# BP-free and hardware-locality contract

This contract applies to every result in the active two-state structured-bias
program. A run cannot be labelled SDIL or hardware-local merely because the
mathematical rule has a local interpretation. The executable learning path
must satisfy the checks below.

## Information available to the debiaser

For one cell, population or physical edge, the debiaser may use only:

- its local neutral state or fixed local basis features `phi(z_neutral)`;
- its locally observed instruction-off teaching channel `a_neutral`;
- its locally observed task-period channel `a`;
- its own predictor coefficients and locally stored traces;
- the native backbone eligibility already available at that synapse or edge;
- a local phase/neutral gate.

The frozen learning rule is

```text
prediction = P phi(z)
r = a - prediction
Delta w = eta_w r eligibility
Delta P = eta_P (a_neutral - P phi(z_neutral)) phi(z_neutral)^T
```

`P` may be an affine or fixed-basis adaptive filter. A multilayer predictor
trained by reverse-mode differentiation is outside the method. Fixed nonlinear
basis functions are allowed only when every adaptive coefficient still has the
local LMS update above.

## Forbidden training information

No SDIL training update may read or be derived from:

- a task-loss gradient or hidden-state BP gradient;
- a copied clean, centered, oracle or BP update;
- a downstream weight, its transpose, or a reverse-mode computation graph;
- a task-period target for the neutral predictor;
- a global loss difference used to supervise the predictor;
- an opposite-sign phase introduced only to create a debiasing target;
- a backbone-specific learned controller trained with BP.

BP, centered/oracle states and clean updates may be computed only in a clearly
separate diagnostic process after the learning update has already been fixed.

## Executable audit

Every backbone adapter must pass all of the following before a task endpoint:

1. **No-grad training:** the SDIL update executes with autograd disabled and
   no learned tensor requiring gradients.
2. **Local replay:** recording the local tuple `(z_neutral, a_neutral, z, a,
   eligibility)` is sufficient to reproduce the update bitwise without the
   model, label, task loss or downstream layers.
3. **Downstream independence:** after the tuple is recorded, randomizing all
   downstream parameters, labels and loss code leaves the update bitwise
   unchanged.
4. **Instruction isolation:** changing the task instruction while holding a
   stored neutral tuple fixed cannot change the predictor update.
5. **Manual/autograd equivalence:** if an author simulator uses autograd to
   evaluate a mathematically local energy derivative, a test-only comparison
   must show that the hand-written local formula agrees. Paper-facing training
   uses the manual path.
6. **Common-mode cancellation:** the same offset in both states cancels before
   SDIL and produces no claimed gain.
7. **Phase and storage audit:** every neutral observation, state copy,
   predictor coefficient, multiplication and update is counted.

Passing these checks establishes algorithmic BP freedom and an executable
local information path. It does not by itself establish that a particular
analog circuit has sufficient precision or energy advantage.

## Hardware primitives

The rule requires only the following primitive operations at each adaptive
site:

| operation | possible local realization |
|---|---|
| store `P` or a trace | capacitor, memristive state, SRAM/register |
| form `a - P phi(z)` | differential amplifier or local subtractor |
| multiply local factors | analog multiplier, coincidence circuit, local MAC |
| integrate `Delta P` and `Delta w` | capacitor current or local accumulator |
| select neutral/task observation | local phase gate or switch |

Dillavou et al.'s coupled-learning hardware already measures local voltage
drops, forms products with AD633 analog multiplier circuitry, and integrates
updates on capacitors. Those are the needed operation classes. SDIL still adds
predictor state, a prediction path, subtraction and a neutral schedule; the
published hardware does not already implement that complete circuit. Until it
is built or circuit-simulated, the correct claim is **implementable from local
analog primitives**, not **demonstrated on hardware**.

For EP, coupled-learning DCHNs and Dual Propagation, relaxation produces the
native local teaching/eligibility variables. The SDIL adapter operates on
those local variables and cannot ask autograd to reconstruct them. An author
implementation that calls `.backward()` for software convenience is acceptable
as a native accuracy reference, but not as the paper-facing SDIL training path
without the manual-equivalence audit.

## Claim language

Allowed after the executable checks:

> SDIL is algorithmically backpropagation-free: its adaptive predictor and
> synaptic updates use local state, instruction-off measurements and native
> local eligibilities, with no task-loss reverse pass or weight transport.

Allowed before a physical circuit demonstration:

> The update decomposes into storage, subtraction, multiplication, integration
> and phase-gating primitives already common in analog local-learning systems.

Not allowed without new evidence:

- “SDIL has been demonstrated on the physical resistor hardware.”
- “SDIL requires no extra observation, state or circuit.”
- “Using autograd internally is irrelevant to the hardware claim.”
- “Every two-state backbone is BP-free because its equations can be written
  locally.”