Pith Number

pith:3XCPUOSG

pith:2012:3XCPUOSGVEOTR4DWFNSXER22QQ

not attested not anchored not stored refs pending

Distribution of residues in approximate subgroups of $\mathbb{F}_p^*$

Francois Hennecart, Norbert Hegyv\'ari

arxiv:1207.2648 v1 · 2012-07-11 · 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{3XCPUOSGVEOTR4DWFNSXER22QQ}

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	2026-05-18T03:51:14.886272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddc4fa3a46a91d38f0762b6572475a843d53531a83b8e1ca6c91265a11d8d444

Aliases

arxiv: 1207.2648 · arxiv_version: 1207.2648v1 · doi: 10.48550/arxiv.1207.2648 · pith_short_12: 3XCPUOSGVEOT · pith_short_16: 3XCPUOSGVEOTR4DW · pith_short_8: 3XCPUOSG

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/3XCPUOSGVEOTR4DWFNSXER22QQ \
  | 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: ddc4fa3a46a91d38f0762b6572475a843d53531a83b8e1ca6c91265a11d8d444

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "249f29052ada0d3279ecb00aed6367b2e747d78b21652c4a3a4dd6491a177901",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-07-11T14:19:10Z",
    "title_canon_sha256": "2a4fd3c3494ba8b0419df77b8c8ad4ccb207f3c79d31ae1231928baed3b2acb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2648",
    "kind": "arxiv",
    "version": 1
  }
}