Pith Number

pith:WLQXHES4

pith:2026:WLQXHES47AEUCZR2DWIEFTKO2A

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New Asymptotic Geometric Quantities in Riemannian Geometry and their Geometric applications

Jiabin Yin, Xiaoshang Jin

On complete noncompact Riemannian manifolds, volume entropy bounds infinity capacity, which bounds the infinity eigenvalue equal to the Maz'ya limit.

arxiv:2604.14600 v2 · 2026-04-16 · math.DG

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\usepackage{pith}
\pithnumber{WLQXHES47AEUCZR2DWIEFTKO2A}

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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

For any compact set Ω subset M, V(M) ≥ C(Ω) ≥ Λ(M) = M(M), where V is volume entropy, C infinity capacity, Λ infinity eigenvalue, and M the Maz'ya limit.

C2weakest assumption

The definitions of the infinity capacity, infinity eigenvalue, and Maz'ya limit are well-posed and the large-p limits exist on complete noncompact Riemannian manifolds.

C3one line summary

On complete noncompact Riemannian manifolds the volume entropy bounds the infinity capacity which bounds the infinity eigenvalue, which equals the Maz'ya limit, with equality under isoperimetric or curvature conditions.

Receipt and verification

First computed	2026-06-01T01:03:53.207685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2e173925cf80941663a1d9042cd4ed03b9b9ab4734a0307048ffe7f9ccfe093

Aliases

arxiv: 2604.14600 · arxiv_version: 2604.14600v2 · doi: 10.48550/arxiv.2604.14600 · pith_short_12: WLQXHES47AEU · pith_short_16: WLQXHES47AEUCZR2 · pith_short_8: WLQXHES4

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/WLQXHES47AEUCZR2DWIEFTKO2A \
  | 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: b2e173925cf80941663a1d9042cd4ed03b9b9ab4734a0307048ffe7f9ccfe093

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "874f009a396497bc70b6f577d8d5212a509bf7666ac896744f768875855c7e98",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-04-16T04:11:19Z",
    "title_canon_sha256": "ae05b4437cbfd1c414b3b322b7543b640f7ef442a96a9385d14359201b42ee79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.14600",
    "kind": "arxiv",
    "version": 2
  }
}