Pith Number

pith:ZKSLKS4J

pith:2026:ZKSLKS4JYWYTTGMZREXQBNGPQE

not attested not anchored not stored refs pending

On a free boundary problem of the Boltzmann equation

Renjun Duan, Shengchuang Chang, Shuangqian Liu

arxiv:2607.24053 v1 · 2026-07-27 · 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{ZKSLKS4JYWYTTGMZREXQBNGPQE}

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	2026-07-28T01:23:43.105092Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caa4b54b89c5b1399999892f00b4cf8133d2cb37e3a51aec7f429c2e52805684

Aliases

arxiv: 2607.24053 · arxiv_version: 2607.24053v1 · doi: 10.48550/arxiv.2607.24053 · pith_short_12: ZKSLKS4JYWYT · pith_short_16: ZKSLKS4JYWYTTGMZ · pith_short_8: ZKSLKS4J

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/ZKSLKS4JYWYTTGMZREXQBNGPQE \
  | 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: caa4b54b89c5b1399999892f00b4cf8133d2cb37e3a51aec7f429c2e52805684

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "350299fce88945f91daa4f69f85503534d38e34b4ffb4cb56f13760cef8c8426",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-27T06:50:04Z",
    "title_canon_sha256": "4bc14b382de9149989b7c9f1b6ff05f9db39c41092853227a9ffa0f447a57ca9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24053",
    "kind": "arxiv",
    "version": 1
  }
}