THM0058canonicalv1Cayley Word Metric (Hinge 7)
The Cayley word metric d_Cay on the DAG, defined as minimal n_1 + n_2 over common reducts, is a genuine metric on AddrTau = Code^NF/teq (reflexive, symmetric, triangle inequality, separation modulo teq). Coincides with Hinge 1's minimal-pass distance. Integer-valued; induces the tau-topology on AddrTau. Effective Bourdon dimension bounded by primorial growth. Source: Hinge 7 section-06-cayley.
Payload
Cayley Word Metric (Hinge 7)
The Cayley word metric d_Cay on the DAG, defined as minimal n_1 + n_2 over common reducts, is a genuine metric on AddrTau = Code^NF/teq (reflexive, symmetric, triangle inequality, separation modulo teq). Coincides with Hinge 1’s minimal-pass distance. Integer-valued; induces the tau-topology on AddrTau. Effective Bourdon dimension bounded by primorial growth. Source: Hinge 7 section-06-cayley.
Cayley Word Metric (Hinge 7)
Summary
The Cayley word metric d_Cay on the DAG, defined as minimal n_1 + n_2 over common reducts, is a genuine metric on AddrTau = Code^NF/teq (reflexive, symmetric, triangle inequality, separation modulo teq). Coincides with Hinge 1’s minimal-pass distance. Integer-valued; induces the tau-topology on AddrTau. Effective Bourdon dimension bounded by primorial growth. Source: Hinge 7 section-06-cayley.
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 258 - Manuscript source: not matched
Lean / Formalization Notes
- Formalization:
planned - Module:
TauLib.BookI.Addressability.CayleyMetric - Name:
None
Dependencies
- Canonical: I.T53, I.T54, I.T55
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.T56cayley-word-metric-hinge-7thm:main-cayleyRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
Sources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.