{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RTET3O5EURVOHQ2SYFQ7LEGULT","short_pith_number":"pith:RTET3O5E","canonical_record":{"source":{"id":"1106.2607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-06-14T04:43:44Z","cross_cats_sorted":["astro-ph.IM"],"title_canon_sha256":"b3a2c7feb6c6b0fa3e611eb19a2074b396b2ecc0599ee41cf7a98be5eef18b58","abstract_canon_sha256":"ceb35c2f20bb586f9f4202b19af1b4a2c5e8100139ecfe3591fd4f3a2746163d"},"schema_version":"1.0"},"canonical_sha256":"8cc93dbba4a46ae3c352c161f590d45cc393da125b6db7829e16035b8f5da59c","source":{"kind":"arxiv","id":"1106.2607","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2607","created_at":"2026-05-18T02:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2607v2","created_at":"2026-05-18T02:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2607","created_at":"2026-05-18T02:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"RTET3O5EURVO","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RTET3O5EURVOHQ2S","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RTET3O5E","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RTET3O5EURVOHQ2SYFQ7LEGULT","target":"record","payload":{"canonical_record":{"source":{"id":"1106.2607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-06-14T04:43:44Z","cross_cats_sorted":["astro-ph.IM"],"title_canon_sha256":"b3a2c7feb6c6b0fa3e611eb19a2074b396b2ecc0599ee41cf7a98be5eef18b58","abstract_canon_sha256":"ceb35c2f20bb586f9f4202b19af1b4a2c5e8100139ecfe3591fd4f3a2746163d"},"schema_version":"1.0"},"canonical_sha256":"8cc93dbba4a46ae3c352c161f590d45cc393da125b6db7829e16035b8f5da59c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:37.654671Z","signature_b64":"fD/+277USvGdN2YfQl8gU272D+5hcz+ccsRYa6uddeZCm2l+ImW7jqJW3hcTCZXgZOluGch6dKcYZHMeOdLoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cc93dbba4a46ae3c352c161f590d45cc393da125b6db7829e16035b8f5da59c","last_reissued_at":"2026-05-18T02:01:37.654081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:37.654081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.2607","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":"2026-05-18T02:01:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U0tqYGxG8p/8D4gkp7YU7MvaM+0M13XeCoPyy4sNAkWy4bM4kSZ5Ic6V6IjJOIUkPHGXit/O9I0rscWfFC6rAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:56:37.397931Z"},"content_sha256":"586591632bcf2b3e9bea435fdf540cb3060e5bac02540208b311129c86599380","schema_version":"1.0","event_id":"sha256:586591632bcf2b3e9bea435fdf540cb3060e5bac02540208b311129c86599380"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RTET3O5EURVOHQ2SYFQ7LEGULT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-linear matter power spectrum from Time Renormalisation Group: efficient computation and comparison with one-loop","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM"],"primary_cat":"astro-ph.CO","authors_text":"Benjamin Audren, Julien Lesgourgues","submitted_at":"2011-06-14T04:43:44Z","abstract_excerpt":"We address the issue of computing the non-linear matter power spectrum on mildly non-linear scales with efficient semi-analytic methods. We implemented M. Pietroni's Time Renormalization Group (TRG) method and its Dynamical 1-Loop (D1L) limit in a numerical module for the new Boltzmann code CLASS. Our publicly released module is valid for LCDM models, and optimized in such a way to run in less than a minute for D1L, or in one hour (divided by number of nodes) for TRG. A careful comparison of the D1L, TRG and Standard 1-Loop approaches reveals that results depend crucially on the assumed initia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2607","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":"2026-05-18T02:01:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5bpMDXC9Lxa47isOYT8hCypPxF73+I7jKoD5Nax5xk6kpjPgDhHRy8sjdaRVfc3BS6OPnnF3R1qV/8Gl+OkLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:56:37.398335Z"},"content_sha256":"59a5ae94754018fd485343e8b3140d777f1804f4ff077ae686811bcd28d605d5","schema_version":"1.0","event_id":"sha256:59a5ae94754018fd485343e8b3140d777f1804f4ff077ae686811bcd28d605d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RTET3O5EURVOHQ2SYFQ7LEGULT/bundle.json","state_url":"https://pith.science/pith/RTET3O5EURVOHQ2SYFQ7LEGULT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RTET3O5EURVOHQ2SYFQ7LEGULT/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":"2026-06-01T19:56:37Z","links":{"resolver":"https://pith.science/pith/RTET3O5EURVOHQ2SYFQ7LEGULT","bundle":"https://pith.science/pith/RTET3O5EURVOHQ2SYFQ7LEGULT/bundle.json","state":"https://pith.science/pith/RTET3O5EURVOHQ2SYFQ7LEGULT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RTET3O5EURVOHQ2SYFQ7LEGULT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RTET3O5EURVOHQ2SYFQ7LEGULT","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":"ceb35c2f20bb586f9f4202b19af1b4a2c5e8100139ecfe3591fd4f3a2746163d","cross_cats_sorted":["astro-ph.IM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-06-14T04:43:44Z","title_canon_sha256":"b3a2c7feb6c6b0fa3e611eb19a2074b396b2ecc0599ee41cf7a98be5eef18b58"},"schema_version":"1.0","source":{"id":"1106.2607","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2607","created_at":"2026-05-18T02:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2607v2","created_at":"2026-05-18T02:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2607","created_at":"2026-05-18T02:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"RTET3O5EURVO","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RTET3O5EURVOHQ2S","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RTET3O5E","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:59a5ae94754018fd485343e8b3140d777f1804f4ff077ae686811bcd28d605d5","target":"graph","created_at":"2026-05-18T02:01:37Z","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 address the issue of computing the non-linear matter power spectrum on mildly non-linear scales with efficient semi-analytic methods. We implemented M. Pietroni's Time Renormalization Group (TRG) method and its Dynamical 1-Loop (D1L) limit in a numerical module for the new Boltzmann code CLASS. Our publicly released module is valid for LCDM models, and optimized in such a way to run in less than a minute for D1L, or in one hour (divided by number of nodes) for TRG. A careful comparison of the D1L, TRG and Standard 1-Loop approaches reveals that results depend crucially on the assumed initia","authors_text":"Benjamin Audren, Julien Lesgourgues","cross_cats":["astro-ph.IM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-06-14T04:43:44Z","title":"Non-linear matter power spectrum from Time Renormalisation Group: efficient computation and comparison with one-loop"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2607","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":"sha256:586591632bcf2b3e9bea435fdf540cb3060e5bac02540208b311129c86599380","target":"record","created_at":"2026-05-18T02:01:37Z","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":"ceb35c2f20bb586f9f4202b19af1b4a2c5e8100139ecfe3591fd4f3a2746163d","cross_cats_sorted":["astro-ph.IM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-06-14T04:43:44Z","title_canon_sha256":"b3a2c7feb6c6b0fa3e611eb19a2074b396b2ecc0599ee41cf7a98be5eef18b58"},"schema_version":"1.0","source":{"id":"1106.2607","kind":"arxiv","version":2}},"canonical_sha256":"8cc93dbba4a46ae3c352c161f590d45cc393da125b6db7829e16035b8f5da59c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cc93dbba4a46ae3c352c161f590d45cc393da125b6db7829e16035b8f5da59c","first_computed_at":"2026-05-18T02:01:37.654081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:37.654081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fD/+277USvGdN2YfQl8gU272D+5hcz+ccsRYa6uddeZCm2l+ImW7jqJW3hcTCZXgZOluGch6dKcYZHMeOdLoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:37.654671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2607","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:586591632bcf2b3e9bea435fdf540cb3060e5bac02540208b311129c86599380","sha256:59a5ae94754018fd485343e8b3140d777f1804f4ff077ae686811bcd28d605d5"],"state_sha256":"59ab6a7e8e419eacb5572c9aa46f95d0173eacc366be5b8591f4e32b0eea5b98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7qTAJdn5iUGEDDvPbqZ4yatTEX6Gw3vwKm7jer3me71Azt5DFbMsH95lrdNTtbQyUT8asuep8QB3E7hflcUhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:56:37.400960Z","bundle_sha256":"859f2d9175c1cd2560d8633f5073d88dff3f8a389024a9c6a72086e42a2daa62"}}