Pith Number

pith:5TMUCTDF

pith:2008:5TMUCTDFK36Z7B32BXWXTAO6L2

not attested not anchored not stored refs pending

The length of unknotting tunnels

Daryl Cooper, Jessica S. Purcell, Marc Lackenby

arxiv:0812.0858 v2 · 2008-12-04 · 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{5TMUCTDFK36Z7B32BXWXTAO6L2}

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	2026-05-18T02:41:51.410863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ecd9414c6556fd9f877a0ded7981de5e896490641c4e4414a092ae34378e8085

Aliases

arxiv: 0812.0858 · arxiv_version: 0812.0858v2 · doi: 10.48550/arxiv.0812.0858 · pith_short_12: 5TMUCTDFK36Z · pith_short_16: 5TMUCTDFK36Z7B32 · pith_short_8: 5TMUCTDF

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/5TMUCTDFK36Z7B32BXWXTAO6L2 \
  | 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: ecd9414c6556fd9f877a0ded7981de5e896490641c4e4414a092ae34378e8085

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed7c23c56e99d474f558d8bac9a34e179ec40613a9378abd0330fb0f42469bb8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-12-04T05:30:01Z",
    "title_canon_sha256": "52c9471929a08e1a28fb4e4a596ca1f1c885acc0b5f4131ef6eb83ff95cbb446"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.0858",
    "kind": "arxiv",
    "version": 2
  }
}