Pith Number

pith:K65YPLWM

pith:2007:K65YPLWMQ6DL5DHWAO4WZWXDAJ

not attested not anchored not stored refs pending

Two Erdos problems on lacunary sequences: Chromatic number and Diophantine approximation

Wilhelm Schlag, Yuval Peres

arxiv:0706.0223 v1 · 2007-06-01 · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K65YPLWMQ6DL5DHWAO4WZWXDAJ}

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	2026-05-18T02:58:12.673107Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57bb87aecc8786be8cf603b96cdae3025a7399634c9d212702d71c620f65e482

Aliases

arxiv: 0706.0223 · arxiv_version: 0706.0223v1 · doi: 10.48550/arxiv.0706.0223 · pith_short_12: K65YPLWMQ6DL · pith_short_16: K65YPLWMQ6DL5DHW · pith_short_8: K65YPLWM

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/K65YPLWMQ6DL5DHWAO4WZWXDAJ \
  | 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: 57bb87aecc8786be8cf603b96cdae3025a7399634c9d212702d71c620f65e482

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa383c01380ab923439498929b7056fd941308ffd3a326e72aea9353403ffcfd",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-06-01T21:39:34Z",
    "title_canon_sha256": "63dde67ddcf707351029a039e8ea299313107d1a6ae57981fdcc464e46ae646b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.0223",
    "kind": "arxiv",
    "version": 1
  }
}