Pith Number

pith:XUCQMQLQ

pith:1998:XUCQMQLQ2WEGKZXDE7NEGEMVG7

not attested not anchored not stored refs pending

A new algorithm for recognizing the unknot

Joan S. Birman, Michael D. Hirsch

arxiv:math/9801126 v3 · 1998-01-28 · 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{XUCQMQLQ2WEGKZXDE7NEGEMVG7}

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	2026-05-18T02:37:59.330567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd05064170d5886566e327da43119537e59c59bb4e95de58fbf05c1a19fb61a6

Aliases

arxiv: math/9801126 · arxiv_version: math/9801126v3 · doi: 10.48550/arxiv.math/9801126 · pith_short_12: XUCQMQLQ2WEG · pith_short_16: XUCQMQLQ2WEGKZXD · pith_short_8: XUCQMQLQ

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/XUCQMQLQ2WEGKZXDE7NEGEMVG7 \
  | 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: bd05064170d5886566e327da43119537e59c59bb4e95de58fbf05c1a19fb61a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc221969d2df049c2e1abe95c0b5711ef665cfaa908b00d6857930bae084a69a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-01-28T16:01:54Z",
    "title_canon_sha256": "f07af64ea1ffd097a508fa706865ad674ab316e878ef61beb8518d0017edc076"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9801126",
    "kind": "arxiv",
    "version": 3
  }
}