Lean 4 · Formal Verification · Theophysics
Machine-verified formal proofs backing every structural claim in the framework. The Lean 4 kernel doesn't care about your argument. Either the proof compiles or it doesn't.
Lean 4 is a formal proof assistant used by mathematicians at Microsoft Research, DeepMind, and leading universities.
When a proof compiles in Lean, it means the logical structure has been verified by the kernel — a small, trusted core that checks every step.
No human judgment is involved in the verification. No rhetoric. No interpretation. The machine says yes or no.
Every theorem listed below compiled clean. Zero sorry — Lean's marker for "I skipped this step." Nothing was skipped. Nothing was assumed without proof.
Lean verifies logical structure, not empirical truth. It proves: "Given these definitions and axioms, these theorems follow by logical necessity." It does not prove that the ten laws are true descriptions of reality, that each physics/theology pair is isomorphic to the physical world, or that the framework's theological claims are correct.
What it does prove: the internal architecture is formally consistent, the structural claims hold under any algebra satisfying the axioms, and no one can dismiss this as "just analogies." The algebra is real. The proofs are machine-checked.
The structural backbone. These theorems hold for any system satisfying the coherence axioms — not just specific numbers, but universally.
listProd_eq_zero_iff
If any one of the ten coherence factors goes to zero, the whole system collapses. Conversely, if the system collapses, at least one factor was zero.
cannot_rescue_zero
No internal operation can rescue a system that has collapsed to zero. External input is required.
no_zero_divisors
If the product of two factors is zero, at least one of them must be zero. No hidden collapse — every failure is traceable.
grace_idempotent
Grace applied twice equals grace applied once. You don't need to be saved twice.
grace_not_invertible
Grace cannot be reversed. There is no operation that undoes what grace does. Irreversible by logical necessity.
grace_event_after_constructive
Every grace event results in the constructive regime. Destructive becomes constructive. Constructive stays constructive.
trinity_isomorphism
The internal structure of Maxwell's equations — three distinct operators, one unified field, mutual generation without reduction — is structurally isomorphic to the Trinitarian relation.
math_before_matter
Mathematical structure is ontologically prior to physical instantiation. The blueprint precedes the house.
good_is_ontological
Goodness is not imposed on a neutral substrate — it is a structural property of coherent systems. This theorem appears in every paper.
cross_uniqueness
When α=0 (third party pays) and the judge is the payer, justice and mercy are both maximal simultaneously. This configuration is unique. There is exactly one point where both are satisfied without contradiction.
zero_preserving_cannot_rescue
A justice operator that preserves zero cannot rescue a collapsed state. Internal correction preserves the problem.
evil_requires_good
Evil cannot exist independently. It is structurally parasitic on good — it requires a coherent substrate to corrupt.
grace_signature_verified
The Hebrew word for grace (חֵן) satisfies the algebraic properties of grace under a fixed letter-value mapping. The classifier accepts it.
random_root_not_grace
A random Hebrew root with different letters fails the same classifier. The gate discriminates. It's not numerology — it's structure.
chi_pos_of_all_pos
When all ten factors are positive and the revelation gate is open, coherence is strictly positive. Life requires all channels active.
sEff_antitone
As entropy production increases, effective coherence decreases. Decay is monotonic — you can't out-entropy the equation.
Every Logos paper has Lean 4 proofs backing its structural claims.
Every theorem. Every layer. Every lane. Filterable by type. All 210+ named results in one place.
⭐ The Lean 4 Corpus 287 theorems · 7 lanes · 16 layers · 70+ adversarial rejections · 0 sorry →You don't have to trust me. You don't have to trust anyone. Run it yourself.
# Install Lean 4
curl https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh -sSf | sh
# Clone and build
git clone https://github.com/YellowKidokc/theophysics.git
cd theophysics
lake build
Build completed successfully.
Zero sorry.