Pith Number

pith:L42LWK35

pith:2004:L42LWK35INL6NEJHKL2P6JS7IF

not attested not anchored not stored refs pending

Notes on Pair Correlation of Zeros and Prime Numbers

D. A. Goldston

arxiv:math/0412313 v1 · 2004-12-16 · 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{L42LWK35INL6NEJHKL2P6JS7IF}

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.

Cited by

1 paper in Pith

A Tsang-range high-moment bound for $\operatorname{Im}\log L(\tfrac12+it,\chi)$ under GRH

Receipt and verification

First computed	2026-07-04T14:39:27.982665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f34bb2b7d4357e6912752f4ff265f41595dc45fb8a7d9b800744eb760657d04

Aliases

arxiv: math/0412313 · arxiv_version: math/0412313v1 · doi: 10.48550/arxiv.math/0412313 · pith_short_12: L42LWK35INL6 · pith_short_16: L42LWK35INL6NEJH · pith_short_8: L42LWK35

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/L42LWK35INL6NEJHKL2P6JS7IF \
  | 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: 5f34bb2b7d4357e6912752f4ff265f41595dc45fb8a7d9b800744eb760657d04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc5ba3f1d1d479369c0318c8ca18fb8895aa1239d8aee71336c178a472b00aba",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-12-16T01:03:00Z",
    "title_canon_sha256": "3a24eefb66a683d0f9ec5490da1c2ad470d836532093aa0d3153528ecb0e312a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412313",
    "kind": "arxiv",
    "version": 1
  }
}