Pith Number

pith:XHSV2V5X

pith:2017:XHSV2V5XTD4YAGKMUMUNU7JF6M

not attested not anchored not stored refs pending

Explicit asymptotic formulae for sub exponentially growing multiplicative structures

Boris Granovsky

arxiv:1705.00438 v2 · 2017-05-01 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XHSV2V5XTD4YAGKMUMUNU7JF6M}

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	2026-05-18T00:45:05.946538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9e55d57b798f980194ca328da7d25f326ac028b491e615d46ac88c84d1af2b6

Aliases

arxiv: 1705.00438 · arxiv_version: 1705.00438v2 · doi: 10.48550/arxiv.1705.00438 · pith_short_12: XHSV2V5XTD4Y · pith_short_16: XHSV2V5XTD4YAGKM · pith_short_8: XHSV2V5X

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/XHSV2V5XTD4YAGKMUMUNU7JF6M \
  | 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: b9e55d57b798f980194ca328da7d25f326ac028b491e615d46ac88c84d1af2b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74225bb46b4ef3c43342155e679d31eea4ce49f2a51891b0f6f48ae97333f5f5",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-05-01T07:53:41Z",
    "title_canon_sha256": "7f2bd4a7f1e1629a317378b8683a04de29cefce1a16ee3aa97d2260371d223ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.00438",
    "kind": "arxiv",
    "version": 2
  }
}