Pith Number

pith:HWISG632

pith:2026:HWISG632UTNZXNMVPTXVIW2O2T

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Linear response for Sinai billiards with small holes

Giovanni Canestrari

The conditional survival probability measure for a Sinai billiard with a small boundary hole is differentiable at zero hole size, with an explicit derivative.

arxiv:2604.19671 v2 · 2026-04-21 · math.DS

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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 that the conditional survival probability measure for a Sinai billiard with a small hole on the boundary of the table is differentiable with respect to the size t of the hole at t = 0 and we compute the derivative.

C2weakest assumption

The Sinai billiard satisfies the standard hyperbolicity, ergodicity, and mixing properties needed for the conditional survival probability measure to exist and for linear response techniques to apply at the zero-hole limit.

C3one line summary

The conditional survival probability measure for a Sinai billiard with a small hole is differentiable with respect to hole size at zero, and the derivative is computed.

Receipt and verification

First computed	2026-05-25T02:01:20.793443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d91237b7aa4db9bb5957cef545b4ed4d49d8499dbb5fbbfbe44eed085398260

Aliases

arxiv: 2604.19671 · arxiv_version: 2604.19671v2 · doi: 10.48550/arxiv.2604.19671 · pith_short_12: HWISG632UTNZ · pith_short_16: HWISG632UTNZXNMV · pith_short_8: HWISG632

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HWISG632UTNZXNMVPTXVIW2O2T \
  | 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: 3d91237b7aa4db9bb5957cef545b4ed4d49d8499dbb5fbbfbe44eed085398260

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40b7452f64f2557fd793ace39ad333e4768a5125c1976ba741564a3d81fc22b4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-04-21T16:51:52Z",
    "title_canon_sha256": "da90617b048a85a628ddc0983343e10a0c737a18225406710a2b046f16137d40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.19671",
    "kind": "arxiv",
    "version": 2
  }
}