Pith Number

pith:36ZOXV2M

pith:2026:36ZOXV2MLGZBV5PU3HHXWTGW7K

not attested not anchored not stored refs resolved

Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow

Hanbing Fang, Yu Li

A Lojasiewicz inequality for the pointed W-entropy establishes strong uniqueness of generalized cylindrical tangent flows in Ricci flow.

arxiv:2605.17001 v1 · 2026-05-16 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{36ZOXV2MLGZBV5PU3HHXWTGW7K}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

We establish a Lojasiewicz inequality for the pointed W-entropy in Ricci flow under the assumption that the geometry near the base point is close to a generalized cylinder R^k × N^{n-k}, where N is an Einstein manifold with obstruction of order three satisfying a suitable spectral condition. As an application, we prove the strong uniqueness of generalized cylindrical tangent flows. Furthermore, we show that the subset S^k_qc(N) is horizontally parabolic k-rectifiable.

C2weakest assumption

The geometry near the base point is close to a generalized cylinder R^k × N^{n-k}, where N is an Einstein manifold with obstruction of order three satisfying a suitable spectral condition (invoked in the statement of the Lojasiewicz inequality and its applications to uniqueness and rectifiability).

C3one line summary

Proves Lojasiewicz inequality for W-entropy near generalized cylinders in Ricci flow, yielding strong uniqueness of tangent flows and horizontal parabolic k-rectifiability of the corresponding singularity set.

References

115 extracted · 115 resolved · 1 Pith anchors

[1] Annals of Mathematics , volume=

[2] Cheeger, J. and Tian, G. , journal=. On the cone structure at infinity of

[3] Sesum, N. , journal=. Linear and dynamical stability of

[4] Colding, T. H. and Minicozzi II, W. P. , journal=. Uniqueness of blowups and. 2015 , publisher= 2015

[5] Colding, T. H. and Minicozzi II, W. P. , title =. Publications Mathématiques de l'IHÉS , year =. doi:10.1007/s10240-025-00145-3 , url = · doi:10.1007/s10240-025-00145-3

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:35.377161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfb2ebd74c59b21af5f4d9cf7b4cd6fa8806176a7324feb5346eebc016ef2599

Aliases

arxiv: 2605.17001 · arxiv_version: 2605.17001v1 · doi: 10.48550/arxiv.2605.17001 · pith_short_12: 36ZOXV2MLGZB · pith_short_16: 36ZOXV2MLGZBV5PU · pith_short_8: 36ZOXV2M

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/36ZOXV2MLGZBV5PU3HHXWTGW7K \
  | 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: dfb2ebd74c59b21af5f4d9cf7b4cd6fa8806176a7324feb5346eebc016ef2599

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7aef4169569e4e9192d17365255e19dcbf98131f70bcd66b53ce4fe3c39a6e1e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-16T13:54:24Z",
    "title_canon_sha256": "5da0dd1ee21e10f6a935ac6440ba5bf5abdb6ae35bbbf1c7d102fb12614c86f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17001",
    "kind": "arxiv",
    "version": 1
  }
}