Pith Number

pith:ZHQYDRIK

pith:2026:ZHQYDRIKX2SDGSM37LPAUXPTEA

not attested not anchored not stored refs pending

Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature

Cuifang Si, Shicheng Xu

The Gromov-Hausdorff limit of orthonormal frame bundles over non-collapsed manifolds with bounded Ricci curvature has a singular set of codimension at least 4.

arxiv:2604.26399 v2 · 2026-04-29 · math.DG

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\usepackage{pith}
\pithnumber{ZHQYDRIKX2SDGSM37LPAUXPTEA}

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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

✓ 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 singular set has codimension ≥4 whose complement contains an open and dense C^{1,α}-Riemannian manifold

C2weakest assumption

The sequence consists of non-collapsed n-manifolds with two-sided bounds on Ricci curvature, and the frame bundles are equipped with an 'almost canonical metric' whose precise definition and properties are required for the limit to behave like a Ricci limit space.

C3one line summary

Gromov-Hausdorff limits of frame bundles of non-collapsed manifolds with two-sided bounded Ricci curvature have singular sets of codimension ≥4 whose complement is an open dense C^{1,α} Riemannian manifold.

Receipt and verification

First computed	2026-05-26T02:04:11.513779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9e181c50abea433499bfade0a5df32014c052047edde2d741de7351c23ea87e

Aliases

arxiv: 2604.26399 · arxiv_version: 2604.26399v2 · doi: 10.48550/arxiv.2604.26399 · pith_short_12: ZHQYDRIKX2SD · pith_short_16: ZHQYDRIKX2SDGSM3 · pith_short_8: ZHQYDRIK

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/ZHQYDRIKX2SDGSM37LPAUXPTEA \
  | 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: c9e181c50abea433499bfade0a5df32014c052047edde2d741de7351c23ea87e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fedd22df3b0ac223c3d1f628967787583ac7eeb1564e6dc8bce95d63d051306",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-04-29T08:08:34Z",
    "title_canon_sha256": "53e5b09c25ae42e012c9da838209dabf25e7d013dfc540e9bf89b5549a6a4cbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26399",
    "kind": "arxiv",
    "version": 2
  }
}