Pith Number

pith:ZGE6QPLJ

pith:2005:ZGE6QPLJUJN7CSEK57L5LSO53S

not attested not anchored not stored refs pending

Sharp bounds for the valence of certain harmonic polynomials

Lukas Geyer

arxiv:math/0510539 v1 · 2005-10-25 · math.CV · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZGE6QPLJUJN7CSEK57L5LSO53S}

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	2026-05-18T02:54:54.616340Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c989e83d69a25bf1488aefd7d5c9dddcb58b7fe93fe5970e815a997a3e9fe379

Aliases

arxiv: math/0510539 · arxiv_version: math/0510539v1 · doi: 10.48550/arxiv.math/0510539 · pith_short_12: ZGE6QPLJUJN7 · pith_short_16: ZGE6QPLJUJN7CSEK · pith_short_8: ZGE6QPLJ

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/ZGE6QPLJUJN7CSEK57L5LSO53S \
  | 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: c989e83d69a25bf1488aefd7d5c9dddcb58b7fe93fe5970e815a997a3e9fe379

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7508daa528c5eefd146826b17d09bf03dc499397ef3a3a182b6d231910cb42a6",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "",
    "primary_cat": "math.CV",
    "submitted_at": "2005-10-25T23:27:13Z",
    "title_canon_sha256": "b834225d07fa0a9acc565c95dee17193e8de80f04b6c1469bede8e51686b6f3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0510539",
    "kind": "arxiv",
    "version": 1
  }
}