Pith Number

pith:XTENRWLW

pith:2006:XTENRWLWCMHC2ZZUIIVP5YGHGZ

not attested not anchored not stored refs pending

Many sets have more sums than differences

Greg Martin, Kevin O'Bryant

arxiv:math/0608131 v3 · 2006-08-04 · 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{XTENRWLWCMHC2ZZUIIVP5YGHGZ}

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

2 papers in Pith

Comparing Left and Right Quotient Sets in Groups

Evaluation-driven Scaling for Scientific Discovery

Receipt and verification

First computed	2026-07-04T17:22:50.344591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcc8d8d976130e2d6734422afee0c73671201078bc3bfc5b98b00d743068a5fa

Aliases

arxiv: math/0608131 · arxiv_version: math/0608131v3 · doi: 10.48550/arxiv.math/0608131 · pith_short_12: XTENRWLWCMHC · pith_short_16: XTENRWLWCMHC2ZZU · pith_short_8: XTENRWLW

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/XTENRWLWCMHC2ZZUIIVP5YGHGZ \
  | 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: bcc8d8d976130e2d6734422afee0c73671201078bc3bfc5b98b00d743068a5fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53b3edd1f8a6fd6a53f2ddac562a15d962a250ed66340b3d5f964339d0ccf37c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-08-04T19:57:11Z",
    "title_canon_sha256": "22d6c9ace9f24e6923dbfb918874cb424879464e663ab23aee25709653476dfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0608131",
    "kind": "arxiv",
    "version": 3
  }
}