Pith Number

pith:MFRTYBTG

pith:2016:MFRTYBTGQZC33RUVOWCDAJVYKJ

not attested not anchored not stored refs pending

Uniform measures on braid monoids and dual braid monoids

Jean Mairesse, Samy Abbes, S\'ebastien Gou\"ezel, Vincent Jug\'e

arxiv:1607.00565 v2 · 2016-07-02 · math.GR · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MFRTYBTGQZC33RUVOWCDAJVYKJ}

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	2026-05-18T00:33:02.426113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61633c06668645bdc69575843026b8525a7a34e7e49f1352007577b88df256d3

Aliases

arxiv: 1607.00565 · arxiv_version: 1607.00565v2 · doi: 10.48550/arxiv.1607.00565 · pith_short_12: MFRTYBTGQZC3 · pith_short_16: MFRTYBTGQZC33RUV · pith_short_8: MFRTYBTG

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/MFRTYBTGQZC33RUVOWCDAJVYKJ \
  | 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: 61633c06668645bdc69575843026b8525a7a34e7e49f1352007577b88df256d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ea0fd2efc57d3afbb98328b2d8efaf7949f7f2fee055ad313697cc31863caf7",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-07-02T21:50:09Z",
    "title_canon_sha256": "c6e635a5d5a533289b1ec630f0839dbce854e4f76882d2fbf55583a01404a1c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.00565",
    "kind": "arxiv",
    "version": 2
  }
}