Pith Number

pith:XD4B7VKP

pith:2016:XD4B7VKP4KOCMC5WVQ5NHR33IC

not attested not anchored not stored refs pending

Root multiplicities for Borcherds algebras and graph coloring

Deniz Kus, G. Arunkumar, R. Venkatesh

arxiv:1612.01320 v1 · 2016-12-05 · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XD4B7VKP4KOCMC5WVQ5NHR33IC}

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	2026-05-18T00:11:11.829439Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8f81fd54fe29c260bb6ac3ad3c77b408de1a683d1fa82994e7cb57e2809a409

Aliases

arxiv: 1612.01320 · arxiv_version: 1612.01320v1 · doi: 10.48550/arxiv.1612.01320 · pith_short_12: XD4B7VKP4KOC · pith_short_16: XD4B7VKP4KOCMC5W · pith_short_8: XD4B7VKP

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/XD4B7VKP4KOCMC5WVQ5NHR33IC \
  | 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: b8f81fd54fe29c260bb6ac3ad3c77b408de1a683d1fa82994e7cb57e2809a409

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4519cb043bd5f28d55932d2aab76e5e967fe977fc67773df8bbad24387b10cce",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-05T11:50:31Z",
    "title_canon_sha256": "2ea14076ab5fa844a507d67fd38ee2da494f5ae5139f05d63900baec69ff76ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01320",
    "kind": "arxiv",
    "version": 1
  }
}