Pith Number

pith:JZESFZEN

pith:2011:JZESFZENQ3GX7SA6KX3XCO56D3

not attested not anchored not stored refs pending

Flat points in zero sets of harmonic polynomials and harmonic measure from two sides

Matthew Badger

arxiv:1109.1427 v2 · 2011-09-07 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JZESFZENQ3GX7SA6KX3XCO56D3}

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	2026-05-18T03:25:16.390246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e4922e48d86cd7fc81e55f7713bbe1edeff7fdca5eb42a2e66cda0e0613c1e3

Aliases

arxiv: 1109.1427 · arxiv_version: 1109.1427v2 · doi: 10.48550/arxiv.1109.1427 · pith_short_12: JZESFZENQ3GX · pith_short_16: JZESFZENQ3GX7SA6 · pith_short_8: JZESFZEN

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/JZESFZENQ3GX7SA6KX3XCO56D3 \
  | 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: 4e4922e48d86cd7fc81e55f7713bbe1edeff7fdca5eb42a2e66cda0e0613c1e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc9803833080a28b780ae89e42c24a58429ec02cf5c89a8c101e6f5fe6761baf",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-09-07T11:43:57Z",
    "title_canon_sha256": "edbc79642584c5ff938187a024503f5c4d8382edc6526c8fe3c91b9625727316"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1427",
    "kind": "arxiv",
    "version": 2
  }
}