Pith Number

pith:V5NTPTHF

pith:2016:V5NTPTHFT5P4VC5KYEYAYAXTAP

not attested not anchored not stored refs pending

Order Quasisymmetric Functions Distinguish Rooted Trees

Shuhei Tsujie, Takahiro Hasebe

arxiv:1610.03908 v3 · 2016-10-13 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V5NTPTHFT5P4VC5KYEYAYAXTAP}

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	2026-05-18T00:05:46.399918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af5b37cce59f5fca8baac1300c02f303f9f800ce4aac2b0d6dc83e6ea1e42039

Aliases

arxiv: 1610.03908 · arxiv_version: 1610.03908v3 · doi: 10.48550/arxiv.1610.03908 · pith_short_12: V5NTPTHFT5P4 · pith_short_16: V5NTPTHFT5P4VC5K · pith_short_8: V5NTPTHF

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/V5NTPTHFT5P4VC5KYEYAYAXTAP \
  | 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: af5b37cce59f5fca8baac1300c02f303f9f800ce4aac2b0d6dc83e6ea1e42039

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a280c209cbb37a5282714f7d3fcdec9f10295fa3022b7e8bd7a82ceee6c81c92",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-10-13T01:38:55Z",
    "title_canon_sha256": "3551995bb5d069ca29c26d3eaec00530b4143a6cfe9a6e719d168fe6d9367cbc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.03908",
    "kind": "arxiv",
    "version": 3
  }
}