Pith Number

pith:JKYHW5NH

pith:2025:JKYHW5NHEFXBRDT3P2NECLCQNZ

not attested not anchored not stored refs pending

Liouville theorem of the subcritical biharmonic equation on complete manifolds

Tian Wu, Wangzhe Wu, Xi-Nan Ma

arxiv:2508.14497 v1 · 2025-08-20 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JKYHW5NHEFXBRDT3P2NECLCQNZ}

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	2026-07-05T11:56:33.063039Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ab07b75a7216e188e7b7e9a412c506e543405d0f46bca4ca6d79c898e2a66aa

Aliases

arxiv: 2508.14497 · arxiv_version: 2508.14497v1 · doi: 10.48550/arxiv.2508.14497 · pith_short_12: JKYHW5NHEFXB · pith_short_16: JKYHW5NHEFXBRDT3 · pith_short_8: JKYHW5NH

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/JKYHW5NHEFXBRDT3P2NECLCQNZ \
  | 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: 4ab07b75a7216e188e7b7e9a412c506e543405d0f46bca4ca6d79c898e2a66aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9db29f571e4a57b1fb8c240afb9d4879c910d58106396d4e655257dee396eabc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-08-20T07:35:12Z",
    "title_canon_sha256": "e0c1c27af69ec4ee1593acfb902df19ca5015a3841b88e016b19bbc1e9af9dee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.14497",
    "kind": "arxiv",
    "version": 1
  }
}