Pith Number

pith:QKCZ2A2T

pith:2010:QKCZ2A2TCYS6HPAN2BQ7Z3RCTP

not attested not anchored not stored refs pending

More than 41% of the zeros of the zeta function are on the critical line

Brian Conrey, Hung Bui, Matthew Young

arxiv:1002.4127 v2 · 2010-02-22 · 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{QKCZ2A2TCYS6HPAN2BQ7Z3RCTP}

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	2026-05-18T03:29:51.398997Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82859d03531625e3bc0dd061fcee229bd6ce126635b1813ac9bd2665b9832866

Aliases

arxiv: 1002.4127 · arxiv_version: 1002.4127v2 · doi: 10.48550/arxiv.1002.4127 · pith_short_12: QKCZ2A2TCYS6 · pith_short_16: QKCZ2A2TCYS6HPAN · pith_short_8: QKCZ2A2T

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/QKCZ2A2TCYS6HPAN2BQ7Z3RCTP \
  | 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: 82859d03531625e3bc0dd061fcee229bd6ce126635b1813ac9bd2665b9832866

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45fdb246d78615faeb282fda13499592d52856dd33a7ed9b5072dfb80a811377",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-02-22T14:43:20Z",
    "title_canon_sha256": "c5c7f35883d4467d5a0cf60bc0a548e9127d26434db430f954df0d293f39e814"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.4127",
    "kind": "arxiv",
    "version": 2
  }
}