Pith Number

pith:IWLCMTFW

pith:2006:IWLCMTFW4E2MWARMNATAZENIUO

not attested not anchored not stored refs pending

The Burau estimate for the entropy of a braid

Gavin Band, Philip Boyland

arxiv:math/0612716 v2 · 2006-12-22 · math.DS · 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{IWLCMTFW4E2MWARMNATAZENIUO}

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	2026-05-18T02:41:26.645127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4596264cb6e134cb022c68260c91a8a3be7c5df8633ae9380d6408fc3cbf08bf

Aliases

arxiv: math/0612716 · arxiv_version: math/0612716v2 · doi: 10.48550/arxiv.math/0612716 · pith_short_12: IWLCMTFW4E2M · pith_short_16: IWLCMTFW4E2MWARM · pith_short_8: IWLCMTFW

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/IWLCMTFW4E2MWARMNATAZENIUO \
  | 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: 4596264cb6e134cb022c68260c91a8a3be7c5df8633ae9380d6408fc3cbf08bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "437d649ec67ea2dafd7f5dd5ca2bfdc13527b360be2d7230efe170fe1910a110",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2006-12-22T17:32:31Z",
    "title_canon_sha256": "69a552cba677b1b73bf5fe789ce20b4f677228d72b7460e1f441e40bc209b211"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612716",
    "kind": "arxiv",
    "version": 2
  }
}