{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AYS3RIVGMK4BAB2MNED2AZBBFG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"60b4cda51497477ad69ec8f4bbdf4d01a37703f8dde8db3426c562d4ecf7b2e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-29T13:34:44Z","title_canon_sha256":"09c38f0e4de88a3f1bfdc068b6812fc667b3076d25cdd65e8b49bdde89971057"},"schema_version":"1.0","source":{"id":"1607.08802","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08802","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08802v2","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08802","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"AYS3RIVGMK4B","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AYS3RIVGMK4BAB2M","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AYS3RIVG","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:b669f37bf71702db07ab991b9b81b59926cf5315f958f9bfd6ccc758058413ed","target":"graph","created_at":"2026-05-18T00:18:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the one-dimensional Fisher-KPP equation, with an initial condition $u_0(x)$ that coincides with the step function except on a compact set. A well-known result of M. Bramson states that, as $t\\to+\\infty$, the solution converges to a traveling wave located at the position $X(t)=2t-(3/2)\\log t+x_0+o(1)$, with the shift $x_0$ that depends on $u_0$. U. Ebert and W. Van Saarloos have formally derived a correction to the Bramson shift, arguing that $X(t)=2t-(3/2)\\log t+x_0-3\\sqrt{\\pi}/\\sqrt{t}+O(1/t)$. Here, we prove that this result does hold, with an error term of the size $O(1/t^{1-\\gamma","authors_text":"James Nolen, Jean-Michel Roquejoffre, Lenya Ryzhik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-29T13:34:44Z","title":"Refined long time asymptotics for Fisher-KPP fronts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08802","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:44e58c319fb138201bc5d4ebbfeec6f2e83651aaef3170e8eb8f423d39bdf5e0","target":"record","created_at":"2026-05-18T00:18:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"60b4cda51497477ad69ec8f4bbdf4d01a37703f8dde8db3426c562d4ecf7b2e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-29T13:34:44Z","title_canon_sha256":"09c38f0e4de88a3f1bfdc068b6812fc667b3076d25cdd65e8b49bdde89971057"},"schema_version":"1.0","source":{"id":"1607.08802","kind":"arxiv","version":2}},"canonical_sha256":"0625b8a2a662b810074c6907a0642129a0bbe7acab1b6082cfc9ab07017a4c26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0625b8a2a662b810074c6907a0642129a0bbe7acab1b6082cfc9ab07017a4c26","first_computed_at":"2026-05-18T00:18:09.926880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:09.926880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M54Fzjw+/bszSXunAUlDG9SZWMVLGUKDB57Czpa8JmxzQ/7DZAyEJu93Lltz2Eeb6jsJpzp8p9N91C7dSMlCDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:09.927507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08802","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44e58c319fb138201bc5d4ebbfeec6f2e83651aaef3170e8eb8f423d39bdf5e0","sha256:b669f37bf71702db07ab991b9b81b59926cf5315f958f9bfd6ccc758058413ed"],"state_sha256":"fb87e59508ff28b32d7e8fc95d7dfd85871aea02c70453c22a10a4b8666bf053"}