Pith Number

pith:7C5XPKOG

pith:2004:7C5XPKOGGUIQ3J7EZEOL6MU6JZ

not attested not anchored not stored refs pending

An uncertainty principle for arithmetic sequences

Andrew Granville, K. Soundararajan

arxiv:math/0406018 v1 · 2004-06-01 · math.NT · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7C5XPKOGGUIQ3J7EZEOL6MU6JZ}

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	2026-07-04T14:38:40.488497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8bb77a9c635110da7e4c91cbf329e4e518c2aa4763fe4d8b271e8d124e8eddc

Aliases

arxiv: math/0406018 · arxiv_version: math/0406018v1 · doi: 10.48550/arxiv.math/0406018 · pith_short_12: 7C5XPKOGGUIQ · pith_short_16: 7C5XPKOGGUIQ3J7E · pith_short_8: 7C5XPKOG

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/7C5XPKOGGUIQ3J7EZEOL6MU6JZ \
  | 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: f8bb77a9c635110da7e4c91cbf329e4e518c2aa4763fe4d8b271e8d124e8eddc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e59680414e493370b46e1ab8cd2649a6c7edb8a6a7b481023a865081b4a4d06",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-06-01T16:00:06Z",
    "title_canon_sha256": "05f47af4bf0bd381fd6680b07ce3463c107008a0c9b348a501072881519cce71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406018",
    "kind": "arxiv",
    "version": 1
  }
}