Benchmark
Exact-GR Benchmark
Read the effective benchmark before interpreting geometry notation.
Open routePhysics Research / Geometry
Flow Geometry
Flow geometry is a dictionary for reading geometry-facing terms. It is not a derivation of the effective metric, matter coupling, field equations, or benchmark promotion.
The Æther Flow Project is a two-part research program about foundational physics and the governed, human-accountable AI research system used to organize and test that work. This Flow Geometry page explains the physics track's dictionary for reading the proposed Æther-Flow interpretation inside its exact general-relativity benchmark.
In that dictionary, g is the adopted GR metric and u is an admissible, generally non-unique observer field used to describe expansion, shear, rotation, and acceleration within the same spacetime geometry. The observer field adds interpretation rather than a second gravitational law, and the page does not derive either the metric or a preferred flow from substrate variables. It helps a general reader distinguish useful geometry vocabulary from the separate work needed to derive matter coupling, recover Einstein equations, or promote the benchmark.
Static diagram
Keep flow-geometry vocabulary below metric promotion.
The metric-response ladder is reused here because it illustrates the same protected boundary: geometry terms and response objects do not jump directly to matter coupling, Einstein equations, or GR promotion.
Visual dictionary
Put each geometry term beside its limit.
The dictionary is intentionally tabular. It keeps meaning, assumption, and limit visible at the same time.
| Term | Meaning here | Assumption | Limit |
|---|---|---|---|
| g | The metric symbol used when discussing the effective benchmark geometry. | Reader-facing shorthand must be tied to its benchmark context. | This page does not derive g from source-side substrate data. |
| u | A congruence or flow-direction marker used to orient geometry language. | It helps readers discuss ordered motion without importing a finished theorem. | It is not by itself a matter-coupling law or field equation. |
| Congruence geometry | A disciplined dictionary for reading flow-aligned geometric language. | The dictionary can clarify terms before formal source work is inspected. | Dictionary clarity is weaker than source-side derivation. |
| Observed geometry | The observer-facing geometric description associated with the benchmark route. | Observed geometry can remain ordinary at the public benchmark level. | Ordinary benchmark behavior does not prove substrate recovery. |
Claim status
Geometry vocabulary is weaker than derivation.
The page can explain the dictionary. It cannot turn a convenient notation into a source-side result.
| Layer | Can safely say | Cannot say |
|---|---|---|
| Vocabulary | Defines symbols and interpretive roles near their use. | Cannot make the symbols source-adopted objects by display alone. |
| Benchmark geometry | Keeps ordinary effective geometry visible for readers. | Cannot claim the effective metric has been derived from ontology. |
| Matter behavior | Names matter coupling as a downstream derivation requirement. | Cannot infer universal same-metric coupling from a geometry dictionary. |
| Field equations | Points toward the equation burden as separate work. | Cannot supply Einstein-equation recovery or benchmark promotion. |
Source basis
The dictionary depends on source-bundle boundaries.
Flow-geometry wording must stay tied to registered source anchors and claim-boundary records. When evidence is incomplete, the page uses weaker language.
| Source area | Used here for | Authority boundary |
|---|---|---|
| Geometry and relativistic-recovery TeX sources | Term orientation and source-bundle provenance. | Registered sources outrank website dictionary copy. |
| Exact-closure TeX notes | Benchmark package context for geometry language. | Generated explanation is not source promotion. |
| GR derivation burden map | Open burden ordering and downstream limits. | The map names burdens; it does not discharge them. |
| Claim-boundary registry | Forbidden overreads for metric, matter, equation, and promotion claims. | Registry constraints keep the page in weaker language. |