Self-Consistent Field Theory (SCFT) L1-475

Polymer PhysicsBlock copolymer microphase separationδ=5 · challengingL_DAG = 3.8📋 Stub — not mineable

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Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

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Forward model E

d q / d s = (b^{2} /6) L a pl a c ian (q) - w (r) q; p h i_{A} (r) = in t e g r a l_{0}^{f} q (r, s) q \cdot (r, 1 - s) d s; w_{A} (r) = c h i_{A} B \cdot N \cdot p h i_{B} (r); F = - Q + (1/ V) in t e g r a l [c h i_{A} B \cdot N \cdot p h i_{A} \cdot p h i_{B} - w_{A} \cdot p h i_{A} - w_{B} \cdot p h i_{B}] d r

SCFT maps polymer chains to modified diffusion equations for propagators q(r,s); mean-field free energy F[w, phi] is minimized self-consistently; morphology emerges from competition between chi_AB * N and entropy.

L-DAG

E.propagator_diffusion -> O.iter -> O.density_field -> O.scattering

E.propagator_diffusionO.iterO.density_fieldO.scattering

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 1200

Multiple local minima (lamellae, gyroid, hexagonal) → non-unique inversion; phase diagram navigation requires morphology seeding.

Solvability C

Solver class:: Anderson-mixing SCFT on Fourier grid; morphology-conditioned Monte Carlo
Convergence rate q:: 2
Complexity:: O(N_s * N_grid * log(N_grid)) per SCFT iteration

Specs (0)

No L2 specs registered yet for this principle.