Pith Number

pith:CMXTUKSO

pith:2012:CMXTUKSO5WZ76LEL2Y224BUDUN

not attested not anchored not stored refs pending

Unrolling residues to avoid progressions

Linyuan Lu, Ron Graham, Steve Butler

arxiv:1209.2687 v1 · 2012-09-12 · 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{CMXTUKSO5WZ76LEL2Y224BUDUN}

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	2026-05-18T03:45:42.357042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

132f3a2a4eedb3ff2c8bd635ae0683a36314848b04adb6abbc6311761ea0f8b1

Aliases

arxiv: 1209.2687 · arxiv_version: 1209.2687v1 · doi: 10.48550/arxiv.1209.2687 · pith_short_12: CMXTUKSO5WZ7 · pith_short_16: CMXTUKSO5WZ76LEL · pith_short_8: CMXTUKSO

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/CMXTUKSO5WZ76LEL2Y224BUDUN \
  | 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: 132f3a2a4eedb3ff2c8bd635ae0683a36314848b04adb6abbc6311761ea0f8b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18816d2918040b1858afdfb5f2b1c7fd1a6655762f1e72a18ba705f93ab46858",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-12T18:40:00Z",
    "title_canon_sha256": "c57e028c82c109618812303e28e1a13ac37b5c8380bb6458a2a4f614790fc453"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2687",
    "kind": "arxiv",
    "version": 1
  }
}