Pith Number

pith:7VM6MTUX

pith:2004:7VM6MTUXV3FKHHT2YGZI6HI3AW

not attested not anchored not stored refs pending

Finite field models in additive combinatorics

Ben Green

arxiv:math/0409420 v1 · 2004-09-22 · 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{7VM6MTUXV3FKHHT2YGZI6HI3AW}

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.

Cited by

1 paper in Pith

Algorithmic Polynomial Freiman-Ruzsa Theorems

Receipt and verification

First computed	2026-07-04T14:39:05.878388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd59e64e97aecaa39e7ac1b28f1d1b05a7ede5aa5cafcdd1af52d1935d87b8d8

Aliases

arxiv: math/0409420 · arxiv_version: math/0409420v1 · doi: 10.48550/arxiv.math/0409420 · pith_short_12: 7VM6MTUXV3FK · pith_short_16: 7VM6MTUXV3FKHHT2 · pith_short_8: 7VM6MTUX

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/7VM6MTUXV3FKHHT2YGZI6HI3AW \
  | 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: fd59e64e97aecaa39e7ac1b28f1d1b05a7ede5aa5cafcdd1af52d1935d87b8d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b47c2edcc7146d562b2b8eb5043d70ced91de85dd805f6e879d40fe061a0a3d8",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-09-22T09:05:36Z",
    "title_canon_sha256": "6219c09aa03ae9aea909c53de5239255aa010032e2540fef413d50588f528dd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409420",
    "kind": "arxiv",
    "version": 1
  }
}