Pith Number

pith:GMC7RYAM

pith:2018:GMC7RYAMNCWFEFKQLLIVL7UHIP

not attested not anchored not stored refs pending

Expansion for the product of matrices in groups

Chun-Yen Shen, Doowon Koh, Le Anh Vinh, Thang Pham

arxiv:1803.03351 v2 · 2018-03-09 · math.NT · 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{GMC7RYAMNCWFEFKQLLIVL7UHIP}

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	2026-05-18T00:19:56.311226Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3305f8e00c68ac5215505ad155fe8743fce5fb092b4d2fdec127ba7a874698b2

Aliases

arxiv: 1803.03351 · arxiv_version: 1803.03351v2 · doi: 10.48550/arxiv.1803.03351 · pith_short_12: GMC7RYAMNCWF · pith_short_16: GMC7RYAMNCWFEFKQ · pith_short_8: GMC7RYAM

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/GMC7RYAMNCWFEFKQLLIVL7UHIP \
  | 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: 3305f8e00c68ac5215505ad155fe8743fce5fb092b4d2fdec127ba7a874698b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3aed4d2fcb0a0fa4fe0b9895da972af82a516ef2952b7619ff781c8247f925da",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-03-09T01:41:43Z",
    "title_canon_sha256": "736e601f0102912e8a553386ea4e95b09660db16f4b33c20c5433dd6b14d0d61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.03351",
    "kind": "arxiv",
    "version": 2
  }
}