{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GNRTLBNDAWA4VE23LQLWZO6JKM","short_pith_number":"pith:GNRTLBND","schema_version":"1.0","canonical_sha256":"33633585a30581ca935b5c176cbbc95316548016ba755cdebc3e85d4ae8d4cac","source":{"kind":"arxiv","id":"2503.01621","version":1},"attestation_state":"computed","paper":{"title":"Multi-index Based Solution Theory to the $\\Phi^4$ Equation in the Full Subcritical Regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Felix Otto, Lucas Broux, Rhys Steele","submitted_at":"2025-03-03T14:54:31Z","abstract_excerpt":"We obtain (small-parameter) well-posedness for the (space-time periodic) $\\Phi^4$ equation in the full subcritical regime in the context of regularity structures based on multi-indices. As opposed to Hairer's more extrinsic tree-based setting, due to the intrinsic description encoded by multi-indices, it is not possible to obtain a solution theory via the standard fixed-point argument. Instead, we develop a more intrinsic approach for existence using a variant of the continuity method from classical PDE theory based on a priori estimates for a new `robust' formulation of the equation. This for"},"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":"2503.01621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-03-03T14:54:31Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"aa3ee09a04bcac605cba91cfdd1df88f531cdc136ae88127cf37492bbfe98d66","abstract_canon_sha256":"e18f9040248cd1058e4024e1072a09ded710322214f20dc900b9e6e6ffac1490"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:23:10.998457Z","signature_b64":"V72P7499vJZMS67QiPnEG4HS+uau9b9iNfxQ1i1GnRe1ZoKIVvhOlMMkfonOCssTesF0wn21ErM+6wFX5GbCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33633585a30581ca935b5c176cbbc95316548016ba755cdebc3e85d4ae8d4cac","last_reissued_at":"2026-07-05T10:23:10.997923Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:23:10.997923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-index Based Solution Theory to the $\\Phi^4$ Equation in the Full Subcritical Regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Felix Otto, Lucas Broux, Rhys Steele","submitted_at":"2025-03-03T14:54:31Z","abstract_excerpt":"We obtain (small-parameter) well-posedness for the (space-time periodic) $\\Phi^4$ equation in the full subcritical regime in the context of regularity structures based on multi-indices. As opposed to Hairer's more extrinsic tree-based setting, due to the intrinsic description encoded by multi-indices, it is not possible to obtain a solution theory via the standard fixed-point argument. Instead, we develop a more intrinsic approach for existence using a variant of the continuity method from classical PDE theory based on a priori estimates for a new `robust' formulation of the equation. This for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.01621","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/2503.01621/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":"2503.01621","created_at":"2026-07-05T10:23:10.997988+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.01621v1","created_at":"2026-07-05T10:23:10.997988+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.01621","created_at":"2026-07-05T10:23:10.997988+00:00"},{"alias_kind":"pith_short_12","alias_value":"GNRTLBNDAWA4","created_at":"2026-07-05T10:23:10.997988+00:00"},{"alias_kind":"pith_short_16","alias_value":"GNRTLBNDAWA4VE23","created_at":"2026-07-05T10:23:10.997988+00:00"},{"alias_kind":"pith_short_8","alias_value":"GNRTLBND","created_at":"2026-07-05T10:23:10.997988+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.14616","citing_title":"A tree-free approach to 3D Yang-Mills Langevin dynamic. Analytic estimates and the existence of a model for a regularity structure","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2605.28677","citing_title":"Weak universality for stochastic reaction-diffusion models with long-range correlated noise","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GNRTLBNDAWA4VE23LQLWZO6JKM","json":"https://pith.science/pith/GNRTLBNDAWA4VE23LQLWZO6JKM.json","graph_json":"https://pith.science/api/pith-number/GNRTLBNDAWA4VE23LQLWZO6JKM/graph.json","events_json":"https://pith.science/api/pith-number/GNRTLBNDAWA4VE23LQLWZO6JKM/events.json","paper":"https://pith.science/paper/GNRTLBND"},"agent_actions":{"view_html":"https://pith.science/pith/GNRTLBNDAWA4VE23LQLWZO6JKM","download_json":"https://pith.science/pith/GNRTLBNDAWA4VE23LQLWZO6JKM.json","view_paper":"https://pith.science/paper/GNRTLBND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.01621&json=true","fetch_graph":"https://pith.science/api/pith-number/GNRTLBNDAWA4VE23LQLWZO6JKM/graph.json","fetch_events":"https://pith.science/api/pith-number/GNRTLBNDAWA4VE23LQLWZO6JKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GNRTLBNDAWA4VE23LQLWZO6JKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GNRTLBNDAWA4VE23LQLWZO6JKM/action/storage_attestation","attest_author":"https://pith.science/pith/GNRTLBNDAWA4VE23LQLWZO6JKM/action/author_attestation","sign_citation":"https://pith.science/pith/GNRTLBNDAWA4VE23LQLWZO6JKM/action/citation_signature","submit_replication":"https://pith.science/pith/GNRTLBNDAWA4VE23LQLWZO6JKM/action/replication_record"}},"created_at":"2026-07-05T10:23:10.997988+00:00","updated_at":"2026-07-05T10:23:10.997988+00:00"}