Pith Number

pith:AVTQ263Y

pith:2026:AVTQ263YHDHGGECMUJWD7VIN3B

not attested not anchored not stored refs pending

Arithmetic Bias in Mersenne Prime Exponents and the Divisor Structure of $p-1$

Jesus Dominguez

arxiv:2603.08994 v3 · 2026-03-09 · 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{AVTQ263YHDHGGECMUJWD7VIN3B}

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	2026-06-02T02:04:15.861453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05670d7b7838ce63104ca26c3fd50dd85b57fca66386558739ab701a960b10e9

Aliases

arxiv: 2603.08994 · arxiv_version: 2603.08994v3 · doi: 10.48550/arxiv.2603.08994 · pith_short_12: AVTQ263YHDHG · pith_short_16: AVTQ263YHDHGGECM · pith_short_8: AVTQ263Y

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/AVTQ263YHDHGGECMUJWD7VIN3B \
  | 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: 05670d7b7838ce63104ca26c3fd50dd85b57fca66386558739ab701a960b10e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c339cba50e1b917c9fb6b74fc7c7b40fc07104f95561c431b7e0de54b864ffa2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-03-09T22:29:55Z",
    "title_canon_sha256": "0074572e3725eb237fff844a46096c665ffcea268f4d63238d1088d9ef5febb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.08994",
    "kind": "arxiv",
    "version": 3
  }
}