THM0059canonicalv1Ontic Ultrametric (Hinge 7)
The Cayley-completion (Ultra, d_inf) = widehat{(AddrTau, d_Cay')} is a complete ultrametric space: strong triangle inequality d_inf(a,c) <= max(d_inf(a,b), d_inf(b,c)), non-archimedean, totally disconnected. Matches the Hinge 4 profinite boundary topology under the primorial ladder (M_k). Ontic (not epistemic) indeterminacy at unstabilised addresses. iota_tau anchors the scale via sigma-fixed endomorphism orbit. This is the tau-native replacement for Euclidean distance in Books II-VII. Source: Hinge 7 section-07-ultrametric.
Payload
Ontic Ultrametric (Hinge 7)
The Cayley-completion (Ultra, d_inf) = widehat{(AddrTau, d_Cay’)} is a complete ultrametric space: strong triangle inequality d_inf(a,c) <= max(d_inf(a,b), d_inf(b,c)), non-archimedean, totally disconnected. Matches the Hinge 4 profinite boundary topology under the primorial ladder (M_k). Ontic (not epistemic) indeterminacy at unstabilised addresses. iota_tau anchors the scale via sigma-fixed endomorphism orbit. This is the tau-native replacement for Euclidean distance in Books II-VII. Source: Hinge 7 section-07-ultrametric.
Ontic Ultrametric (Hinge 7)
Summary
The Cayley-completion (Ultra, d_inf) = widehat{(AddrTau, d_Cay’)} is a complete ultrametric space: strong triangle inequality d_inf(a,c) <= max(d_inf(a,b), d_inf(b,c)), non-archimedean, totally disconnected. Matches the Hinge 4 profinite boundary topology under the primorial ladder (M_k). Ontic (not epistemic) indeterminacy at unstabilised addresses. iota_tau anchors the scale via sigma-fixed endomorphism orbit. This is the tau-native replacement for Euclidean distance in Books II-VII. Source: Hinge 7 section-07-ultrametric.
Statement
No manuscript statement was extracted in this pilot run.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-01.jsonlline 259 - Manuscript source: not matched
Lean / Formalization Notes
- Formalization:
planned - Module:
TauLib.BookI.Addressability.OnticUltrametric - Name:
None
Dependencies
- Canonical: I.T53, I.T54, I.T55, I.T56
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
I.T57ontic-ultrametric-hinge-7thm:main-ultrametricRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
Sources
Version & History
Status disclaimer
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