Pith Number

pith:VRNQP5UE

pith:2009:VRNQP5UEIJ5AYOLTHBAOWBCNNN

not attested not anchored not stored refs pending

How to read the length of a braid from its curve diagram

Bert Wiest (IRMAR)

arxiv:0904.0224 v4 · 2009-04-01 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VRNQP5UEIJ5AYOLTHBAOWBCNNN}

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	2026-05-18T04:05:28.123024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac5b07f684427a0c39733840eb044d6b6e2eef651ba13364fdf50a714943614b

Aliases

arxiv: 0904.0224 · arxiv_version: 0904.0224v4 · doi: 10.48550/arxiv.0904.0224 · pith_short_12: VRNQP5UEIJ5A · pith_short_16: VRNQP5UEIJ5AYOLT · pith_short_8: VRNQP5UE

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/VRNQP5UEIJ5AYOLTHBAOWBCNNN \
  | 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: ac5b07f684427a0c39733840eb044d6b6e2eef651ba13364fdf50a714943614b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8ba7573bf4cdfecd15b5747210fec4362d27c7cc17225a5457f012f2afa3b93",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-04-01T17:23:02Z",
    "title_canon_sha256": "c35f0ee38765e2be38de0d16c3cb1ed82efeb4b140f5238bb8ec7667ac47a86c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.0224",
    "kind": "arxiv",
    "version": 4
  }
}