Step 024 — Master constant ι_τ

The three earned ingredients ${\pi }_{\tau }$,$e_{\tau }$, and the dyadic refinement scalar $2_{\tau }$ meet in the ω-limit as the master coupling ${\iota }_{\tau }$.

Book / layer. Book II · E0
Macro step. CS-02 — Recover Core Mathematics
Short routes. https://prrp.site/s24 · https://prrp.site/s024
Formula checkpoints. ${\iota }_{\tau }$ · ${\iota }_{\tau }$ · ${\iota }_{\tau }$

Status tags. hinge

Construction role

The three earned ingredients ${\pi }_{\tau }$,$e_{\tau }$, and the dyadic refinement scalar $2_{\tau }$ meet in the ω-limit as the master coupling

.

Its closed form is anchored in II.T25/H3 and in TauLib as

. Lobe-swap invariance, refinement-pressure uniqueness, and primorial-stabilized combinatorial linearity force the crossing value; the Central-Theorem route later transports this calibration, it does not rederive the closed form. The numerical value

is therefore presented as a structural calibration constant of the constructed geometry, not as a fitted parameter.

What this step earns

Master constant ${\iota }_{\tau }$ is made addressable as Step 024 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:359)

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 023 — Earned constants π_τ,e_τ,j
• Next: Step 025 — Local Hartogs and mutual determination

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