Pith Number

pith:VKFSXR2M

pith:2026:VKFSXR2M7PQVJXICFQDEX6WPCU

not attested not anchored not stored refs pending

Euler's $\ell$-totients and Riemann hypothesis

Ahmed Gaber

arxiv:2607.26114 v1 · 2026-07-28 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VKFSXR2M7PQVJXICFQDEX6WPCU}

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	2026-07-30T00:08:22.713906Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

aa8b2bc74cfbe154dd022c064bfacf1508f2db7032c28fd7755f55f671463118

Aliases

arxiv: 2607.26114 · arxiv_version: 2607.26114v1 · doi: 10.48550/arxiv.2607.26114 · pith_short_12: VKFSXR2M7PQV · pith_short_16: VKFSXR2M7PQVJXIC · pith_short_8: VKFSXR2M

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/VKFSXR2M7PQVJXICFQDEX6WPCU \
  | 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: aa8b2bc74cfbe154dd022c064bfacf1508f2db7032c28fd7755f55f671463118

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9f33c7ad49beaa876e4124083c4858556bed1fb4bc1e5bcfb98065f77e7b273",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-07-28T15:34:39Z",
    "title_canon_sha256": "f13ecd54d3e3f1b824efd19584bb4c24fd3fbcebf2fa3ec7276d7c851649f7a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26114",
    "kind": "arxiv",
    "version": 1
  }
}