Pith Number

pith:2HQK4WSY

pith:2012:2HQK4WSYUC3UX4YTURLRDZRA2V

not attested not anchored not stored refs pending

On an action of the braid group B_{2g+2} on the free group F_{2g}

Christian Kassel

arxiv:1204.2377 v2 · 2012-04-11 · math.GR · 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{2HQK4WSYUC3UX4YTURLRDZRA2V}

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	2026-05-18T03:10:37.444721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1e0ae5a58a0b74bf313a45711e620d5449380925a019028e923388b079859eb

Aliases

arxiv: 1204.2377 · arxiv_version: 1204.2377v2 · doi: 10.48550/arxiv.1204.2377 · pith_short_12: 2HQK4WSYUC3U · pith_short_16: 2HQK4WSYUC3UX4YT · pith_short_8: 2HQK4WSY

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/2HQK4WSYUC3UX4YTURLRDZRA2V \
  | 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: d1e0ae5a58a0b74bf313a45711e620d5449380925a019028e923388b079859eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2c93b2c718740df193108e596071998764bd17f05db76b1a4a452afd41258c1",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-04-11T09:01:45Z",
    "title_canon_sha256": "643b25535cc510a21b24965e295c2c5f712b912e1266130f34cadc103a5b0665"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2377",
    "kind": "arxiv",
    "version": 2
  }
}