Pith Number

pith:IC6YZD4T

pith:2016:IC6YZD4T2TGZXHXFZGS57BJUD4

not attested not anchored not stored refs pending

Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights

Turgay Bayraktar

arxiv:1611.04695 v2 · 2016-11-15 · math.CV · 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{IC6YZD4T2TGZXHXFZGS57BJUD4}

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	2026-05-18T00:16:50.888427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40bd8c8f93d4cd9b9ee5c9a5df85341f1edec8cbde977251169f78614ab23609

Aliases

arxiv: 1611.04695 · arxiv_version: 1611.04695v2 · doi: 10.48550/arxiv.1611.04695 · pith_short_12: IC6YZD4T2TGZ · pith_short_16: IC6YZD4T2TGZXHXF · pith_short_8: IC6YZD4T

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/IC6YZD4T2TGZXHXFZGS57BJUD4 \
  | 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: 40bd8c8f93d4cd9b9ee5c9a5df85341f1edec8cbde977251169f78614ab23609

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9edd86bca72e8d662d5981482e63f1f20b83ab19b076a254990fd025e420eafb",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2016-11-15T03:49:31Z",
    "title_canon_sha256": "70063da6ecae236bab64bc58e80cad1c1052c77c7eacdf03240e9f2cfb7be359"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04695",
    "kind": "arxiv",
    "version": 2
  }
}