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Capture

Certified endurance — and certified remaining life, with a warrant that voids itself.
CAPTURE · prognostics ISO 13374 lifecycle RUL 18 yr, not simulated

Every solver vendor sells uncertified convergence — run until the residual looks flat, one trajectory, no guarantee. Every condition-monitoring vendor sells an RUL estimate — noisy, uncertified, and silent about its own error. And for a 15-year asset the one number that matters — how long until I must act — is exactly the number you cannot get by simulation: you can't run the mission to find its remaining life.

Noether Capture certifies both ends of that question. It certifies that a system captures into its final state, and by when — one witness covering every trajectory for all time. And on a monitored asset it runs the full lifecycle — detect, classify, trend — to a certified Remaining Useful Life, with a warrant that self-voids the instant the fault outruns its own projection. Certification is a state, not a stamp; unverified change decertifies.

Everyone else's certificate tells you it was true once. This one knows when it has stopped being true, and says so before you ask.

THE ASSET   A tether — the astronaut safety line at parity with the open-source eigensolver, scaled to the lunar space elevator, the most dangerous safety-of-life structure there is, whose mission life no conventional simulation can reach.
THE RESULT   The full ISO 13374 lifecycle, certified end to end:
  • One witness, every trajectory, all time. A verified spectral certificate proves the system captures into steady state for every initial condition and all K — where a referee can step only finitely many trajectories to finite depth. Theorem-grade: no floating point in the verdict.
  • Diagnose by the exact signature. Fault type from the mode comb — mass accretion (modes down), section loss (modes up), distributed — blind, with the sign as the safety call: a tiny up-shift is the life-limiting section loss a naive monitor dismisses.
  • Remaining life, certified, not simulated. On the 56,000-km elevator: a section-loss fray localized to 606 km, trended, and a Remaining Useful Life of 18 years certified without simulating 18 years — where a mission-life FEM is ~30,000 years of wall-clock.
  • The warrant voids itself. A fault on its projection stays certified; one that outruns its trend voids the certificate automatically — act now. Swap a sensor, touch a limit, go blind: the monitor decertifies. Verifiable offline, through the lunar night.
Log-log chart. Horizontal axis is cycles or depth K from ten-cubed to ten-to-the-eighteenth. Vertical axis is flops on a log scale. A grey dashed line, explicit time-stepping at order n-squared K flops per trajectory, rises steeply to a labeled dot near ten-to-the-17 flops per trajectory. A solid green line, the Noether one-Lyapunov-witness certificate at order one, stays flat and low, labeled: one witness certifies every trajectory, all K.
Certify endurance without the endurance run. Explicit stepping is O(n2K) flops per trajectory — ~1017 at a decade-mission depth, and it certifies only the trajectories it runs; one verified Lyapunov witness certifies every trajectory for all K, at constant cost. The exact tier carries no floating point in the verdict.

The lunar-elevator lifecycle — ISO 13374, end to end

BlockWhat was establishedThe number
Detect & locatea section-loss fray on the 56,000-km cable found and localized from one vibration record, through an exactly-subtracted climberlocalized to 606 km
Classifyfault type from the exact modal signature — section loss reads as a mode up-shift (the life-limiting sign), blindtype 7/7 blind
Trendthe growth rate from a monitoring history, with runaway (accelerating) faults flagged automaticallyrate exact · R2 1.00
Remaining lifestate × trend × the design threshold → a certified RUL, where the mission-life FEM is ~30,000 years18 years, certified
Auto-decerta fault on its projection stays certified; one outrunning the trend voids the warrant — liveon-trend / outrunning → VOID

Capture & lifecycle steel threads — measured audits; parity referee the open-source symmetric eigensolver; a spectral-gap constant to 40 digits; the design threshold from the constant-stress tether. A demonstration of the certified-lifecycle capability, not a flight-qualified structural-health system.

How — the witness, the signature, the self-voiding warrant

  1. One witness for all trajectories. A verified certificate bounds the system's contraction to steady state for every initial condition and all time — the composed answer to “does it settle, and by when.” The engine is sealed; the mathematics is published. exact tier: no float in the verdict
  2. Read the fault, name it, trend it. The mode comb gives detection and localization; the exact signature gives the fault type; a sequence of readings gives the growth rate and flags runaway. ISO 13374 Health Assessment
  3. Remaining life is the composition. Current state (resolved), growth (trended), and the design limit combine to a certified Remaining Useful Life — the answer you cannot get by running the mission. state × trend × design threshold
  4. The warrant is a state. It self-voids when the fault outruns its projection, when a component's behavior changes, or when the monitor goes blind — and its whole history is a sealed, offline-checkable chain in which a safety limit cannot change quietly. verify · status · mint