Pith Number

pith:VFPV5UKD

pith:2015:VFPV5UKDDEJZN6GFHFFTXG6YN7

not attested not anchored not stored refs pending

An explicit upper bound for the first $k$-Ramanujan prime

Christian Axler, Thomas Le{\ss}mann

arxiv:1504.05485 v1 · 2015-04-21 · 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{VFPV5UKDDEJZN6GFHFFTXG6YN7}

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	2026-05-18T02:18:14.163121Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a95f5ed143191396f8c5394b3b9bd86fe67a08377c2d47c12a6305694b46f422

Aliases

arxiv: 1504.05485 · arxiv_version: 1504.05485v1 · doi: 10.48550/arxiv.1504.05485 · pith_short_12: VFPV5UKDDEJZ · pith_short_16: VFPV5UKDDEJZN6GF · pith_short_8: VFPV5UKD

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/VFPV5UKDDEJZN6GFHFFTXG6YN7 \
  | 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: a95f5ed143191396f8c5394b3b9bd86fe67a08377c2d47c12a6305694b46f422

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5c9ceddd788bd57ec5ac1b25d39ee5a7abc018739c3334c9486219e0748e362",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-04-21T16:00:27Z",
    "title_canon_sha256": "99091777e3fa5084b4a44538b9a1d3ff174284f4c1249e222de347ee34a198dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05485",
    "kind": "arxiv",
    "version": 1
  }
}