Pith Number

pith:4SBKOVYI

pith:2016:4SBKOVYIV4TMBGDDZLBAPDGZBF

not attested not anchored not stored refs pending

Quasi-shuffle products revisited

Kentaro Ihara, Michael E. Hoffman

arxiv:1610.05180 v3 · 2016-10-17 · math.QA · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4SBKOVYIV4TMBGDDZLBAPDGZBF}

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	2026-05-18T00:45:54.141093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e482a75708af26c09863cac2078cd909547f47d7262f58f88d5e0c898e968a02

Aliases

arxiv: 1610.05180 · arxiv_version: 1610.05180v3 · doi: 10.48550/arxiv.1610.05180 · pith_short_12: 4SBKOVYIV4TM · pith_short_16: 4SBKOVYIV4TMBGDD · pith_short_8: 4SBKOVYI

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/4SBKOVYIV4TMBGDDZLBAPDGZBF \
  | 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: e482a75708af26c09863cac2078cd909547f47d7262f58f88d5e0c898e968a02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecacd01b19299263d275f850f2795d1c5ea83930d11ae51fa8e2c65547485e84",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2016-10-17T16:00:25Z",
    "title_canon_sha256": "0b9c009a4d152b21db4bd24c10b2815549da047370807ba83236c774e190260b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05180",
    "kind": "arxiv",
    "version": 3
  }
}