{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TQKL2BMYYHYHQVSZB47YTFXJ2V","short_pith_number":"pith:TQKL2BMY","schema_version":"1.0","canonical_sha256":"9c14bd0598c1f07856590f3f8996e9d55253da922914bf7516b8474aad212fd2","source":{"kind":"arxiv","id":"1310.6421","version":1},"attestation_state":"computed","paper":{"title":"H\\\"older-continuity for the nonlinear stochastic heat equation with rough initial conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Le Chen, Robert C. Dalang","submitted_at":"2013-10-23T22:40:56Z","abstract_excerpt":"We study space-time regularity of the solution of the nonlinear stochastic heat equation in one spatial dimension driven by space-time white noise, with a rough initial condition. This initial condition is a locally finite measure $\\mu$ with, possibly, exponentially growing tails. We show how this regularity depends, in a neighborhood of $t=0$, on the regularity of the initial condition. On compact sets in which $t>0$, the classical H\\\"older-continuity exponents $\\frac{1}{4}-$ in time and $\\frac{1}{2}-$ in space remain valid. However, on compact sets that include $t=0$, the H\\\"older continuity"},"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":"1310.6421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-23T22:40:56Z","cross_cats_sorted":[],"title_canon_sha256":"5b7dc1993d79965887582d7914ef79067b00de36ffd5a429f62241988d42f0d3","abstract_canon_sha256":"1b311845d0a0e08058f08cb321e379cc7b0d18fd582422b14e878ccc407f2008"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:10.247142Z","signature_b64":"8WRSWzIZDyGKxxwWZ3j5A7i+hpdJ23LcQx2IP69cOARRo2mI8qPucioR+Kif22n+vL0DH8wh/d0LmdRpUNC9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c14bd0598c1f07856590f3f8996e9d55253da922914bf7516b8474aad212fd2","last_reissued_at":"2026-05-18T03:09:10.246495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:10.246495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"H\\\"older-continuity for the nonlinear stochastic heat equation with rough initial conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Le Chen, Robert C. Dalang","submitted_at":"2013-10-23T22:40:56Z","abstract_excerpt":"We study space-time regularity of the solution of the nonlinear stochastic heat equation in one spatial dimension driven by space-time white noise, with a rough initial condition. This initial condition is a locally finite measure $\\mu$ with, possibly, exponentially growing tails. We show how this regularity depends, in a neighborhood of $t=0$, on the regularity of the initial condition. On compact sets in which $t>0$, the classical H\\\"older-continuity exponents $\\frac{1}{4}-$ in time and $\\frac{1}{2}-$ in space remain valid. However, on compact sets that include $t=0$, the H\\\"older continuity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6421","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":""},"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":"1310.6421","created_at":"2026-05-18T03:09:10.246603+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.6421v1","created_at":"2026-05-18T03:09:10.246603+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6421","created_at":"2026-05-18T03:09:10.246603+00:00"},{"alias_kind":"pith_short_12","alias_value":"TQKL2BMYYHYH","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TQKL2BMYYHYHQVSZ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TQKL2BMY","created_at":"2026-05-18T12:28:02.375192+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/TQKL2BMYYHYHQVSZB47YTFXJ2V","json":"https://pith.science/pith/TQKL2BMYYHYHQVSZB47YTFXJ2V.json","graph_json":"https://pith.science/api/pith-number/TQKL2BMYYHYHQVSZB47YTFXJ2V/graph.json","events_json":"https://pith.science/api/pith-number/TQKL2BMYYHYHQVSZB47YTFXJ2V/events.json","paper":"https://pith.science/paper/TQKL2BMY"},"agent_actions":{"view_html":"https://pith.science/pith/TQKL2BMYYHYHQVSZB47YTFXJ2V","download_json":"https://pith.science/pith/TQKL2BMYYHYHQVSZB47YTFXJ2V.json","view_paper":"https://pith.science/paper/TQKL2BMY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.6421&json=true","fetch_graph":"https://pith.science/api/pith-number/TQKL2BMYYHYHQVSZB47YTFXJ2V/graph.json","fetch_events":"https://pith.science/api/pith-number/TQKL2BMYYHYHQVSZB47YTFXJ2V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TQKL2BMYYHYHQVSZB47YTFXJ2V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TQKL2BMYYHYHQVSZB47YTFXJ2V/action/storage_attestation","attest_author":"https://pith.science/pith/TQKL2BMYYHYHQVSZB47YTFXJ2V/action/author_attestation","sign_citation":"https://pith.science/pith/TQKL2BMYYHYHQVSZB47YTFXJ2V/action/citation_signature","submit_replication":"https://pith.science/pith/TQKL2BMYYHYHQVSZB47YTFXJ2V/action/replication_record"}},"created_at":"2026-05-18T03:09:10.246603+00:00","updated_at":"2026-05-18T03:09:10.246603+00:00"}