Pith Number

pith:W735RA66

pith:2016:W735RA66CWHUP7DNBATJSGLEXK

not attested not anchored not stored refs pending

The Growth Rate of Tri-Colored Sum-Free Sets

David E. Speyer, Robert Kleinberg, Will Sawin

arxiv:1607.00047 v3 · 2016-06-30 · 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{W735RA66CWHUP7DNBATJSGLEXK}

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	2026-05-18T00:11:24.025032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7f7d883de158f47fc6d0826991964ba81fa28b773240ef81e2ea52f593f443a

Aliases

arxiv: 1607.00047 · arxiv_version: 1607.00047v3 · doi: 10.48550/arxiv.1607.00047 · pith_short_12: W735RA66CWHU · pith_short_16: W735RA66CWHUP7DN · pith_short_8: W735RA66

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/W735RA66CWHUP7DNBATJSGLEXK \
  | 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: b7f7d883de158f47fc6d0826991964ba81fa28b773240ef81e2ea52f593f443a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43ee2acc1bed633c014f19bac83d2adea15bc97e32bff24dd84e5ef1b073b97c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-30T21:04:11Z",
    "title_canon_sha256": "2ee801314466e5bede813cf94cfb57e6d1ec717c46cfe8c44d8e91d5ee1b2fd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.00047",
    "kind": "arxiv",
    "version": 3
  }
}