# Milestones — Near-Term with Success Criteria

**Last updated:** 2026-07-03

## M1: 3-SAT Spectral Test [NEXT]
**Goal:** Build clause-incidence matrix for a small 3-SAT instance,
compute eigenvalue spectrum, check if satisfiability is spectrally
distinguishable.

**Success criteria:**
- Build matrix for ≥3 different 3-SAT instances (satisfiable + unsatisfiable)
- Compute eigenvalue spectra
- Report: can the spectra distinguish SAT from UNSAT?

**If YES:** First NP-complete data point for the octagon. P=NP route
strengthened. Write up as measurement.

**If NO:** Natural P≠NP witness on the canonical NP-complete problem.
The octagon has a limit. Write up as measurement.

**Estimated effort:** 2-4 hours (Python script, small instances)

## M2: cmix Weight Matrix SVD [NEXT]
**Goal:** Extract cmix's 23×461 layer-0 weight matrix, compute SVD,
check if top-5 singular values capture 95% of compression quality.

**Success criteria:**
- Modify cmix to dump weight matrix after training on enwik8
- Compute SVD (23 singular values)
- Rank-k approximation: does k=5 preserve ≥95% of compression ratio?

**If YES:** Search space reduces from 23×461 to 5D. The octagon
works for cmix (linear system, rich invariants).

**If NO:** cmix's weight structure is genuinely full-rank. No
spectral shortcut for context mixing.

**Estimated effort:** 4-8 hours (C++ modification + SVD computation)

## M3: Quandela SLOS Eigenvalue Product Verification [NEXT]
**Goal:** Verify that eigenvalue products of the Sidon crossing
matrix match the full SLOS output distribution.

**Success criteria:**
- Compute eigenvalue products for the 4-block Sidon matrix
- Compare against SLOS K=2 output
- Report: do they match?

**If YES:** SLOS shortcut confirmed for linear optical. Replace SLOS
with eigenvalue products (400x speedup on block-diagonal circuits).

**If NO:** The K=1 spectrum doesn't determine K=2 output (despite
linearity). Need to find what's missing.

**Estimated effort:** 2-4 hours (Python + Perceval)

## M4: CRT-Coprime Hachimoji Pairing Rules [FUTURE]
**Goal:** Design 8 hachimoji bases with 4 coprime pairing rules.
Verify CRT reconstruction works.

**Success criteria:**
- 4 pairing rules with gcd(L_i, L_j) = 1 for all i≠j
- Each base has a unique partner under each rule
- CRT lift reconstructs the base index from 4 residues

**If YES:** The DNA-CRT bridge is designed. Next: simulate
hybridization energy landscape.

**Estimated effort:** 4-8 hours (design + verification)

## M5: Reaction Prime Existence Proof [FUTURE]
**Goal:** Prove (or disprove) that every DNA computation factors
into reaction-primes.

**Success criteria:**
- Define the reaction algebra formally (generators, relations)
- Prove existence of factorization (or find a counterexample)
- If existence: prove uniqueness (or find non-unique factorization)

**If EXISTS + UNIQUE:** Reaction-prime framework is sound. The
conservation law = FTA for computation.

**If NON-EXISTENT or NON-UNIQUE:** The framework needs refinement.
The prime decomposition isn't universal.

**Estimated effort:** 8-16 hours (Lean formalization)