Pith Number

pith:NFJ3WONW

pith:2014:NFJ3WONW2YSQB72K7QREIJ6RS5

not attested not anchored not stored refs pending

An improved analytic Method for calculating $\pi(x)$

Jan B\"uthe

arxiv:1410.7008 v2 · 2014-10-26 · math.NT · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NFJ3WONW2YSQB72K7QREIJ6RS5}

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	2026-05-18T01:27:38.554904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6953bb39b6d62500ff4afc224427d1975aab1f5a256ecec1b0aba96dbd41ae4b

Aliases

arxiv: 1410.7008 · arxiv_version: 1410.7008v2 · doi: 10.48550/arxiv.1410.7008 · pith_short_12: NFJ3WONW2YSQ · pith_short_16: NFJ3WONW2YSQB72K · pith_short_8: NFJ3WONW

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/NFJ3WONW2YSQB72K7QREIJ6RS5 \
  | 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: 6953bb39b6d62500ff4afc224427d1975aab1f5a256ecec1b0aba96dbd41ae4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bce7af9fb1b075a0872d04a00adb9cd0a20f890563bf5aaf20d5e7954be7fa3",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-10-26T09:51:54Z",
    "title_canon_sha256": "85551b3419922d08e7851e4ac4b15c515c471c72c99ad8019affbe62dc544445"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.7008",
    "kind": "arxiv",
    "version": 2
  }
}