Pith Number

pith:VFSLG5H5

pith:2012:VFSLG5H5V4QQOHW5KVBPYKPSUN

not attested not anchored not stored refs pending

New sum product type estimates

Misha Rudnev, Sergei V. Konyagin

arxiv:1207.6785 v2 · 2012-07-29 · 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{VFSLG5H5V4QQOHW5KVBPYKPSUN}

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	2026-05-18T03:31:30.596952Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a964b374fdaf21071edd5542fc29f2a34320788636f3b63bf292c89a6ec5741b

Aliases

arxiv: 1207.6785 · arxiv_version: 1207.6785v2 · doi: 10.48550/arxiv.1207.6785 · pith_short_12: VFSLG5H5V4QQ · pith_short_16: VFSLG5H5V4QQOHW5 · pith_short_8: VFSLG5H5

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/VFSLG5H5V4QQOHW5KVBPYKPSUN \
  | 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: a964b374fdaf21071edd5542fc29f2a34320788636f3b63bf292c89a6ec5741b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ffc03c74273475fa5f706688f24a5debf0893b1017405617ed5b420358e9c16",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-29T16:59:02Z",
    "title_canon_sha256": "266508cfbcedbf06bd5bb5f3845c701eb2353049cc205df349dbe59f000a8209"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6785",
    "kind": "arxiv",
    "version": 2
  }
}