Pith Number

pith:TGVZIXV4

pith:2026:TGVZIXV4F2UKIUK4ZGAX7YJV5J

not attested not anchored not stored refs pending

Both $AA$ and $(A+1)(A+1)$ can be small

Audie Warren, Oliver Roche-Newton

arxiv:2606.24583 v1 · 2026-06-23 · 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{TGVZIXV4F2UKIUK4ZGAX7YJV5J}

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	2026-06-24T01:15:36.062309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99ab945ebc2ea8a4515cc9817fe135ea69b029a554c20e86304f42f30bb12fea

Aliases

arxiv: 2606.24583 · arxiv_version: 2606.24583v1 · doi: 10.48550/arxiv.2606.24583 · pith_short_12: TGVZIXV4F2UK · pith_short_16: TGVZIXV4F2UKIUK4 · pith_short_8: TGVZIXV4

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/TGVZIXV4F2UKIUK4ZGAX7YJV5J \
  | 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: 99ab945ebc2ea8a4515cc9817fe135ea69b029a554c20e86304f42f30bb12fea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23a3647ec4248e61143f02a10297681d717f4ee3c74ccbf719f5d3bc2ca3e100",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-06-23T13:45:26Z",
    "title_canon_sha256": "d49d495d08db227e2995b8af6d3f35bf5434592e09d845aae6e5b024b8a4cf66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24583",
    "kind": "arxiv",
    "version": 1
  }
}