Pith Number

pith:4NAXKYIH

pith:2016:4NAXKYIH3CBIICVDDTC43BJ7HT

not attested not anchored not stored refs pending

Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables

Adam Doliwa

arxiv:1603.03259 v4 · 2016-03-10 · math.CO · math-ph · math.MP · math.RA · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4NAXKYIH3CBIICVDDTC43BJ7HT}

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.

Cited by

1 paper in Pith

Hopf algebra structure of symmetric and quasisymmetric functions in superspace

Receipt and verification

First computed	2026-07-05T02:54:11.510051Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e341756107d882840aa31cc5cd853f3cccbfe5fd39f2fc48aaa62b5e7d5d489d

Aliases

arxiv: 1603.03259 · arxiv_version: 1603.03259v4 · doi: 10.48550/arxiv.1603.03259 · pith_short_12: 4NAXKYIH3CBI · pith_short_16: 4NAXKYIH3CBIICVD · pith_short_8: 4NAXKYIH

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/4NAXKYIH3CBIICVDDTC43BJ7HT \
  | 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: e341756107d882840aa31cc5cd853f3cccbfe5fd39f2fc48aaa62b5e7d5d489d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8682c9d31b318ffce19b11d8d20413922021be56652c2ec7cb46269ff45e728",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.RA",
      "nlin.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-03-10T13:37:36Z",
    "title_canon_sha256": "15bf5f19d503f8af7b2dd74101afd457b6a4e94bdfe363c24f115e95e8f0f310"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.03259",
    "kind": "arxiv",
    "version": 4
  }
}