Step 025 — Local Hartogs and mutual determination

The boundary grammar now becomes a local continuation principle.

Book / layer. Book II · E0
Macro step. CS-02 — Recover Core Mathematics
Short routes. https://prrp.site/s25 · https://prrp.site/s025

Status tags. formal

Construction role

The boundary grammar now becomes a local continuation principle. The bounded-lift operator BndLift_n certifies that, at each finite depth, refinement tails, spectral tails, ω-germs, boundary characters, and Hartogs continuation are mutually determined. Knowing any one of these data types fixes the others up to the admissible τ-holomorphic grammar. Boundary and interior therefore cease to be independent descriptions: they are two readouts of one stabilized continuation structure. This rigidity is what will later make physical localization non-arbitrary; the carrier cannot choose interior data freely once boundary data are fixed.

What this step earns

Local Hartogs and mutual determination is made addressable as Step 025 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:373)

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 024 — Master constant ι_τ
• Next: Step 026 — Regularity and finite spectral support

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