Pith Number

pith:6LMTHBW6

pith:2015:6LMTHBW6NE5J6SRPU6I3ZJVCU7

not attested not anchored not stored refs pending

On tripling constant of multiplicative subgroups

Ilya D. Shkredov

arxiv:1504.04522 v1 · 2015-04-17 · 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{6LMTHBW6NE5J6SRPU6I3ZJVCU7}

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	2026-05-18T02:18:32.190774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2d93386de693a9f4a2fa791bca6a2a7e457d5538e93dc2d97cbcdaa52af10c7

Aliases

arxiv: 1504.04522 · arxiv_version: 1504.04522v1 · doi: 10.48550/arxiv.1504.04522 · pith_short_12: 6LMTHBW6NE5J · pith_short_16: 6LMTHBW6NE5J6SRP · pith_short_8: 6LMTHBW6

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/6LMTHBW6NE5J6SRPU6I3ZJVCU7 \
  | 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: f2d93386de693a9f4a2fa791bca6a2a7e457d5538e93dc2d97cbcdaa52af10c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1d98ba2e35d7b47d1f9d3de5da23176f8fe5642373bc3dd95efb85923b9115e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-04-17T14:56:12Z",
    "title_canon_sha256": "8effc33ce5a7db0b62b0755f08d7bf16c03fd9cf1bcb88bc973420244b446e54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.04522",
    "kind": "arxiv",
    "version": 1
  }
}