Pith Number

pith:G3J4WPRE

pith:2016:G3J4WPRE5CREZLTGQZFWUS4NRY

not attested not anchored not stored refs pending

A counterexample to a strong variant of the Polynomial Freiman-Ruzsa conjecture in Euclidean space

Oded Regev, Shachar Lovett

arxiv:1612.03332 v2 · 2016-12-10 · 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{G3J4WPRE5CREZLTGQZFWUS4NRY}

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	2026-05-18T00:44:51.924243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36d3cb3e24e8a24cae66864b6a4b8d8e219eb1fe8d8c646a76adabf79cf29daf

Aliases

arxiv: 1612.03332 · arxiv_version: 1612.03332v2 · doi: 10.48550/arxiv.1612.03332 · pith_short_12: G3J4WPRE5CRE · pith_short_16: G3J4WPRE5CREZLTG · pith_short_8: G3J4WPRE

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/G3J4WPRE5CREZLTGQZFWUS4NRY \
  | 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: 36d3cb3e24e8a24cae66864b6a4b8d8e219eb1fe8d8c646a76adabf79cf29daf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0ecbbdd9742e884c317b62c5c0c7db7f1eadb7e14dba185ede82d008b15aeac",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-12-10T18:51:13Z",
    "title_canon_sha256": "b76bc06ead59713a2988272eed6d7ca039f2d6182ff0449b9778680b74512b4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03332",
    "kind": "arxiv",
    "version": 2
  }
}