Pith Number

pith:KFZJUISE

pith:2016:KFZJUISEBU6WJG44FW7PE6B4A7

not attested not anchored not stored refs pending

Twisted Linnik implies optimal covering exponent for $S^3$

R.S. Steiner, T.D. Browning, V. Vinay Kumaraswamy

arxiv:1609.06097 v2 · 2016-09-20 · 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{KFZJUISEBU6WJG44FW7PE6B4A7}

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	2026-05-17T23:43:09.692659Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51729a22440d3d649b9c2dbef2783c07f69ecf34ddc0cbba965adb5e773d3040

Aliases

arxiv: 1609.06097 · arxiv_version: 1609.06097v2 · doi: 10.48550/arxiv.1609.06097 · pith_short_12: KFZJUISEBU6W · pith_short_16: KFZJUISEBU6WJG44 · pith_short_8: KFZJUISE

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/KFZJUISEBU6WJG44FW7PE6B4A7 \
  | 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: 51729a22440d3d649b9c2dbef2783c07f69ecf34ddc0cbba965adb5e773d3040

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d4d5787516152d39707e8751c0abc837a506a39bf1d5e286b5c2489256c8549",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-20T11:11:05Z",
    "title_canon_sha256": "9da06f197cbad36aeaf68e3aecf2a9bf8fa6e3b010194afeaf8b5a4b15f32650"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06097",
    "kind": "arxiv",
    "version": 2
  }
}