Step 028 — Central Theorem route

The Central Theorem assembles the preceding machinery into the bulk – boundary correspondence: 𝒪(${\tau }^3$) ≅ A_spec(𝕃).

Book / layer. Book II · E0
Macro step. CS-03 — Internalize Self-Enrichment
Short routes. https://prrp.site/s28 · https://prrp.site/s028

Status tags. formal hinge

Construction role

The Central Theorem assembles the preceding machinery into the bulk – boundary correspondence:

𝒪(${\tau }^3$) ≅ A_spec(𝕃).

The holomorphic interior, the boundary character ring, and the spectral algebra are not three independent objects; under the theorem they determine one another through a calibrated split-complex isomorphism. Its ${\iota }_{\tau }$-calibration property transports the already-earned H3/II.T25 master-constant calibration from boundary data into the interior; it does not rederive the closed form. The finite rank-(3,15) Lean check and the exact registry dependencies live in the internal source ledger; the main point here is structural: boundary spectral data and holomorphic interior data become one rigid object.

What this step earns

Central Theorem route is made addressable as Step 028 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:410)

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 027 — Sheaf coherence, self-enrichment, Yoneda
• Next: Step 029 — τ-manifold and Book III handoff

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