Step 064 — τ-Einstein identity

The macro field identity is written here as $R^H$, with ${\kappa }_{\tau }$ serving as the τ-gravitational coupling readout, not as an imported PDE.

Book / layer. Book V · E1
Macro step. CS-06 — Build Measurement, Prediction, and Empirical Bridges
Short routes. https://prrp.site/s64 · https://prrp.site/s064
Formula checkpoints. $R^H$

Status tags. bridge readout external-validation-seam

Construction role

The macro field identity is written here as

,

with ${\kappa }_{\tau }$ serving as the τ-gravitational coupling readout, not as an imported PDE. Here H is the holonomy/curvature superscript, not an abbreviation for the Riemann Hypothesis. Its role is to balance curvature-side holonomy data with matter/stress defect data inside the same carrier grammar. Ordinary Einstein gravity appears as a chart/readout shadow of this identity, not as an assumed background equation. Classical GR tests are therefore treated as readout checks of the τ-Einstein structure rather than as axioms of the construction.

What this step earns

τ-Einstein identity is made addressable as Step 064 in the fine-grained Construction Spine routing layer.

• Routing scaffold. Detailed earned-output extraction is pending the source-map pass.

What this step does not yet establish

This route exposes the RC3 construction step for inspection. It does not by itself establish peer review, empirical adequacy, or final manuscript-level source closure.

Source anchors

• Full Construction Spine RC3 whitepaper source (papers/whitepapers/panta-rhei-construction-spine-e0-e3/main.tex:879)

Manuscript extraction state: Detailed source anchors pending extraction.

Anchor classification: whitepaper source resolved; manuscript extraction pending; Registry extraction pending; TauLib extraction pending.

Formalization and verification

Registry links: Registry extraction pending.

TauLib modules: TauLib module extraction pending.

Dependencies

• Previous: Step 063 — Gravity as frame holonomy
• Next: Step 065 — Lorentzian signature from j²=+1

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