{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:D4U3P7VA42Z7PA7CGB7ZEPLUDH","short_pith_number":"pith:D4U3P7VA","schema_version":"1.0","canonical_sha256":"1f29b7fea0e6b3f783e2307f923d7419f9e3dda0fd13f1620816cf9f47dd4f8a","source":{"kind":"arxiv","id":"2606.03860","version":1},"attestation_state":"computed","paper":{"title":"Biased tracers, Hybrid Effective Field Theory and Modified Gravity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph.CO","authors_text":"Baojiu Li, Guilherme Brando, Kazuya Koyama","submitted_at":"2026-06-02T16:34:38Z","abstract_excerpt":"The modelling of the power spectrum of biased tracers has become a central topic in the analysis of modern cosmological galaxy surveys. Perturbative templates formulated in both Eulerian and Lagrangian frameworks have been extensively developed over the last decades, with their implementation in $\\Lambda$CDM thoroughly investigated and validated. In parallel, approaches combining perturbation theory with the output of dark-matter-only simulations have emerged as powerful tools for modelling the nonlinear regime, most notably the Hybrid Effective Field Theory (HEFT) framework~\\cite{Modi:2019qbt"},"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":"2606.03860","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-06-02T16:34:38Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"242b110d8c2ce54a29c25df3070422cea40cdd7d8fd59ae5508737ff579cf306","abstract_canon_sha256":"5b9ce402f9f3bf7f073a3602d7e5110c6bf3b94c70eb407ac0ad2ed69f453ce8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T02:06:04.491034Z","signature_b64":"zVM5Vt4Rw019zwHl1CB8HFxkfMLYKHu91penCi6lBsE8e24/OnKcp9CWU9tfZyMiBswiRsTZi8zz05znurgjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f29b7fea0e6b3f783e2307f923d7419f9e3dda0fd13f1620816cf9f47dd4f8a","last_reissued_at":"2026-06-03T02:06:04.490683Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T02:06:04.490683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biased tracers, Hybrid Effective Field Theory and Modified Gravity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph.CO","authors_text":"Baojiu Li, Guilherme Brando, Kazuya Koyama","submitted_at":"2026-06-02T16:34:38Z","abstract_excerpt":"The modelling of the power spectrum of biased tracers has become a central topic in the analysis of modern cosmological galaxy surveys. Perturbative templates formulated in both Eulerian and Lagrangian frameworks have been extensively developed over the last decades, with their implementation in $\\Lambda$CDM thoroughly investigated and validated. In parallel, approaches combining perturbation theory with the output of dark-matter-only simulations have emerged as powerful tools for modelling the nonlinear regime, most notably the Hybrid Effective Field Theory (HEFT) framework~\\cite{Modi:2019qbt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03860","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/2606.03860/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":"2606.03860","created_at":"2026-06-03T02:06:04.490740+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.03860v1","created_at":"2026-06-03T02:06:04.490740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03860","created_at":"2026-06-03T02:06:04.490740+00:00"},{"alias_kind":"pith_short_12","alias_value":"D4U3P7VA42Z7","created_at":"2026-06-03T02:06:04.490740+00:00"},{"alias_kind":"pith_short_16","alias_value":"D4U3P7VA42Z7PA7C","created_at":"2026-06-03T02:06:04.490740+00:00"},{"alias_kind":"pith_short_8","alias_value":"D4U3P7VA","created_at":"2026-06-03T02:06:04.490740+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/D4U3P7VA42Z7PA7CGB7ZEPLUDH","json":"https://pith.science/pith/D4U3P7VA42Z7PA7CGB7ZEPLUDH.json","graph_json":"https://pith.science/api/pith-number/D4U3P7VA42Z7PA7CGB7ZEPLUDH/graph.json","events_json":"https://pith.science/api/pith-number/D4U3P7VA42Z7PA7CGB7ZEPLUDH/events.json","paper":"https://pith.science/paper/D4U3P7VA"},"agent_actions":{"view_html":"https://pith.science/pith/D4U3P7VA42Z7PA7CGB7ZEPLUDH","download_json":"https://pith.science/pith/D4U3P7VA42Z7PA7CGB7ZEPLUDH.json","view_paper":"https://pith.science/paper/D4U3P7VA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.03860&json=true","fetch_graph":"https://pith.science/api/pith-number/D4U3P7VA42Z7PA7CGB7ZEPLUDH/graph.json","fetch_events":"https://pith.science/api/pith-number/D4U3P7VA42Z7PA7CGB7ZEPLUDH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D4U3P7VA42Z7PA7CGB7ZEPLUDH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D4U3P7VA42Z7PA7CGB7ZEPLUDH/action/storage_attestation","attest_author":"https://pith.science/pith/D4U3P7VA42Z7PA7CGB7ZEPLUDH/action/author_attestation","sign_citation":"https://pith.science/pith/D4U3P7VA42Z7PA7CGB7ZEPLUDH/action/citation_signature","submit_replication":"https://pith.science/pith/D4U3P7VA42Z7PA7CGB7ZEPLUDH/action/replication_record"}},"created_at":"2026-06-03T02:06:04.490740+00:00","updated_at":"2026-06-03T02:06:04.490740+00:00"}