Pith Number

pith:NYTE6BXE

pith:2026:NYTE6BXEHCXCT2K2CASMEOZ7ZN

not attested not anchored not stored refs pending

Beyond the Riemann Hypothesis bounds: A pair-correlation approach to the least prime in arithmetic progression and the smallest quadratic non-residue

Alessandro Languasco, Neelam Kandhil, Pieter Moree

arxiv:2607.14515 v1 · 2026-07-16 · 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{NYTE6BXEHCXCT2K2CASMEOZ7ZN}

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	2026-07-17T01:21:15.742147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e264f06e438ae29e95a1024c23b3fcb56bd43a306bf19239c4add8228f74de4

Aliases

arxiv: 2607.14515 · arxiv_version: 2607.14515v1 · doi: 10.48550/arxiv.2607.14515 · pith_short_12: NYTE6BXEHCXC · pith_short_16: NYTE6BXEHCXCT2K2 · pith_short_8: NYTE6BXE

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/NYTE6BXEHCXCT2K2CASMEOZ7ZN \
  | 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: 6e264f06e438ae29e95a1024c23b3fcb56bd43a306bf19239c4add8228f74de4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09bf923a05208dfda213daeb0b4406699ee24fd4468e8809f3980295cbb41a5b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-16T03:12:02Z",
    "title_canon_sha256": "7dc0b8051d5545677e8b674af957b030b248a2df8e9f0ac92a6694b0a797af70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.14515",
    "kind": "arxiv",
    "version": 1
  }
}