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.
Arun Nadarasa · Selene emulator · 200 shots / slope
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 instrumentModal Projection
Does the SRP class concentrate residue y mod p on 0 while violating slopes spread uniformly?
Two-Window Glue
Does the structural phase survive a mid-circuit measurement between coherent Kuperberg windows?
√p Improvement
Does per-rung Birthday cost drop by √p across p ∈ {2,3,5}, or does it track the naive curve?
Feed-Forward
Does Guppy's in-kernel `if measured_bit: rz(...)` actually fire inside a single compiled shot, no host round-trip?
Qubit Recycling
Can Selene run k ∈ {1,2,4} windows with only n + 1 live qubits by recycling the ancilla slot via measure?
Encoded Parity
Does a 3-qubit GHZ-encoded ancilla survive the naive single-rail parity probe at zero noise?
Transversal Probe
G6 revisited with a transversal probe across all three rails — 0/4800 disagreements, encoded-subspace share = 1.000.
Kernel Fusion
Does compile-once-run-many beat re-compiling per slope, and does Guppy accept parametric entry-point angles?
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}.
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.
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.
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.
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.
Posture
Read firstWhat 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 briefsDihedral / non-abelian HSP
The structural cousin of Shor that has resisted polynomial-time quantum attack for 25 years.
Lattice / LWE
Where every NIST post-quantum standard rests, and where the last serious quantum attack visibly failed at extraction, not preparation.
Isogeny
Half the field collapsed classically in 2022. What survives is non-commutative, and Kuperberg can't reach it cleanly.
Code-based (McEliece, BIKE, HQC)
The most conservative PQC pillar. Quantum gives only modest sub-Grover ISD improvements — and even those need QRAM.
Analogy Wall
8 donor fieldsEach donor field offers a verified historical mechanism. Hover for the transplant hypothesis; the full wall has sources and breakage notes.