Pith Number

pith:2ZLRS2OH

pith:2026:2ZLRS2OHP46UQQ4TIKRSHFE2W7

not attested not anchored not stored refs pending

A Liouville theorem for bounded empirical-harmonic functions on $\mathcal{P}_2(M)$

Hongwei Yuan

arxiv:2605.30756 v1 · 2026-05-29 · 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{2ZLRS2OHP46UQQ4TIKRSHFE2W7}

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	2026-06-01T01:03:14.623740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6571969c77f3d48439342a323949ab7ee2b0a1cd464b91047cddfa17d345bd7

Aliases

arxiv: 2605.30756 · arxiv_version: 2605.30756v1 · doi: 10.48550/arxiv.2605.30756 · pith_short_12: 2ZLRS2OHP46U · pith_short_16: 2ZLRS2OHP46UQQ4T · pith_short_8: 2ZLRS2OH

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/2ZLRS2OHP46UQQ4TIKRSHFE2W7 \
  | 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: d6571969c77f3d48439342a323949ab7ee2b0a1cd464b91047cddfa17d345bd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "323ad1073be9bf3afcb0bc11575d26d4233f125e554e21d19ce895c1718457f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-29T02:37:15Z",
    "title_canon_sha256": "9da88a6bd501185739392dd52b6f7cec9d65b5cf3365762a0636b2295da82e9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.30756",
    "kind": "arxiv",
    "version": 1
  }
}