Pith Number

pith:SGF5QPFU

pith:2016:SGF5QPFUHBMNS3ZMAANQYNJ4WV

not attested not anchored not stored refs pending

The integrally representable trees of norm 3

Jack H. Koolen, Masood Ur Rehman, Qianqian Yang

arxiv:1612.06971 v1 · 2016-12-21 · 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{SGF5QPFUHBMNS3ZMAANQYNJ4WV}

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	2026-05-18T00:54:14.964857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

918bd83cb43858d96f2c001b0c353cb5788348be6c82bfeeda157b03ab1157e3

Aliases

arxiv: 1612.06971 · arxiv_version: 1612.06971v1 · doi: 10.48550/arxiv.1612.06971 · pith_short_12: SGF5QPFUHBMN · pith_short_16: SGF5QPFUHBMNS3ZM · pith_short_8: SGF5QPFU

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/SGF5QPFUHBMNS3ZMAANQYNJ4WV \
  | 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: 918bd83cb43858d96f2c001b0c353cb5788348be6c82bfeeda157b03ab1157e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ad3aaad2c3bb10de921772d384d4c850aa2e80c58d73997ac2168fb318975df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-21T04:32:17Z",
    "title_canon_sha256": "a6a09ed94b0c0e1eed9db3e7ffcba0ad5e4f7873fc08f62e2ac7ab78f51f9792"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.06971",
    "kind": "arxiv",
    "version": 1
  }
}