Pith Number

pith:VE5H6IBF

pith:2002:VE5H6IBFEKKVBVCIWPCROM2OKP

not attested not anchored not stored refs pending

What is a virtual link?

Greg Kuperberg

arxiv:math/0208039 v2 · 2002-08-05 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VE5H6IBFEKKVBVCIWPCROM2OKP}

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	2026-05-18T02:41:32.918959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a93a7f2025229550d448b3c517334e53c55cfa9bf6fdb5f3d1cc6a31a8582c21

Aliases

arxiv: math/0208039 · arxiv_version: math/0208039v2 · doi: 10.48550/arxiv.math/0208039 · pith_short_12: VE5H6IBFEKKV · pith_short_16: VE5H6IBFEKKVBVCI · pith_short_8: VE5H6IBF

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/VE5H6IBFEKKVBVCIWPCROM2OKP \
  | 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: a93a7f2025229550d448b3c517334e53c55cfa9bf6fdb5f3d1cc6a31a8582c21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56d0632de0c59a804bfb761929df1080145b889349c94d0785c969b6d740dffe",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2002-08-05T23:46:31Z",
    "title_canon_sha256": "c98919ca2d1f2ea40096686cd7df223488c8aa9b20263c15aceca2c36a0935cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0208039",
    "kind": "arxiv",
    "version": 2
  }
}