Pith Number

pith:K2B7VZ46

pith:2024:K2B7VZ466CS63TBB3GWOAPQCDX

not attested not anchored not stored refs pending

On Fourier coefficients of sets with small doubling

Ilya D. Shkredov

arxiv:2412.11368 v1 · 2024-12-16 · 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{K2B7VZ466CS63TBB3GWOAPQCDX}

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	2026-07-05T09:49:31.517151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5683fae79ef0a5edcc21d9ace03e021df766a957244eca66bda1d228f6171cf7

Aliases

arxiv: 2412.11368 · arxiv_version: 2412.11368v1 · doi: 10.48550/arxiv.2412.11368 · pith_short_12: K2B7VZ466CS6 · pith_short_16: K2B7VZ466CS63TBB · pith_short_8: K2B7VZ46

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/K2B7VZ466CS63TBB3GWOAPQCDX \
  | 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: 5683fae79ef0a5edcc21d9ace03e021df766a957244eca66bda1d228f6171cf7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d71d0ee8f1f1ea36ec9c8ee66558f9e90d290b65bf89f9a712fca82c53ace58b",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-16T01:50:45Z",
    "title_canon_sha256": "5b4044d1fb9f704f6b1e8181ae72f616f5066469a3bc0c67625627b185fa8e87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.11368",
    "kind": "arxiv",
    "version": 1
  }
}