Pith Number

pith:NVZV3GYL

pith:2005:NVZV3GYLYK2EDHFRTCYI3UZOF3

not attested not anchored not stored refs pending

The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus

Tobias H. Colding, William P. Minicozzi II

arxiv:math/0509647 v2 · 2005-09-27 · math.DG · 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{NVZV3GYLYK2EDHFRTCYI3UZOF3}

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	2026-05-18T03:40:26.037525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d735d9b0bc2b4419cb198b08dd32e2ed9265e87a17fd6bb595a1cc243d1abbe

Aliases

arxiv: math/0509647 · arxiv_version: math/0509647v2 · doi: 10.48550/arxiv.math/0509647 · pith_short_12: NVZV3GYLYK2E · pith_short_16: NVZV3GYLYK2EDHFR · pith_short_8: NVZV3GYL

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/NVZV3GYLYK2EDHFRTCYI3UZOF3 \
  | 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: 6d735d9b0bc2b4419cb198b08dd32e2ed9265e87a17fd6bb595a1cc243d1abbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbee225a4c565645a401651d75fa615c9099cc3ad32823adff1d47e1830f9563",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2005-09-27T21:15:50Z",
    "title_canon_sha256": "77a626e79582b0b0fa08de20179f7e5ac648574312e3e2131e1cf3184f051144"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509647",
    "kind": "arxiv",
    "version": 2
  }
}