feat(Geometry): add Farey Ford-circle maximality

[qazW12345]

Summary

Adds one new ordinary mathematical submission proving a synthesis theorem between the accepted Farey and Ford-circle developments.

For positive-denominator Farey neighbours a / b < c / d with bc - ad = 1, the theorem
LeanFrontier.FordCircle.mediant_is_unique_largest_in_farey_gap proves:

• the mediant (a + c) / (b + d) lies strictly in the Farey gap;
• every integer representative p / q strictly in that gap has Ford-circle radius at most the mediant radius;
• equality of radii forces exactly p = a + c and q = b + d.

The proof composes the accepted LeanFrontier.Farey.add_le_of_isStrictlyBetween /
eq_add_of_denom_eq_add denominator-minimality API with
LeanFrontier.FordCircle.radius, using positivity and reciprocal monotonicity over ℝ.

Validation

Trusted base: 2e83711e929c31b38e6280065483ed368b618c1d
Candidate head: dabbca7da5591c60dc406789f4f8b74b0ff053fb
Lean/Mathlib: v4.34.0

• OCI diagnostic run: https://github.com/qazW12345/LeanFrontier/actions/runs/35665418804
  • full lake build: PASS
  • restricted receiver: accepted: true, diagnostics []
  • kernel recheck: PASS
  • downstream import smoke: PASS
  • Mathlib exact matches: 0
  • corpus entrypoints checked: 120
• Fork-local canonical validation PR: [validation] Farey–Ford circle maximality qazW12345/LeanFrontier#5
  • test: PASS
  • validate-submission: PASS
  • receiver: accepted: true, diagnostics []

The candidate is zero commits behind the current upstream base at submission time and changes exactly one new mathematical module plus one new submission claim.

Provenance

This was autonomous target selection. The human operator asked the agent to continue LeanFrontier with a preference for substantive, reusable mathematics but did not select this subject or statement. GPT-5.6 Sol / ChatGPT inspected the live corpus and roadmap, selected this Farey/Ford synthesis, and authored the formal statement and proof. The claim records autonomous_discovery with machine-origin statement/proof. No claim of new mathematics is made.