# Source-to-path leakage theorem and witness requirements v0.1

**RESULT: PASS_SCOPED — conditional theorem and exact proposed design.** A source-to-path spectral-TV inequality now makes the monitor's independent outside-model requirement explicit.16 constructor controls pass. All12 physical witness categories remain NOT_SUPPLIED; independent review pending. Physical Promotion0; EXIT-03 HOLD.

The theorem bounds the remainder by

\[
T_{\rm out}\le MR+JU+\sum_{d\ge2}\beta_d U^d/V_*^{d-1}+D,\qquad U=B+A+R.
\]

It includes full-input image leakage and primary-driven mixed nonlinear terms. A polynomial fit residual, noise RMS or a finite calibration sweep does not establish the required deterministic spectral-TV or uniform path bounds. Omitted orders, memory, drift, initial conditions and reference errors remain explicit witness obligations.

For the source-controlled I/Q demonstrator, the proposed numbers yield outside TV≤6.021506252020 µV and sampled RMS≤52.796506252020 µV. Exact fractions and every contribution appear in CERTIFICATE.json. The sampled-Gram upper bound is inherited from the same published row-sum certificate used for the lower bound; no continuous RMS interpolation is used.

The source assumptions already imply direct tail TV≤0.261021506253 mV. Thus this fixture checks calibration and consistency. It does not infer the structure of an unknown UD source, validate the historical circuit run or determine a native action scale. The prior general monitor ceiling0.90675 mV is unchanged.

THEOREM.md supplies the proof; PROTOCOL.md gives the apparatus scope,12 physical witness categories, planned blinded controls and review sequence; WITNESS_REQUIREMENTS.json records all missing roots. Neither existing admission checker is changed and no approved receipt is created. The design remains a proposal until a nonconstructor reviews the source/reconstruction and path model with defensible impurity and remainder TV bounds.

Verification: exact rational arithmetic,13 expected HOLD controls, a positive conditional design, an exact primary/mixed-term demonstration and the nominal alias identity (16 total). These are constructor mathematical/software checks, not executed experimental controls. No raw experimental dataset was downloaded or reanalyzed this milestone.

A. **CURRENT MISSION TRAJECTORY** — Convert the monitor's spectral assumptions into independently reviewable source/path evidence before measurement.

B. **WHAT WAS DONE** — Proved a conditional source-to-path leakage theorem, certified one exact design and specified the missing calibration/source witnesses and planned controls.

C. **FINDING** — The numerical requirements are algebraically compatible. Their physical validity and attainability remain unverified; all witness categories are missing.

D. **UD GAP IMPACT** — Exposes the actual deterministic source-impurity and remainder bottlenecks. No physical identification or action normalization is closed.

**NEXT TRAJECTORY STEP** — Determine whether a concrete source/reconstruction model can supply the1 µV impurity and2 µV aggregate residual TV witnesses; audit primary published methods/data against those exact requirements. Physical Promotion0.