Pith Number

pith:2F6V2QYN

pith:2026:2F6V2QYNBOCBY7BKUWHWDP5JOC

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On positivity of the limit F-signature

Suchitra Pande, Yuchen Liu

The limit of F-signatures for KLT singularities stays bounded away from zero in three dimensions for non-weakly exceptional cases and for smooth hypersurfaces of very low degree.

arxiv:2605.16636 v1 · 2026-05-15 · math.AG · math.AC

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\usepackage{pith}
\pithnumber{2F6V2QYNBOCBY7BKUWHWDP5JOC}

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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

We prove that this conjecture holds for three-dimensional non-weakly exceptional singularities by an inductive argument. We also prove that the conjecture holds for smooth hypersurfaces of very low degree by constructing isotrivial normal toric degenerations.

C2weakest assumption

The inductive argument for three-dimensional non-weakly exceptional singularities and the construction of isotrivial normal toric degenerations for low-degree hypersurfaces both rely on the existence of suitable birational models or degenerations whose F-signature behavior can be controlled uniformly in p; this modeling choice is invoked when the authors reduce the problem via K-stability-inspired techniques.

C3one line summary

The authors establish the Carvajal-Rojas-Schwede-Tucker conjecture on positive limiting F-signature for two specific classes of complex KLT singularities using inductive arguments and toric degenerations inspired by K-stability.

References

300 extracted · 300 resolved · 1 Pith anchors

[1] Zhuang, Ziquan , TITLE =. Invent. Math. , FJOURNAL =. 2021 , NUMBER =. doi:10.1007/s00222-021-01046-0 , URL = 2021 · doi:10.1007/s00222-021-01046-0

[2] Paul, Sean Timothy and Tian, Gang , title =. 2006 2006

[3] Starr, Jason , title =. 2006 2006

[4] Ilten, Nathan and Lautsch, Oscar , TITLE =. Canad. Math. Bull. , FJOURNAL =. 2023 , NUMBER =. doi:10.4153/s0008439523000309 , URL = 2023 · doi:10.4153/s0008439523000309

[5] Li, Chi and Liu, Yuchen , TITLE =. Adv. Math. , FJOURNAL =. 2019 , PAGES =. doi:10.1016/j.aim.2018.10.038 , URL = 2019 · doi:10.1016/j.aim.2018.10.038

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:33.579551Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d17d5d430d0b841c7c2aa58f61bfa970b1074c814660931334b3a5a250c43116

Aliases

arxiv: 2605.16636 · arxiv_version: 2605.16636v1 · doi: 10.48550/arxiv.2605.16636 · pith_short_12: 2F6V2QYNBOCB · pith_short_16: 2F6V2QYNBOCBY7BK · pith_short_8: 2F6V2QYN

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/2F6V2QYNBOCBY7BKUWHWDP5JOC \
  | 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: d17d5d430d0b841c7c2aa58f61bfa970b1074c814660931334b3a5a250c43116

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd95b43075ae2adc3b62ee36b903d91442ec9b4c44920c0a65e884a9513c3ee9",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-15T21:06:09Z",
    "title_canon_sha256": "84480bff120d072257e8eb201faad9851ab4d4d10abab004f69105d72a52a4f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16636",
    "kind": "arxiv",
    "version": 1
  }
}