Pith Number

pith:ZR7ORH46

pith:2010:ZR7ORH46ALHTZ52NXRKTIEUIXM

not attested not anchored not stored refs pending

On the speed of approach to equilibrium for a collisionless gas

Fran\c{c}ois Golse, Kazuo Aoki

arxiv:1009.3004 v1 · 2010-09-15 · 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{ZR7ORH46ALHTZ52NXRKTIEUIXM}

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	2026-05-18T03:50:11.121713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc7ee89f9e02cf3cf74dbc55341288bb27d331be4f7383a59c25ef9439e1fcd2

Aliases

arxiv: 1009.3004 · arxiv_version: 1009.3004v1 · doi: 10.48550/arxiv.1009.3004 · pith_short_12: ZR7ORH46ALHT · pith_short_16: ZR7ORH46ALHTZ52N · pith_short_8: ZR7ORH46

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/ZR7ORH46ALHTZ52NXRKTIEUIXM \
  | 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: cc7ee89f9e02cf3cf74dbc55341288bb27d331be4f7383a59c25ef9439e1fcd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0316823d407f8df6fe9d3c723e10b573d4835720f5ebe1c004f23c8171905ac9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-09-15T19:31:33Z",
    "title_canon_sha256": "23db70b3f9b6858b0bfddcccbef0d0e4069f3a7771a13cc52cd6043aa64795ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3004",
    "kind": "arxiv",
    "version": 1
  }
}