Pith Number

pith:BNSDKPLZ

pith:2016:BNSDKPLZFSNWWANL6FU7EHMZK4

not attested not anchored not stored refs pending

On the arithmetic and geometric means of the prime numbers

Christian Axler

arxiv:1609.07934 v2 · 2016-09-26 · 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{BNSDKPLZFSNWWANL6FU7EHMZK4}

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	2026-05-18T00:36:09.566032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b64353d792c9b6b01abf169f21d995739ed09cb99cbf5a0f29cb0e09f010ddb

Aliases

arxiv: 1609.07934 · arxiv_version: 1609.07934v2 · doi: 10.48550/arxiv.1609.07934 · pith_short_12: BNSDKPLZFSNW · pith_short_16: BNSDKPLZFSNWWANL · pith_short_8: BNSDKPLZ

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/BNSDKPLZFSNWWANL6FU7EHMZK4 \
  | 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: 0b64353d792c9b6b01abf169f21d995739ed09cb99cbf5a0f29cb0e09f010ddb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c57379700268f1904b1d17973b19a164899a839d09792c245a3478fa0fd50152",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-26T11:48:33Z",
    "title_canon_sha256": "3ba03f94db4cfa6cecc7815169453eca2261daad14fd472746c4c4b391177eb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07934",
    "kind": "arxiv",
    "version": 2
  }
}