Pith Number

pith:YM2NPQW7

pith:2026:YM2NPQW7APMI2W7DSE4D7VUUCA

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The Hyperboloidal and Spacetime Positive Mass Theorem in All Dimensions

Marcus Khuri, Martin Lesourd, Sven Hirsch, Yiyue Zhang

The spacetime positive mass theorem holds in all dimensions for asymptotically flat and hyperboloidal initial data sets.

arxiv:2604.24746 v2 · 2026-04-27 · math.DG · gr-qc · math.AP

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\usepackage{pith}
\pithnumber{YM2NPQW7APMI2W7DSE4D7VUUCA}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

Using the recent work of Brendle--Wang on the Riemannian positive mass theorem, we prove the spacetime positive mass theorem for asymptotically flat and asymptotically hyperboloidal initial data sets in arbitrary dimension n.

C2weakest assumption

The argument assumes the validity of Brendle-Wang's Riemannian positive mass theorem together with the standard definitions of asymptotic flatness and asymptotic hyperboloidality for the initial data sets.

C3one line summary

The spacetime positive mass theorem holds for asymptotically flat and hyperboloidal initial data in all dimensions.

Cited by

1 paper in Pith

Positive mass theorem for initial data sets with arbitrary ends

Receipt and verification

First computed	2026-05-20T01:05:14.378471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c334d7c2df03d88d5be391383fd694103c77be860c93f7092178aff6ec753755

Aliases

arxiv: 2604.24746 · arxiv_version: 2604.24746v2 · doi: 10.48550/arxiv.2604.24746 · pith_short_12: YM2NPQW7APMI · pith_short_16: YM2NPQW7APMI2W7D · pith_short_8: YM2NPQW7

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/YM2NPQW7APMI2W7DSE4D7VUUCA \
  | 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: c334d7c2df03d88d5be391383fd694103c77be860c93f7092178aff6ec753755

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fea993cb3d68ce7efd3b31603457806d9d782fc617b279d0edcb32b181c5a528",
    "cross_cats_sorted": [
      "gr-qc",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-04-27T17:48:01Z",
    "title_canon_sha256": "2d512ab8b655018807b6df7eca4adcb4ac48837ea4baec7a7279a1c1a8b259b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.24746",
    "kind": "arxiv",
    "version": 2
  }
}