Pith Number

pith:IFEBQR2D

pith:2011:IFEBQR2D36PE4UFE3JMZ4SVCEM

not attested not anchored not stored refs pending

Fast nielsen-thurston classification of braids

Matthieu Calvez

arxiv:1112.0165 v3 · 2011-12-01 · 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{IFEBQR2D36PE4UFE3JMZ4SVCEM}

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	2026-05-18T02:41:43.520781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4148184743df9e4e50a4da599e4aa2230ea9a2d97e0eb3f0210bb9b3e937fd75

Aliases

arxiv: 1112.0165 · arxiv_version: 1112.0165v3 · doi: 10.48550/arxiv.1112.0165 · pith_short_12: IFEBQR2D36PE · pith_short_16: IFEBQR2D36PE4UFE · pith_short_8: IFEBQR2D

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/IFEBQR2D36PE4UFE3JMZ4SVCEM \
  | 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: 4148184743df9e4e50a4da599e4aa2230ea9a2d97e0eb3f0210bb9b3e937fd75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50c1ebf1f7e337e556774fd27d604f8099491d9ecd6645330e2656648b20b811",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-12-01T12:44:28Z",
    "title_canon_sha256": "e8726f65a8e34b1fab33de008618da44643299cac242c6e1ddcfde7e14155d30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0165",
    "kind": "arxiv",
    "version": 3
  }
}