feat(Combinatorics/SimpleGraph/Extremal): the Kővári–Sós–Turán bound

[chy4pro]

This PR adds the Kővári–Sós–Turán bound (Kővári–Sós–Turán 1954) in a bipartite-relation form: if a relation r between finite sets A (size m) and B (size n) contains no K_{s,t} (s elements of A all related to t elements of B), then its number of edges e satisfies (e - (s-1) n)^s ≤ (t-1) m^s n^(s-1) (exact form in ℕ, with truncated subtraction) and hence e ≤ (s-1) n + (t-1)^(1/s) m n^(1-1/s) (real form).

New file Mathlib/Combinatorics/SimpleGraph/Extremal/KovariSosTuran.lean:

• KovariSosTuran.sum_choose_le — the double counting of stars ∑_{b ∈ B} C(deg b, s) ≤ (t-1) C(m, s);
• KovariSosTuran.kovari_sos_turan — the ℕ form of the bound (via (d+1-s)^s ≤ s! C(d,s) and the power-mean inequality);
• KovariSosTuran.kovari_sos_turan_real — the classical real-exponent form.

Mathlib defines SimpleGraph.zarankiewicz but (as far as I could find) does not contain this bound. I kept the statement in the elementary bipartite-relation language; connecting it to SimpleGraph.zarankiewicz / extremalNumber would be a natural follow-up if reviewers prefer that interface.

Checks: the file compiles against the base commit of this branch, #lint reports no issues, #print axioms on the main results shows only propext, Classical.choice, Quot.sound; the import line was added to Mathlib.lean.

AI disclosure (per the Mathlib AI policy): the Lean code was drafted by Claude (Anthropic, Opus/Fable models) in an agentic session directed by me; I re-ran the compiler and the linter myself, reviewed the statements and the proof structure, and I am responsible for the content. Please add the LLM-generated label if that is the right classification.

[github-actions]

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[github-actions]

PR summary 0b27e8799c

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Combinatorics.SimpleGraph.Extremal.KovariSosTuran (new file)	1854

---

Declarations diff (regex)

+ HasKst
+ card_common_le
+ deg
+ kovari_sos_turan
+ kovari_sos_turan_real
+ mem_nbhd
+ nbhd
+ nbhd_subset
+ numEdges
+ sum_choose_le
+ trunc
+ trunc_pow_le

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 0b27e87).

• +13 new declarations
• −0 removed declarations

+KovariSosTuran.HasKst
+KovariSosTuran.card_common_le
+KovariSosTuran.deg
+KovariSosTuran.deg.congr_simp
+KovariSosTuran.kovari_sos_turan
+KovariSosTuran.kovari_sos_turan_real
+KovariSosTuran.mem_nbhd
+KovariSosTuran.nbhd
+KovariSosTuran.nbhd.congr_simp
+KovariSosTuran.nbhd_subset
+KovariSosTuran.numEdges
+KovariSosTuran.numEdges.congr_simp
+KovariSosTuran.sum_choose_le

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
exposed public sections	5049	1

Current commit 0b27e8799c
Reference commit 5aedf732b6

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.py pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[SnirBroshi]

What's the reason for scooping an existing PR by a human contributor?