Pith Number

pith:5MZOFUMD

pith:2026:5MZOFUMDKMIWBINKS7ZYLKLACZ

not attested not anchored not stored refs pending

Positive probability of explosion for stochastic heat equation with superlinear accretive reaction term and polynomially growing multiplicative noise

Michael Salins, Yuyang Zhang

Mild solutions to the stochastic heat equation explode with positive probability for beta in (1,3) with gamma in (beta/2, (beta+3)/4) or beta greater than 1 with gamma up to beta/2.

arxiv:2605.11319 v2 · 2026-05-11 · math.PR

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\usepackage{pith}
\pithnumber{5MZOFUMDKMIWBINKS7ZYLKLACZ}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

if β∈(1,3),γ∈(β/2,(β+3)/4) or β>1,γ∈(0,β/2] then mild solutions can explode with positive probability.

C2weakest assumption

The assumption that σ(u) ≈ u^γ near infinity together with the existence of mild solutions up to the potential explosion time on the periodic interval.

C3one line summary

Mild solutions explode with positive probability when β ∈ (1,3) and γ ∈ (β/2, (β+3)/4), or when β > 1 and γ ∈ (0, β/2].

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-29T02:05:46.475794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb32e2d183531160a1aa97f385a96016415a11b5e8c70465bd3bb93b541c3c89

Aliases

arxiv: 2605.11319 · arxiv_version: 2605.11319v2 · doi: 10.48550/arxiv.2605.11319 · pith_short_12: 5MZOFUMDKMIW · pith_short_16: 5MZOFUMDKMIWBINK · pith_short_8: 5MZOFUMD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5MZOFUMDKMIWBINKS7ZYLKLACZ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: eb32e2d183531160a1aa97f385a96016415a11b5e8c70465bd3bb93b541c3c89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83b2e441061d025f19a6db595da43bcc10c9c6910b332c6e9cf4bef32ebcfd01",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-11T23:11:52Z",
    "title_canon_sha256": "0e18dbef41f1664e5f4e380e554175ca9b1b6d7ff47e5c6605187c30b7472989"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11319",
    "kind": "arxiv",
    "version": 2
  }
}