Step 016 — Global Hartogs
character grammar, CRT reconstruction, tower coherence, and the τ-Identity Theorem now support Global Hartogs: τ-holomorphic data on L K, for primordially thin K, extends uniquely to L, so coherent ω-tail data determine the finite-stage values they project...
character grammar, CRT reconstruction, tower coherence, and the τ-Identity Theorem now support Global Hartogs: τ-holomorphic data on L K, for primordially thin K, extends uniquely to L, so coherent ω-tail data determine the finite-stage values they project…
Book / layer. Book I · E0
Macro step. CS-01 — Build the τ-Kernel
Short routes. https://prrp.site/s16 · https://prrp.site/s016
Status tags. hinge
Construction role
The spectral character grammar, CRT reconstruction, tower coherence, and the τ-Identity Theorem now support Global Hartogs: τ-holomorphic data on L K, for primordially thin K, extends uniquely to L, so coherent ω-tail data determine the finite-stage values they project to. This is not an imported transfinite completion theorem; it is the first internal limit/stage discipline of τ. The construction can speak about its own infinite-stage extensions because boundary data, character grammar, and admissible ω-germ transformers have already been earned. This closes Book I’s mathematical layer by showing that the kernel has enough internal grammar to host limit constructions without leaving the system; proof-substrate audit remains part of the formal trust budget rather than a separate construction step.
What this step earns
Global Hartogs is made addressable as Step 016 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:256)
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 015 — Lemniscate characters
- Next: Step 017 — Boundary-first inversion
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