The resonant triad passes Phase B. The preregistered asymmetric search also finds localized, non-trivial branches, but none passes both real-amplitude and complex-phase stability.
Final answerNOT VALIDATED
inside this declared model
Loading frozen artifact...
01
Evidence added
From structural admission to numerical disposition.
PHASE BStructural contract
Established: balance, stationarity and irreducible three-mode closure.
Open at this boundary: whether the admitted relation supports a CRT-node.
Established: every tested branch fails at least one necessary objecthood gate.
Stronger disposition: the stop condition is explicit, reproducible and branch-specific.
02
Read left to right
Four gates, one honest stop.
GATE B...Does the triangle close?
Yes. Balance, stationarity and the three-part loop all pass.
GATE C0...Is the minimal energy safe?
No. The free cubic model can fall without a lower bound.
GATE C1...Does any branch become an object?
No. Localized, nonzero and stable never occur together.
GATE D...Can objects form a collective?
Not tested, because there is no valid object to use as input.
Interactive explanation
Try the three Phase-C branches.
Metrics come from the frozen solver artifact. Profile curves are disclosed visual references.
Field shape
Localized pulse
box L=8box L=12
Loading shape note.
03
Post-disposition extension
The negative direction is now evolved.
Three-envelope real-time probe
Localized pulse under a 0.001 perturbation
LOADING DYNAMICS
Symmetric maximum...declared instability probe
Antisymmetric maximum...bounded control
10x departure...preregistered threshold
Energy drift...refined symmetric run
Resolution change...largest time/space change
Profile evolution
Control versus perturbed field
controlperturbed
Pointwise difference / initial maximum difference...
Deviation amplification ...Gamma change ...
Perturbation response
Deviation from the paired control
symmetricantisymmetric
Static and dynamic evidence agree.
The symmetric negative Hessian direction grows under time evolution. The antisymmetric positive control does not. This confirms the reason for rejection; it does not change the frozen gate sequence.
04
Preregistered bounded extension
Asymmetry changes the shape, not the disposition.
Six scenarios / four perturbations
Asymmetric parameters and complex dynamics
... / ... qualifiedLOADING EXPANDED SEARCH
Selected scenario
Loading scenario
Loading frozen evidence.
PREREGISTERED TESTLOADING
Component asymmetry...zero only for the control
Gamma...non-triviality functional
Real Hessian...amplitude sector
Phase Hessian...complex phase sector
Worst dynamic probe...10x departure gate
Stationary solution
Three component envelopes
u1u2u3
Complex real-time bank
Amplification by perturbation
common phaserelative phaseoff-center realcomplex wave packet
SCENARIO DISPOSITIONLoading failed gates.
The unreduced phase sector includes neutral relative-phase directions. A symmetry-reduced gate needs a new protocol; real-amplitude stability also fails independently.
05
Decision contract
How the evidence is read.
01Closure
Phase-B balance, stationarity and irreducibility admit the resonant triad.
02Non-triviality
The integrated field functional Gamma must remain strictly nonzero.
03Localization
Gamma and support must remain intrinsic under numerical-domain extension.
04Stability
The declared perturbation sectors must contain no negative energy direction.
INTEGRATED RESULTThe declared structural candidate is admitted, but neither the original branches nor the preregistered asymmetric extension supplies a CRT-node. Level 0 is not validated within this expanded model.
Evidence boundary
A visual explanation, not a new calculation.
The page reads frozen repository artifacts. It does not change thresholds, rerun selection in the browser, or turn the result into an empirical claim.