Pith Number

pith:Q5UTZPHK

pith:2018:Q5UTZPHKH4TDIUDA54NSPTW324

not attested not anchored not stored refs pending

The lemniscate tree of a random polynomial

Boris Hanin, Erik Lundberg, Michael Epstein

arxiv:1806.00521 v1 · 2018-06-01 · math.PR · math.CO · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q5UTZPHKH4TDIUDA54NSPTW324}

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	2026-05-18T00:14:20.990816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87693cbcea3f26345060ef1b27cedbd716ca1fb2526dd9445d70db2ea35a987a

Aliases

arxiv: 1806.00521 · arxiv_version: 1806.00521v1 · doi: 10.48550/arxiv.1806.00521 · pith_short_12: Q5UTZPHKH4TD · pith_short_16: Q5UTZPHKH4TDIUDA · pith_short_8: Q5UTZPHK

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/Q5UTZPHKH4TDIUDA54NSPTW324 \
  | 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: 87693cbcea3f26345060ef1b27cedbd716ca1fb2526dd9445d70db2ea35a987a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0a055a3761aea96600f168c71881baa957d50214096b1d70a65c73dbaf4eb99",
    "cross_cats_sorted": [
      "math.CO",
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-06-01T19:45:21Z",
    "title_canon_sha256": "741c9799990ee01d88b042134ccdc1f9a065904502ef3c244ec386e15c367b09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.00521",
    "kind": "arxiv",
    "version": 1
  }
}