Pith Number

pith:COY2HEYN

pith:2025:COY2HEYNORMSVPV5V74K4JIKK4

not attested not anchored not stored refs pending

On the arithmetic average of the first $n$ primes

Matt Visser (Victoria University of Wellington)

arxiv:2505.04951 v3 · 2025-05-08 · 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{COY2HEYNORMSVPV5V74K4JIKK4}

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.

Cited by

1 paper in Pith

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$

Receipt and verification

First computed	2026-07-05T11:37:44.672865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13b1a3930d74592abebdaff8ae250a57331d5fe0b5bbd2d0c88210aa65f6ca1c

Aliases

arxiv: 2505.04951 · arxiv_version: 2505.04951v3 · doi: 10.48550/arxiv.2505.04951 · pith_short_12: COY2HEYNORMS · pith_short_16: COY2HEYNORMSVPV5 · pith_short_8: COY2HEYN

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/COY2HEYNORMSVPV5V74K4JIKK4 \
  | 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: 13b1a3930d74592abebdaff8ae250a57331d5fe0b5bbd2d0c88210aa65f6ca1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78ab80d41311153dfa1ea493e5152dd4df3138c718ac8df380e21f4b1d6d7fba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-05-08T05:10:43Z",
    "title_canon_sha256": "de3f62fe4d796848db10f23619cd5799d40e0a5b082ecdbaa1a9bae41a0d1fcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.04951",
    "kind": "arxiv",
    "version": 3
  }
}