Pith Number

pith:3KT52ZTK

pith:1999:3KT52ZTKWF7GCRBFUGY64FTJLZ

not attested not anchored not stored refs pending

Dynamical Evolution in Noncommutative Discrete Phase Space and the Derivation of Classical Kinetic Equations

A. Dimakis, C. Tzanakis

arxiv:math-ph/9912016 v1 · 1999-12-20 · 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{3KT52ZTKWF7GCRBFUGY64FTJLZ}

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	2026-05-18T02:35:38.646851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daa7dd666ab17e614425a1b1ee16695e6620d7a6b7c2ca38c1ab542a4db9f72d

Aliases

arxiv: math-ph/9912016 · arxiv_version: math-ph/9912016v1 · doi: 10.48550/arxiv.math-ph/9912016 · pith_short_12: 3KT52ZTKWF7G · pith_short_16: 3KT52ZTKWF7GCRBF · pith_short_8: 3KT52ZTK

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/3KT52ZTKWF7GCRBFUGY64FTJLZ \
  | 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: daa7dd666ab17e614425a1b1ee16695e6620d7a6b7c2ca38c1ab542a4db9f72d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "112e3ece6ef76140be2ee0edafe072ecbe2a00b53f819c1c0975febd279ef918",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "1999-12-20T16:29:14Z",
    "title_canon_sha256": "f42b9b7cae9c15057fbea824b6f108978cc79bc23ecc4e618ab33543ed6524de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/9912016",
    "kind": "arxiv",
    "version": 1
  }
}