Pith Number

pith:VBIPW7Q2

pith:2014:VBIPW7Q24PRA5WMK3O3GSA7JW2

not attested not anchored not stored refs pending

An Elementary Proof of an Asymptotic Formula of Ramanujan

Adrian Dudek

arxiv:1401.1514 v1 · 2014-01-07 · 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{VBIPW7Q24PRA5WMK3O3GSA7JW2}

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	2026-05-18T03:02:58.709856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a850fb7e1ae3e20ed98adbb66903e9b694bd571ad38a8366db8db399acd63e2f

Aliases

arxiv: 1401.1514 · arxiv_version: 1401.1514v1 · doi: 10.48550/arxiv.1401.1514 · pith_short_12: VBIPW7Q24PRA · pith_short_16: VBIPW7Q24PRA5WMK · pith_short_8: VBIPW7Q2

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/VBIPW7Q24PRA5WMK3O3GSA7JW2 \
  | 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: a850fb7e1ae3e20ed98adbb66903e9b694bd571ad38a8366db8db399acd63e2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdb38d6d271b1e27498f17cf036bbf7a2ce10cf675076492a5748646bb3dee9b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-01-07T21:28:09Z",
    "title_canon_sha256": "cfd3e4ab816a867bfd713327df76b08354e030acdaec9dd27d8bcc8f2d41ae36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.1514",
    "kind": "arxiv",
    "version": 1
  }
}