Pith Number

pith:2VG5SVXE

pith:1999:2VG5SVXEE7BQTBQ3DTEJBKDQZA

not attested not anchored not stored refs pending

Notions of denseness

Greg Kuperberg

arxiv:math/9908003 v3 · 1999-08-01 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2VG5SVXEE7BQTBQ3DTEJBKDQZA}

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	2026-05-18T02:37:59.207140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d54dd956e427c309861b1cc890a870c83c27866930a1187d8247be7e9c8b93af

Aliases

arxiv: math/9908003 · arxiv_version: math/9908003v3 · doi: 10.48550/arxiv.math/9908003 · pith_short_12: 2VG5SVXEE7BQ · pith_short_16: 2VG5SVXEE7BQTBQ3 · pith_short_8: 2VG5SVXE

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/2VG5SVXEE7BQTBQ3DTEJBKDQZA \
  | 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: d54dd956e427c309861b1cc890a870c83c27866930a1187d8247be7e9c8b93af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af23a9688916c3d3ed92a853f707b13b33461b863c5f39a395f77a523dcafb4d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "1999-08-01T19:07:21Z",
    "title_canon_sha256": "caaec3a33b054ff2f8359826f502b39c882a9d1d76622b575c9b24f8fe586d44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9908003",
    "kind": "arxiv",
    "version": 3
  }
}