Pith Number

pith:MSNK3TCE

pith:2015:MSNK3TCE7HIK3OGJN5CKHL2M75

not attested not anchored not stored refs pending

$\sum_{p\le n} 1/p = \ln(\ln n) + O(1)$: An Exposition

Larry Washington, William Gasarch

arxiv:1511.01823 v2 · 2015-11-05 · math.HO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MSNK3TCE7HIK3OGJN5CKHL2M75}

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	2026-05-18T01:26:57.061332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

649aadcc44f9d0adb8c96f44a3af4cff7c4aaad5ad6df819ec86c61b7132b0ca

Aliases

arxiv: 1511.01823 · arxiv_version: 1511.01823v2 · doi: 10.48550/arxiv.1511.01823 · pith_short_12: MSNK3TCE7HIK · pith_short_16: MSNK3TCE7HIK3OGJ · pith_short_8: MSNK3TCE

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/MSNK3TCE7HIK3OGJN5CKHL2M75 \
  | 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: 649aadcc44f9d0adb8c96f44a3af4cff7c4aaad5ad6df819ec86c61b7132b0ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4937a205d8382fe6b726fe662ef8e97d643fc22b22988ee3bc45ca1b92f4e3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2015-11-05T17:34:32Z",
    "title_canon_sha256": "10d8ad8d933d5825bf4257978c51c34c80725838a17c7931edbd9656bcc01b2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.01823",
    "kind": "arxiv",
    "version": 2
  }
}