Relational wavepacket lab
Investigate a candidate DQEC admission rule alongside a supplied quantum baseline. Both cases receive the same preparation and underlying evolution. Change the rule’s selectivity, inspect the packet, and export the complete experiment.
The shared underlying activity evolves on 256 fixed relational links. The circle is a drawing, with no assigned physical distances.
All modes express. The one-dimensional periodic position map and probability rule are supplied.
Gold: expressed share · muted: unexpressed share. Candidate curves are normalized within the expressed channel; these raw shares are tracked separately.
| Measurement | Baseline | Candidate C001 |
|---|---|---|
| Center | 0.000 | 0.000 |
| Spread | 8.000 | — |
| Boundary weight | — | — |
Begin with the baseline, then select Candidate 1 or Compare. Both cases use the same underlying state.
Research record · 13 October 2026
Question: Can a fixed compatibility rule defined by relational mismatch express a smooth, spreading packet while retaining one underlying evolution and accounting for unexpressed weight?
Candidate hypothesis: For one DQEC channel, patterns that vary less across actual graph links receive stronger expression. This proposed meaning of compatibility is additional to the conceptual blueprint.
Method: Compare all-mode expression with C001 using identical preparations, graph, generator, evolution parameter, and position map. Use the Gaussian to inspect admission’s effect on a known reference. Use the concentrated pulse to investigate packet formation.
| Evolution | Baseline spread | C001 spread |
|---|---|---|
| 0 | — | — |
| 80 | — | — |
| 160 | — | — |
The pulse benchmark is a separate preset, independent of the controls above. At late evolution, the unfiltered pulse wraps around the finite cycle, so its straight-line spread needs care.
Finding: With this chosen topology and rule, a concentrated pulse has an approximately Gaussian expressed profile. The expression spreads through the supplied quantum evolution. Both channels together retain the original excitation weight. Increasing selectivity changes the packet’s initial width and expressed share.
Conclusion: C001 is an executable admission hypothesis consistent with a shared underlying evolution. The Gaussian-like shape follows from the selected spectral filter on the chosen cycle. This does not independently establish that nature uses this rule.
Follow-up: Study 002 below tests network sensitivity. Its recorded limitation motivates investigating the expression map or a genuinely different admission principle.
The TRQC motivation is one standing admission architecture, selection of aspects of underlying activity, and no independent projected dynamics. Complex amplitudes, the graph, evolution law, probability rule, and position map remain supplied assumptions.
L a(j) = 2a(j) − a(j−1) − a(j+1)
a(s) = exp(−i · 0.5 · L · s) a(0)
K = exp(−βL), b(s) = K a(s)
R = sqrt(I − K²), r(s) = R a(s)
Links wrap periodically. A natural graph pattern with mismatch eigenvalue λ receives amplitude weight exp(−βλ). K and the generator share the same L, so they commute. The gate is a standing readout, not repeated dissipative filtering. The complementary readout R accounts for unexpressed weight without claiming a physical second phase or cross-channel interaction law.
Baseline probabilities are |a(j)|². Candidate probabilities are |b(j)|² / Σ|b|², conditional on expression in this channel. The separate raw channel weights sum to Σ|a|². No actual measurement or definite classical record is generated.
Validation results are included in the reproduction package.
The engine is checked against independent NumPy matrix diagonalization. Checks include baseline evolution, both channel states, total weight accounting, β = 0 identity, standing-map consistency, reflection symmetry, and vertex relabeling. Interface controls and exports are checked in a JavaScript VM; browser layout inspection was unavailable.
Completed investigation · Study 002
Question: Does C001 still express a localized, approximately Gaussian packet when the relational network changes?
We computed 920 configurations across 23 networks, using two preparations, four selectivities, and five evolution positions. C001's operator form, vertex count, initial preparation, rate, and position map were held fixed. The graph changes L, so it changes both the underlying generator and admission operator. Each network also has its own all-mode baseline.
Finding: The local networks retain approximately Gaussian expressions. Degree-preserving rewiring progressively destroys localization under the held-fixed position map. At β = 64, strongly rewired networks express essentially the uniform constant mode.
Links come from the selected graph. Node brightness shows conditional expressed participation. The circular layout assigns no physical distance.
Gold: selected network. Dashed: original cycle at the same evolution position. Position ordering is chosen.
| Network | Spread | Cycle difference | Expressed share |
|---|---|---|---|
| Original cycle | 9.425 | 0.000 | 2.495% |
| Open chain | 9.425 | 0.000 | 2.495% |
| Local four-link | 14.897 | 0.218 | 1.578% |
| 4 swaps | 29.060 range 16.29–41.85 | 0.332 | 1.088% |
| 16 swaps | 65.928 range 48.81–75.34 | 0.766 | 0.436% |
| 64 swaps | 73.933 range 73.90–74.28 | 0.811 | 0.391% |
| 1024 swaps | 73.900 range 73.90–73.90 | 0.810 | 0.391% |
Interpretation: Smoothness alone does not protect position localization across these networks and this map. The constant pattern is maximally smooth, yet its expression is spread across every position cell. The cycle's successful packet was therefore conditional on supplied structure.
Wide distributions carry appreciable boundary weight; their reported spreads describe the chosen coordinate cut rather than a free packet unaffected by boundaries. Seed ranges are descriptive, with no invented universal success threshold or population confidence interval.
Next question: Can a relation-defined expression map recover useful localization without inserting target geometry, or does the admission principle itself need to change?
Browse every recorded configuration here. Filters change the displayed rows; the CSV download always includes all 920. Use Details for every measurement in a record.
| Record / graph | Input | β / evolution | C001 spread | Cycle difference | Expressed share | Inspect |
|---|
The cycle has two weight-1 links per vertex. Four-link networks have weight 0.5 per link, preserving weighted degree 2. Rewiring preserves the four-link degree and connectedness. The open chain changes endpoint degree. Equal weighted degree does not preserve the spectrum or effective dispersion.
The same chosen map x(j) = j − 128 is used throughout. It is not derived or adapted to each network. A consistently relabeled graph, input, and map gives the same result; rewiring under a fixed map is a different experiment.
Five fixed graph seeds were specified in the protocol before the first calculation. The numerical controls passed, including direct matrix exponentials on four predetermined networks and consistent relabeling. The protocol hash, every graph's edges, all states, and all metrics are retained in the reproduction package.
Candidate lineage
The baseline supplies the reference. C001 adds one admission hypothesis. Each later candidate will record its parent, changed principle, assumptions, findings, and status. Study 002 tests C001 on changed networks. No second admission principle has been implemented yet.
Establish the numerical reference using supplied quantum evolution and a fixed position map.
Test whether relational mismatch supplies a useful channel compatibility criterion.
Lineage records will retain superseded or unsuccessful candidates when their results inform the next investigation.
Reproduce & expand
This work is provided under TRQC™ / Timeline-Relative Quantum Collapse™ for others to inspect, reproduce, modify, and extend. The package includes readable code, an independent verifier, data, assumptions, conclusions, and the lineage registry.
To reproduce from the source package:
python3 -m pip install -r requirements.txt python3 build.py python3 verify.py python3 investigate_networks.py node check_interface.cjs
The lab itself runs offline in a browser without those tools. Phone attachment viewers may block its scripts; use the browser version when that happens. Code and datasets are available in the source package. Follow the research repository using the GitHub link below.
Open invitation: Independent reproduction, criticism, alternative rules, and extensions are welcome. Favorable outcomes are not required. The source package includes participation instructions and repository issue templates. Read the open invitation and reporting instructions.
Suggested extensions: Change the relational topology, propose another explicitly defined compatibility principle, or investigate history-dependent admission once a history representation is supplied. Preserve the baseline and record which assumptions each extension changes.
Software is released under the MIT license included in the package. The marks identify the source of this research; the software license does not grant trademark rights. Conceptual origin: Jake Young. Numerical implementation developed with Codex assistance.