Pith Number

pith:MF7GZAXF

pith:2012:MF7GZAXFLGQ3U3RJLPBLAEMKUW

not attested not anchored not stored refs pending

Min-max minimal hypersurface in $(M^{n+1}, g)$ with $Ric_{g}>0$ and $2\leq n\leq 6$

Xin Zhou

arxiv:1210.2112 v2 · 2012-10-07 · 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{MF7GZAXFLGQ3U3RJLPBLAEMKUW}

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	2026-05-18T03:42:45.812910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

617e6c82e559a1ba6e295bc2b0118aa5881560bc0430464c9245ab814845b3ef

Aliases

arxiv: 1210.2112 · arxiv_version: 1210.2112v2 · doi: 10.48550/arxiv.1210.2112 · pith_short_12: MF7GZAXFLGQ3 · pith_short_16: MF7GZAXFLGQ3U3RJ · pith_short_8: MF7GZAXF

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/MF7GZAXFLGQ3U3RJLPBLAEMKUW \
  | 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: 617e6c82e559a1ba6e295bc2b0118aa5881560bc0430464c9245ab814845b3ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5895583859ecae13620f2a5a0285c52d707a4bfbf224eb13761dc2e7354d219",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-10-07T22:18:58Z",
    "title_canon_sha256": "41183065387ea4853049382f1a1908cd6d3e488dcf8421ee58d9789ba835fe57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2112",
    "kind": "arxiv",
    "version": 2
  }
}