Pith Number

pith:ZD3E6YGY

pith:2026:ZD3E6YGYON6EXRJTPRVYWM3AL4

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Geometric uncertainty principles for Schr\"odinger evolutions on negatively curved manifolds

Changxing Miao, Ruihan Zhou, Yilin Song

Schrödinger solutions with Gaussian decay at two times are identically zero on asymptotic hyperbolic manifolds.

arxiv:2605.17233 v1 · 2026-05-17 · math.AP · math.DG

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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 a similar rigidity persists in the setting of hyperbolic geometry, despite the absence of translation invariance and Fourier representation.

C2weakest assumption

The manifolds are Cartan-Hadamard and endowed with an asymptotic hyperbolic metric, allowing the construction of a new weight function and mollifier via the exponential map and Jacobi fields that yield the required Carleman estimates and logarithmic convexity.

C3one line summary

The paper establishes a Hardy-type uncertainty principle showing Gaussian decay at two times implies the solution is identically zero for Schrödinger equations on Cartan-Hadamard manifolds with asymptotic hyperbolic metrics.

References

24 extracted · 24 resolved · 0 Pith anchors

[1] Almgren, Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents, inMinimal submanifolds and geodesics (Proc 1977

[2] Anderson, Hardy’s uncertainty principle on hyperbolic spaces, Bull 2002

[3] Anderson,L p versions of Hardy type uncertainty principle on hyperbolic space, Proc 2003

[4] J.-P. Anker and V. Pierfelice, Nonlinear Schr¨ odinger equation on real hyperbolic spaces, Ann. Inst. H. Poincar´ e C Anal. Non Lin´ eaire26(2009), no. 5, 1853-1869. 3 2009

[5] Banica, The nonlinear Schr¨ odinger equation on hyperbolic space, Comm 2007

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:46.727154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8f64f60d8737c4bc5337c6b8b33605f182a55df32e89d95cc48a3723f1362eb

Aliases

arxiv: 2605.17233 · arxiv_version: 2605.17233v1 · doi: 10.48550/arxiv.2605.17233 · pith_short_12: ZD3E6YGYON6E · pith_short_16: ZD3E6YGYON6EXRJT · pith_short_8: ZD3E6YGY

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZD3E6YGYON6EXRJTPRVYWM3AL4 \
  | 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: c8f64f60d8737c4bc5337c6b8b33605f182a55df32e89d95cc48a3723f1362eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4791534c74d5c5bf559f1a78a6a08ff9d3a0b35fc60c2e168a6d99f8cc85a07",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-17T03:01:00Z",
    "title_canon_sha256": "14bf027e79644a9acf16e99a5fc790dacaacc0c3c95d9f178fb079f4c0f51e66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17233",
    "kind": "arxiv",
    "version": 1
  }
}