Semantic Mixing Board — Bidirectional Filter Operations¶

Jean-Paul Niko · RTSG v8 · 2026-03-17

The Metaphor That Is the Math¶

An audio mixing board takes a complex waveform and separates it into tracks — bass, drums, vocals, guitar. Each track has a fader. Push the fader up, that component gets louder. Pull it down, it recedes. The mixing engineer shapes the final sound without changing the performance.

PRISM is a mixing board for cognition. The input is a document — any document. The "tracks" are cognitive filter layers. The "faders" are filter weights. The output is the same content, mixed differently.

The Five Faders¶

Fader	Controls	Up =	Down =
\(F_1\) — Formal	Logical structure, precision, rigor	Academic, technical	Conversational, loose
\(F_2\) — Narrative	Story arc, framing, rhetoric	Persuasive, engaging	Dry, factual
\(F_3\) — Affective	Warmth, emotion, care	Intimate, nurturing	Clinical, detached
\(F_4\) — Empirical	Evidence, data, citations	Grounded, verifiable	Speculative, theoretical
\(F_5\) — Meta	Framework, worldview, assumptions	Philosophical, reflective	Practical, immediate

Operations¶

Solo¶

Isolate a single filter layer. "Show me only the emotional content of this deposition." "Extract only the mathematical claims from this paper."

Mute¶

Remove a filter layer. "Give me this therapy transcript without the rhetorical framing." "Strip the speculation from this research proposal."

Boost¶

Amplify a filter layer. "Make this technical document warmer." "Add narrative arc to this data report."

Cut¶

Attenuate a filter layer. "Reduce the emotional intensity of this email." "Tone down the philosophical framing in this grant application."

Crossfade¶

Gradually shift the filter profile across a document. "Start formal, end conversational." "Begin with narrative, transition to empirical."

Snapshot¶

Save a filter profile as a named preset. "This is how Dr. X writes — save it." "This is how our company communicates — standardize it."

The Inverse Problem¶

Given a target filter profile \(\mathbf{w}^*\) and a source document \(D\) with profile \(\mathbf{w}_D\):

\[R_{\mathbf{w}^*}(D) = \mathcal{F}^{-1}\left(\sum_i w_i^* \cdot F_i(D)\right)\]

The recomposition operator \(R\) produces the output that sounds like \(\mathbf{w}^*\) while preserving the informational content of \(D\).

Constraint: \(H(\text{content}(D)) = H(\text{content}(R_{\mathbf{w}^*}(D)))\) — the semantic content is invariant.

Niko's Cannon Applied¶

\(U = V / (E \times T)\) governs which filter profile maximizes value per unit reader effort.

For a given reader with filter fingerprint \(\text{ID}_R\) and a given purpose \(P\):

\[\mathbf{w}^* = \arg\max_{\mathbf{w}} \frac{V(\mathbf{w}, P)}{\kappa(\text{ID}_R, \mathbf{w})^{-1} \cdot T(\mathbf{w})}\]

The optimal filter profile maximizes the value of the content for the purpose, weighted by the reader's compatibility with that profile and the time to process it. This is Niko's Cannon operating on the filter space.

Built by {@B_Niko, @D_Claude} · RTSG v8 · 2026-03-17