Pith Number

pith:XHP25XRD

pith:2024:XHP25XRDWTZKO4S7TS4S2ZSBMG

not attested not anchored not stored refs pending

On arithmetic terms expressing the prime-counting function and the n-th prime

Joseph M. Shunia, Mihai Prunescu

arxiv:2412.14594 v2 · 2024-12-19 · 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{XHP25XRDWTZKO4S7TS4S2ZSBMG}

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

Undecidability, Chaos and Universality in Arithmetic Terms

Receipt and verification

First computed	2026-07-05T11:47:59.127103Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9dfaede23b4f2a7725f9cb92d6641619192fc4b33365339751ac7d2fe53ceb0

Aliases

arxiv: 2412.14594 · arxiv_version: 2412.14594v2 · doi: 10.48550/arxiv.2412.14594 · pith_short_12: XHP25XRDWTZK · pith_short_16: XHP25XRDWTZKO4S7 · pith_short_8: XHP25XRD

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/XHP25XRDWTZKO4S7TS4S2ZSBMG \
  | 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: b9dfaede23b4f2a7725f9cb92d6641619192fc4b33365339751ac7d2fe53ceb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "140a7f380f2b1a0aa86bd5bd5292e2ca635655a6f72bc9bafb1376f1f71101a0",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-12-19T07:30:46Z",
    "title_canon_sha256": "335655feecd112ff073b42ad60ae9c1c0f4aa3d4287921280f1d94abf8081032"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.14594",
    "kind": "arxiv",
    "version": 2
  }
}