Pith Number

pith:VNGFUP3W

pith:2013:VNGFUP3W7PZJADIOSXPAFV4U45

not attested not anchored not stored refs pending

On exponential sums over multiplicative subgroups of medium size

Ilya D. Shkredov

arxiv:1311.5726 v1 · 2013-11-22 · math.NT · 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{VNGFUP3W7PZJADIOSXPAFV4U45}

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	2026-05-18T03:06:23.456215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab4c5a3f76fbf2900d0e95de02d794e75a58650e3c7f54783de156c6e8df2197

Aliases

arxiv: 1311.5726 · arxiv_version: 1311.5726v1 · doi: 10.48550/arxiv.1311.5726 · pith_short_12: VNGFUP3W7PZJ · pith_short_16: VNGFUP3W7PZJADIO · pith_short_8: VNGFUP3W

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/VNGFUP3W7PZJADIOSXPAFV4U45 \
  | 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: ab4c5a3f76fbf2900d0e95de02d794e75a58650e3c7f54783de156c6e8df2197

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e27fd9e933ec71d91e9da0bc60c5b367eb7c12e14e6b989492c679c30087a0b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-22T12:00:57Z",
    "title_canon_sha256": "ea2583567610db096b050ab7700528298aa3baa53e4fd537f83a03c00ca02ebf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5726",
    "kind": "arxiv",
    "version": 1
  }
}