Pith Number

pith:GVVL2JLY

pith:2008:GVVL2JLYFAUMADFNISEPROD3UD

not attested not anchored not stored refs pending

Solymosi's multiplicative energy bound for complex numbers

Misha Rudnev, Tim Jones

arxiv:0812.1454 v4 · 2008-12-08 · 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{GVVL2JLYFAUMADFNISEPROD3UD}

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	2026-05-18T02:48:34.107211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

356abd25782828c00cad4488f8b87ba0d981601baacaf4fc8019358a1d979e4e

Aliases

arxiv: 0812.1454 · arxiv_version: 0812.1454v4 · doi: 10.48550/arxiv.0812.1454 · pith_short_12: GVVL2JLYFAUM · pith_short_16: GVVL2JLYFAUMADFN · pith_short_8: GVVL2JLY

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/GVVL2JLYFAUMADFNISEPROD3UD \
  | 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: 356abd25782828c00cad4488f8b87ba0d981601baacaf4fc8019358a1d979e4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7647b567433f7d07fa6a3763518b737fa5d1dfcfaf2247426a081bdf2982f2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-12-08T10:33:51Z",
    "title_canon_sha256": "17a678f2a989ca7a8c0fa1e3cd15eeadbe73040e74318472e29aa1aa869d5f25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.1454",
    "kind": "arxiv",
    "version": 4
  }
}