Pith Number

pith:D4TCTIYD

pith:2011:D4TCTIYDNIG5LTOY5X4NK66Y5W

not attested not anchored not stored refs pending

New Proofs of Pl\"unnecke-type Estimates for Product Sets in Groups

Giorgis Petridis

arxiv:1101.3507 v3 · 2011-01-18 · math.CO · 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{D4TCTIYDNIG5LTOY5X4NK66Y5W}

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	2026-05-18T03:13:56.542418Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f2629a3036a0dd5cdd8edf8d57bd8edbd40a0b223b957f394173e7496e063c8

Aliases

arxiv: 1101.3507 · arxiv_version: 1101.3507v3 · doi: 10.48550/arxiv.1101.3507 · pith_short_12: D4TCTIYDNIG5 · pith_short_16: D4TCTIYDNIG5LTOY · pith_short_8: D4TCTIYD

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/D4TCTIYDNIG5LTOY5X4NK66Y5W \
  | 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: 1f2629a3036a0dd5cdd8edf8d57bd8edbd40a0b223b957f394173e7496e063c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c28f2f0ea6923a665decd5d15751b3b0f68f66e92d22772a6e28516ebf01eed",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-01-18T17:18:44Z",
    "title_canon_sha256": "f0da586d1e98b927c5193da8f417d8486766bb08152768ca1902f01b4dba6b9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3507",
    "kind": "arxiv",
    "version": 3
  }
}