01 / CHANNEL
Momentum p
Published K*≈ 1.507
Reference only✳ PERSISTENCE COLLAPSE REPLICATION 01 / 03
Same system.
Different
answers.
We tested one mathematical system three ways. Two measurements detected a change. The third did not. Explore the moving system, then see what the original data reveal.
STANDARD MAP / INTERACTIVE MOTION
LIVE MATHEMATICAL MOTION
θ angular coordinate0.00
p momentum+0.00
ONE SYSTEM ∕ ONE MOTION
A visual model of the real standard-map equations—not a physical pendulum or a measured persistence result.
KICK STRENGTH · K
1.51
DRAG TO ROTATE THE MODEL · MOVE THE K SLIDER TO CHANGE HOW STRONGLY IT KICKS · SPACE TO PAUSE
✧
Here is the question. If you look at the same system in different ways, will every measurement notice the same change? In this published test, the answer was no.
See the data ↓THE RESULT, IN PLAIN ENGLISH 02 / 03
Three ways
to measure.
We looked at movement, a value calculated from movement, and position. Each had its own pre-set allowed range. Only the first two showed the benchmark’s defined drop.
01 / MOMENTUM p1.507Change detected near K = 1.507
02 / ACTION PROXY J1.508Change detected near K = 1.508
03 / POSITION θNot detectedDid not cross the 50% mark for K = 0 to 2
PUBLISHED PERSISTENCE COLLAPSE BENCHMARK · 300 paths at each of 40 K settings · This does not mean position can never detect change.
THE KEY POINTNot seeing a change does not always mean no change occurred.
Sometimes your measurement simply is not sensitive to the change that this particular test is trying to find.
SEE IT. TEST IT. QUESTION IT. 03 / 03
Now try
the experiment.
Start with the real published results. Then try a smaller test on your device, or bring results from the original Python code. We keep these separate so you always know what you’re seeing.
01
STEP 1
Choose what to see
You are looking at real measurements from the published study, not an animation made to resemble them. The pale bands show how uncertain each measured fraction is.
What does “detected near K = 1.5” mean?
For each kick strength K, the experiment checked how many simulated paths stayed within a predefined range. The reported K* is where that share first dropped below half, estimated between two tested K values. It is not the mathematical last-torus destruction value near K = 0.9716.
The original width estimator may use a nearest-grid fallback if a 20% crossing is missing. Such widths are not fully bracketed 80%-to-20% intervals.
ORIGINAL V6 DATA · VERIFIED300 simulated paths per K value · 40 settingsArchive checksums checked. The original code was not changed.
Research details, extra measurements, and known exceptions
Rotation-number proxy (exploratory): K* = 1.52095. Torus-distance heuristic (exploratory): no clean 0.5 crossing. The three main graphs show the primary momentum, standardizable action proxy, and negative-reference position observables.
Also documented in the original package: five Baker-map sign-operator execution failures; the Baker Q2 manifest writer incorrectly reports failure despite the underlying CSV data; 167 no-clean-bracket transition records and one additional warning in the log. The revised manuscript lists Baker v5_native baseline mean hard persistence as 0.190, whereas the supplied summary_v6.csv gives 0.3294167 across all 40 fixed-corridor baseline cells; this remains an unresolved source-to-text discrepancy. The later reviewer-requested robustness experiments are post-review, not preregistered.
02
STEP 2
Save or share the result
No sign-in needed. Your experiments and imported CSVs stay in this browser.
WHAT THE ORIGINAL EXPERIMENT ACTUALLY MEASURED
Published references · no run yetSee where the lines fall.
How to read these: Higher lines mean more paths stayed within their allowed range. The halfway line is the key. We mark a detection when the share drops below 50% as K rises.
TRACKS THE SYSTEM’S MOMENTUM · PRESET RANGE
02 / CHANNEL
Action proxy J
Published K*≈ 1.508
Reference only03 / CHANNEL
Position θ
Published findingNo crossing
K ∈ [0, 2]WHAT TO TAKE AWAY
Two saw the change. One did not.
The original data show a clear halfway crossing for momentum and the action proxy near K = 1.5. Position never crosses halfway in the tested range. This is about what the test can detect—not proof that position could never detect a change.
OBSERVABLEPUBLISHED VALUEARCHIVED V6
Momentum1.5067—
Action1.5077—
Positionno crossing—
OPTIONAL MOTION VIEW
See the paths
These dots follow the mathematical map. They help you picture the motion, but they are not the experiment’s detection results.
HOW THE EXPERIMENT WORKS
Three simple steps.
One careful test.
It is not asking whether the system is chaotic in every possible sense. It asks when a chosen measurement stops staying inside its pre-set range during a fixed period.
Run the same mathematical system
A simulated point receives a series of kicks. Turn up K to make each kick stronger. We use many starting points, not just one.
Measure three different things
Watch momentum, a value calculated from momentum, or position. Each measurement has a predefined allowed range. Count how many paths stay inside it.
Look for the halfway drop
As K increases, ask: have fewer than half the paths stayed in range? Where the measured share first falls below half is the estimated threshold.
FOR SCIENTISTS Full equations, locked settings, and limitations
Standard-map equations
pn+1 = pn + K sin θn
θn+1 = (θn + pn+1) mod 2π
θn+1 = (θn + pn+1) mod 2π
Discrete-time mathematical dynamics. The interactive optical instrument is an illustration of these updates, not a literal pendulum.
Locked V6 protocol
40 K values across [0, 2]; N = 300 trajectories per cell; 12,000 steps; 1,000 burn-in; seed 12345. The fixed anchor is built from one 50-step block after burn-in, then 50-step measurement blocks are tested against the specified corridor for each observable: ε = 2.00 (momentum), 0.30 (action proxy), 1.50 (position). These are different prespecified tolerances.
Estimator and limits
Hard persistence is the share of trajectories with no block-mean corridor exit during the measurement horizon. K* is linearly interpolated at a strictly descending 0.50 crossing between neighboring points. No bracket means no detected crossing within this scan.
The standard-map transition near 1.507 is a finite-time measurement threshold, not the last-KAM-torus destruction value near 0.9716. The action observable J = p²/(2π) is a proxy, not a canonical action-angle variable. Browser tests use different random sampling and are exploratory.
ABOUT THE EVIDENCE
Original code and data ↗Original data first. Visual effects second.
The graphs use the archived V6 measurements and 99% Wilson confidence bands. A shorter browser experiment is clearly labeled exploratory. For a true full-size replication, use the original Python code and check the resulting files.