Pith Number

pith:TM7ZVAZY

pith:2026:TM7ZVAZYJSPQOUJ6ORBVITDEX6

not attested not anchored not stored refs pending

Fine projection complex and subsurface homeomorphisms with positive stable commutator length

Yongsheng Jia, Yusen Long

Some surface homeomorphisms that preserve a non-sporadic essential subsurface or a once-bordered torus have positive stable commutator length inside the identity component of the homeomorphism group of a closed surface.

arxiv:2604.12974 v2 · 2026-04-14 · math.GT · math.DS · math.GR

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\usepackage{pith}
\pithnumber{TM7ZVAZYJSPQOUJ6ORBVITDEX6}

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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

some surface homeomorphisms preserving a non-sporadic essential subsurface or an essential subsurface homeomorphic to a once-bordered torus can have positive stable commutator length in Homeo_0(S_g)

C2weakest assumption

The family of unbounded quasi-trees exists with the stated cobounded isometric action for every closed oriented surface of genus g >= 2, and the projection complex construction succeeds without the usual finiteness conditions on the subsurface data.

C3one line summary

A finiteness-free projection complex yields unbounded quasi-trees for Homeo_0(S_g) with cobounded isometric actions, proving positive scl for subsurface-preserving homeomorphisms.

Receipt and verification

First computed	2026-05-25T02:02:15.250862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b3f9a83384c9f07513e7443544c64bf9e27010ba25a7158ec7f62be8fb21f95

Aliases

arxiv: 2604.12974 · arxiv_version: 2604.12974v2 · doi: 10.48550/arxiv.2604.12974 · pith_short_12: TM7ZVAZYJSPQ · pith_short_16: TM7ZVAZYJSPQOUJ6 · pith_short_8: TM7ZVAZY

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/TM7ZVAZYJSPQOUJ6ORBVITDEX6 \
  | 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: 9b3f9a83384c9f07513e7443544c64bf9e27010ba25a7158ec7f62be8fb21f95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fc5b675b54567ed0445281818fb68807b9f5450e0bb8e5e794696260aad9b25",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-04-14T17:08:10Z",
    "title_canon_sha256": "d147b15c64deb46ed8be28b7afaeda1c6679a989ea0fa9c4a660e33e14f09c46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.12974",
    "kind": "arxiv",
    "version": 2
  }
}