{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NCL2ZYVBYB4HNMKBDA462GCOAZ","short_pith_number":"pith:NCL2ZYVB","canonical_record":{"source":{"id":"1509.02120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-09-07T16:54:18Z","cross_cats_sorted":[],"title_canon_sha256":"2621d0e5d63e9b5f1462d94a624ab04db948615c1959f263fb878a9087567e48","abstract_canon_sha256":"905e850c37dc44a866193886c177c2e3eb208e87bc9a0775c5ca96747127b28d"},"schema_version":"1.0"},"canonical_sha256":"6897ace2a1c07876b1411839ed184e06505ec6a910e1dec1c2624ed3581995d9","source":{"kind":"arxiv","id":"1509.02120","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02120","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02120v2","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02120","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"NCL2ZYVBYB4H","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NCL2ZYVBYB4HNMKB","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NCL2ZYVB","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NCL2ZYVBYB4HNMKBDA462GCOAZ","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-09-07T16:54:18Z","cross_cats_sorted":[],"title_canon_sha256":"2621d0e5d63e9b5f1462d94a624ab04db948615c1959f263fb878a9087567e48","abstract_canon_sha256":"905e850c37dc44a866193886c177c2e3eb208e87bc9a0775c5ca96747127b28d"},"schema_version":"1.0"},"canonical_sha256":"6897ace2a1c07876b1411839ed184e06505ec6a910e1dec1c2624ed3581995d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:58.255073Z","signature_b64":"aPvx5VYVoGPjPf5UwO1RdgsojE2L5YwMpeAg9pRi/dPEcQfQImhIGZHczZ64da7YmB8125yyQnYPN5oV73snCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6897ace2a1c07876b1411839ed184e06505ec6a910e1dec1c2624ed3581995d9","last_reissued_at":"2026-05-18T01:15:58.254577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:58.254577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02120","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":"2026-05-18T01:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z7WXXjg6gn7GkHiUI9zoVJsLtyHDKp7hF0K8VY1WA+76yFDBH3kXOFoVTVh/oz3GrUClp0SUDXteNntXrTwGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:44:58.528679Z"},"content_sha256":"095f8ff6f6454335235b47ad478c158f6adb9a3440236662d6b1809795207da9","schema_version":"1.0","event_id":"sha256:095f8ff6f6454335235b47ad478c158f6adb9a3440236662d6b1809795207da9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NCL2ZYVBYB4HNMKBDA462GCOAZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbation theory, effective field theory, and oscillations in the power spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Man Yat Chu, Uro\\v{s} Seljak, Yu Feng, Zvonimir Vlah","submitted_at":"2015-09-07T16:54:18Z","abstract_excerpt":"We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02120","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":"2026-05-18T01:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PVlOXaGML62v8G9uEGYWxm3uVBVoJOdDDsMBvDIkE5kyzfMcYXCNhSEjl992aXCWYoMH6M1tD8mpfruhnqFJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:44:58.529402Z"},"content_sha256":"889361062b6689a9a336729b1aaec747a27122f09283a507f7c686e67bf822f2","schema_version":"1.0","event_id":"sha256:889361062b6689a9a336729b1aaec747a27122f09283a507f7c686e67bf822f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NCL2ZYVBYB4HNMKBDA462GCOAZ/bundle.json","state_url":"https://pith.science/pith/NCL2ZYVBYB4HNMKBDA462GCOAZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NCL2ZYVBYB4HNMKBDA462GCOAZ/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":"2026-05-29T21:44:58Z","links":{"resolver":"https://pith.science/pith/NCL2ZYVBYB4HNMKBDA462GCOAZ","bundle":"https://pith.science/pith/NCL2ZYVBYB4HNMKBDA462GCOAZ/bundle.json","state":"https://pith.science/pith/NCL2ZYVBYB4HNMKBDA462GCOAZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NCL2ZYVBYB4HNMKBDA462GCOAZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NCL2ZYVBYB4HNMKBDA462GCOAZ","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":"905e850c37dc44a866193886c177c2e3eb208e87bc9a0775c5ca96747127b28d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-09-07T16:54:18Z","title_canon_sha256":"2621d0e5d63e9b5f1462d94a624ab04db948615c1959f263fb878a9087567e48"},"schema_version":"1.0","source":{"id":"1509.02120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02120","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02120v2","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02120","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"NCL2ZYVBYB4H","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NCL2ZYVBYB4HNMKB","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NCL2ZYVB","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:889361062b6689a9a336729b1aaec747a27122f09283a507f7c686e67bf822f2","target":"graph","created_at":"2026-05-18T01:15:58Z","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 explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the res","authors_text":"Man Yat Chu, Uro\\v{s} Seljak, Yu Feng, Zvonimir Vlah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-09-07T16:54:18Z","title":"Perturbation theory, effective field theory, and oscillations in the power spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02120","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":"sha256:095f8ff6f6454335235b47ad478c158f6adb9a3440236662d6b1809795207da9","target":"record","created_at":"2026-05-18T01:15:58Z","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":"905e850c37dc44a866193886c177c2e3eb208e87bc9a0775c5ca96747127b28d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-09-07T16:54:18Z","title_canon_sha256":"2621d0e5d63e9b5f1462d94a624ab04db948615c1959f263fb878a9087567e48"},"schema_version":"1.0","source":{"id":"1509.02120","kind":"arxiv","version":2}},"canonical_sha256":"6897ace2a1c07876b1411839ed184e06505ec6a910e1dec1c2624ed3581995d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6897ace2a1c07876b1411839ed184e06505ec6a910e1dec1c2624ed3581995d9","first_computed_at":"2026-05-18T01:15:58.254577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:58.254577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aPvx5VYVoGPjPf5UwO1RdgsojE2L5YwMpeAg9pRi/dPEcQfQImhIGZHczZ64da7YmB8125yyQnYPN5oV73snCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:58.255073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:095f8ff6f6454335235b47ad478c158f6adb9a3440236662d6b1809795207da9","sha256:889361062b6689a9a336729b1aaec747a27122f09283a507f7c686e67bf822f2"],"state_sha256":"dfaa11f84ca1a6fae21cbedb54b88bfb4ff1910a11639725bc29c33fd631ff29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f+OYpCUmVzIbvH8ORh/D9G2OYIrEzw2Qt/RNbxq40Aes19ln4CdX/lL9QUjfh2LxwTu31jJ8KDvLAa7mw4huAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T21:44:58.533150Z","bundle_sha256":"e290641e77fb3d9977f52c43ae8fb08d412c3515bbd32b857f5bddfa8c3fff3c"}}