Irreversible Gradient-Ratcheting Composites (IGRC)
Structural evolution is irreversible and path-dependent. Endpoint equivalence is invalid.
Core Statement
IGRC defines a class of composite architectures in which sustained environmental gradients irreversibly increase internal structural order through interfacial mechanochemistry.
Structural state is a function of exposure trajectory—not endpoint condition.
Doctrine Constraint
Durability or improvement claims are valid only if internal state evolution is tracked as a function of gradient exposure history.
Endpoint-equivalent treatments cannot reproduce trajectory-dependent states.
Architectural Requirements
- Semi-crystalline or partially ordered matrix
- Mechanically anisotropic secondary phase
- Irreversible mechanochemical interfacial linkages
- No reversible or externally actuated mechanisms
Governing Mechanism
- Localized interfacial bond rupture
- Irreversible re-bonding in new topology
- Directional alignment and trapping
Each activation event ratchets internal structure irreversibly.
State Representation (MTI-1)
- ψ_if — irreversible interfacial bond density
- Φ_al — alignment order parameter
- Λ_cr — ordered domain fraction
These must evolve monotonically with exposure trajectory.
Non-Commutativity Constraint
Identical endpoints reached via different gradient histories produce different internal states.
If states are reproducible by endpoint treatment, IGRC is invalid.
Failure Condition
Failure initiates at the interface if ratcheting is absent or unstable.
Decisive Falsification
The system fails if:
- No irreversible state evolution occurs
- State variables are endpoint-reproducible
- Trajectory dependence is absent
Invariant Framework
G: Gradient-preserving transformations
Q: Material mass and chemistry
S: Irreversible internal state spectrum
Failure: S is endpoint-reproducible or non-monotonic
Claim Eligibility Boundary
Durability, improvement, or safety claims that are not expressed as a function of trajectory over S are invalid.
Properties do not exist independently of history in this regime.
Boundary Judgment
Improvement is not a property. It is a trajectory. Any claim that ignores path-dependent state accumulation exceeds its epistemic authority.