Pith Number

pith:7I2CSU33

pith:2026:7I2CSU33OAZKJB5KEIZ6KC4YJ3

not attested not anchored not stored refs pending

Multiplicative dependence in the sumset of multiplicative groups

Florian Luca, Yuri Bilu

arxiv:2607.28857 v1 · 2026-07-30 · 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{7I2CSU33OAZKJB5KEIZ6KC4YJ3}

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	2026-08-03T01:17:13.451949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa3429537b7032a487aa2233e50b984ed1ec23218b07fed36024abecf1d43ef6

Aliases

arxiv: 2607.28857 · arxiv_version: 2607.28857v1 · doi: 10.48550/arxiv.2607.28857 · pith_short_12: 7I2CSU33OAZK · pith_short_16: 7I2CSU33OAZKJB5K · pith_short_8: 7I2CSU33

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/7I2CSU33OAZKJB5KEIZ6KC4YJ3 \
  | 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: fa3429537b7032a487aa2233e50b984ed1ec23218b07fed36024abecf1d43ef6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efce3effb53b4ade4ca9dc5c3ca51d88116e5a482ad4a7155ece63c2f1b806d5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-30T21:44:54Z",
    "title_canon_sha256": "ccd9a3131d8e51d36f0a40dd9c408d726b2fed01ea7ea3c4de155404e660414e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.28857",
    "kind": "arxiv",
    "version": 1
  }
}