Step 043 — Layered equivalence

The enrichment ladder changes what “the same” can mean.

Book / layer. Book IV · E1
Macro step. CS-05 — Recover Internal Physical Grammar
Short routes. https://prrp.site/s43 · https://prrp.site/s043

Status tags. readout

Construction role

The enrichment ladder changes what “the same” can mean. At $E_0$, sameness is identity of generated objects, addresses, and normal forms. At $E_1$, physics introduces physical-kind equivalence: two distinct carrier realizations count as the same particle or mode when they preserve the same defect-bundle, holonomy, charge, mass, spin, and transport invariants under admissible readout. Thus “this is a neutron” does not assert numerical identity of substrate pieces; it asserts membership in the neutron equivalence class. Higher-layer analogues – code equivalence at $E_2$, semantic/proof equivalence at $E_3$ – appear below as the construction continues into Books VI – VII.

What this step earns

Layered equivalence is made addressable as Step 043 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:643)

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 042 — Hinge Theorem export
• Next: Step 044 — No stage/actor split

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• Ten-step Construction Spine