{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:6N7BW4FH66SQCYNAXLOLCXVYVO","short_pith_number":"pith:6N7BW4FH","canonical_record":{"source":{"id":"astro-ph/0002240","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-11T11:13:12Z","cross_cats_sorted":[],"title_canon_sha256":"edbff32c4859fc44c08ecbce8077bdbb519e487663720255cfd85a2e44ea4bd2","abstract_canon_sha256":"b80edaab77a684135a641b3dab119fd7a8ca98eef8222592de136c598c44ef91"},"schema_version":"1.0"},"canonical_sha256":"f37e1b70a7f7a50161a0badcb15eb8ab96b52d14e57782ab969b710ef932cac9","source":{"kind":"arxiv","id":"astro-ph/0002240","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0002240","created_at":"2026-05-18T01:40:48Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0002240v2","created_at":"2026-05-18T01:40:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0002240","created_at":"2026-05-18T01:40:48Z"},{"alias_kind":"pith_short_12","alias_value":"6N7BW4FH66SQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"6N7BW4FH66SQCYNA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"6N7BW4FH","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:6N7BW4FH66SQCYNAXLOLCXVYVO","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0002240","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-11T11:13:12Z","cross_cats_sorted":[],"title_canon_sha256":"edbff32c4859fc44c08ecbce8077bdbb519e487663720255cfd85a2e44ea4bd2","abstract_canon_sha256":"b80edaab77a684135a641b3dab119fd7a8ca98eef8222592de136c598c44ef91"},"schema_version":"1.0"},"canonical_sha256":"f37e1b70a7f7a50161a0badcb15eb8ab96b52d14e57782ab969b710ef932cac9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:48.327207Z","signature_b64":"ltv2i075Q/fYinnQ2xZKCrUH5FfXfu+sct1CiG9G3vOGSB8he+l8/BVYIXD8IyDHSRED/45nPkez9t0wutHBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f37e1b70a7f7a50161a0badcb15eb8ab96b52d14e57782ab969b710ef932cac9","last_reissued_at":"2026-05-18T01:40:48.326527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:48.326527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0002240","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":"2026-05-18T01:40:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"80xkdxFTVgjGJhBPaVFOJDwHxcBKLRYp/sXvYkDjeS1q8j/dKaZtm1e5o3N+iwsV5T2iTphIixcz5GRkRb1EDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T03:20:47.633336Z"},"content_sha256":"57d67ef349d76f38b22baf83113ffedbf71bb19f61ea2d342884a91657d0c0fa","schema_version":"1.0","event_id":"sha256:57d67ef349d76f38b22baf83113ffedbf71bb19f61ea2d342884a91657d0c0fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:6N7BW4FH66SQCYNAXLOLCXVYVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projected bispectrum in spherical harmonics and its application to angular galaxy catalogues","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Alan F. Heavens (IfA, Edinburgh), Licia Verde (IfA, Sabino Matarrese (Padova & MPA)","submitted_at":"2000-02-11T11:13:12Z","abstract_excerpt":"We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic microwave background and gravitational lensing studies. By expanding the 2D distribution of galaxies on the sky in spherical harmonics, we show how the 3-point function of the coefficients can be used in principle to determine the bias parameter of the galaxy sample. If this can be achieved, it would allow a lifting of the degeneracy between the bias and the mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0002240","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:40:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WX2oWUY8f9MquH4WmGYn4hx+oD1PqYOp4U2VO+L4bMRDDp01CYvNyvqty/rblbxZZD/v1Z2TmUFU3hrrDltHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T03:20:47.633936Z"},"content_sha256":"5c8bab40fa8e84f3094ac482d93a708400f10623573dc78785de9aab4fca67fa","schema_version":"1.0","event_id":"sha256:5c8bab40fa8e84f3094ac482d93a708400f10623573dc78785de9aab4fca67fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6N7BW4FH66SQCYNAXLOLCXVYVO/bundle.json","state_url":"https://pith.science/pith/6N7BW4FH66SQCYNAXLOLCXVYVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6N7BW4FH66SQCYNAXLOLCXVYVO/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":"2026-07-02T03:20:47Z","links":{"resolver":"https://pith.science/pith/6N7BW4FH66SQCYNAXLOLCXVYVO","bundle":"https://pith.science/pith/6N7BW4FH66SQCYNAXLOLCXVYVO/bundle.json","state":"https://pith.science/pith/6N7BW4FH66SQCYNAXLOLCXVYVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6N7BW4FH66SQCYNAXLOLCXVYVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:6N7BW4FH66SQCYNAXLOLCXVYVO","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":"b80edaab77a684135a641b3dab119fd7a8ca98eef8222592de136c598c44ef91","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-11T11:13:12Z","title_canon_sha256":"edbff32c4859fc44c08ecbce8077bdbb519e487663720255cfd85a2e44ea4bd2"},"schema_version":"1.0","source":{"id":"astro-ph/0002240","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0002240","created_at":"2026-05-18T01:40:48Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0002240v2","created_at":"2026-05-18T01:40:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0002240","created_at":"2026-05-18T01:40:48Z"},{"alias_kind":"pith_short_12","alias_value":"6N7BW4FH66SQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"6N7BW4FH66SQCYNA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"6N7BW4FH","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:5c8bab40fa8e84f3094ac482d93a708400f10623573dc78785de9aab4fca67fa","target":"graph","created_at":"2026-05-18T01:40:48Z","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 present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic microwave background and gravitational lensing studies. By expanding the 2D distribution of galaxies on the sky in spherical harmonics, we show how the 3-point function of the coefficients can be used in principle to determine the bias parameter of the galaxy sample. If this can be achieved, it would allow a lifting of the degeneracy between the bias and the mat","authors_text":"Alan F. Heavens (IfA, Edinburgh), Licia Verde (IfA, Sabino Matarrese (Padova & MPA)","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2000-02-11T11:13:12Z","title":"Projected bispectrum in spherical harmonics and its application to angular galaxy catalogues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0002240","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":"sha256:57d67ef349d76f38b22baf83113ffedbf71bb19f61ea2d342884a91657d0c0fa","target":"record","created_at":"2026-05-18T01:40:48Z","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":"b80edaab77a684135a641b3dab119fd7a8ca98eef8222592de136c598c44ef91","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-11T11:13:12Z","title_canon_sha256":"edbff32c4859fc44c08ecbce8077bdbb519e487663720255cfd85a2e44ea4bd2"},"schema_version":"1.0","source":{"id":"astro-ph/0002240","kind":"arxiv","version":2}},"canonical_sha256":"f37e1b70a7f7a50161a0badcb15eb8ab96b52d14e57782ab969b710ef932cac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f37e1b70a7f7a50161a0badcb15eb8ab96b52d14e57782ab969b710ef932cac9","first_computed_at":"2026-05-18T01:40:48.326527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:48.326527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ltv2i075Q/fYinnQ2xZKCrUH5FfXfu+sct1CiG9G3vOGSB8he+l8/BVYIXD8IyDHSRED/45nPkez9t0wutHBCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:48.327207Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0002240","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57d67ef349d76f38b22baf83113ffedbf71bb19f61ea2d342884a91657d0c0fa","sha256:5c8bab40fa8e84f3094ac482d93a708400f10623573dc78785de9aab4fca67fa"],"state_sha256":"ea1edb8fa78ff7aa96d78c51c896bebc2f01e330bc700334a0d6185e32b7c07b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BmfL+yRxQtYNceci7jB7KMy/ajfxlqe/1Xt654zc02opwYNd9mSLpZ7RFNM/NMRrUBkqDDVvx/Ixk88kNuz+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T03:20:47.636901Z","bundle_sha256":"576d0359f2979a5fb2b3d27882c1795498ee733f7bf9fb07d1b38eb66e8e1bc8"}}