Obstacle Class K

Class K — Bias/Generation Decoupling

Class K is the case where a source direction looks writable to the bias-path readout but not to the generation-path readout.

In the survey language, the bias probe is a coarse instrument. It can report a real sensitivity effect, but that is not yet a content-generation symmetry or steering certificate.

Explainer

The Lean model has one propagated source vector and two covectors: \(c_{\mathrm{bias}}\) for completion-side sensitivity and \(c_{\mathrm{gen}}\) for free-generation presence. Class K fires when the same intervention gives \(|\sigma\kappa_{\mathrm{bias}}|\) above threshold while \(|\sigma\kappa_{\mathrm{gen}}|\) stays below the generation gate. This is a concrete fake-symmetry pattern. The coarse bias readout makes a direction look writable; refining the observable to the generation path collapses that writable region. The important distinction from Class A is that K is not merely one null covector. It is a two-readout mismatch at the same site.

probe-fake symmetry generation-path readout required falsifier: nonzero gen response

Theorem Table

Theorem name	File:line	What it proves
`ClassKDecoupled`	`BiasGenDecoupling.lean:115`	Defines the two-readout decoupling predicate.
`bias_decomposition`	`BiasGenDecoupling.lean:92`	Expands the bias readout into baseline plus source coupling.
`gen_decomposition`	`BiasGenDecoupling.lean:100`	Expands the generation readout with the matching covector.
`classK_realised_of_kappa_gen_zero`	`BiasGenDecoupling.lean:129`	Shows zero generation coupling is enough for Class K.
`equal_readouts_collapses`	`BiasGenDecoupling.lean:142`	Shows the nontrivial K case vanishes when readouts coincide.
`falsifier_negates_decoupling`	`BiasGenDecoupling.lean:165`	A generation response above threshold refutes Class K.
`decoupled_at_zero_gen_iff_kappa_gen_zero`	`BiasGenDecoupling.lean:176`	Gives the strict-zero generation form of decoupling.
`inverse_source_under_decoupled`	`BiasGenDecoupling.lean:197`	Bias lift can be fitted while generation response stays zero.

Empirical Witnesses

The QK/OV chart family and SAE chart probes repeatedly show bias-side lift with target-presence \(\Delta=0\) under generation readouts. The LFS_K5 downstream closure keeps LFS2/LFS4 blocked because no trap-clean source/readout/site triple survives; see the steerability mega-postmortem.

Reopen Criteria

Reopen requires a preregistered, trap-clean generation-path witness: the same branch must preserve the bias-path signal while pushing generation presence above the matched-null threshold. A stronger bias readout alone is not a Class K falsifier.