Pith Number

pith:PIIYSDP7

pith:2010:PIIYSDP7OLOZZKUEZZHCKWATDV

not attested not anchored not stored refs pending

On parabolicity and area growth of minimal surfaces

Robert W. Neel

arxiv:1004.4544 v2 · 2010-04-26 · math.DG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PIIYSDP7OLOZZKUEZZHCKWATDV}

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	2026-05-18T03:11:24.344098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a11890dff72dd9caa84ce4e2558131d7322e396901be3c3939ebaf62f36fe87

Aliases

arxiv: 1004.4544 · arxiv_version: 1004.4544v2 · doi: 10.48550/arxiv.1004.4544 · pith_short_12: PIIYSDP7OLOZ · pith_short_16: PIIYSDP7OLOZZKUE · pith_short_8: PIIYSDP7

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/PIIYSDP7OLOZZKUEZZHCKWATDV \
  | 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: 7a11890dff72dd9caa84ce4e2558131d7322e396901be3c3939ebaf62f36fe87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c19a949e1ee690c072bc66b6564898b62ba16eba2943669538e4a7360045985a",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-04-26T14:49:08Z",
    "title_canon_sha256": "035b1fc99135c3afd3582a527b741bba62b69f16086f5bbf0b52c4b2952124d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4544",
    "kind": "arxiv",
    "version": 2
  }
}