Pith. sign in
Pith Number

pith:ZO7ZQCCA

pith:2010:ZO7ZQCCA2ODHZCWQ5JLGIENQOM
not attested not anchored not stored refs pending

Both real and imaginary parts of the function F(s)=zeta(s)*Gamma(s/2)*pi**(-s/2)=xi(s)/(s*(s-1)), whose zeroes exactly coincide with the non-trivial zeroes of the Riemann zeta-function, have infinitely many zeroes for any value of Re(s)

S. K. Sekatskii

arxiv:1007.0926 v1 · 2010-06-02 · 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{ZO7ZQCCA2ODHZCWQ5JLGIENQOM}

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 2026-07-04T17:31:22.329402Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05) · public key
Schema pith-number/v1.0

Canonical hash

cbbf980840d3867c8ad0ea566411b073320d8144a380332f0490635fd8e5c438

Aliases

arxiv: 1007.0926 · arxiv_version: 1007.0926v1 · doi: 10.48550/arxiv.1007.0926 · pith_short_12: ZO7ZQCCA2ODH · pith_short_16: ZO7ZQCCA2ODHZCWQ · pith_short_8: ZO7ZQCCA
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/ZO7ZQCCA2ODHZCWQ5JLGIENQOM \
  | 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: cbbf980840d3867c8ad0ea566411b073320d8144a380332f0490635fd8e5c438
Canonical record JSON 
{
  "metadata": {
    "abstract_canon_sha256": "5963df0872b7b68298fca2ca144d2dc97638d087c9ee4f15d7cb7226b16b377b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-06-02T13:36:40Z",
    "title_canon_sha256": "7dd8f06dd7246ffbd20463f01e8c7b987ca4373ad6a3e8f98eb43758a93a3d1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0926",
    "kind": "arxiv",
    "version": 1
  }
}