Pith Number

pith:7WJHG4RB

pith:2001:7WJHG4RBYLZH6GTDUVRGL7XW46

not attested not anchored not stored refs pending

Commensurability of 1-cusped hyperbolic 3-manifolds

Danny Calegari, Nathan M. Dunfield

arxiv:math/0102024 v2 · 2001-02-03 · 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{7WJHG4RBYLZH6GTDUVRGL7XW46}

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	2026-07-04T14:35:03.967490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd92737221c2f27f1a63a56265fef6e7a0d13118db8b6a5b8dd782f375abbc5f

Aliases

arxiv: math/0102024 · arxiv_version: math/0102024v2 · doi: 10.48550/arxiv.math/0102024 · pith_short_12: 7WJHG4RBYLZH · pith_short_16: 7WJHG4RBYLZH6GTD · pith_short_8: 7WJHG4RB

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/7WJHG4RBYLZH6GTDUVRGL7XW46 \
  | 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: fd92737221c2f27f1a63a56265fef6e7a0d13118db8b6a5b8dd782f375abbc5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83411ac00068f1fe6015c24f15120fa6f194ac0ed5eb192864742b2bbf084a57",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2001-02-03T17:52:09Z",
    "title_canon_sha256": "36d3d762268e45e7d4107f2447b43be45c1e666e98b85bad09d5fa949caa35b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0102024",
    "kind": "arxiv",
    "version": 2
  }
}