The Fourth Proof-Carrying Rescue

The fourth v0 rescue lane is:

saturation_shelf -> saturation_deshelf -> corner_concentration

This one is different from the first three. It does not move directly into an interior-good event. It moves from a bad finite flatline back into measurable boundary structure.

The Function Family

The fixture is:

saturated_response(x) = clamp(exp(x), 0, 1)

Large positive inputs are finite and bounded, but they collapse onto the same output:

output = 1

That is a saturation shelf. It is safe-looking, but it destroys optimizer information.

The Trace

Forge emits the packet with:

tools/saturation_deshelf_rescue.py

It records:

examples/saturation_deshelf_rescue.eml

The deshelf replay inspects pre-clamp pressure. High-pressure shelf samples move back into boundary structure:

The packet is intentionally modest. It does not claim a global optimizer win. It claims the clamp invariant stayed intact while replay recovered measurable boundary pressure.

The Obligation

The packet points at:

ClampInvariantObligation

MachLib now has the matching bridge:

ValidBoundaryRunPacket p
  -> PacketHasEvent p saturationShelf
  -> PacketHasTransition p saturationShelf cornerConcentration
  -> ClampInvariantObligation p
     and a nonempty transition-graph witness

That completes the v0 proof-carrying rescue suite.