Pith Number

pith:Q3BEO6GS

pith:2026:Q3BEO6GS24QYWJENHS3D4267IR

not attested not anchored not stored refs resolved

From Hilbert's Tenth Problem to Quantum Speedup: Explicit Oracles for Bounded Diophantine Systems

Gabriel Escrig, M. A. Martin-Delgado

A reversible quantum oracle framework solves bounded Diophantine equations with quadratic speedup and O((n + d²) log N) qubits.

arxiv:2605.13980 v1 · 2026-05-13 · quant-ph

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\usepackage{pith}
\pithnumber{Q3BEO6GS24QYWJENHS3D4267IR}

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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

✓ 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 overall spatial complexity is bounded by q = O((n + d²)log₂ N) logical qubits ... quadratic speedup over classical exhaustive search, whether retrieving a unique assignment or dynamically enumerating an unknown number of solutions.

C2weakest assumption

That the in-place two's complement arithmetic and routing operations into a single recycled accumulator can be synthesized gate-by-gate without introducing hidden overhead or non-reversibility for arbitrary polynomial degrees and coefficient sizes.

C3one line summary

Explicit reversible quantum oracles for bounded Diophantine systems achieve quadratic speedup with qubit count O((n + d²) log₂ N) and Toffoli depth O(q²).

References

39 extracted · 39 resolved · 3 Pith anchors

[1] Let the variablex i be encoded in aw- bit register,|x i,w−1

[2] Instead of a variable controlling its own shifted addition, the qubits ofx i act as controls for the logically shifted additions of the dis- joint registerx j

[3] Specifically, we adopt the BBHT search strategy [22]

[4] Quantum Counting Alternatively, when the primary goal is to deter- mine the exact number of solutions, the operatorGis integrated into a Quantum Counting framework [23]. This framework interpretsGas a 2024

[5] G. H. Hardy and E. M. Wright,An Introduction to the Theory of Numbers, 4th ed. (Oxford University Press, 1975) 1975

Receipt and verification

First computed	2026-05-17T23:39:13.387462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86c24778d2d7218b248d3cb63e6bdf446ba8fd9ad6e0079bdb77ebd4779567f3

Aliases

arxiv: 2605.13980 · arxiv_version: 2605.13980v1 · doi: 10.48550/arxiv.2605.13980 · pith_short_12: Q3BEO6GS24QY · pith_short_16: Q3BEO6GS24QYWJEN · pith_short_8: Q3BEO6GS

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/Q3BEO6GS24QYWJENHS3D4267IR \
  | 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: 86c24778d2d7218b248d3cb63e6bdf446ba8fd9ad6e0079bdb77ebd4779567f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b5e600c58b8ca3c537b0d3ea5a0ee86981c5b76710e95d8d77a95e6db77c6f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-13T18:01:01Z",
    "title_canon_sha256": "83766f2db151ee9544b04b2cbd08f1152ef565d48245ae2f50aba990a04005c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13980",
    "kind": "arxiv",
    "version": 1
  }
}