Pith Number

pith:54HO7U5E

pith:2011:54HO7U5EZL4VO7VQE7NCDDMGE4

not attested not anchored not stored refs pending

New Bounds on cap sets

Michael Bateman, Nets Hawk Katz

arxiv:1101.5851 v2 · 2011-01-31 · math.CA · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{54HO7U5EZL4VO7VQE7NCDDMGE4}

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	2026-05-18T04:25:10.882220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef0eefd3a4caf9577eb027da218d862712650acb3a90c3a8f856aa9a6830c8cf

Aliases

arxiv: 1101.5851 · arxiv_version: 1101.5851v2 · doi: 10.48550/arxiv.1101.5851 · pith_short_12: 54HO7U5EZL4V · pith_short_16: 54HO7U5EZL4VO7VQ · pith_short_8: 54HO7U5E

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/54HO7U5EZL4VO7VQE7NCDDMGE4 \
  | 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: ef0eefd3a4caf9577eb027da218d862712650acb3a90c3a8f856aa9a6830c8cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "512a905f5a9d48c8cb57dd83d328b1b8c309374b2483eae1975f2c1246ac52d7",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-01-31T05:23:55Z",
    "title_canon_sha256": "f5d681faa3ca9b8a066f73efbdd13c8b902213fe33bb95f22f414b6baf1cb7cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5851",
    "kind": "arxiv",
    "version": 2
  }
}