Pith Number

pith:VEYFWZPY

pith:2000:VEYFWZPYQX3AYZZUTLF5NO6N3L

not attested not anchored not stored refs pending

Taut ideal triangulations of 3-manifolds

Marc Lackenby

arxiv:math/0003132 v2 · 2000-03-22 · 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{VEYFWZPYQX3AYZZUTLF5NO6N3L}

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	2026-05-18T02:38:01.025679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9305b65f885f60c67349acbd6bbcddaf2352ed726b6202110d4b270d8f115c1

Aliases

arxiv: math/0003132 · arxiv_version: math/0003132v2 · doi: 10.48550/arxiv.math/0003132 · pith_short_12: VEYFWZPYQX3A · pith_short_16: VEYFWZPYQX3AYZZU · pith_short_8: VEYFWZPY

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/VEYFWZPYQX3AYZZUTLF5NO6N3L \
  | 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: a9305b65f885f60c67349acbd6bbcddaf2352ed726b6202110d4b270d8f115c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fda632b9bca7225e6c377ce625bc85b32be66e2cd13faf37f23432961db3ca5a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2000-03-22T17:07:24Z",
    "title_canon_sha256": "648823a61d14e12f7f0f51c383558b27acb243f3ab35737a9e3fe4c32461749e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0003132",
    "kind": "arxiv",
    "version": 2
  }
}