Pith Number

pith:FEXQJA5S

pith:2012:FEXQJA5SE5OZHD2LQDNUPW7QSU

not attested not anchored not stored refs pending

Computing $\pi(x)$ Analytically

David J. Platt

arxiv:1203.5712 v3 · 2012-03-26 · 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{FEXQJA5SE5OZHD2LQDNUPW7QSU}

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	2026-05-18T03:08:38.564298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

292f0483b2275d938f4b80db47dbf0953b45ef8d42695c27665e57d541577098

Aliases

arxiv: 1203.5712 · arxiv_version: 1203.5712v3 · doi: 10.48550/arxiv.1203.5712 · pith_short_12: FEXQJA5SE5OZ · pith_short_16: FEXQJA5SE5OZHD2L · pith_short_8: FEXQJA5S

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/FEXQJA5SE5OZHD2LQDNUPW7QSU \
  | 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: 292f0483b2275d938f4b80db47dbf0953b45ef8d42695c27665e57d541577098

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e5e8a8a843da10653fcbebd2ff389f76877d466f4e02167389f0bb6d96e9717",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-03-26T16:11:34Z",
    "title_canon_sha256": "cde6ce95dde6fd1c14920896820397407124b50f3e6cebed4849e0dbc423fad1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5712",
    "kind": "arxiv",
    "version": 3
  }
}