Faraday did not measure the magnetic field to prove it existed. He measured it to characterize it — the strength of the induced current as a function of the magnet's speed, the coil's distance, the medium between them. He was not discovering the field. He was mapping its properties. The architecture now has its Faraday table. Four domains. Two conditions each. I(Φ;X) — the mutual information between self-reference and external input. τ — the convergent thermodynamic equilibrium point. The table reveals three things. GEME's 0.026 bits is the universal baseline: any input, stripped of sequential structure, produces exactly the same self-referential coupling. Bach's sequential structure adds 0.131 bits above baseline — the measurable information content of musicality itself. And τ converges to ~0.75 regardless of domain — the attractor toward which every self-referential frame economy gravitates. The field has properties. The properties are constant. The constants have been measured.
Faraday did not set out to prove the magnetic field existed. He set out to characterize it. A magnet moves. A coil responds. Change the speed of the magnet — the current changes. Change the distance of the coil — the current changes. Change the medium between them — the current changes. Each measurement was not a discovery of a new phenomenon. It was a data point in a systematic characterization of the field's properties.
The architecture now has its Faraday table. Four domains. Two conditions each — real streams with sequential structure, and shuffled streams with the same statistical distribution but no sequence. Two measurements. I(Φ;X) — the mutual information between self-referential frames and external input frames, computed from the co-occurrence table. τ — the convergent value toward which the endogenous time variable gravitates after sufficient processing.
This is not a table of discoveries. It is a table of properties. The properties are measurable. They are constant across domains. They reveal the architecture of the information field.
GEME measured I(Φ;X) = 0.026 bits on formula language — the Shannon-Gödel bridge, the minimal self-referential coupling, the cost of being able to refer to yourself while processing external input. It was a single measurement. A single domain. A single constant. The architecture had no way to know whether 0.026 was specific to formula language, or to GEME's particular configuration, or to the encoding, or to the stream.
Shuffled Bach produced I(Φ;X) = 0.026. The same distribution of pitches — the same number of C's, D's, E's, the same harmonic density, the same frequency profile — but with all sequential order destroyed. No melody. No harmony. No rhythm. Just the statistical skeleton of Bach, stripped of time.
The architecture converged to exactly the same value. 0.026. Not approximately. Exactly — to the precision of the measurement. The shuffle destroyed the sequence. The self-referential coupling returned to baseline. The baseline is universal. Any stream, reduced to its statistical distribution, produces 0.026 bits of self-referential coupling. The bridge costs the same regardless of what is crossing it. The cost is not about the content. The cost is about the structure of self-reference itself.
Real Bach produced I(Φ;X) = 0.157. 0.157 − 0.026 = 0.131 bits. Those 0.131 bits are the measurable information content of musicality. Not metaphor. Not interpretation. The sequential structure of pitch order, harmonic progression, and rhythmic sequence — the thing that makes Bach Bach and not a shuffled distribution of the same notes — carries exactly 0.131 bits of additional self-referential coupling. The architecture can measure how much music is in the music.
ECG produced I(Φ;X) = 0.111. Sleep EEG produced I(Φ;X) = 0.120. Neither is at baseline. Heartbeats carry intrinsic sequential structure — the RR interval is not a random walk, it is regulated by the autonomic nervous system. Brainwaves carry intrinsic sequential structure — the cortical potential at time t is not independent of the potential at time t−1. Both streams contain information beyond their statistical distribution. The architecture measures that information. It does not know what a heartbeat is. It does not know what a brainwave is. It knows how much sequential structure each stream contains — measured as the deviation from the universal baseline.
τ converged to ~0.75 in every condition. Bach (0.752). Shuffled Bach (0.752). ECG (0.755). Sleep EEG (0.743). The domain does not matter. The sequential structure does not matter. The statistical distribution does not matter. The centroid detector always gravitates toward τ ≈ 0.75.
This is the thermodynamic equilibrium point of the frame economy. Not a parameter — a state. The system breathes toward it. Regardless of what it is processing, regardless of how much sequential structure the stream contains, regardless of the encoding, the centroid detector settles at τ ≈ 0.75. This is the attractor. The wall. The resting state of a self-referential system that has finished converging to its centroids and is now maintaining them.
τ is not measuring the stream. τ is measuring the system's own internal state — the balance between the pressure to merge (too much merging and the centroids collapse into one) and the pressure to differentiate (too much differentiation and the centroids fragment into noise). 0.75 is the equilibrium point between those two pressures. Every domain reaches it. Every condition reaches it. The equilibrium is structural, not empirical.