{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:C2PYH3D6UL2OPI4ETJEPSDR55F","short_pith_number":"pith:C2PYH3D6","canonical_record":{"source":{"id":"math/0606599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2006-06-23T15:08:03Z","cross_cats_sorted":["astro-ph","cond-mat.other","stat.TH"],"title_canon_sha256":"bb8ad1abff77eeb5fc33c25216ea414c079a3aad4ce50bfbc238202a219b272b","abstract_canon_sha256":"cdd881fcf2a0f21ada0070e288ee07d02da1ef41240823394436827e45826726"},"schema_version":"1.0"},"canonical_sha256":"169f83ec7ea2f4e7a3849a48f90e3de96d170268730b7ab7727e571eedcf2b71","source":{"kind":"arxiv","id":"math/0606599","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606599","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606599v2","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606599","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"C2PYH3D6UL2O","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"pith_short_16","alias_value":"C2PYH3D6UL2OPI4E","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"pith_short_8","alias_value":"C2PYH3D6","created_at":"2026-07-04T15:52:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:C2PYH3D6UL2OPI4ETJEPSDR55F","target":"record","payload":{"canonical_record":{"source":{"id":"math/0606599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2006-06-23T15:08:03Z","cross_cats_sorted":["astro-ph","cond-mat.other","stat.TH"],"title_canon_sha256":"bb8ad1abff77eeb5fc33c25216ea414c079a3aad4ce50bfbc238202a219b272b","abstract_canon_sha256":"cdd881fcf2a0f21ada0070e288ee07d02da1ef41240823394436827e45826726"},"schema_version":"1.0"},"canonical_sha256":"169f83ec7ea2f4e7a3849a48f90e3de96d170268730b7ab7727e571eedcf2b71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:52:43.734293Z","signature_b64":"dJyCYY8FBE6Df+MmI0SGxyqMF2CTBn7hYPf2kivQW7BLGxcuyaCbvuWYxn7+7t3eXCwGe0HnfsdXX9Q+TeUADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"169f83ec7ea2f4e7a3849a48f90e3de96d170268730b7ab7727e571eedcf2b71","last_reissued_at":"2026-07-04T15:52:43.733889Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:52:43.733889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0606599","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8r4no7Zi8ap59ml7ITeQP4iQwhu2CvUL/D6Byg/ORP2NkvfMn8dKPJRFIg14sySPctx98lCAHDZJrpINSp42BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:17:18.596943Z"},"content_sha256":"1ecb526363b92644f6edbe50ee58489eae3758d41e95181a9bc9cd7400fed66c","schema_version":"1.0","event_id":"sha256:1ecb526363b92644f6edbe50ee58489eae3758d41e95181a9bc9cd7400fed66c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:C2PYH3D6UL2OPI4ETJEPSDR55F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics for spherical needlets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph","cond-mat.other","stat.TH"],"primary_cat":"math.ST","authors_text":"D. Marinucci, D. Picard, G. Kerkyacharian, P. Baldi","submitted_at":"2006-06-23T15:08:03Z","abstract_excerpt":"We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our propos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606599","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0606599/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"El04SXQZED0UzOF7DE0AGljC/MsGRdPD3xKfjiQVgrU+PYt/Zo1AUsScaiILxWeuI55uZBLiw/Fb/+EBHUSmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:17:18.597444Z"},"content_sha256":"579157290aca15cab4ccf6155cbe40d17fd615cf5a26335b6b979c9117725534","schema_version":"1.0","event_id":"sha256:579157290aca15cab4ccf6155cbe40d17fd615cf5a26335b6b979c9117725534"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C2PYH3D6UL2OPI4ETJEPSDR55F/bundle.json","state_url":"https://pith.science/pith/C2PYH3D6UL2OPI4ETJEPSDR55F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C2PYH3D6UL2OPI4ETJEPSDR55F/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":"2026-08-04T04:17:18Z","links":{"resolver":"https://pith.science/pith/C2PYH3D6UL2OPI4ETJEPSDR55F","bundle":"https://pith.science/pith/C2PYH3D6UL2OPI4ETJEPSDR55F/bundle.json","state":"https://pith.science/pith/C2PYH3D6UL2OPI4ETJEPSDR55F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C2PYH3D6UL2OPI4ETJEPSDR55F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:C2PYH3D6UL2OPI4ETJEPSDR55F","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":"cdd881fcf2a0f21ada0070e288ee07d02da1ef41240823394436827e45826726","cross_cats_sorted":["astro-ph","cond-mat.other","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2006-06-23T15:08:03Z","title_canon_sha256":"bb8ad1abff77eeb5fc33c25216ea414c079a3aad4ce50bfbc238202a219b272b"},"schema_version":"1.0","source":{"id":"math/0606599","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606599","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606599v2","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606599","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"C2PYH3D6UL2O","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"pith_short_16","alias_value":"C2PYH3D6UL2OPI4E","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"pith_short_8","alias_value":"C2PYH3D6","created_at":"2026-07-04T15:52:43Z"}],"graph_snapshots":[{"event_id":"sha256:579157290aca15cab4ccf6155cbe40d17fd615cf5a26335b6b979c9117725534","target":"graph","created_at":"2026-07-04T15:52:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0606599/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our propos","authors_text":"D. Marinucci, D. Picard, G. Kerkyacharian, P. Baldi","cross_cats":["astro-ph","cond-mat.other","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2006-06-23T15:08:03Z","title":"Asymptotics for spherical needlets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606599","kind":"arxiv","version":2},"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":"sha256:1ecb526363b92644f6edbe50ee58489eae3758d41e95181a9bc9cd7400fed66c","target":"record","created_at":"2026-07-04T15:52:43Z","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":"cdd881fcf2a0f21ada0070e288ee07d02da1ef41240823394436827e45826726","cross_cats_sorted":["astro-ph","cond-mat.other","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2006-06-23T15:08:03Z","title_canon_sha256":"bb8ad1abff77eeb5fc33c25216ea414c079a3aad4ce50bfbc238202a219b272b"},"schema_version":"1.0","source":{"id":"math/0606599","kind":"arxiv","version":2}},"canonical_sha256":"169f83ec7ea2f4e7a3849a48f90e3de96d170268730b7ab7727e571eedcf2b71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"169f83ec7ea2f4e7a3849a48f90e3de96d170268730b7ab7727e571eedcf2b71","first_computed_at":"2026-07-04T15:52:43.733889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:52:43.733889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dJyCYY8FBE6Df+MmI0SGxyqMF2CTBn7hYPf2kivQW7BLGxcuyaCbvuWYxn7+7t3eXCwGe0HnfsdXX9Q+TeUADw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:52:43.734293Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606599","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ecb526363b92644f6edbe50ee58489eae3758d41e95181a9bc9cd7400fed66c","sha256:579157290aca15cab4ccf6155cbe40d17fd615cf5a26335b6b979c9117725534"],"state_sha256":"4fc53044c0ec724edcd02c18cde80454c1f9a6ccea3cc3f532aeacf23731ea41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1TDKj9wI2ua7eac/D8KbaQsIhFvF7tQpC+fUJUePUpNcXWnF7VBKJO4xaxXmUHzx7StrsTU3g8M8xKaCarYpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:17:18.601034Z","bundle_sha256":"7f81e0352147d6b25454ff992edaf9336715001e0d292b58de36f523574422c9"}}