Pith Number

pith:VDI53VZO

pith:2014:VDI53VZODVNJEN3HFXT2FYK5VR

not attested not anchored not stored refs pending

New bounds for the prime counting function \pi(x)

Christian Axler

arxiv:1409.1780 v7 · 2014-09-05 · 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{VDI53VZODVNJEN3HFXT2FYK5VR}

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	2026-05-18T01:23:04.439347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8d1ddd72e1d5a9237672de7a2e15dac4e063f1374fa000f55a1d07eb7eaead5

Aliases

arxiv: 1409.1780 · arxiv_version: 1409.1780v7 · doi: 10.48550/arxiv.1409.1780 · pith_short_12: VDI53VZODVNJ · pith_short_16: VDI53VZODVNJEN3H · pith_short_8: VDI53VZO

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/VDI53VZODVNJEN3HFXT2FYK5VR \
  | 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: a8d1ddd72e1d5a9237672de7a2e15dac4e063f1374fa000f55a1d07eb7eaead5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75165b5783caf5e2ed63585d7daa1032ff3d6036128b6e11c0d1287448ef59fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-09-05T13:09:55Z",
    "title_canon_sha256": "d0bab7eca40657e8748e8c475e193fd0acb80544f59ac66ac77ade6f7919f70a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.1780",
    "kind": "arxiv",
    "version": 7
  }
}