Pith Number

pith:PS5JVNTG

pith:2009:PS5JVNTG3XNGFQEJKWORXCBD72

not attested not anchored not stored refs pending

On the dimension of iterated sumsets

J\"org Schmeling, Pablo Shmerkin

arxiv:0906.1537 v2 · 2009-06-08 · math.CA · 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{PS5JVNTG3XNGFQEJKWORXCBD72}

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	2026-05-18T03:30:26.296825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cba9ab666ddda62c089559d1b8823fe9190c8e2a60dda8c2611d7e863d7191d

Aliases

arxiv: 0906.1537 · arxiv_version: 0906.1537v2 · doi: 10.48550/arxiv.0906.1537 · pith_short_12: PS5JVNTG3XNG · pith_short_16: PS5JVNTG3XNGFQEJ · pith_short_8: PS5JVNTG

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/PS5JVNTG3XNGFQEJKWORXCBD72 \
  | 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: 7cba9ab666ddda62c089559d1b8823fe9190c8e2a60dda8c2611d7e863d7191d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "875f922e2544726c80e96dd03516d38f7bd844e4e1ba18b69a66d5f4a54268fc",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-06-08T16:58:01Z",
    "title_canon_sha256": "ee84a3b62b751ff06b9af1915a41112ccc56605339db6fe992c50dee2bafa5a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.1537",
    "kind": "arxiv",
    "version": 2
  }
}