Pith Number

pith:WJMXKWHC

pith:2026:WJMXKWHCSMHTZV2CUJHQOGJCVD

not attested not anchored not stored refs pending

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems

Wenpeng Yin, Wenrui Hao, Zhipeng Chang

arxiv:2608.12286 v1 · 2026-08-12 · math-ph · 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{WJMXKWHCSMHTZV2CUJHQOGJCVD}

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	2026-08-13T01:30:43.268704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2597558e2930f3cd742a24f071922a8e0833a97344ccfef09d05c6c35f5ad6a

Aliases

arxiv: 2608.12286 · arxiv_version: 2608.12286v1 · doi: 10.48550/arxiv.2608.12286 · pith_short_12: WJMXKWHCSMHT · pith_short_16: WJMXKWHCSMHTZV2C · pith_short_8: WJMXKWHC

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/WJMXKWHCSMHTZV2CUJHQOGJCVD \
  | 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: b2597558e2930f3cd742a24f071922a8e0833a97344ccfef09d05c6c35f5ad6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5873209c4696e00cfc6e482a9832757cd42b0e728d244155f9dcdb6897e6eb0",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-08-12T17:31:38Z",
    "title_canon_sha256": "e070cb82b2ce2349fe1047a1358465b70458c01e4a855f64eac5e7ce68222c80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.12286",
    "kind": "arxiv",
    "version": 1
  }
}