Pith Number

pith:FDH52V7S

pith:2016:FDH52V7SLVEBJUTHOPD3POJ7HP

not attested not anchored not stored refs pending

On The Energy Variant of the Sum-Product Conjecture

Ilya D. Shkredov, Misha Rudnev, Sophie Stevens

arxiv:1607.05053 v5 · 2016-07-18 · 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{FDH52V7SLVEBJUTHOPD3POJ7HP}

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	2026-05-18T00:43:09.287074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28cfdd57f25d4814d26773c7b7b93f3be9cffe6964808bc4ef91db3d51edf3d2

Aliases

arxiv: 1607.05053 · arxiv_version: 1607.05053v5 · doi: 10.48550/arxiv.1607.05053 · pith_short_12: FDH52V7SLVEB · pith_short_16: FDH52V7SLVEBJUTH · pith_short_8: FDH52V7S

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/FDH52V7SLVEBJUTHOPD3POJ7HP \
  | 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: 28cfdd57f25d4814d26773c7b7b93f3be9cffe6964808bc4ef91db3d51edf3d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a51aad88bc9197c9f2f07536cfe67b345ce5c9cf38347ddf95a88dc6058d14a",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-07-18T12:59:19Z",
    "title_canon_sha256": "d04931189b10eb0ae176376aa5277742a2a268341ff39c2b3c844ab59544acc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.05053",
    "kind": "arxiv",
    "version": 5
  }
}