---
title: "twin-forecast — Mova code model"
description: "Mova code model of tools/twin/src/lib.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/tools/twin/src/lib.rs.groupant/forecast.groupant/"
---
Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants**

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# twin-forecast

The groupant beside tools/twin/src/lib.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

## Facts

- **kind:** groupant_fragment
- **status:** partial source bound model
- **source:** [`tools/twin/src/lib.rs`](https://github.com/ElamurAI/mova-free/blob/main/tools/twin/src/lib.rs)
- **source SHA-256:** `89a5a0b5a5dc0fde…`
- **covers:** Prediction and observed-support projection (bytes 3501–4386)
- **part of:** [mathematical-twin-library](https://md.groupants.elamur.ai/free/en/mova/tools/twin/src/lib.rs.groupant/)
- **repository folder:** [`tools/twin/src/lib.rs.groupant/forecast.groupant`](https://github.com/ElamurAI/mova-free/tree/main/tools/twin/src/lib.rs.groupant/forecast.groupant)
- **repository commit:** `855da7bd4a7b`

> **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.

## Components

| component | label | where |
|---|---|---|
| **approximant** | partial | [forward](#forward) |
| **ast** | not materialized |  |
| **cost** | partial | [cost](#cost) |
| **descriptant** | present | [epoch-memory](#epoch-memory) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | existing checks referenced | [checks](#checks) |

## Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

| id | type | label | where |
|---|---|---|---|
| `twin-forecast-behavior-complement` | behavior_complement | partial source model | [behavior-complement](#behavior-complement) |
| `twin-forecast-reverse-reconstruction` | reverse_reconstruction | partial source model | [reverse-reconstruction](#reverse-reconstruction) |
| `twin-forecast-rmse-observation` | history_projection | partial source model | [rmse-observation](#rmse-observation) |
| `twin-forecast-box-boundary` | support_relation | partial source model | [box-boundary](#box-boundary) |

## Model text


### catalog

## Prediction and observed-support projection

Subject: `tools/twin/src/lib.rs`, exact SHA-256 in manifest; modeling epoch 2026-10-29.

Every relation below is scoped to the named observation, holding other input/state coordinates fixed unless quantified. U is its stated input/output (or finite trace) Cartesian universe, R the described reachable relation. Complement targets U \ R; converse retains every compatible antecedent, never an invented unique cause. Source-derived formulas are partial hypotheses about Rust; floating-point expressions use evaluation order where stated, ideal real identities are conditional. Checks marked proposed were not executed.

### forward

validate M, require finite x of matching length; compute px/h/seconds, reject unstable projections and return n/RMSE/box summary.

### invariant

Validation requires finite vectors/SSE>=0 and approximate symmetry plus successful finite positive Cholesky pivots. It does not certify an exact symmetric matrix, box ordering, n/SSE consistency or observational reachability. Constructor does not call validate: subnormal positive ridge may yield infinite P. Predict may return negative seconds. n+1 overflow is not guarded: debug panic or release wrapping is outside the n<u64::MAX model.

### cost

At dimension d<=32, validation uses O(d^3) arithmetic and O(d^2) allocation. Predict adds O(d^2); observe calls predict and another validate, hence O(d^3), not merely the O(d^2) rank-one kernel. State memory O(d^2). No wall-clock estimate is calibrated.

### composition

Leaf fragment. Its validation dependency lies in the sibling initial-state fragment; cost includes that call.

### epoch-memory

Initial source review, 2026-10-29. Default Rust source remains unchanged. These models record mechanisms and gaps rather than claiming statistical calibration, semantic proof or a complete AST. CLI evidence is trusted local data, not authenticated provenance. Preserve these limits when refreshing bindings.

### checks

Existing `cargo test -p mova-twin --locked`: three library tests compare online updates with independent 2D ridge, reject invalid information and preserve prospective residuals; three ledger integration tests exercise forecast-before-execution, parent replay/tamper rejection, rejected runs, timeout, input mutation and predict without launch. Integration commands are bounded local fixtures, not live benchmarks or teacher calls. See checks.md at the file root for execution evidence. Other oracles below are proposals. Structural validation checks hashes, references and bounds, not equations.

### behavior-complement

U is (M,x,Result Prediction). Source-derived U\R excludes successful nonfinite seconds/leverage or negative leverage and mismatched feature length. Negative finite seconds and zero feature vectors are allowed by library predict. Proposed oracle distinguishes this library domain from CLI nonzero-feature validation.

### reverse-reconstruction

At fixed M and prediction z, B(z)={x:dot(x,theta)=z.seconds, dot(x,Px)=z.leverage, box predicate=z.outside, all Rust guards pass}; n and RMSE are fixed state projections. In real SPD geometry this intersects a hyperplane with an ellipsoid plus box inequalities; rounding modifies boundaries. Proposed oracle groups a small feature grid and preserves all ties.

### rmse-observation

Observation n=0 maps any validate-accepted SSE to historical_rmse=None; n>0 maps to sqrt(SSE/(n as f64)). Thus None loses SSE, and floating casts/sqrt can merge distinct history values. Proposed oracle contrasts two n=0 loaded states with unequal SSE; validate permits both.

### box-boundary

For n>0, outside is OR_i(x_i<min_i or x_i>max_i), using strict inequalities. Boundary equality is inside; n=0 always outside. Observed box coverage is not density, hull membership or uncertainty. Existing ridge test exercises x5 outside and x2 inside after maximum4.