Pith Number

pith:5VPOAWZ3

pith:2016:5VPOAWZ3276ZDIL6JN7JN4XM64

not attested not anchored not stored refs pending

Improved upper bound on A(18,8)

Sven Polak

arxiv:1612.02178 v2 · 2016-12-07 · math.CO · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5VPOAWZ3276ZDIL6JN7JN4XM64}

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	2026-05-18T00:49:36.363311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed5ee05b3bd7fd91a17e4b7e96f2ecf70049cf9073b46bd4d66a92b5c6b78424

Aliases

arxiv: 1612.02178 · arxiv_version: 1612.02178v2 · doi: 10.48550/arxiv.1612.02178 · pith_short_12: 5VPOAWZ3276Z · pith_short_16: 5VPOAWZ3276ZDIL6 · pith_short_8: 5VPOAWZ3

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/5VPOAWZ3276ZDIL6JN7JN4XM64 \
  | 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: ed5ee05b3bd7fd91a17e4b7e96f2ecf70049cf9073b46bd4d66a92b5c6b78424

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "678f22d57cea2ad74ae2fd4d51779d9287a80676ab6ff3360c52b539e38f6ff4",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-07T10:10:20Z",
    "title_canon_sha256": "4d93b092a56aa02e6b1c07fe76a0cbc39764196d9fc33a1019fdb4407e218efa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.02178",
    "kind": "arxiv",
    "version": 2
  }
}