{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4BNWOSN4UD6LBXOBWSDKMYW6P4","short_pith_number":"pith:4BNWOSN4","schema_version":"1.0","canonical_sha256":"e05b6749bca0fcb0ddc1b486a662de7f193d4a28bdc6ae605b02237621413d7a","source":{"kind":"arxiv","id":"2608.12819","version":1},"attestation_state":"computed","paper":{"title":"Waterfall-modulated $\\alpha$-attractors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Andrei Linde, Renata Kallosh, Yusuke Yamada","submitted_at":"2026-08-13T04:48:51Z","abstract_excerpt":"Hybrid $\\alpha$-attractor models \\cite{Kallosh:2022ggf} can have significantly greater values of $n_{s}$ and smaller $r$, while preserving the relation $r\\cong 3\\alpha (1-n_s)^2$, which is valid for exponential T- and E-models at large values of the inflaton field. Here we study single-field $\\alpha$-attractors with features inspired by hybrid models: one can uplift the potential, and one can also have a waterfall regime that leads to a premature termination of inflation near the critical point $\\varphi_c$. This allows one to increase the effective number of e-foldings $N_c$ in formulas like $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.12819","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-13T04:48:51Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"ca4a31a7bbff7b3828fe1c6a1f8d4aa84b04bd7110a14f6812005682ba8b94cd","abstract_canon_sha256":"fc695f7297d8bff2a6f0739cfb40dd55edd089d75b6191de7f2826c7536c0e88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-14T00:48:38.873370Z","signature_b64":"C+9TaZqRnFLOtmsRHBjE4GcvZAffQkq8+H37n+AXM/KUDbz81/i06QfvuPI/UGqQgqhPYxs2EmAQ1hfg7wBOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e05b6749bca0fcb0ddc1b486a662de7f193d4a28bdc6ae605b02237621413d7a","last_reissued_at":"2026-08-14T00:48:38.866465Z","signature_status":"signed_v1","first_computed_at":"2026-08-14T00:48:38.866465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Waterfall-modulated $\\alpha$-attractors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Andrei Linde, Renata Kallosh, Yusuke Yamada","submitted_at":"2026-08-13T04:48:51Z","abstract_excerpt":"Hybrid $\\alpha$-attractor models \\cite{Kallosh:2022ggf} can have significantly greater values of $n_{s}$ and smaller $r$, while preserving the relation $r\\cong 3\\alpha (1-n_s)^2$, which is valid for exponential T- and E-models at large values of the inflaton field. Here we study single-field $\\alpha$-attractors with features inspired by hybrid models: one can uplift the potential, and one can also have a waterfall regime that leads to a premature termination of inflation near the critical point $\\varphi_c$. This allows one to increase the effective number of e-foldings $N_c$ in formulas like $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12819","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.12819/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.12819","created_at":"2026-08-14T00:48:38.872091+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.12819v1","created_at":"2026-08-14T00:48:38.872091+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.12819","created_at":"2026-08-14T00:48:38.872091+00:00"},{"alias_kind":"pith_short_12","alias_value":"4BNWOSN4UD6L","created_at":"2026-08-14T00:48:38.872091+00:00"},{"alias_kind":"pith_short_16","alias_value":"4BNWOSN4UD6LBXOB","created_at":"2026-08-14T00:48:38.872091+00:00"},{"alias_kind":"pith_short_8","alias_value":"4BNWOSN4","created_at":"2026-08-14T00:48:38.872091+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4BNWOSN4UD6LBXOBWSDKMYW6P4","json":"https://pith.science/pith/4BNWOSN4UD6LBXOBWSDKMYW6P4.json","graph_json":"https://pith.science/api/pith-number/4BNWOSN4UD6LBXOBWSDKMYW6P4/graph.json","events_json":"https://pith.science/api/pith-number/4BNWOSN4UD6LBXOBWSDKMYW6P4/events.json","paper":"https://pith.science/paper/4BNWOSN4"},"agent_actions":{"view_html":"https://pith.science/pith/4BNWOSN4UD6LBXOBWSDKMYW6P4","download_json":"https://pith.science/pith/4BNWOSN4UD6LBXOBWSDKMYW6P4.json","view_paper":"https://pith.science/paper/4BNWOSN4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.12819&json=true","fetch_graph":"https://pith.science/api/pith-number/4BNWOSN4UD6LBXOBWSDKMYW6P4/graph.json","fetch_events":"https://pith.science/api/pith-number/4BNWOSN4UD6LBXOBWSDKMYW6P4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4BNWOSN4UD6LBXOBWSDKMYW6P4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4BNWOSN4UD6LBXOBWSDKMYW6P4/action/storage_attestation","attest_author":"https://pith.science/pith/4BNWOSN4UD6LBXOBWSDKMYW6P4/action/author_attestation","sign_citation":"https://pith.science/pith/4BNWOSN4UD6LBXOBWSDKMYW6P4/action/citation_signature","submit_replication":"https://pith.science/pith/4BNWOSN4UD6LBXOBWSDKMYW6P4/action/replication_record"}},"created_at":"2026-08-14T00:48:38.872091+00:00","updated_at":"2026-08-14T00:48:38.872091+00:00"}