Pith Number

pith:I4ZBTYY4

pith:2014:I4ZBTYY4DBWZVRK5U6XJFIC4JH

not attested not anchored not stored refs pending

Dual Garside structure of braids and free cumulants of products

Patrick Dehornoy (LMNO), Philippe Biane (LIGM)

arxiv:1407.1604 v1 · 2014-07-07 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I4ZBTYY4DBWZVRK5U6XJFIC4JH}

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	2026-05-18T02:48:10.933474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

473219e31c186d9ac55da7ae92a05c49d80c5e43e023b92a86490b010d54f83a

Aliases

arxiv: 1407.1604 · arxiv_version: 1407.1604v1 · doi: 10.48550/arxiv.1407.1604 · pith_short_12: I4ZBTYY4DBWZ · pith_short_16: I4ZBTYY4DBWZVRK5 · pith_short_8: I4ZBTYY4

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/I4ZBTYY4DBWZVRK5U6XJFIC4JH \
  | 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: 473219e31c186d9ac55da7ae92a05c49d80c5e43e023b92a86490b010d54f83a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be9f75d487df5eefd4deb587aa6cbe15ebe8d3b8cb0f1c166cb7fcac7241ed51",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-07-07T07:05:44Z",
    "title_canon_sha256": "528a8f887b5f748fd7f5b3a156138a33c6824b88971853e33cd4943aa3209b18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.1604",
    "kind": "arxiv",
    "version": 1
  }
}