Draft · v0.2 · Unreviewed
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NADARASA
REDUCTION

A refutation-first quantum research notebook. The draft conjecture C1 currently sits in tension with all three of its own Selene experiments — and the data is on the page.

C1 · In Tension · G1 · G2 · G3

Arun Nadarasa · Selene emulator · 200 shots / slope

Draft Conjecture v0.2

Conditional on the Structured Reflection Promise (SRP), the dihedral hidden subgroup problem on ZN ⋊ Z2 admits a windowed Kuperberg sieve whose per-rung Birthday cost improves by √p when sliced into k coherent windows stitched by a classical glue layer.

Three Selene experiments test the load-bearing claims. Each currently shows tension. The draft is not retracted — the toys are wind-tunnel scale — but the refutation is what you see first.

Experimental Series · Refutation Status

3 draft + 5 frontier + 1 instrument
Ref. ID: S · G1

Modal Projection

Does the SRP class concentrate residue y mod p on 0 while violating slopes spread uniformly?

Selene · 200 shotsWorks when p | N
Ref. ID: S · G2

Two-Window Glue

Does the structural phase survive a mid-circuit measurement between coherent Kuperberg windows?

Selene · 200 shotsKernel can't test
Ref. ID: S · G3

√p Improvement

Does per-rung Birthday cost drop by √p across p ∈ {2,3,5}, or does it track the naive curve?

Selene · 200 shotsTension
Ref. ID: F · G4

Feed-Forward

Does Guppy's in-kernel `if measured_bit: rz(...)` actually fire inside a single compiled shot, no host round-trip?

Selene · 200 shotsVerified
Ref. ID: F · G5

Qubit Recycling

Can Selene run k ∈ {1,2,4} windows with only n + 1 live qubits by recycling the ancilla slot via measure?

Selene · 200 shotsVerified
Ref. ID: F · G6

Encoded Parity

Does a 3-qubit GHZ-encoded ancilla survive the naive single-rail parity probe at zero noise?

Selene · 200 shotsBlocked
Ref. ID: F · G6b

Transversal Probe

G6 revisited with a transversal probe across all three rails — 0/4800 disagreements, encoded-subspace share = 1.000.

Selene · 200 shotsVerified
Ref. ID: F · G7

Kernel Fusion

Does compile-once-run-many beat re-compiling per slope, and does Guppy accept parametric entry-point angles?

Selene · 200 shotsPartial
Ref. ID: P · G8

Amplitude Estimation

Canonical QPE on a 1-qubit eigenstate. m=4 estimation + 1 target, halfturn cphase + IQFT-no-swap. Worst |peak−a| = 0 bins across a ∈ {2,4,6,7}.

Selene · 200 shotsVerified
Ref. ID: P · G9

LCU Block-Encoding

PREP / SELECT / UNPREP on 1 prep + 1 data encoding H = c0·I + c1·X. Post-selected stats match closed form within 1.2% across an 8-row (θ × ψ) grid.

Selene · 200 shotsVerified
Ref. ID: P · G10

QSP Execution

Single-signal-qubit QSP with hand-chosen phases (d=3). Measured P(0) tracks the exact NumPy reference within |Δ|=0.0176 across 8 x-points.

Selene · 200 shotsPartial
Ref. ID: P · G11

Shor Period Decode

QPE/IQFT backend for r = ord₁₅(7) = 4. 100% of 2048 shots land on {0,4,8,12}; continued-fractions decode recovers r=4. Modular exponentiation stays open.

Selene · 200 shotsPartial
Ref. ID: F · Stream

Live Shot Replay

SSE drip of pre-recorded G4 shots into a converging in-browser histogram. Real in-loop Selene blocked by the edge runtime.

Selene · 200 shotsPartial

Posture

Read first

What this is

  • 01

    A draft conjecture with every [GAP] marked.

  • 02

    Real Guppy kernels compiled and run on the Selene emulator.

  • 03

    Three adversarial refutation experiments — data on the page.

  • 04

    A reproducible artifact — install, run, regenerate the JSON yourself.

What this is not

  • 01

    Not a proof. Not peer-reviewed.

  • 02

    Not a Quantinuum H-series hardware run. Selene is the emulator.

  • 03

    Not a speedup claim. The conjecture is conditional on SRP.

  • 04

    Not a priority claim. Chen 2024 is the methodological warning.

Four Frontiers

4 briefs

Analogy Wall

8 donor fields

Each donor field offers a verified historical mechanism. Hover for the transplant hypothesis; the full wall has sources and breakage notes.

April 1989 (Game Boy launch) – October 1990 (Game Gear)
Consumer electronics — Game Boy vs Game Gear
Stop chasing Regev's fully general LWE-to-lattice reduction. Pick a narrower lattice family (ideal lattices over a fixed cyclotomic with structured modulus q = 2^k + small) and prove a quantum sieve that exploits the structure. CRYSTALS-Kyber's NIST selection arguably already vindicates this — it met hard ceilings on key size, ciphertext expansion, and decapsulation cycles simultaneously.
1959 (Kind of Blue)
Music — Miles Davis modal improvisation
Replace the generic dihedral coset-combination step with a 'modal' restriction: only combine coset states whose labels lie in a fixed residue mode mod some small prime. The quantum walk lives inside one mode; the modes are stitched classically at the end. Total query count may drop because each modal walk has smaller effective spectral gap to fight.
1950s–present (Ellis–Delbrück onward); modern formalism Bull 2006
Biology — bacteriophage lysis timing
In Kuperberg's sieve, do not combine coset states greedily. Accumulate until a measurable information-theoretic density threshold is crossed (a quantum analogue of Bull's optimum), then combine in a synchronized batch. The batch exploits the higher density to produce a sharper label.
26 April 1956 (SS Ideal X, Newark → Houston); ISO 668 codified 1968
Logistics — Malcolm McLean's shipping container
A standard 'coset-state interface' (qubit register width, label register width, ancilla protocol) that dihedral, lattice, and isogeny sieves all conform to — so a single hardware-tuned combination subroutine improves all three at once.
1990s sleep-deprivation literature (Stampi, et al.)
Chronobiology — polyphasic / ultradian consolidation
Replace one monolithic Kuperberg sieve (O(2^√n) coset states held coherently) with many short 'windowed' sieves of size 2^(√n / k), with classical glue between windows. Each window fits well inside a coherence budget, and the classical glue is cheap. Total query count is comparable in theory; hardware feasibility is much better.
1978–1989
Software — Donald Knuth's TeX
Publish the draft as a proof scaffold with explicit [GAP] markers — not as a polished narrative. Collaborators (or future Arun) fill the gaps one by one, each a self-contained lemma. This trades immediate prestige for long-term composability.
October–December 1901, Dayton bicycle shop
Aviation — Wright brothers wind tunnel
Before claiming an asymptotic sieve improvement, run the toy on Selene at N = 16 or 32 and confirm empirical scaling. Selene IS the wind tunnel for quantum cryptanalysis — the falsifier, not the confirmer.
1950s–present
Manufacturing — Toyota Production System Andon cord
Each [GAP] marker in the draft has an explicit refutation experiment attached. If the experiment fails, that branch of the proof is dead and the draft is retracted (or branched) — fast. No silent rot.