Pith Number

pith:F4NKOWHZ

pith:2011:F4NKOWHZ6NFOVJ5XF25MLN366K

not attested not anchored not stored refs pending

Some properties of lower level-sets of convolutions

Ernie Croot

arxiv:1108.1578 v4 · 2011-08-07 · 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{F4NKOWHZ6NFOVJ5XF25MLN366K}

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	2026-05-18T04:01:49.609010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f1aa758f9f34aeaa7b72ebac5b77ef2a63b437311326faad5bbfaf8bed45d10

Aliases

arxiv: 1108.1578 · arxiv_version: 1108.1578v4 · doi: 10.48550/arxiv.1108.1578 · pith_short_12: F4NKOWHZ6NFO · pith_short_16: F4NKOWHZ6NFOVJ5X · pith_short_8: F4NKOWHZ

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/F4NKOWHZ6NFOVJ5XF25MLN366K \
  | 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: 2f1aa758f9f34aeaa7b72ebac5b77ef2a63b437311326faad5bbfaf8bed45d10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5fa0a0978b6087d99ab9e4b555f96d175fe03d92a5e31e4452afa861cf249e4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-07T21:55:46Z",
    "title_canon_sha256": "436677abf11875cdce39272dd39f17f6208e2c7a5e3a492b25f095fa454e3c6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1578",
    "kind": "arxiv",
    "version": 4
  }
}