Pith Number

pith:4M22FN2D

pith:2012:4M22FN2D2565RZKOKDQG2IKS3A

not attested not anchored not stored refs pending

A Probabilistic Threshold for Monochromatic Arithmetic Progressions

Aaron Robertson

arxiv:1206.2885 v2 · 2012-06-13 · 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{4M22FN2D2565RZKOKDQG2IKS3A}

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	2026-05-18T02:48:26.218011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e335a2b743d77dd8e54e50e06d2152d833393e80c2a173fbccfa4cbab1952db2

Aliases

arxiv: 1206.2885 · arxiv_version: 1206.2885v2 · doi: 10.48550/arxiv.1206.2885 · pith_short_12: 4M22FN2D2565 · pith_short_16: 4M22FN2D2565RZKO · pith_short_8: 4M22FN2D

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/4M22FN2D2565RZKOKDQG2IKS3A \
  | 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: e335a2b743d77dd8e54e50e06d2152d833393e80c2a173fbccfa4cbab1952db2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e792aeecdfda8b126a383b0e730d29f67f034a4ffebc98a9103262ddf98864a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-06-13T17:57:59Z",
    "title_canon_sha256": "4421d26fa104ce53e2c2dd417fba7671493a16614ce7a71c78847ff8407e0165"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.2885",
    "kind": "arxiv",
    "version": 2
  }
}