Pith Number

pith:4V7R7AL4

pith:2026:4V7R7AL4USRQQMBW74FDGVBUFR

not attested not anchored not stored refs resolved

Boundary-Aware QFT Block-Encoding of Fractional Laplacians

Sina Kazemian, Younes Javanmard

Zero-padding a state into a larger QFT register recovers the open-boundary fractional Laplacian from a circulant encoding up to a kernel-tail error.

arxiv:2605.16749 v1 · 2026-05-16 · quant-ph

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\usepackage{pith}
\pithnumber{4V7R7AL4USRQQMBW74FDGVBUFR}

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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

The resulting compressed block satisfies P_{N→M}^† Ã^{(M)}_{α,h} P_{N→M} = A^{(N)}_{α,h} + E^{(M)}, where E^{(M)} is controlled by the tail of the semi-discrete convolution kernel.

C2weakest assumption

That zero-padding into an M-point register followed by compression recovers the open-boundary Toeplitz action up to an error term whose size is governed solely by the kernel tail (abstract, section on the aliasing identity).

C3one line summary

The paper presents a zero-padding method to make QFT block-encodings match open-boundary Toeplitz truncations of fractional Laplacians instead of periodic circulant surrogates.

References

42 extracted · 42 resolved · 1 Pith anchors

[1] R. Metzler and J. Klafter, Phys. Rep.339, 1 (2000) 2000

[2] Applebaum,L´ evy Processes and Stochastic Calculus, 2nd ed 2009

[3] N. Laskin, Phys. Rev. E66, 056108 (2002) 2002

[4] S. Duo, H.-W. van Wyk, and Y. Zhang, J. Comput. Phys.355, 233 (2018) 2018

[5] Y. Huang and A. Oberman, SIAM J. Numer. Anal.52, 3056 (2014) 2014

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:19.596548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e57f1f817ca4a3083036ff0a3354342c4bd468ee73b7920397e6c9cbeb9f1347

Aliases

arxiv: 2605.16749 · arxiv_version: 2605.16749v1 · doi: 10.48550/arxiv.2605.16749 · pith_short_12: 4V7R7AL4USRQ · pith_short_16: 4V7R7AL4USRQQMBW · pith_short_8: 4V7R7AL4

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/4V7R7AL4USRQQMBW74FDGVBUFR \
  | 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: e57f1f817ca4a3083036ff0a3354342c4bd468ee73b7920397e6c9cbeb9f1347

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "529534859ffee6cf071dce8a1ba7a522aaa95a252ca6396fb4dc2826c18a1799",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-16T02:06:47Z",
    "title_canon_sha256": "534f247259bee13164317d67d71e494f19fd7e7992a5e918c510721601d3c269"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16749",
    "kind": "arxiv",
    "version": 1
  }
}