Pith Number

pith:X6PE2YDM

pith:2008:X6PE2YDMW2KZHTJGVMQPJX3XMG

not attested not anchored not stored refs pending

Examples of stable embedded minimal spheres without area bounds

Joel I. Kramer

arxiv:0812.3841 v2 · 2008-12-19 · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X6PE2YDMW2KZHTJGVMQPJX3XMG}

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.

Cited by

1 paper in Pith

Closed minimal surfaces of index one in Riemannian manifolds

Receipt and verification

First computed	2026-07-04T15:49:05.853402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf9e4d606cb69593cd26ab20f4df7761b2f4ac88624734516092fe0cb6130f51

Aliases

arxiv: 0812.3841 · arxiv_version: 0812.3841v2 · doi: 10.48550/arxiv.0812.3841 · pith_short_12: X6PE2YDMW2KZ · pith_short_16: X6PE2YDMW2KZHTJG · pith_short_8: X6PE2YDM

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/X6PE2YDMW2KZHTJGVMQPJX3XMG \
  | 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: bf9e4d606cb69593cd26ab20f4df7761b2f4ac88624734516092fe0cb6130f51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84a4c31601d9bc0e1509c506e1134f0756d75f9873ec74f056c1429592590754",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2008-12-19T19:13:13Z",
    "title_canon_sha256": "4a60f38380261ef076998a5496e5ca461f913849843471bbb4520a7fdc5c3d3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.3841",
    "kind": "arxiv",
    "version": 2
  }
}