Pith Number

pith:GVI4BRRJ

pith:2026:GVI4BRRJU6PPCGC3DT4YI7L6C6

not attested not anchored not stored refs pending

Pair correlation of $\alpha n^{\theta}$ for random $\theta$

Andrei Shubin

arxiv:2606.03781 v1 · 2026-06-02 · 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{GVI4BRRJU6PPCGC3DT4YI7L6C6}

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	2026-06-03T02:06:02.256147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3551c0c629a79ef1185b1cf9847d7e17997f1e45990003e903b050eda9f72ac1

Aliases

arxiv: 2606.03781 · arxiv_version: 2606.03781v1 · doi: 10.48550/arxiv.2606.03781 · pith_short_12: GVI4BRRJU6PP · pith_short_16: GVI4BRRJU6PPCGC3 · pith_short_8: GVI4BRRJ

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/GVI4BRRJU6PPCGC3DT4YI7L6C6 \
  | 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: 3551c0c629a79ef1185b1cf9847d7e17997f1e45990003e903b050eda9f72ac1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e095532193150a6e0b02dd64cbf3077ef6382dc71aef5893d787b3f12f00320",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-06-02T15:36:08Z",
    "title_canon_sha256": "5c6df680c4e0b7a32847658be598c9eaf71866decea6a4f6a52b96a5e854e4c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.03781",
    "kind": "arxiv",
    "version": 1
  }
}