{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6VJ3V4PN2UUZPDXINCX4BLCFWN","short_pith_number":"pith:6VJ3V4PN","schema_version":"1.0","canonical_sha256":"f553baf1edd529978ee868afc0ac45b37637e2a3716d1ccc2c81bc97f9224c0e","source":{"kind":"arxiv","id":"2603.21151","version":2},"attestation_state":"computed","paper":{"title":"Solving Functional Renormalization Group Equations with Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Lianyi He, Lingxiao Wang, Wei-jie Fu, Yang-yang Tan","submitted_at":"2026-03-22T10:03:22Z","abstract_excerpt":"We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow equations directly into the loss function, the network parameters are determined so as to provide a continuous and differentiable representation of the scale- and field-dependent effective potential without relying on precomputed training data. Focusing on the $O(N)$ scalar field theory within the local potential approximation at finite temperature, we demonstrate t"},"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":"2603.21151","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2026-03-22T10:03:22Z","cross_cats_sorted":[],"title_canon_sha256":"9780f2d8061992505b7cef783dd30438bed7901741b79b94795d26954c229d32","abstract_canon_sha256":"ee882e6409e4d662cacaf1043bbf47eb10584dc6bf1c97d808d1a34e940722be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T02:23:28.578031Z","signature_b64":"Os2NUY8cO20Qhbvp0MMG4xHOFcwKC2cNDV//zq+adJZPnKr63jTkPtjxp5DRLZumQ2PmxwhaqBCKfpyDZ4vmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f553baf1edd529978ee868afc0ac45b37637e2a3716d1ccc2c81bc97f9224c0e","last_reissued_at":"2026-07-28T02:23:28.577059Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T02:23:28.577059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving Functional Renormalization Group Equations with Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Lianyi He, Lingxiao Wang, Wei-jie Fu, Yang-yang Tan","submitted_at":"2026-03-22T10:03:22Z","abstract_excerpt":"We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow equations directly into the loss function, the network parameters are determined so as to provide a continuous and differentiable representation of the scale- and field-dependent effective potential without relying on precomputed training data. Focusing on the $O(N)$ scalar field theory within the local potential approximation at finite temperature, we demonstrate t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.21151","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.21151/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":"2603.21151","created_at":"2026-07-28T02:23:28.577523+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.21151v2","created_at":"2026-07-28T02:23:28.577523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.21151","created_at":"2026-07-28T02:23:28.577523+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VJ3V4PN2UUZ","created_at":"2026-07-28T02:23:28.577523+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VJ3V4PN2UUZPDXI","created_at":"2026-07-28T02:23:28.577523+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VJ3V4PN","created_at":"2026-07-28T02:23:28.577523+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08505","citing_title":"Diffusion Models for Sampling Near Criticality in Lattice Field Theories","ref_index":36,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6VJ3V4PN2UUZPDXINCX4BLCFWN","json":"https://pith.science/pith/6VJ3V4PN2UUZPDXINCX4BLCFWN.json","graph_json":"https://pith.science/api/pith-number/6VJ3V4PN2UUZPDXINCX4BLCFWN/graph.json","events_json":"https://pith.science/api/pith-number/6VJ3V4PN2UUZPDXINCX4BLCFWN/events.json","paper":"https://pith.science/paper/6VJ3V4PN"},"agent_actions":{"view_html":"https://pith.science/pith/6VJ3V4PN2UUZPDXINCX4BLCFWN","download_json":"https://pith.science/pith/6VJ3V4PN2UUZPDXINCX4BLCFWN.json","view_paper":"https://pith.science/paper/6VJ3V4PN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.21151&json=true","fetch_graph":"https://pith.science/api/pith-number/6VJ3V4PN2UUZPDXINCX4BLCFWN/graph.json","fetch_events":"https://pith.science/api/pith-number/6VJ3V4PN2UUZPDXINCX4BLCFWN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VJ3V4PN2UUZPDXINCX4BLCFWN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VJ3V4PN2UUZPDXINCX4BLCFWN/action/storage_attestation","attest_author":"https://pith.science/pith/6VJ3V4PN2UUZPDXINCX4BLCFWN/action/author_attestation","sign_citation":"https://pith.science/pith/6VJ3V4PN2UUZPDXINCX4BLCFWN/action/citation_signature","submit_replication":"https://pith.science/pith/6VJ3V4PN2UUZPDXINCX4BLCFWN/action/replication_record"}},"created_at":"2026-07-28T02:23:28.577523+00:00","updated_at":"2026-07-28T02:23:28.577523+00:00"}