Pith Number

pith:62PKXRMK

pith:1999:62PKXRMKEOTAO63Z6YVAQIGLCB

not attested not anchored not stored refs pending

Levelling an unknotting tunnel

Abigail Thompson, Hiroshi Goda, Martin Scharlemann

arxiv:math/9910099 v2 · 1999-10-19 · 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{62PKXRMKEOTAO63Z6YVAQIGLCB}

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	2026-05-18T02:37:59.199504Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f69eabc58a23a6077b79f62a0820cb105565f49be614dcbdfb3da02e0b3cbc79

Aliases

arxiv: math/9910099 · arxiv_version: math/9910099v2 · doi: 10.48550/arxiv.math/9910099 · pith_short_12: 62PKXRMKEOTA · pith_short_16: 62PKXRMKEOTAO63Z · pith_short_8: 62PKXRMK

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/62PKXRMKEOTAO63Z6YVAQIGLCB \
  | 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: f69eabc58a23a6077b79f62a0820cb105565f49be614dcbdfb3da02e0b3cbc79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cd1cac4598936f47b763adfd620dbdf69055b7efebb07bceeee04387a3a772e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1999-10-19T18:09:16Z",
    "title_canon_sha256": "c2a11c6057ed399c257be0a41a437d281f427183e4b06e7727c765daa64af9f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9910099",
    "kind": "arxiv",
    "version": 2
  }
}