Pith Number

pith:CO46USJD

pith:2013:CO46USJDLI5MDE3VOM2OUKOT3R

not attested not anchored not stored refs pending

Combinatorics of $\phi$-deformed stuffle Hopf algebras

B\`ui Chi\^en (LIPN), Christophe Tollu (LIPN), G\'erard Henry Edmond Duchamp (LIPN), Nguyen Hoang Nghia (LIPN), Vincel Hoang Ngoc Minh (LIPN)

arxiv:1302.5391 v7 · 2013-02-21 · math.CO · cs.SC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CO46USJDLI5MDE3VOM2OUKOT3R}

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	2026-05-18T02:57:33.780069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13b9ea49235a3ac193757334ea29d3dc6d99b8daa7fdbbe4218d326ed38ecce9

Aliases

arxiv: 1302.5391 · arxiv_version: 1302.5391v7 · doi: 10.48550/arxiv.1302.5391 · pith_short_12: CO46USJDLI5M · pith_short_16: CO46USJDLI5MDE3V · pith_short_8: CO46USJD

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/CO46USJDLI5MDE3VOM2OUKOT3R \
  | 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: 13b9ea49235a3ac193757334ea29d3dc6d99b8daa7fdbbe4218d326ed38ecce9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "999251645ee6a51fb22465f73472d7b1503d190ab8c1533a7a7750499277f747",
    "cross_cats_sorted": [
      "cs.SC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-21T19:53:26Z",
    "title_canon_sha256": "dbc764a005895b09a33b49e6b594d3d75e1f15c0392539872f752fd689681bf2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5391",
    "kind": "arxiv",
    "version": 7
  }
}