Pith Number

pith:MSNMBTRR

pith:2010:MSNMBTRRMEWPP73TODCJ5B6ZX5

not attested not anchored not stored refs pending

Optimal estimates for the gradient of harmonic functions in the unit disk

David Kalaj, Marijan Markovic

arxiv:1012.3153 v2 · 2010-12-14 · 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{MSNMBTRRMEWPP73TODCJ5B6ZX5}

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	2026-05-18T04:25:02.901049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

649ac0ce31612cf7ff7370c49e87d9bf5dd555f1a1ce636e5e476d47f43f81b0

Aliases

arxiv: 1012.3153 · arxiv_version: 1012.3153v2 · doi: 10.48550/arxiv.1012.3153 · pith_short_12: MSNMBTRRMEWP · pith_short_16: MSNMBTRRMEWPP73T · pith_short_8: MSNMBTRR

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/MSNMBTRRMEWPP73TODCJ5B6ZX5 \
  | 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: 649ac0ce31612cf7ff7370c49e87d9bf5dd555f1a1ce636e5e476d47f43f81b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e038915622a2cf950d2deb02a3fcbf23f5538152d451b6342de308eb030057f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2010-12-14T20:08:05Z",
    "title_canon_sha256": "57a40ac8b2a0eb2080c5183675c4413ce2061754fc1e0acaee016b4b2a474510"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3153",
    "kind": "arxiv",
    "version": 2
  }
}