Pith Number

pith:3OPQYJRQ

pith:2026:3OPQYJRQXCWTVMREYAIWF3K5MX

not attested not anchored not stored refs pending

A turning point principle for liquid Lane-Emden stars

King Ming Lam

arxiv:2607.24530 v1 · 2026-07-27 · math-ph · math.AP · 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{3OPQYJRQXCWTVMREYAIWF3K5MX}

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	2026-07-28T02:24:08.385728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db9f0c2630b8ad3ab224c01162ed5d65e5e624ac02ac26786b292db94d5ad686

Aliases

arxiv: 2607.24530 · arxiv_version: 2607.24530v1 · doi: 10.48550/arxiv.2607.24530 · pith_short_12: 3OPQYJRQXCWT · pith_short_16: 3OPQYJRQXCWTVMRE · pith_short_8: 3OPQYJRQ

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/3OPQYJRQXCWTVMREYAIWF3K5MX \
  | 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: db9f0c2630b8ad3ab224c01162ed5d65e5e624ac02ac26786b292db94d5ad686

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72e09e8d8abe1c0abb6fd7b8a213c01f88f537970083be031ad769922ecf328d",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-27T15:08:37Z",
    "title_canon_sha256": "2e636413f89f62dc93bc5a0da443b3b1829c0d5420765683c1a9ff00663ed068"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24530",
    "kind": "arxiv",
    "version": 1
  }
}