Pith Number

pith:BUJ5EKKE

pith:2026:BUJ5EKKE3R5IJXI3AJ5BMVWDKM

not attested not anchored not stored refs pending

Minimizing the volume of globally hyperbolic anti-de Sitter 3-manifolds

Gabriele Mondello, Nicolas Tholozan

The volume of any maximal globally hyperbolic Cauchy-compact anti-de Sitter 3-manifold is at least π² times the absolute value of its Euler characteristic, achieved only for Fuchsian manifolds.

arxiv:2602.14806 v3 · 2026-02-16 · math.DG

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\usepackage{pith}
\pithnumber{BUJ5EKKE3R5IJXI3AJ5BMVWDKM}

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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.

Claims

C1strongest claim

the volume of a maximal globally hyperbolic Cauchy-compact anti-de Sitter 3-manifold M is at least π²|χ(M)|, and that this minimum value is attained if and only if M is Fuchsian.

C2weakest assumption

The manifold must be maximal, globally hyperbolic, and Cauchy-compact within anti-de Sitter space, relying on the standard definitions and properties of these structures from prior literature.

C3one line summary

The volume of maximal globally hyperbolic Cauchy-compact anti-de Sitter 3-manifolds is at least π²|χ(M)|, attained if and only if M is Fuchsian.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-03T01:05:48.902749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d13d22944dc7a84dd1b027a1656c353312ba6a71966ab05195ad470b98bc2ce

Aliases

arxiv: 2602.14806 · arxiv_version: 2602.14806v3 · doi: 10.48550/arxiv.2602.14806 · pith_short_12: BUJ5EKKE3R5I · pith_short_16: BUJ5EKKE3R5IJXI3 · pith_short_8: BUJ5EKKE

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/BUJ5EKKE3R5IJXI3AJ5BMVWDKM \
  | 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: 0d13d22944dc7a84dd1b027a1656c353312ba6a71966ab05195ad470b98bc2ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c93a37bb21b56d334454cc44101460b11d6ff5acf1eda13bda15f3996282fcbf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-02-16T14:58:44Z",
    "title_canon_sha256": "28f13652974efeef399294b81509cb1db4c35a134dca363a3332db81ce2cc12b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.14806",
    "kind": "arxiv",
    "version": 3
  }
}