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erkan Nane, Mirko D'Ovidio","submitted_at":"2012-05-29T07:13:11Z","abstract_excerpt":"We introduce a class of isotropic time dependent random fields on the non-homogeneous sphere represented by a time-changed spherical Brownian motion of order \\nu \\in (0,1] with which some anisotrophies can be captured in Cosmology. This process is a time-changed rotational diffusion (TRD) or the stochastic solution to the equation involving the spherical Laplace operator and a time-fractional derivative of order \\nu. TRD is a diffusion on the non-homogeneous sphere and therefore, the spherical coordinates given by TRD represent the coordinates of a non-homogeneous sphere by means of which an i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6280","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.6280","created_at":"2026-05-18T03:44:02.347775+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.6280v2","created_at":"2026-05-18T03:44:02.347775+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6280","created_at":"2026-05-18T03:44:02.347775+00:00"},{"alias_kind":"pith_short_12","alias_value":"CH2N6XPM2KCL","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CH2N6XPM2KCLVMLL","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CH2N6XPM","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CH2N6XPM2KCLVMLL4VJSEFP7OZ","json":"https://pith.science/pith/CH2N6XPM2KCLVMLL4VJSEFP7OZ.json","graph_json":"https://pith.science/api/pith-number/CH2N6XPM2KCLVMLL4VJSEFP7OZ/graph.json","events_json":"https://pith.science/api/pith-number/CH2N6XPM2KCLVMLL4VJSEFP7OZ/events.json","paper":"https://pith.science/paper/CH2N6XPM"},"agent_actions":{"view_html":"https://pith.science/pith/CH2N6XPM2KCLVMLL4VJSEFP7OZ","download_json":"https://pith.science/pith/CH2N6XPM2KCLVMLL4VJSEFP7OZ.json","view_paper":"https://pith.science/paper/CH2N6XPM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.6280&json=true","fetch_graph":"https://pith.science/api/pith-number/CH2N6XPM2KCLVMLL4VJSEFP7OZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CH2N6XPM2KCLVMLL4VJSEFP7OZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CH2N6XPM2KCLVMLL4VJSEFP7OZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CH2N6XPM2KCLVMLL4VJSEFP7OZ/action/storage_attestation","attest_author":"https://pith.science/pith/CH2N6XPM2KCLVMLL4VJSEFP7OZ/action/author_attestation","sign_citation":"https://pith.science/pith/CH2N6XPM2KCLVMLL4VJSEFP7OZ/action/citation_signature","submit_replication":"https://pith.science/pith/CH2N6XPM2KCLVMLL4VJSEFP7OZ/action/replication_record"}},"created_at":"2026-05-18T03:44:02.347775+00:00","updated_at":"2026-05-18T03:44:02.347775+00:00"}