Pith Number

pith:RYSVJNHQ

pith:2026:RYSVJNHQTJVDL6TVRQUS2B2B7F

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Uniform spectral gap of scl in $2$-orbifolds

Lvzhou Chen, Nicolaus Heuer

Compact hyperbolic 2-orbifolds have a uniform spectral gap for stable commutator length relative to peripheral subgroups.

arxiv:2604.21059 v2 · 2026-04-22 · math.GT · math.GR

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\usepackage{pith}
\pithnumber{RYSVJNHQTJVDL6TVRQUS2B2B7F}

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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 show a uniform spectral gap of stable commutator length for all compact hyperbolic 2-orbifolds relative to the peripheral subgroups. Except for the case of a sphere with three cone points, we have an explicit uniform gap 1/36.

C2weakest assumption

The assumption that the orbifolds are compact and hyperbolic, together with the existence of sufficiently many explicit quasimorphisms or pleated surfaces that achieve the gap without depending on the particular orbifold.

C3one line summary

Stable commutator length admits a uniform spectral gap of 1/36 relative to peripheral subgroups in all compact hyperbolic 2-orbifolds except the sphere with three cone points.

Receipt and verification

First computed	2026-05-28T01:04:40.644673Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e2554b4f09a6a35fa758c292d0741f9517e54e1fecc7c61ab19591d7187e11e

Aliases

arxiv: 2604.21059 · arxiv_version: 2604.21059v2 · doi: 10.48550/arxiv.2604.21059 · pith_short_12: RYSVJNHQTJVD · pith_short_16: RYSVJNHQTJVDL6TV · pith_short_8: RYSVJNHQ

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/RYSVJNHQTJVDL6TVRQUS2B2B7F \
  | 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: 8e2554b4f09a6a35fa758c292d0741f9517e54e1fecc7c61ab19591d7187e11e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cede8df943108355a84852d3740ff1afdc1bd421950b5413772c79b636f82208",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-04-22T20:02:16Z",
    "title_canon_sha256": "c47d97322942366926c216819e5412a673ddc00d83a592aae06e4439cb86d57e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.21059",
    "kind": "arxiv",
    "version": 2
  }
}