{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:52A5WEOLOWTXMKORDZXS5ROYIA","short_pith_number":"pith:52A5WEOL","canonical_record":{"source":{"id":"1312.2697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-10T08:01:35Z","cross_cats_sorted":[],"title_canon_sha256":"034fbd246ecc31bd18229a6e90d1c4dd848bd63023f49c4210c38c035866dca2","abstract_canon_sha256":"54e804f5d9f32ad96847a21e212a4edba64926eeb581589bd3e7021d7b9eb339"},"schema_version":"1.0"},"canonical_sha256":"ee81db11cb75a77629d11e6f2ec5d840321cb67cc2ebb87f315989bc3fc8fdd3","source":{"kind":"arxiv","id":"1312.2697","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2697","created_at":"2026-05-18T01:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2697v2","created_at":"2026-05-18T01:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2697","created_at":"2026-05-18T01:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"52A5WEOLOWTX","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"52A5WEOLOWTXMKOR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"52A5WEOL","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:52A5WEOLOWTXMKORDZXS5ROYIA","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-10T08:01:35Z","cross_cats_sorted":[],"title_canon_sha256":"034fbd246ecc31bd18229a6e90d1c4dd848bd63023f49c4210c38c035866dca2","abstract_canon_sha256":"54e804f5d9f32ad96847a21e212a4edba64926eeb581589bd3e7021d7b9eb339"},"schema_version":"1.0"},"canonical_sha256":"ee81db11cb75a77629d11e6f2ec5d840321cb67cc2ebb87f315989bc3fc8fdd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:45:52.254596Z","signature_b64":"BYaJEubHaOag5f+f5H/UTqCKXWmQIe++b4fOVbWAl4Pl6ONhnH9gE6ixTv4hUWjEZtOyNp2182jh7qtFmWi4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee81db11cb75a77629d11e6f2ec5d840321cb67cc2ebb87f315989bc3fc8fdd3","last_reissued_at":"2026-05-18T01:45:52.254135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:45:52.254135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2697","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":"2026-05-18T01:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NyPW6WfZCuEwLs3DzQWomCJg0DGpNinf8AgtMsRPCjY9JUR9q09ZbxIy2ccqVrmEZej9RnM2tyKISwHgZnE9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:15:55.748795Z"},"content_sha256":"aa738add9f66fa5aa32a437f78a38ce3f5faeba54ee2d79c3dcf6ff279a046ef","schema_version":"1.0","event_id":"sha256:aa738add9f66fa5aa32a437f78a38ce3f5faeba54ee2d79c3dcf6ff279a046ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:52A5WEOLOWTXMKORDZXS5ROYIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast and accurate CMB computations in non-flat FLRW universes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Julien Lesgourgues, Thomas Tram","submitted_at":"2013-12-10T08:01:35Z","abstract_excerpt":"We present a new method for calculating CMB anisotropies in a non-flat Friedmann universe, relying on a very stable algorithm for the calculation of hyperspherical Bessel functions, that can be pushed to arbitrary precision levels. We also introduce a new approximation scheme which gradually takes over in the flat space limit, and significant speeds-up calculations. Our method is implemented in the Boltzmann code CLASS. It can be used to benchmark the accuracy of the CAMB code in curved space, which is found to match expectations. For default precision settings, corresponding to 0.1% for scala"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2697","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":"2026-05-18T01:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUKt78tvKc4QoPvaujcR664pN7tF++q9z+V7u29kZ51+7JhM2suRLoO5YwXpZrEVOqFWNubALQM2bKbyTzRRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:15:55.749475Z"},"content_sha256":"8381bd4b489dcafb60ebb961cbe3b8fb22ccb8c86f680eaf27c15d5fc0e01ac3","schema_version":"1.0","event_id":"sha256:8381bd4b489dcafb60ebb961cbe3b8fb22ccb8c86f680eaf27c15d5fc0e01ac3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52A5WEOLOWTXMKORDZXS5ROYIA/bundle.json","state_url":"https://pith.science/pith/52A5WEOLOWTXMKORDZXS5ROYIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52A5WEOLOWTXMKORDZXS5ROYIA/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":"2026-05-23T03:15:55Z","links":{"resolver":"https://pith.science/pith/52A5WEOLOWTXMKORDZXS5ROYIA","bundle":"https://pith.science/pith/52A5WEOLOWTXMKORDZXS5ROYIA/bundle.json","state":"https://pith.science/pith/52A5WEOLOWTXMKORDZXS5ROYIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52A5WEOLOWTXMKORDZXS5ROYIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:52A5WEOLOWTXMKORDZXS5ROYIA","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":"54e804f5d9f32ad96847a21e212a4edba64926eeb581589bd3e7021d7b9eb339","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-10T08:01:35Z","title_canon_sha256":"034fbd246ecc31bd18229a6e90d1c4dd848bd63023f49c4210c38c035866dca2"},"schema_version":"1.0","source":{"id":"1312.2697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2697","created_at":"2026-05-18T01:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2697v2","created_at":"2026-05-18T01:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2697","created_at":"2026-05-18T01:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"52A5WEOLOWTX","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"52A5WEOLOWTXMKOR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"52A5WEOL","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:8381bd4b489dcafb60ebb961cbe3b8fb22ccb8c86f680eaf27c15d5fc0e01ac3","target":"graph","created_at":"2026-05-18T01:45:52Z","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 new method for calculating CMB anisotropies in a non-flat Friedmann universe, relying on a very stable algorithm for the calculation of hyperspherical Bessel functions, that can be pushed to arbitrary precision levels. We also introduce a new approximation scheme which gradually takes over in the flat space limit, and significant speeds-up calculations. Our method is implemented in the Boltzmann code CLASS. It can be used to benchmark the accuracy of the CAMB code in curved space, which is found to match expectations. For default precision settings, corresponding to 0.1% for scala","authors_text":"Julien Lesgourgues, Thomas Tram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-10T08:01:35Z","title":"Fast and accurate CMB computations in non-flat FLRW universes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2697","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:aa738add9f66fa5aa32a437f78a38ce3f5faeba54ee2d79c3dcf6ff279a046ef","target":"record","created_at":"2026-05-18T01:45:52Z","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":"54e804f5d9f32ad96847a21e212a4edba64926eeb581589bd3e7021d7b9eb339","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-10T08:01:35Z","title_canon_sha256":"034fbd246ecc31bd18229a6e90d1c4dd848bd63023f49c4210c38c035866dca2"},"schema_version":"1.0","source":{"id":"1312.2697","kind":"arxiv","version":2}},"canonical_sha256":"ee81db11cb75a77629d11e6f2ec5d840321cb67cc2ebb87f315989bc3fc8fdd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee81db11cb75a77629d11e6f2ec5d840321cb67cc2ebb87f315989bc3fc8fdd3","first_computed_at":"2026-05-18T01:45:52.254135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:52.254135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BYaJEubHaOag5f+f5H/UTqCKXWmQIe++b4fOVbWAl4Pl6ONhnH9gE6ixTv4hUWjEZtOyNp2182jh7qtFmWi4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:52.254596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa738add9f66fa5aa32a437f78a38ce3f5faeba54ee2d79c3dcf6ff279a046ef","sha256:8381bd4b489dcafb60ebb961cbe3b8fb22ccb8c86f680eaf27c15d5fc0e01ac3"],"state_sha256":"26f449668fd8c3fabb0252b8125c3a3733820887e3f87bda5746f36cbbb58d8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HtNJHfQ2nQh0YDH20MTaePxY7Hjf+/AauM4faOwS0DJewsPkFlSbsemBnR9N6QrG7sVfzYq0SsIPvnOiIZFbAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T03:15:55.753284Z","bundle_sha256":"16059a6921a3e91cbfbf61ffa75618f040042af933bd667434df4b05ee345d2e"}}