Pith Number

pith:FG5Y5PFY

pith:2025:FG5Y5PFYJB42W7QOJ4FP2G7XDJ

not attested not anchored not stored refs pending

Chromatic MacMahon symmetric functions of graphs

Jeremy L. Martin, May B. Trist

arxiv:2508.00157 v1 · 2025-07-31 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FG5Y5PFYJB42W7QOJ4FP2G7XDJ}

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	2026-07-05T11:46:50.079870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29bb8ebcb84879ab7e0e4f0afd1bf71a51b5de818fab171d84c0976be2e24f86

Aliases

arxiv: 2508.00157 · arxiv_version: 2508.00157v1 · doi: 10.48550/arxiv.2508.00157 · pith_short_12: FG5Y5PFYJB42 · pith_short_16: FG5Y5PFYJB42W7QO · pith_short_8: FG5Y5PFY

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/FG5Y5PFYJB42W7QOJ4FP2G7XDJ \
  | 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: 29bb8ebcb84879ab7e0e4f0afd1bf71a51b5de818fab171d84c0976be2e24f86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4bc607bf00a93575ff2c0929b274e9b8a16c71a33d5cb0dad36e3d82ab7f8a34",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-31T20:53:12Z",
    "title_canon_sha256": "206f17c4bddb65d618b13f9f1e55a82fd95358b2b389a3b063f2fe500f29e2b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.00157",
    "kind": "arxiv",
    "version": 1
  }
}