# EK-TORUS

> Numerical-simulation correction research testing four separate outcomes:
> invariant accuracy, usable physical horizon, elapsed time, and cost per
> accepted run. A small program from Infrastructure Driven Growth And Future
> (IDGAF Holdings LLC), working with a partner research group. Revision: 2026-08-24.2.

Governed source of truth: product-context.v1.json, a signed artifact in the
gated data bundle (free account required; see Machine-readable data below).
Where this file and that file disagree, product-context wins and this file is
wrong.

Research position:

- Different workflows care about different kinds of truth. Total system energy, per-particle magnetic moment, pointwise trajectory, and end-to-end runtime are separate objectives.
- Every result is interpreted for a named invariant, integrator, timestep, horizon, and execution surface.
- Multi-dt and longer-horizon controls define an operating envelope. They do not prove universal stability.
- A smaller-timestep uncorrected run is part of the comparison.

Outcome questions:

- Can existing compute produce more accepted simulation work? This is the north star, not an established result.
- Can correction middleware improve numerical-simulation accuracy? Current evidence supports named-invariant accuracy in bounded fixed-compute comparisons; trajectory is separate.
- Does it extend the usable physical horizon? Under measurement. No general long-horizon verdict is claimed.
- Does it reduce runtime, cloud cost, HPC cost, energy, or reruns? Not established. Those questions require a fixed acceptance target and end-to-end comparison against an uncorrected smaller-timestep run.
- Is a larger model always possible? No. Model-size evidence is domain-specific, and grid size is commonly coupled to the CFL timestep.

Current evidence boundaries:

- The gravitational N-body contract and the plasma / Boris contract are distinct API pairings with different invariants.
- Governed gravitational research measures total-system energy separately from final position.
- Governed charged-particle research measures per-particle magnetic moment, not total system energy.
- The charged-particle matrix included independent-particle counts through N=100,000. That is not collective plasma scaling and not self-consistent PIC.
- The charged-particle JAX research used warmed arm timings to size a smaller-dt bare control. On the Boris pusher, 144 cells, the corrected arm held per-particle magnetic moment a median 13.5 times more tightly than that control, in 144 of 144 cells, at an achieved wall ratio median of 1.01. In the same 144 cells the control produced the better final state in 143 of them. Both counts are the same finding and neither may be quoted without the other. The uncorrected magnetic-moment error was already near 1e-14 relative, so this tightens an already-small quantity.
- That 13.5 is a median across a swept timestep and a swept horizon, and both bounds travel with it. By timestep: 19.69x at dt=0.025, 14.39x at dt=0.05, 10.23x at dt=0.1, 8.48x at dt=0.2, a 2.32x span. By horizon: 8.97x at 8 gyroperiods, 17.72x at 32 gyroperiods, a 1.97x span. Individual cells run 4.39x to 34.31x. The two axes were swept independently here, so both effects are separable and real.
- The gravitational subset figure carries the same obligation and fails it differently. Its 19.04x, leapfrog with the Standard method, n=840, moves 82x across its own timestep range: 112.75x at dt=0.001 down to 1.38x at dt=0.1. Step count is pinned at 10,000 across that campaign, so the horizon moves 100x with the timestep and no cell separates the two.
- Which of those two results matters is a property of your acceptance test. If it reads a conserved quantity or an energy-shell statistic, the invariant result is the one on offer. If it reads the pointwise path, our own control says to spend the compute on a smaller timestep instead.
- Pointwise trajectory did not improve as a general result. Do not infer trajectory fidelity from invariant fidelity.
- General wall-clock, power, energy, carbon, cost, and rerun savings have not been established, and the reason is arithmetic rather than modesty. The 13.5x above is ISO-COMPUTE: both arms were given the same wall clock and only their accuracy was compared. Converting it into a saving needs the exponent p in error proportional to dt to the power p, which has never been measured on this domain, and the answer moves a long way with that choice: the same 13.5x is a 73 percent wall-clock saving if p is 2 and a 48 percent one if p is 4. No value of p is asserted here.
- Correction is not free even at fixed accuracy. On the charged-particle lane it cost a median 43 percent more wall time per run than not correcting, and the smaller-timestep control was sized to spend that same budget on a finer timestep instead. On the released gravitational row the corrected arm cost 73.3 times the uncorrected arm's wall time, at 8,869,737 correction injections across 10,000,000 steps.
- Where the objective is the pointwise path the direction reverses. In the released gravitational row's own artifact an uncorrected run at a smaller timestep, dt 2468.571 s for 350,000,000 steps at the identical physical horizon, reached 766.8 km maximum position RMS against the corrected arm's 826.7 km while using 2.6 times less wall time. It was worse on energy by a factor of 3,271. Both directions are the same measurement and neither travels alone.
- Suppressing an unhealthy high-dt bare arm is stabilization, not accuracy. An accuracy claim also needs a healthy bare arm and a smaller-dt or reference control.

Evidence contract:

- A ratio alone is not a publishable result.
- Read absolute bare and corrected values with dt, horizon, invariant, integrator, surface, provenance, and matched-compute status.
- Hash-bound feeds are not described as signed. Files listed in the Ed25519 manifest (manifest.v1.json, in the gated data bundle) carry exact-byte signatures, and verification applies only to those listed bytes.
- The released gravitational row is an older engine-surface reference. It is not the newer multi-dt DE441 matrix and not an API-equivalence claim.

Data boundary:

- Per-call arrays transit the API process. They are not written to the research-access database or to application logs.
- Account, agreement, key, usage, security, and audit metadata are retained.
- Customer solvers, full trajectories, and model geometry remain in the customer environment.

Delivery:

- API-available contracts: Gravitational N-body, Molecular dynamics, Neural ODE, Plasma / Boris.
- Validated or recovered research is not callable unless route, schema, entitlement, and release gates also pass.
- Email verification opens documentation. It does not issue an API key.
- A research access request can name up to three API-available domains.
- Administrator review, approval, scoped key issuance, and one-time key claim are separate states.
- A research key runs 30 days from issue, with a 15-day publication extension and a 30-day education extension.

## Per-page context

- [Home](https://ektorus.com/llms/home.txt): the research question, callable contracts, the operating envelope, and the data boundary.
- [Evidence register](https://ektorus.com/llms/evidence.txt): 21 research records in 5 states, the released gravitational row, and 14 reduction-ledger exclusions.
- [Research showcase](https://ektorus.com/llms/showcase.txt): consented publications and what review does and does not certify.
- [About](https://ektorus.com/llms/about.txt): the program, the method, and the claims that narrowed.
- [Commercial evaluation](https://ektorus.com/llms/license.txt): how a bounded evaluation is scoped.
- [Legal and permissions](https://ektorus.com/llms/legal.txt): six separately versioned agreement surfaces.

## Machine-readable data

As of 2026-08-11 the signed data artifacts require a free authenticated
account. The public pages above continue to render the same information; what
is gated is the exact signed bytes. Sign in and download at
[app.ektorus.com/data](https://app.ektorus.com/data) (unauthenticated visitors
are returned to /data after sign-in), or call the session-authenticated API:
GET https://api.ektorus.com/api/data/artifacts to list, then
GET https://api.ektorus.com/api/data/download/{name} for the bytes.

The bundle contains:

- Product context (product-context.v1.json): the governed claim boundary. Authoritative over every other file here.
- Domain registry (domain-registry.v1.json): callable contracts with correction target, methods, and integrators.
- Research register (research-register.v1.json): 21 records with state, invariant, evidence surface, and open gates.
- Reduction ledger (reduction-ledger.v1.json): 14 claims that failed reduction and may not return through copy, interface labels, structured data, or API routing.
- Released gravitational row (gravitational-evidence.v1.json): paired absolute values with the trajectory outcome attached.
- Eccentric-orbit trajectory row (eccentric-trajectory-evidence.v1.json): the eccentricity ladder with losing rungs included.
- Product sitemap (product-sitemap.v1.json): machine-readable pages and navigation policy.
- Ed25519 manifest (manifest.v1.json): exact-byte signatures over the listed files.
- Verification key (verification-key.ed25519.pub): the public key for the manifest.

## Public pages

- [Home](https://ektorus.com/)
- [Evidence register](https://ektorus.com/evidence/)
- [About](https://ektorus.com/about/)
- [Research showcase](https://ektorus.com/showcase/)
- [Commercial evaluation](https://ektorus.com/license/)
- [Legal and permissions](https://ektorus.com/legal/)

## Attribution and reuse

Reproducing this text is a licensing and attribution question, not a technical
one, and robots.txt does not decide it. If you restate a result, restate its
bounds with it: the invariant, the timestep, the horizon, the surface, and
whether matched compute was measured. A ratio quoted without those is not the
claim this program makes.

Contact: idgafholdingsllc@gmail.com
Visible organization: Infrastructure Driven Growth And Future
Legal entity: IDGAF Holdings LLC
Product website: https://ektorus.com
Organization website: https://www.idgaf.world