Pith Number

pith:TTZ4EYEO

pith:2016:TTZ4EYEO3TFPSRXIVYZBF4T4JD

not attested not anchored not stored refs pending

Pairing of Zeros and Critical Points for Random Polynomials

Boris Hanin

arxiv:1601.06417 v1 · 2016-01-24 · math.PR · math-ph · math.CV · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TTZ4EYEO3TFPSRXIVYZBF4T4JD}

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	2026-05-18T01:22:04.534449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cf3c2608edccaf946e8ae3212f27c48c10abdc5681b33251378f678dd31954b

Aliases

arxiv: 1601.06417 · arxiv_version: 1601.06417v1 · doi: 10.48550/arxiv.1601.06417 · pith_short_12: TTZ4EYEO3TFP · pith_short_16: TTZ4EYEO3TFPSRXI · pith_short_8: TTZ4EYEO

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/TTZ4EYEO3TFPSRXIVYZBF4T4JD \
  | 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: 9cf3c2608edccaf946e8ae3212f27c48c10abdc5681b33251378f678dd31954b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85803dd447a2072ea4ff9cdbe6a2a938a1aad9450b3b96c34ce3da80d1fca26b",
    "cross_cats_sorted": [
      "math-ph",
      "math.CV",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-01-24T18:59:37Z",
    "title_canon_sha256": "b24bfa1fbe692c21398d26d4651000067d238bdd59b6a484c3ecec97e921d8d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.06417",
    "kind": "arxiv",
    "version": 1
  }
}