Power Law Time Contours
Same-day fair value with empirical cycle references. Four daily-close cycle lows came within 18.44% of the lower reference; five selected cycle peaks came within 13.88% of the upper reference. The upper curve rises in dollars with the trend; what declines is its relative premium over fair value, and that premium stops declining at the last measured cycle-peak gap, about 15% above fair value. Retrospective calibration, not guaranteed support or resistance.
What is it?
Same-day centre C(t) = 10^-17.04 × days_since_genesis^5.83. The lower reference uses a constant log10(price/C) residual calibrated on four cycle lows; the upper reference uses a residual declining linearly with network age, fitted to five selected cycle peaks. Daily-close lows came within 18.44% of the lower reference, and selected peaks within 13.88% of the upper reference. These are retrospective empirical references, not guaranteed support or resistance.
How to read
Compare price, fair value and cycle references on the same day and price axis. All curves share the LOG toggle. The upper price reference can rise while its ratio to fair value declines. Below the centre means below the model for that day, not an observed market fair price.
Key zones
Lower reference: four measured lows, maximum absolute relative gap 18.44%, so the 15% contact criterion is not met. Centre: same-day fair value. Upper reference: five selected peaks, maximum gap 13.88%. These curves do not contain every daily close. The declining upper residual is held at the last measured cycle-peak residual, about 15% above the centre, so the upper reference never extrapolates below the observed peaks.
What to observe
Compare actual daily-close extremes with the references. The secondary spring peak of the double-top cycle came within 14.63%; the high before the following halving missed the upper reference by 30.84%. They were checked separately and were not fitted cycle peaks. A new cycle can depart from this calibration.
Historical context
The public power-law framework relates price to network age. Calibration uses canonical cycle-low dates and the highest daily close between the preceding halving and the registered low, with the first market cycle and the latest registered peak included. Prices come from the daily-close series, not indicative anchor prices. Measured contact on fitted peaks is not independent predictive validation.
Expert notes
With q=price/C at the four lows, lower=C×(min(q)+max(q))/2 minimises the maximum absolute relative gap. Upper=C×10^max(0,a+b×days), with a=1.5648545079806284 and b=-0.00023947533369732092, fitted by OLS to five peak log residuals. The lower residual is -0.2809547624546829. Coefficients stay fixed across syncs and display periods. A constant lower residual cannot fit all four lows within 15%.
Common mistakes to avoid
These are daily-close cycle references, not intraday extrema, future targets or a point-in-time backtest. Contact at selected calibration peaks does not establish a universal resistance. Fitting only the first four peaks misses the fifth by 21.97%. The lower reference misses the requested 15% criterion; the upper fit also misses the separate pre-halving high. Do not extrapolate its calibrated contact beyond its convergence with the centre.
Programmatic access
REST API
curl -sS \
'https://api.trinityinsights.io/api/v1/cycle-intelligence/metrics/cycle-power-law-time-contours/data?timeframe=90d' \
-H 'X-API-Key: $TRINITY_API_KEY'MCP server
{
"tool": "get_chart_value",
"metric_id": "cycle-power-law-time-contours",
"timeframe": "1y"
}Required tier: pro. See the pricing grid for the tier list and the MCP documentation for multi-client configuration.
Related metrics
Institutional disclaimer
Trinity Insights is an educational and analytical tool. The metric above does not constitute investment advice. Trinity Insights is not a Crypto-Asset Service Provider (CASP) registered under MiCA Regulation (EU) 2023/1114. See the full disclaimer.