Pith Number

pith:DGSDPNJU

pith:2026:DGSDPNJUWSSPKDXXIB5ZTRYLOU

not attested not anchored not stored refs pending

Sharp $H_{x}^{s}$ Ill-posedness of the Hard-sphere Boltzmann Equation

Shunlin Shen, Xuwen Chen, Zhifei Zhang

arxiv:2606.01331 v1 · 2026-05-31 · math.AP · 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{DGSDPNJUWSSPKDXXIB5ZTRYLOU}

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	2026-06-02T02:04:30.442652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19a437b534b4a4f50ef7407b99c70b752b1821210ef481b0e536400e8ff2d10e

Aliases

arxiv: 2606.01331 · arxiv_version: 2606.01331v1 · doi: 10.48550/arxiv.2606.01331 · pith_short_12: DGSDPNJUWSSP · pith_short_16: DGSDPNJUWSSPKDXX · pith_short_8: DGSDPNJU

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/DGSDPNJUWSSPKDXXIB5ZTRYLOU \
  | 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: 19a437b534b4a4f50ef7407b99c70b752b1821210ef481b0e536400e8ff2d10e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f360582dd83c7de396b35fc4bc27d14944c106f4d7a1987752da394a67080e14",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-31T16:33:08Z",
    "title_canon_sha256": "1bfb3d0dbfe87ed1aeb3383502193ce8ac87179e41dae7dec660bd82ad5f0e99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.01331",
    "kind": "arxiv",
    "version": 1
  }
}