mathematical-twin

The groupant beside models/mathematical-twin.groupant 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

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 approximant
ast	not materialized
composition	partial	Composition
descriptant	present	Epoch memory
invariant	partial	Invariant
tests	existing checks referenced	tests

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
`excluded-observations`	behavior_complement	partial source derived	excluded-observations
`compatible-histories`	reverse_reconstruction	partial source derived	compatible-histories
`cohort-boundary`	cohort_partition	partial source derived	cohort-boundary
`finite-update-domain`	numerical_domain	partial source derived	finite-update-domain
`replay-converse`	evidence_replay_preimage	partial source derived	replay-converse
`cost-decomposition`	resource_approximation	partial source derived	cost-decomposition

Model text

model

Mathematical twin interaction model

Forward approximant

For model M=(theta,P,n,SSE,lo,hi), input x and positive observed duration y, the ideal update uses h=x^T P x, e=y-x^T theta and d=1+h:

theta' = theta + P*x*e/d
P' = P - (P*x)*(P*x)^T/d
n' = n+1; SSE' = SSE+e^2.

The implementation clones, updates and validates the candidate before replacing M. The residual is prospective: it compares y to the earlier forecast. The matrix is inverse information, not calibrated predictive covariance. Prediction may be negative even though accepted observed durations must be positive.

Composition

CLI validate/fingerprint/domain -> library prediction -> forecast persistence -> explicit requested command -> output/fingerprint checks -> observation persistence -> library observation update -> checkpoint persistence. Predict mode stops before execution. Failed observations retain evidence and reject the normal update path; I/O errors can leave partial directories and files.

Cohort identity includes named context, fixed arguments/settings, feature names, prior, ridge, output checks and fingerprints. Variable feature values and named environment axes are allowed within a cohort. Parent preparation checks evidence hashes and replays the previous update; filesystem trust and collision resistance remain assumptions. This is a source-derived composition, not a new process run.

Invariant

Feature ordering uses BTreeMap keys. Model dimensions, finite values and positive information are checked at prediction/update boundaries. Forecast persistence precedes command launch on the normal run path. Hash binding establishes byte identity; it does not establish scientific adequacy or arbitrary external state. No default clipping makes a negative forecast physically meaningful.

Epoch memory

2026-10-29: this group registers the existing mathematical-twin library and CLI. Their source snapshots and child contracts now participate in root closure. Known limits include a tiny-ridge constructor result later rejected by validation, unvalidated min/max ordering/history consistency, count-overflow assumptions, and the replay helper's zip-based comparison. These are scoped observations, not newly fixed code or an end-to-end correctness claim. Exact arithmetic and finite-precision behavior remain distinct.

References

Sherman and Morrison (1950), doi:10.1214/aoms/1177729893, rank-one inverse. Kalman (1960), doi:10.1115/1.3662552, sequential correction. These are already cited in the library; neither source grants the runtime model calibrated prediction intervals.

catalog

Typed interaction models

All relations have the assumptions and dependency limits in model.md. These are source-derived partial models; check references do not imply universal proof.

excluded-observations

Type: behavior_complement.

U consists of fixed-snapshot CLI run records and model transitions; an inner bound on U minus actual R contains a normal updated checkpoint after a rejected observation, or admitted prediction with invalid feature dimensions. I/O failures may retain prefixes.