Pith Number

pith:NV4FHZUB

pith:2004:NV4FHZUBFO7DPDEWEM2MPQ66R2

not attested not anchored not stored refs pending

On the Zappa-Szep Product

Matthew G. Brin

arxiv:math/0406044 v1 · 2004-06-02 · math.GR · math.CT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NV4FHZUBFO7DPDEWEM2MPQ66R2}

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	2026-05-18T03:16:30.509808Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d7853e6812bbe378c962334c7c3de8eb7e0c0d542cc5b578e7c500242ab04a5

Aliases

arxiv: math/0406044 · arxiv_version: math/0406044v1 · doi: 10.48550/arxiv.math/0406044 · pith_short_12: NV4FHZUBFO7D · pith_short_16: NV4FHZUBFO7DPDEW · pith_short_8: NV4FHZUB

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/NV4FHZUBFO7DPDEWEM2MPQ66R2 \
  | 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: 6d7853e6812bbe378c962334c7c3de8eb7e0c0d542cc5b578e7c500242ab04a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed6075dc76d8da972f58b7e9494a13eef09d8ce506e28f38e64c785e9e63b161",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2004-06-02T18:43:11Z",
    "title_canon_sha256": "37a24a04c38fa2dea1d1f0cb581eec633eae78e0c6ac07a41669ba3901afb1de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406044",
    "kind": "arxiv",
    "version": 1
  }
}