Pith Number

pith:WBW37I7Z

pith:2015:WBW37I7ZPW5CIWC53I72OZ5NRO

not attested not anchored not stored refs pending

Universality of the mean number of real zeros of random trigonometric polynomials under a weak Cramer condition

Guillaume Poly, J\"urgen Angst

arxiv:1511.08750 v1 · 2015-11-27 · 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{WBW37I7ZPW5CIWC53I72OZ5NRO}

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	2026-05-18T01:25:48.181523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b06dbfa3f97dba24585dda3fa767ad8b919cc9ac31e01dded10652aeb7b99ba2

Aliases

arxiv: 1511.08750 · arxiv_version: 1511.08750v1 · doi: 10.48550/arxiv.1511.08750 · pith_short_12: WBW37I7ZPW5C · pith_short_16: WBW37I7ZPW5CIWC5 · pith_short_8: WBW37I7Z

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/WBW37I7ZPW5CIWC53I72OZ5NRO \
  | 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: b06dbfa3f97dba24585dda3fa767ad8b919cc9ac31e01dded10652aeb7b99ba2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93fa41ade07551015305ac78fd75617a95f6b1f6c5ebc40beb92563df99bd9fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-27T17:24:13Z",
    "title_canon_sha256": "4d0f3e0168c3044182d190325509bb07a6f96a3c82678bf24dba4aa3f408ea3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08750",
    "kind": "arxiv",
    "version": 1
  }
}