Pith Number

pith:7K36JE3X

pith:2005:7K36JE3XW2R6SA3R75V4AIYGQQ

not attested not anchored not stored refs pending

Sharpenings of Li's criterion for the Riemann Hypothesis

Andr\'e Voros

arxiv:math/0506326 v2 · 2005-06-16 · math.NT · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7K36JE3XW2R6SA3R75V4AIYGQQ}

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	2026-05-18T01:41:44.430508Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fab7e49377b6a3e90371ff6bc023068409727b289c3704f478e91575cfa85976

Aliases

arxiv: math/0506326 · arxiv_version: math/0506326v2 · doi: 10.48550/arxiv.math/0506326 · pith_short_12: 7K36JE3XW2R6 · pith_short_16: 7K36JE3XW2R6SA3R · pith_short_8: 7K36JE3X

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/7K36JE3XW2R6SA3R75V4AIYGQQ \
  | 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: fab7e49377b6a3e90371ff6bc023068409727b289c3704f478e91575cfa85976

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8df8aed3454e6f54a6d03f85287c706029c70547c110dd40cde9b610d1b1678e",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-06-16T11:17:55Z",
    "title_canon_sha256": "66ed69d522e0dfd16a9b62fdf3cf8911167e102da1633dcb77566c8683458db0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0506326",
    "kind": "arxiv",
    "version": 2
  }
}