{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GLXO44R4DOBAR4OENFPOAC2HKO","short_pith_number":"pith:GLXO44R4","schema_version":"1.0","canonical_sha256":"32eeee723c1b8208f1c4695ee00b47538d2a37638d6cf06890dbfc2328ab41e3","source":{"kind":"arxiv","id":"1707.04386","version":2},"attestation_state":"computed","paper":{"title":"Tensor Minkowski Functionals for random fields on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Changbom Park, Joby P. K., K P Yogendran, Pravabati Chingangbam, Stephen Appleby, Vidhya Ganesan","submitted_at":"2017-07-14T05:16:25Z","abstract_excerpt":"We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We obtain analytic expressions for the ensemble expectation values for the matrix elements of the tensor-valued Minkowski Functionals for isotropic Gaussian and Rayleigh fields. We elucidate the way in which the elements of the tensor Minkowski Functionals encode information about the"},"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":"1707.04386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-07-14T05:16:25Z","cross_cats_sorted":[],"title_canon_sha256":"8a5860f7d26f968902c001e8b1ec7ab9bfc218be6fe0678b7afe381ef6f29b0a","abstract_canon_sha256":"c22bc9595b5b3a9e645869ab8bc290b31b3617fecd4b59bb2212bc4ce311f884"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:21.177111Z","signature_b64":"4kMrp04aMUql7FKMVfOF0ZAerRcVCJ09DtPZg47QW6nvB4tRPvXcVyf/UOPk0N0glM6ql02WpVfG5azqbSjnDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32eeee723c1b8208f1c4695ee00b47538d2a37638d6cf06890dbfc2328ab41e3","last_reissued_at":"2026-05-18T00:27:21.176534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:21.176534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor Minkowski Functionals for random fields on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Changbom Park, Joby P. K., K P Yogendran, Pravabati Chingangbam, Stephen Appleby, Vidhya Ganesan","submitted_at":"2017-07-14T05:16:25Z","abstract_excerpt":"We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We obtain analytic expressions for the ensemble expectation values for the matrix elements of the tensor-valued Minkowski Functionals for isotropic Gaussian and Rayleigh fields. We elucidate the way in which the elements of the tensor Minkowski Functionals encode information about the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04386","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":"1707.04386","created_at":"2026-05-18T00:27:21.176614+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.04386v2","created_at":"2026-05-18T00:27:21.176614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04386","created_at":"2026-05-18T00:27:21.176614+00:00"},{"alias_kind":"pith_short_12","alias_value":"GLXO44R4DOBA","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GLXO44R4DOBAR4OE","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GLXO44R4","created_at":"2026-05-18T12:31:18.294218+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/GLXO44R4DOBAR4OENFPOAC2HKO","json":"https://pith.science/pith/GLXO44R4DOBAR4OENFPOAC2HKO.json","graph_json":"https://pith.science/api/pith-number/GLXO44R4DOBAR4OENFPOAC2HKO/graph.json","events_json":"https://pith.science/api/pith-number/GLXO44R4DOBAR4OENFPOAC2HKO/events.json","paper":"https://pith.science/paper/GLXO44R4"},"agent_actions":{"view_html":"https://pith.science/pith/GLXO44R4DOBAR4OENFPOAC2HKO","download_json":"https://pith.science/pith/GLXO44R4DOBAR4OENFPOAC2HKO.json","view_paper":"https://pith.science/paper/GLXO44R4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.04386&json=true","fetch_graph":"https://pith.science/api/pith-number/GLXO44R4DOBAR4OENFPOAC2HKO/graph.json","fetch_events":"https://pith.science/api/pith-number/GLXO44R4DOBAR4OENFPOAC2HKO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GLXO44R4DOBAR4OENFPOAC2HKO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GLXO44R4DOBAR4OENFPOAC2HKO/action/storage_attestation","attest_author":"https://pith.science/pith/GLXO44R4DOBAR4OENFPOAC2HKO/action/author_attestation","sign_citation":"https://pith.science/pith/GLXO44R4DOBAR4OENFPOAC2HKO/action/citation_signature","submit_replication":"https://pith.science/pith/GLXO44R4DOBAR4OENFPOAC2HKO/action/replication_record"}},"created_at":"2026-05-18T00:27:21.176614+00:00","updated_at":"2026-05-18T00:27:21.176614+00:00"}