Pith Number

pith:ZYJHLKCQ

pith:2013:ZYJHLKCQ3PZUS23BU7VWTGCYLS

not attested not anchored not stored refs pending

A gradient estimate for harmonic functions sharing the same zeros

Dan Mangoubi

arxiv:1306.0565 v1 · 2013-06-03 · 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{ZYJHLKCQ3PZUS23BU7VWTGCYLS}

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	2026-05-18T01:25:39.987782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce1275a850dbf3496b61a7eb6998585cad82d26efddd9b22f2e786900ffcbdbe

Aliases

arxiv: 1306.0565 · arxiv_version: 1306.0565v1 · doi: 10.48550/arxiv.1306.0565 · pith_short_12: ZYJHLKCQ3PZU · pith_short_16: ZYJHLKCQ3PZUS23B · pith_short_8: ZYJHLKCQ

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/ZYJHLKCQ3PZUS23BU7VWTGCYLS \
  | 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: ce1275a850dbf3496b61a7eb6998585cad82d26efddd9b22f2e786900ffcbdbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1fb31d0aa2634c43ae3603f2e641f6723881e24dafd6e85d6cc6dfbaae84a549",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-03T20:00:02Z",
    "title_canon_sha256": "1a244799aaaea492e29985b3cff107c9958e01c8f6f20b80fef06afef16f097c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0565",
    "kind": "arxiv",
    "version": 1
  }
}