{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MK5O5ZJARQI5D7ZXPHB2ZV2VEQ","short_pith_number":"pith:MK5O5ZJA","canonical_record":{"source":{"id":"1412.1650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-12-04T12:56:44Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"8d1870309a7b672e37c796ba898342623b33f59e4a7d6cd3f009b7965bf3e889","abstract_canon_sha256":"2dc9a72ac2e0c9e628dfe9dbce06ff5bdcbe43f60cbe655eeb2c2722c221c966"},"schema_version":"1.0"},"canonical_sha256":"62baeee5208c11d1ff3779c3acd75524042e6f28c1a661323ad1ccc1dc529654","source":{"kind":"arxiv","id":"1412.1650","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1650","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1650v1","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1650","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"MK5O5ZJARQI5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MK5O5ZJARQI5D7ZX","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MK5O5ZJA","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MK5O5ZJARQI5D7ZXPHB2ZV2VEQ","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-12-04T12:56:44Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"8d1870309a7b672e37c796ba898342623b33f59e4a7d6cd3f009b7965bf3e889","abstract_canon_sha256":"2dc9a72ac2e0c9e628dfe9dbce06ff5bdcbe43f60cbe655eeb2c2722c221c966"},"schema_version":"1.0"},"canonical_sha256":"62baeee5208c11d1ff3779c3acd75524042e6f28c1a661323ad1ccc1dc529654","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:12.117530Z","signature_b64":"V4imn9wyOgCN00vpyzqh1ymG5aTWayVWZm7LhRIsPIo5kLCQaV2Q+Vu17ILDGEnUbZppdaSsfplNfhZ52eWNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62baeee5208c11d1ff3779c3acd75524042e6f28c1a661323ad1ccc1dc529654","last_reissued_at":"2026-05-18T01:20:12.116786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:12.116786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1650","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZBvgA7FXMRsl/VM0OpZDm5mZ3fBbp91dtWz1tHXMLGzxEBLkkEy+ojSF1tiiDRSUdvH5Py5CWIkyCng/lmbeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:36:14.954797Z"},"content_sha256":"e28f27e627154dd838a3ebd256270dae5283e41e342c533fbe248b2f99f92663","schema_version":"1.0","event_id":"sha256:e28f27e627154dd838a3ebd256270dae5283e41e342c533fbe248b2f99f92663"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MK5O5ZJARQI5D7ZXPHB2ZV2VEQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient implementation of the Time Renormalization Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"astro-ph.CO","authors_text":"(2) Institut f\\\"ur Theoretische Physik, 37077 G\\\"ottingen, 69120 Heidelberg, Adrian Vollmer (1), Friedrich-Hund-Platz 1, Georg-August-Universit\\\"at G\\\"ottingen, Germany, Germany), Luca Amendola (1), Philosophenweg 16, Riccardo Catena (2) ((1) Institut f\\\"ur Theoretische Physik, Ruprecht-Karls-Universit\\\"at Heidelberg","submitted_at":"2014-12-04T12:56:44Z","abstract_excerpt":"The Time Renormalization Group (TRG) is an effective method for accurate calculations of the matter power spectrum at the scale of the first baryonic acoustic oscillations. By using a particular variable transformation in the TRG formalism, we can reduce the 2D integral in the source term of the equations of motion for the power spectrum into a series of 1D integrals. The shape of the integrand allows us to pre-compute only thirteen antiderivatives numerically, which can then be reused when evaluating the outer integral. While this introduces a few challenges to keep numerical noise under cont"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1650","kind":"arxiv","version":1},"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":"2026-05-18T01:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hIV25MmxqnlrflOy0gQLZdYe7fuyDgeYA58s4cxt6nUO7x7T8QbU5Uh2vHqu6VAjTy6OOZvFyTyx+TtyU20eDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:36:14.955492Z"},"content_sha256":"e1ff95d83868fbbfb111ba2a6f459c79685d8257b2dceca84a4fee0eeb1478cc","schema_version":"1.0","event_id":"sha256:e1ff95d83868fbbfb111ba2a6f459c79685d8257b2dceca84a4fee0eeb1478cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MK5O5ZJARQI5D7ZXPHB2ZV2VEQ/bundle.json","state_url":"https://pith.science/pith/MK5O5ZJARQI5D7ZXPHB2ZV2VEQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MK5O5ZJARQI5D7ZXPHB2ZV2VEQ/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":"2026-05-25T22:36:14Z","links":{"resolver":"https://pith.science/pith/MK5O5ZJARQI5D7ZXPHB2ZV2VEQ","bundle":"https://pith.science/pith/MK5O5ZJARQI5D7ZXPHB2ZV2VEQ/bundle.json","state":"https://pith.science/pith/MK5O5ZJARQI5D7ZXPHB2ZV2VEQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MK5O5ZJARQI5D7ZXPHB2ZV2VEQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MK5O5ZJARQI5D7ZXPHB2ZV2VEQ","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":"2dc9a72ac2e0c9e628dfe9dbce06ff5bdcbe43f60cbe655eeb2c2722c221c966","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-12-04T12:56:44Z","title_canon_sha256":"8d1870309a7b672e37c796ba898342623b33f59e4a7d6cd3f009b7965bf3e889"},"schema_version":"1.0","source":{"id":"1412.1650","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1650","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1650v1","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1650","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"MK5O5ZJARQI5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MK5O5ZJARQI5D7ZX","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MK5O5ZJA","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:e1ff95d83868fbbfb111ba2a6f459c79685d8257b2dceca84a4fee0eeb1478cc","target":"graph","created_at":"2026-05-18T01:20:12Z","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 Time Renormalization Group (TRG) is an effective method for accurate calculations of the matter power spectrum at the scale of the first baryonic acoustic oscillations. By using a particular variable transformation in the TRG formalism, we can reduce the 2D integral in the source term of the equations of motion for the power spectrum into a series of 1D integrals. The shape of the integrand allows us to pre-compute only thirteen antiderivatives numerically, which can then be reused when evaluating the outer integral. While this introduces a few challenges to keep numerical noise under cont","authors_text":"(2) Institut f\\\"ur Theoretische Physik, 37077 G\\\"ottingen, 69120 Heidelberg, Adrian Vollmer (1), Friedrich-Hund-Platz 1, Georg-August-Universit\\\"at G\\\"ottingen, Germany, Germany), Luca Amendola (1), Philosophenweg 16, Riccardo Catena (2) ((1) Institut f\\\"ur Theoretische Physik, Ruprecht-Karls-Universit\\\"at Heidelberg","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-12-04T12:56:44Z","title":"Efficient implementation of the Time Renormalization Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1650","kind":"arxiv","version":1},"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:e28f27e627154dd838a3ebd256270dae5283e41e342c533fbe248b2f99f92663","target":"record","created_at":"2026-05-18T01:20:12Z","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":"2dc9a72ac2e0c9e628dfe9dbce06ff5bdcbe43f60cbe655eeb2c2722c221c966","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2014-12-04T12:56:44Z","title_canon_sha256":"8d1870309a7b672e37c796ba898342623b33f59e4a7d6cd3f009b7965bf3e889"},"schema_version":"1.0","source":{"id":"1412.1650","kind":"arxiv","version":1}},"canonical_sha256":"62baeee5208c11d1ff3779c3acd75524042e6f28c1a661323ad1ccc1dc529654","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62baeee5208c11d1ff3779c3acd75524042e6f28c1a661323ad1ccc1dc529654","first_computed_at":"2026-05-18T01:20:12.116786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:12.116786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V4imn9wyOgCN00vpyzqh1ymG5aTWayVWZm7LhRIsPIo5kLCQaV2Q+Vu17ILDGEnUbZppdaSsfplNfhZ52eWNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:12.117530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e28f27e627154dd838a3ebd256270dae5283e41e342c533fbe248b2f99f92663","sha256:e1ff95d83868fbbfb111ba2a6f459c79685d8257b2dceca84a4fee0eeb1478cc"],"state_sha256":"d059987acc61d6ca66f86e04f809e42f26d09965c3cede859ab9624661fbc882"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f2OYKhQa+UFYEJV9SyrP3hrGqLTYdvC5xUVWp1I/4XVOhDcuA9jxIne1vZ6MvYhR7zKBCEiRsPEQkmS3JaEaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:36:14.959033Z","bundle_sha256":"d0a196c630e2bf520f8d19d10b7f795ce5305416407aaded951456e80ba5f631"}}