Pith Number

pith:PIEWRAYZ

pith:2026:PIEWRAYZR55UBV6XRKQ4ZZKXQ7

not attested not anchored not stored refs pending

Decay estimates for the two-dimensional Beam equation with potentials

Han Cheng, Shuangshuang Chen, Xiaohua Yao, Zijun Wan

arxiv:2606.16793 v2 · 2026-06-15 · 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{PIEWRAYZR55UBV6XRKQ4ZZKXQ7}

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	2026-07-31T01:33:52.355255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

7a096883198f7b40d7d78aa1cce55787c304169ed5b2ee2bc1eea9beacde10d9

Aliases

arxiv: 2606.16793 · arxiv_version: 2606.16793v2 · doi: 10.48550/arxiv.2606.16793 · pith_short_12: PIEWRAYZR55U · pith_short_16: PIEWRAYZR55UBV6X · pith_short_8: PIEWRAYZ

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/PIEWRAYZR55UBV6XRKQ4ZZKXQ7 \
  | 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: 7a096883198f7b40d7d78aa1cce55787c304169ed5b2ee2bc1eea9beacde10d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b436bb6f7051718a56ca69976a10d58268431218fc063cf2f81279688a8e21a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-15T14:36:47Z",
    "title_canon_sha256": "47c803a2d28078fb8d4fa0af39fc2359e618e7d770282161bfed2d8f563a4d3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.16793",
    "kind": "arxiv",
    "version": 2
  }
}