Pith Number

pith:BUTCH77T

pith:2018:BUTCH77TLPQNT4STG7I6FSR722

not attested not anchored not stored refs pending

The kernel of chromatic quasisymmetric functions on graphs and hypergraphic polytopes

Raul Penaguiao

arxiv:1803.08824 v4 · 2018-03-23 · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BUTCH77TLPQNT4STG7I6FSR722}

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	2026-07-05T00:51:00.604571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d2623fff35be0d9f25337d1e2ca3fd69fe0fbf977da566976766b2271997a89

Aliases

arxiv: 1803.08824 · arxiv_version: 1803.08824v4 · doi: 10.48550/arxiv.1803.08824 · pith_short_12: BUTCH77TLPQN · pith_short_16: BUTCH77TLPQNT4ST · pith_short_8: BUTCH77T

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/BUTCH77TLPQNT4STG7I6FSR722 \
  | 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: 0d2623fff35be0d9f25337d1e2ca3fd69fe0fbf977da566976766b2271997a89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed2d644b71ccc2106e8b2814a71004ff299f1790ca5aa07789e332d392862d6c",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-03-23T14:58:07Z",
    "title_canon_sha256": "d357cf5f139568f63017188309eea28d76f1e5987502a62c80f96e287236ab42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.08824",
    "kind": "arxiv",
    "version": 4
  }
}