Pith Number

pith:TW2BS5GF

pith:2013:TW2BS5GFBT5HG2DDHSE2I2D4K4

not attested not anchored not stored refs pending

The Cardinality of Sumsets: Different Summands

Brendan Murphy, Eyvindur Ari Palsson, Giorgis Petridis

arxiv:1309.2191 v3 · 2013-09-09 · 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{TW2BS5GFBT5HG2DDHSE2I2D4K4}

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	2026-05-18T00:50:36.123886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9db41974c50cfa7368633c89a4687c57200ed4dda7efc60b21271a6ddfbf0658

Aliases

arxiv: 1309.2191 · arxiv_version: 1309.2191v3 · doi: 10.48550/arxiv.1309.2191 · pith_short_12: TW2BS5GFBT5H · pith_short_16: TW2BS5GFBT5HG2DD · pith_short_8: TW2BS5GF

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/TW2BS5GFBT5HG2DDHSE2I2D4K4 \
  | 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: 9db41974c50cfa7368633c89a4687c57200ed4dda7efc60b21271a6ddfbf0658

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f32a8c0b19ffdcae58bc57ea98a1fcd8a67cdfda1cc5573e31927e127085bbd4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-09T15:23:56Z",
    "title_canon_sha256": "e11e3c6e79d99ef941fd92625d66052d384f728bb4c6c61afbc2d213fc88e799"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.2191",
    "kind": "arxiv",
    "version": 3
  }
}