Pith Number

pith:A7NQJNR2

pith:2005:A7NQJNR2EUN5AAKGI25THR354B

not attested not anchored not stored refs pending

Lower bounds on volumes of hyperbolic Haken 3-manifolds

Ian Agol, Nathan M. Dunfield, Peter A. Storm, William P. Thurston

arxiv:math/0506338 v2 · 2005-06-17 · math.DG · 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{A7NQJNR2EUN5AAKGI25THR354B}

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	2026-07-04T15:05:25.322180Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07db04b63a251bd0014646bb33c77de05402522fa948046f5146ceda55a8a5fb

Aliases

arxiv: math/0506338 · arxiv_version: math/0506338v2 · doi: 10.48550/arxiv.math/0506338 · pith_short_12: A7NQJNR2EUN5 · pith_short_16: A7NQJNR2EUN5AAKG · pith_short_8: A7NQJNR2

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/A7NQJNR2EUN5AAKGI25THR354B \
  | 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: 07db04b63a251bd0014646bb33c77de05402522fa948046f5146ceda55a8a5fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5573b549645678416c3c76d35d15b9a6fb04681e25e5b53620e57cba62a4533b",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2005-06-17T15:37:12Z",
    "title_canon_sha256": "c4d13d5643fccb1604bc2368bdae127b6e3d2e52f6cf03853db89ec77243dd5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0506338",
    "kind": "arxiv",
    "version": 2
  }
}