Pith Number

pith:ZVBC7LZ3

pith:2004:ZVBC7LZ36NF6HIDOEGIWTTRXKA

not attested not anchored not stored refs pending

Phase Space Reduction of Star Products on Cotangent Bundles

Markus J. Pflaum, Niels Kowalzig, Nikolai Neumaier

arxiv:math/0403239 v1 · 2004-03-15 · math.SG · 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{ZVBC7LZ36NF6HIDOEGIWTTRXKA}

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	2026-05-18T01:33:49.547283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd422faf3bf34be3a06e219169ce375024eaddba191ac03e88800976459464aa

Aliases

arxiv: math/0403239 · arxiv_version: math/0403239v1 · doi: 10.48550/arxiv.math/0403239 · pith_short_12: ZVBC7LZ36NF6 · pith_short_16: ZVBC7LZ36NF6HIDO · pith_short_8: ZVBC7LZ3

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/ZVBC7LZ36NF6HIDOEGIWTTRXKA \
  | 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: cd422faf3bf34be3a06e219169ce375024eaddba191ac03e88800976459464aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "757f9acdb6dcf1c75cb64b958191e19db4a445a982741a99f2e32a1eafc5e803",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SG",
    "submitted_at": "2004-03-15T11:42:54Z",
    "title_canon_sha256": "952b00f10cd706579189ebc8a3467949ef4afa3260890b940792f3f5832ea64c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0403239",
    "kind": "arxiv",
    "version": 1
  }
}