Pith Number

pith:CVRPHM4E

pith:2024:CVRPHM4EH5CI7NPHV2VCZSOZWD

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Some splitting and rigidity results for sub-static spaces

Allan Freitas, Giulio Colombo, Luciano Mari, Marco Rigoli

Sub-static systems split locally and globally when suitable compact minimal hypersurfaces are present.

arxiv:2412.05238 v3 · 2024-12-06 · math.DG

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Record completeness

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4 Citations open

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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

Local and global splitting theorems hold for sub-static systems assuming suitable compact minimal hypersurfaces; boundary integral inequalities extend and improve prior results of Chruściel and Boucher-Gibbons-Horowitz even in the vacuum case; a Liouville theorem holds for the sigma-model coupled system allowing positively curved targets, generalizing Reiris.

C2weakest assumption

The existence of suitable compact minimal hypersurfaces is assumed to obtain the splitting theorems; the precise definition of the sub-static system and the sigma-model coupling must satisfy the structural equations stated in the paper for the inequalities and Liouville result to apply.

C3one line summary

Establishes local and global splitting theorems under minimal hypersurface assumptions, derives improved boundary inequalities for sub-static systems, and proves a Liouville theorem allowing positive curvature in sigma-model targets.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-28T02:04:39.559795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1562f3b3843f448fb5e7aeaa2cc9d9b0c25fc8105cc289d2cdeb46c4acc6f222

Aliases

arxiv: 2412.05238 · arxiv_version: 2412.05238v3 · doi: 10.48550/arxiv.2412.05238 · pith_short_12: CVRPHM4EH5CI · pith_short_16: CVRPHM4EH5CI7NPH · pith_short_8: CVRPHM4E

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/CVRPHM4EH5CI7NPHV2VCZSOZWD \
  | 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: 1562f3b3843f448fb5e7aeaa2cc9d9b0c25fc8105cc289d2cdeb46c4acc6f222

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33ade4c051a9bd2aef2d41be5b39e56ca4ffe6ac7a3b1b16b828f9dd2888a678",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2024-12-06T18:14:42Z",
    "title_canon_sha256": "bd2710839b1fc0c4ae4a31e6bbe0e04b355183b388e9d3752c094e0e8c55dde2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.05238",
    "kind": "arxiv",
    "version": 3
  }
}