Pith Number

pith:HI5AUH4U

pith:2019:HI5AUH4U72TNAQVFT46KW5VGML

not attested not anchored not stored refs pending

Chromatic symmetric function of graphs from Borcherds algebras

G. Arunkumar

arxiv:1908.08198 v2 · 2019-08-22 · 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{HI5AUH4U72TNAQVFT46KW5VGML}

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	2026-07-05T02:41:46.113841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a3a0a1f94fea6d042a59f3cab76a662c4e1d6fbb70f45dce58e5d66a916d1bb

Aliases

arxiv: 1908.08198 · arxiv_version: 1908.08198v2 · doi: 10.48550/arxiv.1908.08198 · pith_short_12: HI5AUH4U72TN · pith_short_16: HI5AUH4U72TNAQVF · pith_short_8: HI5AUH4U

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/HI5AUH4U72TNAQVFT46KW5VGML \
  | 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: 3a3a0a1f94fea6d042a59f3cab76a662c4e1d6fbb70f45dce58e5d66a916d1bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca48c924597c6972b95ea2e6659e1cac4e22634b6007ffc6f0bbb566dd92f508",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-22T04:24:44Z",
    "title_canon_sha256": "2388f703a1e4d81fee7476997c504d7e1c9470b735a9f403e489142df7173ad0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08198",
    "kind": "arxiv",
    "version": 2
  }
}