{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LQRKWUNXVIDXXEOKIYN5MBJQWU","short_pith_number":"pith:LQRKWUNX","canonical_record":{"source":{"id":"1405.5301","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-05-21T05:13:52Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"c1444f5a49cd34729ad15d60cd6129cfeaa30159d5ddce6da96e20870557432e","abstract_canon_sha256":"89b2e0789e679e7b157a72c0ddc750968767d3c570b96d0855c68ace60692753"},"schema_version":"1.0"},"canonical_sha256":"5c22ab51b7aa077b91ca461bd60530b529f9b16a35fd74df64b9e9cf85358742","source":{"kind":"arxiv","id":"1405.5301","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5301","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5301v3","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5301","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"pith_short_12","alias_value":"LQRKWUNXVIDX","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LQRKWUNXVIDXXEOK","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LQRKWUNX","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LQRKWUNXVIDXXEOKIYN5MBJQWU","target":"record","payload":{"canonical_record":{"source":{"id":"1405.5301","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-05-21T05:13:52Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"c1444f5a49cd34729ad15d60cd6129cfeaa30159d5ddce6da96e20870557432e","abstract_canon_sha256":"89b2e0789e679e7b157a72c0ddc750968767d3c570b96d0855c68ace60692753"},"schema_version":"1.0"},"canonical_sha256":"5c22ab51b7aa077b91ca461bd60530b529f9b16a35fd74df64b9e9cf85358742","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:25.925471Z","signature_b64":"cmi2myTIiKBijyk2p3h1qfKyFhf8T3jViciKuYHv2U+DiEccEdjmmR03CUjFV2Xo8GVN4Y6B5p0neAHuXOrJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c22ab51b7aa077b91ca461bd60530b529f9b16a35fd74df64b9e9cf85358742","last_reissued_at":"2026-05-18T02:43:25.924737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:25.924737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.5301","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S2rfPORkB2Hw99RtfuC4qA1YiobGbu3SHgdmGt+9+9HsxOpf1ArH7OIVfqabowQGcSWWvgHwTfXztkP/TwRnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:19:49.463706Z"},"content_sha256":"a34eaee477f71e7b212ce11e495d75945597b3716acfef300212822815e698e1","schema_version":"1.0","event_id":"sha256:a34eaee477f71e7b212ce11e495d75945597b3716acfef300212822815e698e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LQRKWUNXVIDXXEOKIYN5MBJQWU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravitational quantum effects on power spectra and spectral indices with higher-order corrections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-ph","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Anzhong Wang, Gerald Cleaver, Klaus Kirsten, Qin Sheng, Tao Zhu","submitted_at":"2014-05-21T05:13:52Z","abstract_excerpt":"The uniform asymptotic approximation method provides a powerful, systematically-improved, and error-controlled approach to construct accurate analytical approximate solutions of mode functions of perturbations of the Friedmann-Robertson-Walker universe, designed especially for the cases where the relativistic linear dispersion relation is modified after gravitational quantum effects are taken into account. These include models from string/M-Theory, loop quantum cosmology and Ho\\v{r}ava-Lifshitz quantum gravity. In this paper, we extend our previous studies of the first-order approximations to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5301","kind":"arxiv","version":3},"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":"2026-05-18T02:43:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AyCNi/OJAEuDtt5tyD39g063A+/qThAq8OoAiMx/vwW/tTBsag/tsNSK3JrDCGju+nJLx5i8ILiMn3GHQK/MDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:19:49.464365Z"},"content_sha256":"f64075fd0973dec899666e1d9e61eefa4abaf8925b7ebab9cff87f711f0a0931","schema_version":"1.0","event_id":"sha256:f64075fd0973dec899666e1d9e61eefa4abaf8925b7ebab9cff87f711f0a0931"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQRKWUNXVIDXXEOKIYN5MBJQWU/bundle.json","state_url":"https://pith.science/pith/LQRKWUNXVIDXXEOKIYN5MBJQWU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQRKWUNXVIDXXEOKIYN5MBJQWU/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":"2026-05-25T17:19:49Z","links":{"resolver":"https://pith.science/pith/LQRKWUNXVIDXXEOKIYN5MBJQWU","bundle":"https://pith.science/pith/LQRKWUNXVIDXXEOKIYN5MBJQWU/bundle.json","state":"https://pith.science/pith/LQRKWUNXVIDXXEOKIYN5MBJQWU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQRKWUNXVIDXXEOKIYN5MBJQWU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LQRKWUNXVIDXXEOKIYN5MBJQWU","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":"89b2e0789e679e7b157a72c0ddc750968767d3c570b96d0855c68ace60692753","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-05-21T05:13:52Z","title_canon_sha256":"c1444f5a49cd34729ad15d60cd6129cfeaa30159d5ddce6da96e20870557432e"},"schema_version":"1.0","source":{"id":"1405.5301","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5301","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5301v3","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5301","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"pith_short_12","alias_value":"LQRKWUNXVIDX","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LQRKWUNXVIDXXEOK","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LQRKWUNX","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:f64075fd0973dec899666e1d9e61eefa4abaf8925b7ebab9cff87f711f0a0931","target":"graph","created_at":"2026-05-18T02:43:25Z","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":"The uniform asymptotic approximation method provides a powerful, systematically-improved, and error-controlled approach to construct accurate analytical approximate solutions of mode functions of perturbations of the Friedmann-Robertson-Walker universe, designed especially for the cases where the relativistic linear dispersion relation is modified after gravitational quantum effects are taken into account. These include models from string/M-Theory, loop quantum cosmology and Ho\\v{r}ava-Lifshitz quantum gravity. In this paper, we extend our previous studies of the first-order approximations to ","authors_text":"Anzhong Wang, Gerald Cleaver, Klaus Kirsten, Qin Sheng, Tao Zhu","cross_cats":["gr-qc","hep-ph","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-05-21T05:13:52Z","title":"Gravitational quantum effects on power spectra and spectral indices with higher-order corrections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5301","kind":"arxiv","version":3},"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:a34eaee477f71e7b212ce11e495d75945597b3716acfef300212822815e698e1","target":"record","created_at":"2026-05-18T02:43:25Z","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":"89b2e0789e679e7b157a72c0ddc750968767d3c570b96d0855c68ace60692753","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-05-21T05:13:52Z","title_canon_sha256":"c1444f5a49cd34729ad15d60cd6129cfeaa30159d5ddce6da96e20870557432e"},"schema_version":"1.0","source":{"id":"1405.5301","kind":"arxiv","version":3}},"canonical_sha256":"5c22ab51b7aa077b91ca461bd60530b529f9b16a35fd74df64b9e9cf85358742","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c22ab51b7aa077b91ca461bd60530b529f9b16a35fd74df64b9e9cf85358742","first_computed_at":"2026-05-18T02:43:25.924737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:25.924737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cmi2myTIiKBijyk2p3h1qfKyFhf8T3jViciKuYHv2U+DiEccEdjmmR03CUjFV2Xo8GVN4Y6B5p0neAHuXOrJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:25.925471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5301","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a34eaee477f71e7b212ce11e495d75945597b3716acfef300212822815e698e1","sha256:f64075fd0973dec899666e1d9e61eefa4abaf8925b7ebab9cff87f711f0a0931"],"state_sha256":"5e1527a3d87b834d3a8302dcaef297880cab35f1656b8b66d0dd04324cca0958"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NXY1iR290CgHH/IZ+8LxTGEDfUMYT09MR7VMHzxMAuWTcTjHXjGLzhZ800+Q+HqqR0NBNoJopLKFwchrZzlZDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:19:49.467988Z","bundle_sha256":"e7634b6463c44662fe8899cc180bc97cad196dbb0111a531f746d8635f00161a"}}