{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2QM3WKLE4W4YY2NWTHUZ3WKQ27","short_pith_number":"pith:2QM3WKLE","schema_version":"1.0","canonical_sha256":"d419bb2964e5b98c69b699e99dd950d7fed1cc11523893e8e4ed06c27c5a49f9","source":{"kind":"arxiv","id":"1504.04143","version":2},"attestation_state":"computed","paper":{"title":"Piecewise linear approximation for the dynamical $\\Phi^4_3$ model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Rongchan Zhu, Xiangchan Zhu","submitted_at":"2015-04-16T08:54:07Z","abstract_excerpt":"We construct a piecewise linear approximation for the dynamical $\\Phi_3^4$ model on $\\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed in order to define the nonlinear term. Compared to the results in [Hai14] we consider piecewise linear approximations to space-time white noise and prove that the solutions to the approximating equations converge to the solution to the dynamical $\\Phi^4_3$ model. The renormalisation in this case corresponds to adding the solution multiplied by a "},"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":"1504.04143","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-16T08:54:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c63fbf6b9fe4908f84764867bcd0513371e231e71640454b9b708d7b6351b5d4","abstract_canon_sha256":"b556ea474423db39aaf204220bb71e2e50444c64892271b6990aff0a173130f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:21.739992Z","signature_b64":"9GpPvypwDmKLOoy1u4yt+vY0jTNqGFAblVtTvMsuMUAP5QWkpC+MURW3e/e58/aT507vpBv7xH8gsvtuj4R3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d419bb2964e5b98c69b699e99dd950d7fed1cc11523893e8e4ed06c27c5a49f9","last_reissued_at":"2026-05-18T00:32:21.739414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:21.739414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Piecewise linear approximation for the dynamical $\\Phi^4_3$ model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Rongchan Zhu, Xiangchan Zhu","submitted_at":"2015-04-16T08:54:07Z","abstract_excerpt":"We construct a piecewise linear approximation for the dynamical $\\Phi_3^4$ model on $\\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed in order to define the nonlinear term. Compared to the results in [Hai14] we consider piecewise linear approximations to space-time white noise and prove that the solutions to the approximating equations converge to the solution to the dynamical $\\Phi^4_3$ model. The renormalisation in this case corresponds to adding the solution multiplied by a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04143","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":""},"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":"1504.04143","created_at":"2026-05-18T00:32:21.739497+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04143v2","created_at":"2026-05-18T00:32:21.739497+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04143","created_at":"2026-05-18T00:32:21.739497+00:00"},{"alias_kind":"pith_short_12","alias_value":"2QM3WKLE4W4Y","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2QM3WKLE4W4YY2NW","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2QM3WKLE","created_at":"2026-05-18T12:29:02.477457+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/2QM3WKLE4W4YY2NWTHUZ3WKQ27","json":"https://pith.science/pith/2QM3WKLE4W4YY2NWTHUZ3WKQ27.json","graph_json":"https://pith.science/api/pith-number/2QM3WKLE4W4YY2NWTHUZ3WKQ27/graph.json","events_json":"https://pith.science/api/pith-number/2QM3WKLE4W4YY2NWTHUZ3WKQ27/events.json","paper":"https://pith.science/paper/2QM3WKLE"},"agent_actions":{"view_html":"https://pith.science/pith/2QM3WKLE4W4YY2NWTHUZ3WKQ27","download_json":"https://pith.science/pith/2QM3WKLE4W4YY2NWTHUZ3WKQ27.json","view_paper":"https://pith.science/paper/2QM3WKLE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04143&json=true","fetch_graph":"https://pith.science/api/pith-number/2QM3WKLE4W4YY2NWTHUZ3WKQ27/graph.json","fetch_events":"https://pith.science/api/pith-number/2QM3WKLE4W4YY2NWTHUZ3WKQ27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2QM3WKLE4W4YY2NWTHUZ3WKQ27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2QM3WKLE4W4YY2NWTHUZ3WKQ27/action/storage_attestation","attest_author":"https://pith.science/pith/2QM3WKLE4W4YY2NWTHUZ3WKQ27/action/author_attestation","sign_citation":"https://pith.science/pith/2QM3WKLE4W4YY2NWTHUZ3WKQ27/action/citation_signature","submit_replication":"https://pith.science/pith/2QM3WKLE4W4YY2NWTHUZ3WKQ27/action/replication_record"}},"created_at":"2026-05-18T00:32:21.739497+00:00","updated_at":"2026-05-18T00:32:21.739497+00:00"}