lin-0087

6.5 A bracket-enriched CSQL schema

The construction can be presented through a tangent expansion \(\tau \mathbb S\). The exact physical tables are application dependent, but the logical roles are stable.

Logical relation

Representative fields

Mathematical role

Typical query

Context

regime, source, population, chart, version

site over which an instance is interpreted

where was the field estimated?

Generator

field id, target, protocol, anchor, estimator

registered natural vector field

which intervention directions are visible?

Transport witness

schema arrow, source field, target field, residual

naturality of a database section

which fields fail under migration?

Bracket witness

ordered pair, context, coefficients, bracket value

antisymmetric interaction

which pairs interact by order?

Closure witness

visible span, quotient class, residual, uncertainty

factorization through \(\mathcal D_{\mathrm{vis}}\)

where does the span fail to close?

Evidence

data slice, probe, seed, estimator, confidence, provenance

observer and admission record

can the witness be reproduced?

Repair ticket

proposed generator, latent augmentation, invariant, status

typed change awaiting admission

which repair explains the obstruction?

Table 6.1 A logical schema for a bracket-enriched infinitesimal database. The relations store typed witnesses and provenance rather than only scalar bracket scores.

For a local frame \(V_1,\ldots ,V_r\), a bracket row may retain

\[ [V_i,V_j] = \sum _{k=1}^{r}c_{ij}^{k}V_k + R_{ij}, \]

together with the coefficient chart, quotient convention, uncertainty, and provenance of \(R_{ij}\). The database should not treat the coefficients as globally comparable unless their frame-transport maps have been declared. The same geometric bracket can have different coordinates in different charts.

This yields CSQL-like questions that an ordinary causal graph cannot answer:

  • Which intervention-field pairs fail closure in more than one regime?

  • Does a closure witness survive quotienting of nuisance or gauge directions?

  • Which schema migrations preserve a field but not its estimated bracket?

  • Can one proposed latent generator repair several localized residuals?

  • Does the repaired span close on held-out contexts without changing admitted causal effects?