{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:GTCYQP74KPXRFEPTDWX5HLOVEY","short_pith_number":"pith:GTCYQP74","canonical_record":{"source":{"id":"2404.16797","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-04-25T17:43:29Z","cross_cats_sorted":[],"title_canon_sha256":"5ac72f291ecb747966a24ddb818c4b2be964b532d4f1aef354f1b1a1f075918a","abstract_canon_sha256":"20ede18e9e06c1b9b02002dae373a72f81439cae275c074a3d1f1b3f6f5ed85d"},"schema_version":"1.0"},"canonical_sha256":"34c5883ffc53ef1291f31dafd3add52621b38516e8cf5320d5bcfa53900c66cd","source":{"kind":"arxiv","id":"2404.16797","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.16797","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"arxiv_version","alias_value":"2404.16797v2","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.16797","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"pith_short_12","alias_value":"GTCYQP74KPXR","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"pith_short_16","alias_value":"GTCYQP74KPXRFEPT","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"pith_short_8","alias_value":"GTCYQP74","created_at":"2026-07-05T08:46:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:GTCYQP74KPXRFEPTDWX5HLOVEY","target":"record","payload":{"canonical_record":{"source":{"id":"2404.16797","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-04-25T17:43:29Z","cross_cats_sorted":[],"title_canon_sha256":"5ac72f291ecb747966a24ddb818c4b2be964b532d4f1aef354f1b1a1f075918a","abstract_canon_sha256":"20ede18e9e06c1b9b02002dae373a72f81439cae275c074a3d1f1b3f6f5ed85d"},"schema_version":"1.0"},"canonical_sha256":"34c5883ffc53ef1291f31dafd3add52621b38516e8cf5320d5bcfa53900c66cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:46:54.705291Z","signature_b64":"H/JfUtT1A6NZHq9oh4Rth4qgwz9LWhLx7GSO+r7eOlNVAdR+6wlrkIpmSrezAbM53WNHmb7RXSFGE03NKUzsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34c5883ffc53ef1291f31dafd3add52621b38516e8cf5320d5bcfa53900c66cd","last_reissued_at":"2026-07-05T08:46:54.704716Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:46:54.704716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.16797","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":"2026-07-05T08:46:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GvN22N7jGH9MJmvu7GjkB0pfSRBZjRZBgryaG8B38Eyj72fREk7rcUS+xDG4fiJToGs8hEFsY98eS3jLPe8eDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:07:22.582316Z"},"content_sha256":"b941c37c27f67953f8db0001d4fcb9b5eb133fa502ee6021013fcfc1e3b44ead","schema_version":"1.0","event_id":"sha256:b941c37c27f67953f8db0001d4fcb9b5eb133fa502ee6021013fcfc1e3b44ead"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:GTCYQP74KPXRFEPTDWX5HLOVEY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical bispectrum expansion and quadratic estimators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Antony Lewis, Julien Carron","submitted_at":"2024-04-25T17:43:29Z","abstract_excerpt":"We describe a general expansion of spherical (full-sky) bispectra into a set of orthogonal modes. For squeezed shapes, the basis separates physically-distinct signals and is dominated by the lowest moments. In terms of reduced bispectra, we identify a set of discrete polynomials that are pairwise orthogonal with respect to the relevant Wigner 3j symbol, and reduce to Chebyshev polynomials in the flat-sky (high-momentum) limit for both parity-even and parity-odd cases. For squeezed shapes, the flat-sky limit is equivalent to previous moment expansions used for CMB bispectra and quadratic estima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16797","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/2404.16797/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":"2026-07-05T08:46:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IkEmKO8MQlqxtoB1g6ALMVvIrWpwu6/k0blh6N29Dn+a6mhX22qseNCvm0kMVvU154HM9B+Ld1HuZbJcGRHoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:07:22.582895Z"},"content_sha256":"ca24410211f388d425a63596d1dd9ce4b9d4926e9dd61493213a34085c5b707b","schema_version":"1.0","event_id":"sha256:ca24410211f388d425a63596d1dd9ce4b9d4926e9dd61493213a34085c5b707b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTCYQP74KPXRFEPTDWX5HLOVEY/bundle.json","state_url":"https://pith.science/pith/GTCYQP74KPXRFEPTDWX5HLOVEY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTCYQP74KPXRFEPTDWX5HLOVEY/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":"2026-08-05T04:07:22Z","links":{"resolver":"https://pith.science/pith/GTCYQP74KPXRFEPTDWX5HLOVEY","bundle":"https://pith.science/pith/GTCYQP74KPXRFEPTDWX5HLOVEY/bundle.json","state":"https://pith.science/pith/GTCYQP74KPXRFEPTDWX5HLOVEY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTCYQP74KPXRFEPTDWX5HLOVEY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GTCYQP74KPXRFEPTDWX5HLOVEY","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":"20ede18e9e06c1b9b02002dae373a72f81439cae275c074a3d1f1b3f6f5ed85d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-04-25T17:43:29Z","title_canon_sha256":"5ac72f291ecb747966a24ddb818c4b2be964b532d4f1aef354f1b1a1f075918a"},"schema_version":"1.0","source":{"id":"2404.16797","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.16797","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"arxiv_version","alias_value":"2404.16797v2","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.16797","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"pith_short_12","alias_value":"GTCYQP74KPXR","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"pith_short_16","alias_value":"GTCYQP74KPXRFEPT","created_at":"2026-07-05T08:46:54Z"},{"alias_kind":"pith_short_8","alias_value":"GTCYQP74","created_at":"2026-07-05T08:46:54Z"}],"graph_snapshots":[{"event_id":"sha256:ca24410211f388d425a63596d1dd9ce4b9d4926e9dd61493213a34085c5b707b","target":"graph","created_at":"2026-07-05T08:46:54Z","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/2404.16797/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe a general expansion of spherical (full-sky) bispectra into a set of orthogonal modes. For squeezed shapes, the basis separates physically-distinct signals and is dominated by the lowest moments. In terms of reduced bispectra, we identify a set of discrete polynomials that are pairwise orthogonal with respect to the relevant Wigner 3j symbol, and reduce to Chebyshev polynomials in the flat-sky (high-momentum) limit for both parity-even and parity-odd cases. For squeezed shapes, the flat-sky limit is equivalent to previous moment expansions used for CMB bispectra and quadratic estima","authors_text":"Antony Lewis, Julien Carron","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-04-25T17:43:29Z","title":"Spherical bispectrum expansion and quadratic estimators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16797","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:b941c37c27f67953f8db0001d4fcb9b5eb133fa502ee6021013fcfc1e3b44ead","target":"record","created_at":"2026-07-05T08:46:54Z","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":"20ede18e9e06c1b9b02002dae373a72f81439cae275c074a3d1f1b3f6f5ed85d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-04-25T17:43:29Z","title_canon_sha256":"5ac72f291ecb747966a24ddb818c4b2be964b532d4f1aef354f1b1a1f075918a"},"schema_version":"1.0","source":{"id":"2404.16797","kind":"arxiv","version":2}},"canonical_sha256":"34c5883ffc53ef1291f31dafd3add52621b38516e8cf5320d5bcfa53900c66cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34c5883ffc53ef1291f31dafd3add52621b38516e8cf5320d5bcfa53900c66cd","first_computed_at":"2026-07-05T08:46:54.704716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:46:54.704716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H/JfUtT1A6NZHq9oh4Rth4qgwz9LWhLx7GSO+r7eOlNVAdR+6wlrkIpmSrezAbM53WNHmb7RXSFGE03NKUzsCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:46:54.705291Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.16797","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b941c37c27f67953f8db0001d4fcb9b5eb133fa502ee6021013fcfc1e3b44ead","sha256:ca24410211f388d425a63596d1dd9ce4b9d4926e9dd61493213a34085c5b707b"],"state_sha256":"f21e429d54543d0870910cd7ed093f8feee76593098f353554e1f8cc74e6b2c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RYl7e/uk7Wd5iNCJLZXZr/wpFoVkAXO3gzvr9IQctL4Z0pZJQsBzfYRatiKHe8bMkgutwIddDS7dhezKvHSfAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T04:07:22.590094Z","bundle_sha256":"be763c1d774b98cf70b271d7a1aac20c9d3bf37b9ddbbbb57f8b2267ec622292"}}