Pith Number

pith:PH6WG7YA

pith:2019:PH6WG7YAPYTYL2DZLCPHA2ZST4

not attested not anchored not stored refs pending

On the density or measure of sets and their sumsets in the integers or the circle

Fran\c{c}ois Hennecart, Pierre-Yves Bienvenu

arxiv:1905.07938 v1 · 2019-05-20 · 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{PH6WG7YAPYTYL2DZLCPHA2ZST4}

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	2026-05-17T23:45:48.022111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79fd637f007e2785e879589e706b329f2fc6cfa1365bd999aeffbc73268478dd

Aliases

arxiv: 1905.07938 · arxiv_version: 1905.07938v1 · doi: 10.48550/arxiv.1905.07938 · pith_short_12: PH6WG7YAPYTY · pith_short_16: PH6WG7YAPYTYL2DZ · pith_short_8: PH6WG7YA

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/PH6WG7YAPYTYL2DZLCPHA2ZST4 \
  | 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: 79fd637f007e2785e879589e706b329f2fc6cfa1365bd999aeffbc73268478dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60d838a460185706b89ed789bb6bd80dd5daa9e0cfd48a4782d3ed5896b0e0af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-05-20T08:21:57Z",
    "title_canon_sha256": "1128901d4d91b1e8f5ec6316e2c0615f4a420850bddc3fe37319b7f1f31ea28f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.07938",
    "kind": "arxiv",
    "version": 1
  }
}