Pith Number

pith:MPIW6HV7

pith:2007:MPIW6HV7OI4O7T5YHW6YOMFIY4

not attested not anchored not stored refs pending

On the maximal number of three-term arithmetic progressions in subsets of Z/pZ

Ben Green, Olof Sisask

arxiv:0709.4432 v1 · 2007-09-27 · 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{MPIW6HV7OI4O7T5YHW6YOMFIY4}

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	2026-05-18T02:58:12.267276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63d16f1ebf7238efcfb83dbd8730a8c73c6b166c739ab98ddcd30db4cebe3f34

Aliases

arxiv: 0709.4432 · arxiv_version: 0709.4432v1 · doi: 10.48550/arxiv.0709.4432 · pith_short_12: MPIW6HV7OI4O · pith_short_16: MPIW6HV7OI4O7T5Y · pith_short_8: MPIW6HV7

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/MPIW6HV7OI4O7T5YHW6YOMFIY4 \
  | 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: 63d16f1ebf7238efcfb83dbd8730a8c73c6b166c739ab98ddcd30db4cebe3f34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "882c21f7bfbc6d306ce2f44a81799d0885cb7d10588cf7c2eb5fee3e5c5d5f90",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-09-27T15:34:21Z",
    "title_canon_sha256": "14114a077e2f372377d9164eb42741d73a9608a67f96882e0d79f36d0a29bb9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.4432",
    "kind": "arxiv",
    "version": 1
  }
}