Pith Number

pith:XV33EITY

pith:1998:XV33EITYRYDYG2QD2BUI3NZ2I5

not attested not anchored not stored refs pending

Word hyperbolic Dehn surgery

Marc Lackenby (Cambridge)

arxiv:math/9808120 v2 · 1998-08-28 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XV33EITYRYDYG2QD2BUI3NZ2I5}

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	2026-07-04T14:40:46.180075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd77b222788e07836a03d0688db73a476e3b9db5999739d5e914a248c210451c

Aliases

arxiv: math/9808120 · arxiv_version: math/9808120v2 · doi: 10.48550/arxiv.math/9808120 · pith_short_12: XV33EITYRYDY · pith_short_16: XV33EITYRYDYG2QD · pith_short_8: XV33EITY

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/XV33EITYRYDYG2QD2BUI3NZ2I5 \
  | 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: bd77b222788e07836a03d0688db73a476e3b9db5999739d5e914a248c210451c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5a3d3f41604e95d4bcfa4d9e5f15db67a430a31ab5e264e381050cec4eff43e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-08-28T19:38:18Z",
    "title_canon_sha256": "3dbec9c0fadf0e62aad3b189f1c9574d0432de0ae34f617332b171bf8d1c4e92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9808120",
    "kind": "arxiv",
    "version": 2
  }
}