Pith Number

pith:HUKRPPXJ

pith:2019:HUKRPPXJOVXGQJD7C3TSAU7LEF

not attested not anchored not stored refs pending

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC

Aaron M. Yeager

arxiv:1908.02234 v1 · 2019-08-06 · math.CA · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HUKRPPXJOVXGQJD7C3TSAU7LEF}

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	2026-07-04T23:51:52.300536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d1517bee9756e68247f16e72053eb21645daa67c64287aeed667d5fca882125

Aliases

arxiv: 1908.02234 · arxiv_version: 1908.02234v1 · doi: 10.48550/arxiv.1908.02234 · pith_short_12: HUKRPPXJOVXG · pith_short_16: HUKRPPXJOVXGQJD7 · pith_short_8: HUKRPPXJ

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/HUKRPPXJOVXGQJD7C3TSAU7LEF \
  | 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: 3d1517bee9756e68247f16e72053eb21645daa67c64287aeed667d5fca882125

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa92c5861b85efeb1a9201268ddb97898623d54cdef360adb4eb8b7ac91565e6",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-08-06T16:19:22Z",
    "title_canon_sha256": "d77fa7b6fa74ca9b2b3e255684bb1d30d1a15c8ee0d7be050f45b3bf66968da6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02234",
    "kind": "arxiv",
    "version": 1
  }
}