Analogy wall

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.

Cryptographic security is set by worst-case in the family; a speedup on a sub-family doesn't break a primitive unless deployments use that structure. Also: the Game Boy won partly because Henk Rogers bundled Tetris (April 1989) — an exogenous content win that no amount of engineering discipline guarantees in cryptography.

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.

If the hidden subgroup is not aligned with the chosen mode lattice, the modal restriction throws away the signal entirely. Need a promise that the hidden structure respects the mode, which restricts the cryptographic instances this attacks.

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.

Quantum coset states decohere while waiting; the density threshold must be reached before noise dominates. Bull's δ and r are stationary; the quantum 'environment' is the device noise profile, which is neither stationary nor measurable to high precision.

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.

ISO 668 works because container security is captured by geometry; cryptographic security is NOT captured by an API signature. Two functions with identical encapsulate(pk) -> (ct, ss) signatures can have radically different IND-CCA2 properties. Contents bleed through. McLean's steel and grain didn't interact; in crypto, algorithm and protocol interact structurally.

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.

The classical glue must not destroy quantum interference advantage. If gluing reduces to pure classical sieving, the quantum subroutine becomes a Grover-style polynomial speedup and the dihedral subexponential is lost.

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.

Academic incentive structures reward complete papers, not scaffolds. A draft published as gaps may not be cited until those gaps are closed by someone else, who then gets the credit.

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.

Aerodynamics scales via Reynolds number; quantum computers do NOT scale cleanly from NISQ to fault-tolerant. Current devices are noise-dominated above ~100 gate depth; a 16-bit lattice toy may say nothing about a 256-bit attack because error-correction overhead changes the effective algorithm.

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.

Refutation experiments themselves need correctness. A buggy Selene script can falsely 'refute' a correct lemma.