{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HGKLDZBKZWUT3G6EX7X2BQMYVS","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":"b0904da7d18b1bd3b760ff7cd5c04d679f0977c60ccba014c9c61e14b0809c54","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":"2016-06-07T15:20:44Z","title_canon_sha256":"aade18299273d960696216354384ed9fdbe744746eef58a70ebfce023c4b7f6d"},"schema_version":"1.0","source":{"id":"1606.02176","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02176","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02176v3","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02176","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"HGKLDZBKZWUT","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HGKLDZBKZWUT3G6E","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HGKLDZBK","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:9ad919d44a1c009274d5e11f6e32206253df40cd95fe409818d0143c27418ff3","target":"graph","created_at":"2026-05-18T01:03:36Z","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":"In single field slow-roll inflation, one expects that the spectral index $n_s -1$ is first order in slow-roll parameters. Similarly, its running $\\alpha_s = dn_s/d \\log k$ and the running of the running $\\beta_s = d\\alpha_s/d \\log k$ are second and third order and therefore expected to be progressively smaller, and usually negative. Hence, such models of inflation are in considerable tension with a recent analysis hinting that $\\beta_s$ may actually be positive, and larger than $\\alpha_s$. Motivated by this, in this work we ask the question of what kinds of inflationary models may be useful in","authors_text":"Carsten van de Bruck, Chris Longden","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":"2016-06-07T15:20:44Z","title":"Running of the Running and Entropy Perturbations During Inflation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02176","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:b41aab510e09880402016854af35f63b508fb01ecebd2a520f0c73a6e1a71db6","target":"record","created_at":"2026-05-18T01:03:36Z","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":"b0904da7d18b1bd3b760ff7cd5c04d679f0977c60ccba014c9c61e14b0809c54","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":"2016-06-07T15:20:44Z","title_canon_sha256":"aade18299273d960696216354384ed9fdbe744746eef58a70ebfce023c4b7f6d"},"schema_version":"1.0","source":{"id":"1606.02176","kind":"arxiv","version":3}},"canonical_sha256":"3994b1e42acda93d9bc4bfefa0c198acafb7edcbb5fb8bed40d7f309704588e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3994b1e42acda93d9bc4bfefa0c198acafb7edcbb5fb8bed40d7f309704588e0","first_computed_at":"2026-05-18T01:03:36.276817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:36.276817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gxIX+nCQ9hIyL1negUq7iI/q1F/WkaLPWaas+u60+qRCIpdQqW/K+HmqHa5DsPRmFKRzO2VxbtHcwRG+mDLbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:36.277776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02176","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b41aab510e09880402016854af35f63b508fb01ecebd2a520f0c73a6e1a71db6","sha256:9ad919d44a1c009274d5e11f6e32206253df40cd95fe409818d0143c27418ff3"],"state_sha256":"c58420ee32d3839d67ca9d8a0703d37399e8a0ed961e8006068b20efb3847eb7"}