What we did
We started with 256 participants connected in a cycle. Each participant carries a complex amplitude. The baseline expresses every mode; candidate C001 admits smoother patterns more strongly. Both receive the same input, network, evolution, and assigned positions.
Two inputs answer different questions: an already smooth Gaussian packet, and a concentrated pulse at one participant. The pulse is useful because no Gaussian shape is inserted into that input.
What happened
At selectivity 64, the pulse expressed as an approximately Gaussian packet. Its initial width was 7.992 model cells. At evolution position 80 it was 9.425 cells wide; at 160 it was 12.794. With no directional bias its center stayed fixed while the packet spread.
About 2.495% of the pulse's original weight was admitted into the expressed channel. The rest remained in the complementary accounting. The plotted candidate shape is normalized within the expressed share, so its visible height must not be confused with the amount of original weight admitted.
What we learned
One standing admission rule can express the packet shape on this cycle. Its smoothing effect is explained by the supplied mathematical operator; subsequent spreading follows the supplied quantum evolution. This gave us an executable first candidate to test under changed relational connections.
The exact candidate rule
The network Laplacian L measures how amplitudes vary across graph connections. The chosen position map assigns participant j to x(j) = j − 128. All quantities use dimensionless model units.
Underlying evolution: H = 0.5 L
a(s) = exp(−i H s) a(0)
B000 reference: all modes express
C001 admission: K = exp(−β L)
Expressed state: b(s) = K a(s)
Complement: R = sqrt(I − K²)
Unexpressed accounting: r(s) = R a(s)
||b(s)||² + ||r(s)||² = ||a(s)||²The readout is fixed during a run. Moving the evolution slider reads the original evolving state at that position; it does not repeatedly smooth the previous frame. Complex amplitudes, quantum evolution, the probability rule, and the position map are supplied.
How this uses TRQC
The TRQC connection is the architecture: one underlying activity, selective standing expression through a candidate DQEC channel, and expressed behavior inherited from that same activity. The particular choice “compatibility means smoothness” is C001's research hypothesis. It is not a settled rule of the conceptual framework.
How it was checked
The numerical implementation was compared with independent matrix calculations across 112 configurations. All 16 recorded checks passed, including conservation, channel accounting, identity admission, and relabeling. The validation record contains the exact values and tolerances.
Download validation results · Download candidate traces · Download recorded distributions
Where we went next
The obvious next test was whether this packet depended on the chosen connections. We ran that test in Study 002, keeping its unfavorable outcomes in the record.