Pith Number

pith:XLW4NRPQ

pith:2011:XLW4NRPQFE45SQJPNNOY324GI2

not attested not anchored not stored refs pending

Dehn filling and the geometry of unknotting tunnels

Daryl Cooper, David Futer, Jessica S. Purcell

arxiv:1105.3461 v3 · 2011-05-17 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XLW4NRPQFE45SQJPNNOY324GI2}

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	2026-05-18T02:38:18.149763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

baedc6c5f02939d9412f6b5d8deb86469ca30ad322a7e8ab0c93729b486dde9d

Aliases

arxiv: 1105.3461 · arxiv_version: 1105.3461v3 · doi: 10.48550/arxiv.1105.3461 · pith_short_12: XLW4NRPQFE45 · pith_short_16: XLW4NRPQFE45SQJP · pith_short_8: XLW4NRPQ

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/XLW4NRPQFE45SQJPNNOY324GI2 \
  | 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: baedc6c5f02939d9412f6b5d8deb86469ca30ad322a7e8ab0c93729b486dde9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7edab0242922e012eacc767077e787d1a566924b8dd2f68b60a7aa38fce84d62",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-05-17T19:28:42Z",
    "title_canon_sha256": "92c5ecb5b73608e4e87a4d7d4e63b9a8c2811f7bb38ed2d979db2b5eec1ba342"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.3461",
    "kind": "arxiv",
    "version": 3
  }
}