Pith Number

pith:U2F3IMFH

pith:2026:U2F3IMFHJRLB6Y7TD3XXHX3VQD

not attested not anchored not stored refs pending

The four-dimensional Anderson model: a case study for critical SPDEs

Hao Shen, Yu Deng

arxiv:2607.10105 v1 · 2026-07-11 · math.PR · math-ph · math.AP · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U2F3IMFHJRLB6Y7TD3XXHX3VQD}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-07-14T00:18:51.916442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a68bb430a74c561f63f31eef73df7580da21c7be1b58541bb22a437001d80d27

Aliases

arxiv: 2607.10105 · arxiv_version: 2607.10105v1 · doi: 10.48550/arxiv.2607.10105 · pith_short_12: U2F3IMFHJRLB · pith_short_16: U2F3IMFHJRLB6Y7T · pith_short_8: U2F3IMFH

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/U2F3IMFHJRLB6Y7TD3XXHX3VQD \
  | 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: a68bb430a74c561f63f31eef73df7580da21c7be1b58541bb22a437001d80d27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88cd14572c169b6b711c4bb23ecb730bca2f96c77ad5963342cbe6782585de42",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-11T03:45:48Z",
    "title_canon_sha256": "c0d337c9d07fc87571875495120be5d3fda6b015ef71fc4a644cb9380b1f008d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10105",
    "kind": "arxiv",
    "version": 1
  }
}