Extensional–projective
How is the object constructed, transformed, viewed, projected, and reconstructed? What survives and what is lost?
Unified geometry-thinking kernel
From Views to Operational Phases
E7G-T makes construction, projection, preservation, loss, reconstruction, operational sameness, material boundaries, transition paths, bridge mode, and admissible use visible.
One kernel, two complementary routes.
The phase layer does not replace projection geometry. It completes it.
Operational phase
Which configurations count as equivalent for this inquiry? Which change crosses a material boundary?
Combined route
Does a lossy view support one operational phase, several possible phases, or no admissible phase?
The practical sequence.
Use the smallest profile that changes the next responsible move without hiding risk.
1. Frame
Name the entity, semantic context, inquiry, model boundary, and intended use.
2. View
Declare viewing or projection, preserved structure, loss, distortion, and source candidates.
3. Define sameness
State tolerated differences and the relations, invariants, behaviours, or interfaces that define the phase.
4. Test sufficiency
Determine whether the reconstruction fibre maps to one phase, several phases, none, or an unknown set.
5. Navigate
Inspect typed transitions, phase boundaries, path choice, operation order, and representative dependence.
6. Act or stop
Classify, narrow, source-return, obtain another view, compare paths, repair, rely within scope, or stop.
Where the phase layer matters.
AI answers
Different source and support states can produce the same fluent answer while belonging to different reliance phases.
Translation QA
Different wording may be harmless variation—or may cross a legal-force, identity, or usability boundary.
Dashboards
The same green tile may be compatible with source configurations in different readiness or health phases.
Software
A refactoring claim requires behavioural equivalence, representative checks, and path-sensitive validation.
Proof work
A visible proof state may not uniquely determine proof readiness or discharged-obligation status.
Documents and decisions
A summary, status, or approval-looking view may not carry the phase required for operational reliance.
Start testing.
The unified kernel is a candidate. Its value must be demonstrated by better next moves.
Start here
Use the worksheet
Run the pilot
Public caution
E7G-T is not established mathematics as a whole, empirical physics, a proof system, an authority decision, or a replacement for domain expertise. Formal-looking notation does not create evidence, proof, authorisation, validation, or performed work.