Pith Number

pith:WMAXIYDN

pith:2024:WMAXIYDN6YX2WINGYQHYPDKEZW

not attested not anchored not stored refs pending

A Birkhoff Normal Form Theorem for Partial Differential Equations on torus

Duohui Xiang, Jianjun Liu

arxiv:2411.13312 v1 · 2024-11-20 · math.AP · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WMAXIYDN6YX2WINGYQHYPDKEZW}

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	2026-07-05T09:38:08.639388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b30174606df62fab21a6c40f878d44cd8a12343780b470cb6e6c0a5bcdbc0130

Aliases

arxiv: 2411.13312 · arxiv_version: 2411.13312v1 · doi: 10.48550/arxiv.2411.13312 · pith_short_12: WMAXIYDN6YX2 · pith_short_16: WMAXIYDN6YX2WING · pith_short_8: WMAXIYDN

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/WMAXIYDN6YX2WINGYQHYPDKEZW \
  | 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: b30174606df62fab21a6c40f878d44cd8a12343780b470cb6e6c0a5bcdbc0130

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e8f01d6a59652906a8d0dd83c19d7d292f18e34ebdf18e6565ce867af998267",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-11-20T13:28:32Z",
    "title_canon_sha256": "e4b941713d923785db48c0487e596dd6f315050b55d5592e0560f2fb84b6f84a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.13312",
    "kind": "arxiv",
    "version": 1
  }
}