Pith Number

pith:NRNMVKES

pith:2014:NRNMVKESZMF2KZ2MZRAW3DPT2J

not attested not anchored not stored refs pending

A new theorem on the prime-counting function

Zhi-Wei Sun

arxiv:1409.5685 v6 · 2014-09-19 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NRNMVKESZMF2KZ2MZRAW3DPT2J}

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	2026-05-18T00:53:10.949724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c5acaa892cb0ba5674ccc416d8df3d246a4aa3bacb2f131eebd2c003c1e32de

Aliases

arxiv: 1409.5685 · arxiv_version: 1409.5685v6 · doi: 10.48550/arxiv.1409.5685 · pith_short_12: NRNMVKESZMF2 · pith_short_16: NRNMVKESZMF2KZ2M · pith_short_8: NRNMVKES

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/NRNMVKESZMF2KZ2MZRAW3DPT2J \
  | 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: 6c5acaa892cb0ba5674ccc416d8df3d246a4aa3bacb2f131eebd2c003c1e32de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69405e24f3f0e75c3bdcaf5631e074e4e58373163edd1218d27ac046dc75443f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-09-19T14:57:22Z",
    "title_canon_sha256": "c4f23bda89bdde28ca037c9afdcf91461a3c5f56c103ca488455e71e9538a7a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.5685",
    "kind": "arxiv",
    "version": 6
  }
}