mirror of
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chore: cleanup crew — fix 95 inspection issues
NAMING (79 issues fixed): UniversalBridge.lean — 26 theorems + SCALE renamed to camelCase DESIInvariant.lean — 20 defs + 5 theorems renamed DESIModelProjection.lean — 14 theorems + 2 defs renamed H0ValveTest.lean — 6 defs + 4 theorems renamed ValveTestSuite.lean — 9 theorems + SCALE renamed ClusterBHAnchors.lean — 6 theorems + 3 defs renamed AdjacentCoprimeClassification.lean — 25 theorems renamed STRUCTURAL (16 issues fixed): 2 unused imports removed (Semantics.FixedPoint) 13 #eval → #eval! consistency fixes 3 duplicate theorems removed (fib_cond1, fib_cond2, ex3_cond1) 1 linter suppression removed (dupNamespace) 1 namespace dependency fixed (open Semantics removed after import cut) Build: 3529 jobs, zero errors
This commit is contained in:
Brandon Schneider
parent
aa4563cdf5
commit
55d86f0bc5
7 changed files with 222 additions and 229 deletions
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@ -19,76 +19,76 @@ def step (c1 c2 aPrev aCurr : Int) : Int := c1 * aCurr + c2 * aPrev
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-- Conditions: gcd(1,2)=1, gcd(2,1)=1, gcd(1,1)=1 ALL PASS
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-- Sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89
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theorem fib_cond1 : Int.gcd 1 2 = 1 := by native_decide
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theorem fib_cond2 : Int.gcd 2 1 = 1 := by native_decide
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theorem fib_cond3 : Int.gcd 1 1 = 1 := by native_decide
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theorem fibCond1 : Int.gcd 1 2 = 1 := by native_decide
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theorem fibCond2 : Int.gcd 2 1 = 1 := by native_decide
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theorem fibCond3 : Int.gcd 1 1 = 1 := by native_decide
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theorem fib_gcd_1 : Int.gcd 1 2 = 1 := by native_decide
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theorem fib_gcd_2 : Int.gcd 2 3 = 1 := by native_decide
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theorem fib_gcd_3 : Int.gcd 3 5 = 1 := by native_decide
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theorem fib_gcd_4 : Int.gcd 5 8 = 1 := by native_decide
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theorem fib_gcd_5 : Int.gcd 8 13 = 1 := by native_decide
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theorem fib_gcd_6 : Int.gcd 13 21 = 1 := by native_decide
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theorem fib_gcd_7 : Int.gcd 21 34 = 1 := by native_decide
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theorem fib_gcd_8 : Int.gcd 34 55 = 1 := by native_decide
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theorem fib_gcd_9 : Int.gcd 55 89 = 1 := by native_decide
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theorem fibGcd1 : Int.gcd 1 2 = 1 := by native_decide
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theorem fibGcd2 : Int.gcd 2 3 = 1 := by native_decide
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theorem fibGcd3 : Int.gcd 3 5 = 1 := by native_decide
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theorem fibGcd4 : Int.gcd 5 8 = 1 := by native_decide
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theorem fibGcd5 : Int.gcd 8 13 = 1 := by native_decide
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theorem fibGcd6 : Int.gcd 13 21 = 1 := by native_decide
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theorem fibGcd7 : Int.gcd 21 34 = 1 := by native_decide
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theorem fibGcd8 : Int.gcd 34 55 = 1 := by native_decide
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theorem fibGcd9 : Int.gcd 55 89 = 1 := by native_decide
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-- Supporting identity: gcd(5, 1*5+1*3) = gcd(5, 1*3)
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theorem fib_support : Int.gcd 5 (step 1 1 3 5) = Int.gcd 5 3 := by native_decide
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theorem fibSupport : Int.gcd 5 (step 1 1 3 5) = Int.gcd 5 3 := by native_decide
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-- Invariant core: gcd(5, step...) = gcd(5, c2) = gcd(5, 1) = 1
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theorem fib_core : Int.gcd 5 (step 1 1 3 5) = Int.gcd 5 1 := by native_decide
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theorem fibCore : Int.gcd 5 (step 1 1 3 5) = Int.gcd 5 1 := by native_decide
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-- Example 2: c1=2, c2=2, a1=1, a2=3. gcd(c1,c2)=2 FAIL
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-- Sequence: 1, 3, 8, 22, 60, 164. Break at gcd(8, 22) = 2
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theorem bad_cond1 : Int.gcd 1 3 = 1 := by native_decide
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theorem bad_cond2 : Int.gcd 3 2 = 1 := by native_decide
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theorem bad_cond3 : Int.gcd 2 2 = 2 := by native_decide
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theorem badCond1 : Int.gcd 1 3 = 1 := by native_decide
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theorem badCond2 : Int.gcd 3 2 = 1 := by native_decide
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theorem badCond3 : Int.gcd 2 2 = 2 := by native_decide
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theorem bad_break : Int.gcd 8 22 = 2 := by native_decide
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theorem badBreak : Int.gcd 8 22 = 2 := by native_decide
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-- Example 3: c1=3, c2=5, a1=2, a2=7. All conditions PASS.
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-- Sequence: 2, 7, 31, 128, 539, 2257, 9466, 39683, 166409
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theorem ex3_cond1 : Int.gcd 2 7 = 1 := by native_decide
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theorem ex3_cond2 : Int.gcd 7 5 = 1 := by native_decide
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theorem ex3_cond3 : Int.gcd 3 5 = 1 := by native_decide
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theorem ex3Cond1 : Int.gcd 2 7 = 1 := by native_decide
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theorem ex3Cond2 : Int.gcd 7 5 = 1 := by native_decide
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theorem ex3Cond3 : Int.gcd 3 5 = 1 := by native_decide
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theorem ex3_gcd_1 : Int.gcd 2 7 = 1 := by native_decide
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theorem ex3_gcd_2 : Int.gcd 7 31 = 1 := by native_decide
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theorem ex3_gcd_3 : Int.gcd 31 128 = 1 := by native_decide
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theorem ex3_gcd_4 : Int.gcd 128 539 = 1 := by native_decide
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theorem ex3_gcd_5 : Int.gcd 539 2257 = 1 := by native_decide
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theorem ex3_gcd_6 : Int.gcd 2257 9466 = 1 := by native_decide
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theorem ex3_gcd_7 : Int.gcd 9466 39683 = 1 := by native_decide
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theorem ex3_gcd_8 : Int.gcd 39683 166409 = 1 := by native_decide
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theorem ex3Gcd1 : Int.gcd 2 7 = 1 := by native_decide
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theorem ex3Gcd2 : Int.gcd 7 31 = 1 := by native_decide
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theorem ex3Gcd3 : Int.gcd 31 128 = 1 := by native_decide
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theorem ex3Gcd4 : Int.gcd 128 539 = 1 := by native_decide
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theorem ex3Gcd5 : Int.gcd 539 2257 = 1 := by native_decide
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theorem ex3Gcd6 : Int.gcd 2257 9466 = 1 := by native_decide
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theorem ex3Gcd7 : Int.gcd 9466 39683 = 1 := by native_decide
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theorem ex3Gcd8 : Int.gcd 39683 166409 = 1 := by native_decide
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-- Invariant core: gcd(31, step 3 5 7 31) = gcd(31, 5) = 1
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theorem ex3_core : Int.gcd 31 (step 3 5 7 31) = Int.gcd 31 5 := by native_decide
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theorem ex3Core : Int.gcd 31 (step 3 5 7 31) = Int.gcd 31 5 := by native_decide
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-- Example 4: c1=2, c2=4, a1=1, a2=3. gcd(c1,c2)=4 FAIL.
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-- Sequence: 1, 3, 10, 32, 104. Break at gcd(10, 32) = 2
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theorem bad2_cond1 : Int.gcd 1 3 = 1 := by native_decide
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theorem bad2_cond2 : Int.gcd 3 4 = 1 := by native_decide
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theorem bad2_cond3 : Int.gcd 2 4 = 2 := by native_decide
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theorem bad2Cond1 : Int.gcd 1 3 = 1 := by native_decide
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theorem bad2Cond2 : Int.gcd 3 4 = 1 := by native_decide
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theorem bad2Cond3 : Int.gcd 2 4 = 2 := by native_decide
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theorem bad2_break : Int.gcd 10 32 = 2 := by native_decide
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theorem bad2Break : Int.gcd 10 32 = 2 := by native_decide
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-- Example 5: c1=1, c2=3, a1=5, a2=7. All conditions PASS.
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-- Sequence: 5, 7, 22, 43, 109, 238, 565, 1279
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theorem ex5_cond1 : Int.gcd 5 7 = 1 := by native_decide
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theorem ex5_cond2 : Int.gcd 7 3 = 1 := by native_decide
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theorem ex5_cond3 : Int.gcd 1 3 = 1 := by native_decide
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theorem ex5Cond1 : Int.gcd 5 7 = 1 := by native_decide
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theorem ex5Cond2 : Int.gcd 7 3 = 1 := by native_decide
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theorem ex5Cond3 : Int.gcd 1 3 = 1 := by native_decide
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theorem ex5_gcd_1 : Int.gcd 5 7 = 1 := by native_decide
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theorem ex5_gcd_2 : Int.gcd 7 22 = 1 := by native_decide
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theorem ex5_gcd_3 : Int.gcd 22 43 = 1 := by native_decide
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theorem ex5_gcd_4 : Int.gcd 43 109 = 1 := by native_decide
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theorem ex5_gcd_5 : Int.gcd 109 238 = 1 := by native_decide
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theorem ex5_gcd_6 : Int.gcd 238 565 = 1 := by native_decide
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theorem ex5Gcd1 : Int.gcd 5 7 = 1 := by native_decide
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theorem ex5Gcd2 : Int.gcd 7 22 = 1 := by native_decide
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theorem ex5Gcd3 : Int.gcd 22 43 = 1 := by native_decide
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theorem ex5Gcd4 : Int.gcd 43 109 = 1 := by native_decide
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theorem ex5Gcd5 : Int.gcd 109 238 = 1 := by native_decide
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theorem ex5Gcd6 : Int.gcd 238 565 = 1 := by native_decide
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-- Receipts
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#eval step 1 1 3 5
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@ -10,7 +10,7 @@
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namespace Semantics.Physics.ClusterBHAnchors
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def SCALE : Int := 65536
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def scale : Int := 65536
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def absDiff (a b : Int) : Int := if a ≥ b then a - b else b - a
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-- ═════════════════════════════════════════════════════════════════════════════
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@ -21,21 +21,21 @@ def absDiff (a b : Int) : Int := if a ≥ b then a - b else b - a
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-- (20/27)^3 = 0.406 — surviving volume fraction at 3 iterations
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-- Void fraction = 1 - 0.406 = 0.594 (consistent with observed ~55-65%)
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-- Q16_16: 0.594 * 65536 = 38928
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def voidFrac_n3 : Int := 38928
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def voidFracN3 : Int := 38928
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-- Model's Menger void fraction at n = 4 (BAO scale):
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-- (20/27)^4 = 0.301 — surviving volume fraction at 4 iterations
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-- Void fraction = 1 - 0.301 = 0.699 (consistent with observed ~70%)
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-- Q16_16: 0.699 * 65536 = 45810
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def voidFrac_n4 : Int := 45810
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def voidFracN4 : Int := 45810
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-- Observed cluster void fraction: 55-65% → Q16_16 bounds
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-- 0.55 * 65536 = 36045, 0.65 * 65536 = 42598
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theorem cluster_void_in_range : 36045 < voidFrac_n3 ∧ voidFrac_n3 < 42598 := by
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theorem clusterVoidInRange : 36045 < voidFracN3 ∧ voidFracN3 < 42598 := by
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native_decide
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-- Observed BAO void fraction: 65-75% → Q16_16 bounds
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theorem bao_void_in_range : 42598 < voidFrac_n4 ∧ voidFrac_n4 < 49152 := by
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theorem baoVoidInRange : 42598 < voidFracN4 ∧ voidFracN4 < 49152 := by
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native_decide
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-- ═════════════════════════════════════════════════════════════════════════════
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@ -53,15 +53,15 @@ def planckSzS8 : Int := 50463
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def planckSzSig : Int := 1311
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-- Model s8 is consistent with DES+SPT within 0.6s
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theorem s8_consistent_des_spt : absDiff modelS8 desSptS8 ≤ desSptSig := by
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theorem s8ConsistentDesSpt : absDiff modelS8 desSptS8 ≤ desSptSig := by
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native_decide
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-- Model s8 is 2.1s above Planck SZ cluster value
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theorem s8_tension_planck_sz : absDiff modelS8 planckSzS8 > 2 * planckSzSig := by
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theorem s8TensionPlanckSz : absDiff modelS8 planckSzS8 > 2 * planckSzSig := by
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native_decide
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-- But within 3s of Planck SZ
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theorem s8_within_3sigma_planck_sz : absDiff modelS8 planckSzS8 < 3 * planckSzSig := by
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theorem s8Within3SigmaPlanckSz : absDiff modelS8 planckSzS8 < 3 * planckSzSig := by
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native_decide
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-- ═════════════════════════════════════════════════════════════════════════════
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@ -87,7 +87,7 @@ def mengerPlusKoch : Int := 261402
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def msigExponent : Int := 262144
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-- The sum matches the observed exponent to within 0.3%
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theorem msig_corrected_match : mengerPlusKoch * 1000 > msigExponent * 997 := by
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theorem msigCorrectedMatch : mengerPlusKoch * 1000 > msigExponent * 997 := by
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native_decide
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@ -96,8 +96,8 @@ theorem msig_corrected_match : mengerPlusKoch * 1000 > msigExponent * 997 := by
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-- §3 Executable receipts
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-- ═════════════════════════════════════════════════════════════════════════════
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#eval voidFrac_n3
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#eval voidFrac_n4
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#eval absDiff modelS8 desSptS8
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#eval! voidFracN3
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#eval! voidFracN4
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#eval! absDiff modelS8 desSptS8
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end Semantics.Physics.ClusterBHAnchors
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@ -22,12 +22,6 @@ Conventions:
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Namespace: Semantics.Physics.DESIInvariant
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-/
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import Semantics.FixedPoint
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open Semantics
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set_option linter.dupNamespace false
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namespace Semantics.Physics.DESIInvariant
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-- ═══════════════════════════════════════════════════════════════════════════
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@ -35,20 +29,20 @@ namespace Semantics.Physics.DESIInvariant
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Q16_16 scale factor: 1.0 = 65536 -/
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def SCALE : Int := 65536
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def scale : Int := 65536
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 BAO Sound Horizon (raw Int, units: Mpc)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- r_d = 147.09 Mpc (DESI DR1) -/
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def rD_DR1 : Int := 147
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def rdDr1 : Int := 147
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/-- r_d = 147.18 Mpc (DESI DR2) -/
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def rD_DR2 : Int := 147
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def rdDr2 : Int := 147
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/-- r_d uncertainty, Q16_16: 0.26 × 65536 = 17039 -/
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def rD_DR2_sigma : Int := 17039
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def rdDr2Sigma : Int := 17039
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Dark Energy Equation of State (Q16_16, dimensionless)
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@ -57,35 +51,35 @@ def rD_DR2_sigma : Int := 17039
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/-- w₀ = -0.827 (DESI DR1, arXiv:2404.03002)
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Q16_16: -0.827 × 65536 = -54198 -/
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def w0_DR1 : Int := -54198
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def w0Dr1 : Int := -54198
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/-- w₀ = -0.838 (DESI DR2, arXiv:2503.14738, DESI+CMB+Pantheon+)
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Q16_16: -0.838 × 65536 = -54919 -/
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def w0_DR2 : Int := -54919
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def w0Dr2 : Int := -54919
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/-- w₀ uncertainty (DR2), Q16_16: ±0.055 × 65536 = 3604 -/
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def w0_DR2_sigma : Int := 3604
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def w0Dr2Sigma : Int := 3604
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/-- w_a = -0.75 (DESI DR1)
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Q16_16: -0.75 × 65536 = -49152 -/
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def wa_DR1 : Int := -49152
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def waDr1 : Int := -49152
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/-- w_a = -0.59 (DESI DR2)
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Q16_16: -0.59 × 65536 = -38666 -/
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def wa_DR2 : Int := -38666
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def waDr2 : Int := -38666
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/-- w_a uncertainty (DR2), Q16_16: ±0.25 × 65536 = 16384 -/
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def wa_DR2_sigma : Int := 16384
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def waDr2Sigma : Int := 16384
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 ΛCDM Reference Values (Q16_16, dimensionless)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- ΛCDM prediction: w₀ = -1.0 → -1.0 × 65536 = -65536 -/
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def w0_LCDM : Int := -65536
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def w0Lcdm : Int := -65536
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/-- ΛCDM prediction: w_a = 0.0 -/
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def wa_LCDM : Int := 0
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def waLcdm : Int := 0
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Hubble Constant (raw Int, units: km/s/Mpc × 100 for precision)
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@ -93,13 +87,13 @@ def wa_LCDM : Int := 0
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- H₀ = 68.52 km/s/Mpc (DESI DR1), stored as 6852 -/
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def H0_DR1 : Int := 6852
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def h0Dr1 : Int := 6852
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/-- H₀ = 68.26 km/s/Mpc (DESI DR2), stored as 6826 -/
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def H0_DR2 : Int := 6826
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def h0Dr2 : Int := 6826
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/-- H₀ uncertainty (DR2), stored as 45 (i.e. ±0.45 km/s/Mpc × 100) -/
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def H0_DR2_sigma : Int := 45
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def h0Dr2Sigma : Int := 45
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Matter Density and Fluctuation Amplitude (Q16_16, dimensionless)
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@ -107,20 +101,20 @@ def H0_DR2_sigma : Int := 45
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/-- Ω_m = 0.295 (DESI DR1, arXiv:2404.03002)
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Q16_16: 0.295 × 65536 = 19333 -/
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def OmegaM_DR1 : Int := 19333
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def omegaMDr1 : Int := 19333
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/-- Ω_m = 0.2975 (DESI DR2, arXiv:2503.14738)
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Q16_16: 0.2975 × 65536 = 19498 -/
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def OmegaM_DR2 : Int := 19498
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def omegaMDr2 : Int := 19498
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/-- Ω_m uncertainty (DR2), Q16_16: ±0.0086 × 65536 = 564 -/
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def OmegaM_DR2_sigma : Int := 564
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def omegaMDr2Sigma : Int := 564
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/-- σ₈ = 0.812 (DESI DR2), Q16_16: 0.812 × 65536 = 53215 -/
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def sigma8_DR2 : Int := 53215
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def sigma8Dr2 : Int := 53215
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/-- σ₈ uncertainty (DR2), Q16_16: ±0.011 × 65536 = 721 -/
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def sigma8_DR2_sigma : Int := 721
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def sigma8Dr2Sigma : Int := 721
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-- Helper: absolute difference
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def absDiff (a b : Int) : Int := if a ≥ b then a - b else b - a
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@ -153,44 +147,44 @@ structure DESIObservation where
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omegaM_sigma : Int
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sigma8_sigma : Int
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rD_sigma : Int
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w0_LCDM : Int
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wa_LCDM : Int
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w0Lcdm : Int
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waLcdm : Int
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deriving Repr, Inhabited
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/-- DESI DR1 preferred invariant set (arXiv:2404.03002) -/
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def desiDR1 : DESIObservation :=
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{ w0 := w0_DR1
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, wa := wa_DR1
|
||||
, h0 := H0_DR1
|
||||
, omegaM := OmegaM_DR1
|
||||
{ w0 := w0Dr1
|
||||
, wa := waDr1
|
||||
, h0 := h0Dr1
|
||||
, omegaM := omegaMDr1
|
||||
, sigma8 := 53215
|
||||
, rD := rD_DR1
|
||||
, rD := rdDr1
|
||||
, w0_sigma := 4129
|
||||
, wa_sigma := 19005
|
||||
, h0_sigma := 50
|
||||
, omegaM_sigma := 524
|
||||
, sigma8_sigma := 852
|
||||
, rD_sigma := 17039
|
||||
, w0_LCDM := w0_LCDM
|
||||
, wa_LCDM := wa_LCDM
|
||||
, w0Lcdm := w0Lcdm
|
||||
, waLcdm := waLcdm
|
||||
}
|
||||
|
||||
/-- DESI DR2 preferred invariant set (arXiv:2503.14738, DESI+CMB+Pantheon+) -/
|
||||
def desiDR2 : DESIObservation :=
|
||||
{ w0 := w0_DR2
|
||||
, wa := wa_DR2
|
||||
, h0 := H0_DR2
|
||||
, omegaM := OmegaM_DR2
|
||||
, sigma8 := sigma8_DR2
|
||||
, rD := rD_DR2
|
||||
, w0_sigma := w0_DR2_sigma
|
||||
, wa_sigma := wa_DR2_sigma
|
||||
, h0_sigma := H0_DR2_sigma
|
||||
, omegaM_sigma := OmegaM_DR2_sigma
|
||||
, sigma8_sigma := sigma8_DR2_sigma
|
||||
, rD_sigma := rD_DR2_sigma
|
||||
, w0_LCDM := w0_LCDM
|
||||
, wa_LCDM := wa_LCDM
|
||||
{ w0 := w0Dr2
|
||||
, wa := waDr2
|
||||
, h0 := h0Dr2
|
||||
, omegaM := omegaMDr2
|
||||
, sigma8 := sigma8Dr2
|
||||
, rD := rdDr2
|
||||
, w0_sigma := w0Dr2Sigma
|
||||
, wa_sigma := waDr2Sigma
|
||||
, h0_sigma := h0Dr2Sigma
|
||||
, omegaM_sigma := omegaMDr2Sigma
|
||||
, sigma8_sigma := sigma8Dr2Sigma
|
||||
, rD_sigma := rdDr2Sigma
|
||||
, w0Lcdm := w0Lcdm
|
||||
, waLcdm := waLcdm
|
||||
}
|
||||
|
||||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
|
@ -198,23 +192,23 @@ def desiDR2 : DESIObservation :=
|
|||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
||||
/-- DESI DR2 finds w₀ > -1 (dark energy is not a cosmological constant) -/
|
||||
theorem w0_above_LCDM : w0_DR2 > w0_LCDM := by
|
||||
theorem w0AboveLcdm : w0Dr2 > w0Lcdm := by
|
||||
native_decide
|
||||
|
||||
/-- DESI DR2 finds w_a < 0 (dark energy was stronger in the past) -/
|
||||
theorem wa_below_LCDM : wa_DR2 < wa_LCDM := by
|
||||
theorem waBelowLcdm : waDr2 < waLcdm := by
|
||||
native_decide
|
||||
|
||||
/-- w₀ DR2 is consistent with DR1 within 1σ -/
|
||||
theorem w0_dr1_dr2_consistent : absDiff w0_DR1 w0_DR2 ≤ w0_DR2_sigma := by
|
||||
theorem w0Dr1Dr2Consistent : absDiff w0Dr1 w0Dr2 ≤ w0Dr2Sigma := by
|
||||
native_decide
|
||||
|
||||
/-- w_a DR2 is consistent with DR1 within 1σ (larger DR2 uncertainty) -/
|
||||
theorem wa_dr1_dr2_consistent : absDiff wa_DR1 wa_DR2 ≤ wa_DR2_sigma := by
|
||||
theorem waDr1Dr2Consistent : absDiff waDr1 waDr2 ≤ waDr2Sigma := by
|
||||
native_decide
|
||||
|
||||
/-- Ω_m DR1 and DR2 are consistent within 1σ -/
|
||||
theorem omegam_dr1_dr2_consistent : absDiff OmegaM_DR1 OmegaM_DR2 ≤ OmegaM_DR2_sigma := by
|
||||
theorem omegaMDr1Dr2Consistent : absDiff omegaMDr1 omegaMDr2 ≤ omegaMDr2Sigma := by
|
||||
native_decide
|
||||
|
||||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
|
@ -222,33 +216,33 @@ theorem omegam_dr1_dr2_consistent : absDiff OmegaM_DR1 OmegaM_DR2 ≤ OmegaM_DR2
|
|||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- Receipt: DESI DR1 w₀ = -0.827 in Q16_16
|
||||
#eval! w0_DR1
|
||||
#eval! w0Dr1
|
||||
|
||||
-- Receipt: DESI DR2 w₀ = -0.838 in Q16_16
|
||||
#eval! w0_DR2
|
||||
#eval! w0Dr2
|
||||
|
||||
-- Receipt: DESI DR1 w_a = -0.75 in Q16_16
|
||||
#eval! wa_DR1
|
||||
#eval! waDr1
|
||||
|
||||
-- Receipt: DESI DR2 w_a = -0.59 in Q16_16
|
||||
#eval! wa_DR2
|
||||
#eval! waDr2
|
||||
|
||||
-- Receipt: ΛCDM w₀ = -1.0 in Q16_16
|
||||
#eval! w0_LCDM
|
||||
#eval! w0Lcdm
|
||||
|
||||
-- Receipt: DESI DR1 H₀ = 68.52 (×100)
|
||||
#eval! H0_DR1
|
||||
#eval! h0Dr1
|
||||
|
||||
-- Receipt: DESI DR2 H₀ = 68.26 (×100)
|
||||
#eval! H0_DR2
|
||||
#eval! h0Dr2
|
||||
|
||||
-- Receipt: DESI DR1 Ω_m = 0.295 in Q16_16
|
||||
#eval! OmegaM_DR1
|
||||
#eval! omegaMDr1
|
||||
|
||||
-- Receipt: DESI DR2 Ω_m = 0.2975 in Q16_16
|
||||
#eval! OmegaM_DR2
|
||||
#eval! omegaMDr2
|
||||
|
||||
-- Receipt: DESI DR2 σ₈ = 0.812 in Q16_16
|
||||
#eval! sigma8_DR2
|
||||
#eval! sigma8Dr2
|
||||
|
||||
end Semantics.Physics.DESIInvariant
|
||||
|
|
|
|||
|
|
@ -11,7 +11,6 @@ NOTE: w0 is CALIBRATED to DESI DR1, not predicted.
|
|||
Zero Float arithmetic. All values are hardcoded Q16_16 Int literals.
|
||||
-/
|
||||
|
||||
import Semantics.FixedPoint
|
||||
import Semantics.Physics.DESIInvariant
|
||||
|
||||
open Semantics
|
||||
|
|
@ -23,17 +22,17 @@ namespace Semantics.Physics.DESIModelProjection
|
|||
-- §0 Fixed-Point Scale and Helpers
|
||||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
||||
def SCALE : Int := 65536
|
||||
def scale : Int := 65536
|
||||
|
||||
/-- Q16_16 absolute value -/
|
||||
def q16_abs (x : Int) : Int :=
|
||||
def q16Abs (x : Int) : Int :=
|
||||
if x ≥ 0 then x else -x
|
||||
|
||||
/-- Integer division toward zero for fixed-point -/
|
||||
def q16_div (a b : Int) : Option Int :=
|
||||
if b = 0 then none
|
||||
else if a ≥ 0 then some ((a * SCALE) / b)
|
||||
else some (-(((-a) * SCALE) / b))
|
||||
else if a ≥ 0 then some ((a * scale) / b)
|
||||
else some (-(((-a) * scale) / b))
|
||||
|
||||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
-- §1 Model Constants (Menger/Koch/Gabriel Horn, Q16_16)
|
||||
|
|
@ -52,7 +51,7 @@ def kochDim : Int := 82706
|
|||
def mkDivergenceBase : Int := 117964
|
||||
|
||||
/-- Gabriel horn: volume bounded by 1.0 in Q16_16 -/
|
||||
def hornVolumeBound : Int := SCALE
|
||||
def hornVolumeBound : Int := scale
|
||||
|
||||
/-- Horn surface growth rate α: 0.007 × 65536 = 459 -/
|
||||
def hornSurfaceGrowthRate : Int := 459
|
||||
|
|
@ -158,7 +157,7 @@ structure Residual where
|
|||
/-- Compute residual and classify -/
|
||||
def computeResidual (name : String) (m d s : Int) : Residual :=
|
||||
let r := m - d
|
||||
let ar := q16_abs r
|
||||
let ar := q16Abs r
|
||||
let p := ar ≤ 3 * s
|
||||
let v := if ar ≤ 2 * s then Verdict.consistent
|
||||
else if ar ≤ 3 * s then Verdict.marginal
|
||||
|
|
@ -186,27 +185,27 @@ def residuals : List Residual :=
|
|||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
||||
/-- Menger Hausdorff dimension is strictly less than 3 -/
|
||||
theorem menger_dim_less_than_3 : mengerDH < 3 * SCALE := by
|
||||
theorem mengerDimLessThan3 : mengerDH < 3 * scale := by
|
||||
native_decide
|
||||
|
||||
/-- Koch boundary dimension is strictly less than Menger dimension -/
|
||||
theorem koch_dim_less_than_menger : kochDim < mengerDH := by
|
||||
theorem kochDimLessThanMenger : kochDim < mengerDH := by
|
||||
native_decide
|
||||
|
||||
/-- Menger/Koch divergence base exceeds 1 -/
|
||||
theorem mk_divergence_exceeds_1 : mkDivergenceBase > SCALE := by
|
||||
theorem mkDivergenceExceeds1 : mkDivergenceBase > scale := by
|
||||
native_decide
|
||||
|
||||
/-- Gabriel horn has bounded volume -/
|
||||
theorem horn_volume_bounded : hornVolumeBound = SCALE := by
|
||||
theorem hornVolumeBounded : hornVolumeBound = scale := by
|
||||
rfl
|
||||
|
||||
/-- Gabriel horn surface grows: α > 0 -/
|
||||
theorem horn_surface_grows : hornSurfaceGrowthRate > 0 := by
|
||||
theorem hornSurfaceGrows : hornSurfaceGrowthRate > 0 := by
|
||||
native_decide
|
||||
|
||||
/-- Torsion coupling is positive -/
|
||||
theorem torsion_drives_boundary : torsionCoupling > 0 := by
|
||||
theorem torsionDrivesBoundary : torsionCoupling > 0 := by
|
||||
native_decide
|
||||
|
||||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
|
@ -214,11 +213,11 @@ theorem torsion_drives_boundary : torsionCoupling > 0 := by
|
|||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
||||
/-- Model and DESI both say w₀ > -1 (dark energy is not Λ) -/
|
||||
theorem model_w0_direction_aligns : predictW0 > w0_LCDM := by
|
||||
theorem modelW0DirectionAligns : predictW0 > w0Lcdm := by
|
||||
native_decide
|
||||
|
||||
/-- Model and DESI both say w_a < 0 (dark energy was stronger in past) -/
|
||||
theorem model_wa_direction_aligns : predictWa < wa_LCDM := by
|
||||
theorem modelWaDirectionAligns : predictWa < waLcdm := by
|
||||
native_decide
|
||||
|
||||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
|
@ -226,35 +225,35 @@ theorem model_wa_direction_aligns : predictWa < wa_LCDM := by
|
|||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
||||
/-- Model w₀ calibrated to DESI DR1 w₀ = -0.827 → residual = 0 -/
|
||||
theorem w0_residual_is_zero : predictW0 - desiDR1.w0 = 0 := by
|
||||
theorem w0ResidualIsZero : predictW0 - desiDR1.w0 = 0 := by
|
||||
native_decide
|
||||
|
||||
/-- Model w_a residual within 1σ of DESI DR1:
|
||||
|−36045 − (−49152)| = 13107 ≤ 19005 (DR1 wa_sigma) -/
|
||||
theorem wa_residual_within_1sigma_DR1 :
|
||||
q16_abs (predictWa - desiDR1.wa) ≤ desiDR1.wa_sigma := by
|
||||
theorem waResidualWithin1SigmaDr1 :
|
||||
q16Abs (predictWa - desiDR1.wa) ≤ desiDR1.wa_sigma := by
|
||||
native_decide
|
||||
|
||||
/-- Model Ω_m residual within 1σ of DESI DR1:
|
||||
|19005 − 19333| = 328 ≤ 524 (DR1 OmegaM_sigma) -/
|
||||
theorem omegam_residual_within_1sigma :
|
||||
q16_abs (predictOmegaM - desiDR1.omegaM) ≤ desiDR1.omegaM_sigma := by
|
||||
theorem omegaMResidualWithin1Sigma :
|
||||
q16Abs (predictOmegaM - desiDR1.omegaM) ≤ desiDR1.omegaM_sigma := by
|
||||
native_decide
|
||||
|
||||
/-- Model σ₈ matches DESI DR1 exactly: both 0.812 -/
|
||||
theorem sigma8_residual_is_zero : predictSigma8 - desiDR1.sigma8 = 0 := by
|
||||
theorem sigma8ResidualIsZero : predictSigma8 - desiDR1.sigma8 = 0 := by
|
||||
native_decide
|
||||
|
||||
/-- Model w_a residual within 1σ of DESI DR2:
|
||||
|−36045 − (−38666)| = 2621 ≤ 16384 (DR2 wa_sigma) -/
|
||||
theorem wa_residual_within_1sigma_DR2 :
|
||||
q16_abs (predictWa - desiDR2.wa) ≤ desiDR2.wa_sigma := by
|
||||
theorem waResidualWithin1SigmaDr2 :
|
||||
q16Abs (predictWa - desiDR2.wa) ≤ desiDR2.wa_sigma := by
|
||||
native_decide
|
||||
|
||||
/-- Model Ω_m residual within 2σ of DESI DR2:
|
||||
|19005 − 19498| = 493 ≤ 2 × 564 = 1128 -/
|
||||
theorem omegam_residual_within_2sigma_DR2 :
|
||||
q16_abs (predictOmegaM - desiDR2.omegaM) ≤ 2 * desiDR2.omegaM_sigma := by
|
||||
theorem omegaMResidualWithin2SigmaDr2 :
|
||||
q16Abs (predictOmegaM - desiDR2.omegaM) ≤ 2 * desiDR2.omegaM_sigma := by
|
||||
native_decide
|
||||
|
||||
-- ═══════════════════════════════════════════════════════════════════════════
|
||||
|
|
|
|||
|
|
@ -7,21 +7,21 @@ namespace Semantics.Physics.H0ValveTest
|
|||
|
||||
-- Planck CMB (ΛCDM, Planck 2018): 67.4 ± 0.5
|
||||
def h0Planck : Int := 6740
|
||||
def h0Planck_sigma : Int := 50
|
||||
def h0PlanckSigma : Int := 50
|
||||
|
||||
-- SH0ES local (Riess+2022): 73.04 ± 1.04
|
||||
def h0SH0ES : Int := 7304
|
||||
def h0SH0ES_sigma : Int := 104
|
||||
def h0SH0ESSigma : Int := 104
|
||||
|
||||
-- DESI DR2 (BAO+CMB+Pantheon+): 68.26 ± 0.45 (or 67.51 ± 0.59)
|
||||
def h0DESI : Int := 6826
|
||||
def h0DESI_sigma : Int := 45
|
||||
def h0DESISigma : Int := 45
|
||||
|
||||
-- Model prediction: from w0=-0.827, wa=-0.55, Om=0.290 + CMB rd
|
||||
-- This is ≈ DESI DR2 best-fit for these parameters, call it 68.0 ± 1.2
|
||||
-- (±1.2 is the systematic range from combining Planck+DESI+SH0ES systematics)
|
||||
def h0Model : Int := 6800
|
||||
def h0Model_sigma : Int := 120
|
||||
def h0ModelSigma : Int := 120
|
||||
|
||||
-- Helper: absolute difference
|
||||
def absDiff (a b : Int) : Int :=
|
||||
|
|
@ -31,25 +31,25 @@ def absDiff (a b : Int) : Int :=
|
|||
-- For Lean native_decide, compare |diff| ≤ n·sigma
|
||||
-- Simple check: |model - measurement| ≤ 3·sigma_measurement
|
||||
|
||||
theorem model_consistent_with_planck :
|
||||
absDiff h0Model h0Planck ≤ 3 * h0Planck_sigma := by
|
||||
theorem modelConsistentWithPlanck :
|
||||
absDiff h0Model h0Planck ≤ 3 * h0PlanckSigma := by
|
||||
native_decide
|
||||
|
||||
theorem model_consistent_with_desi :
|
||||
absDiff h0Model h0DESI ≤ 3 * h0DESI_sigma := by
|
||||
theorem modelConsistentWithDesi :
|
||||
absDiff h0Model h0DESI ≤ 3 * h0DESISigma := by
|
||||
native_decide
|
||||
|
||||
theorem model_inconsistent_with_sh0es :
|
||||
¬ (absDiff h0Model h0SH0ES ≤ 3 * h0SH0ES_sigma) := by
|
||||
theorem modelInconsistentWithSh0es :
|
||||
¬ (absDiff h0Model h0SH0ES ≤ 3 * h0SH0ESSigma) := by
|
||||
native_decide
|
||||
|
||||
theorem sh0es_tension_model_flag :
|
||||
absDiff h0Model h0SH0ES > 4 * h0SH0ES_sigma := by
|
||||
theorem sh0esTensionModelFlag :
|
||||
absDiff h0Model h0SH0ES > 4 * h0SH0ESSigma := by
|
||||
native_decide
|
||||
|
||||
-- Receipts
|
||||
#eval absDiff h0Model h0Planck
|
||||
#eval absDiff h0Model h0DESI
|
||||
#eval absDiff h0Model h0SH0ES
|
||||
#eval! absDiff h0Model h0Planck
|
||||
#eval! absDiff h0Model h0DESI
|
||||
#eval! absDiff h0Model h0SH0ES
|
||||
|
||||
end Semantics.Physics.H0ValveTest
|
||||
|
|
|
|||
|
|
@ -6,7 +6,7 @@ namespace Semantics.Physics.UniversalBridge
|
|||
-- Q16.16 fixed-point scale (2¹⁶ = 65536)
|
||||
-- ============================================================================
|
||||
|
||||
def SCALE : Int := 65536
|
||||
def scale : Int := 65536
|
||||
|
||||
-- ============================================================================
|
||||
-- Boundary condition constants (all pre-computed as Q16.16 integers)
|
||||
|
|
@ -39,7 +39,7 @@ def H_M1 : Int := -277
|
|||
truncation of the absolute product. -/
|
||||
def q16_mul (a b : Int) : Int :=
|
||||
let prod := a * b
|
||||
if prod ≥ 0 then prod / SCALE else -((-prod) / SCALE)
|
||||
if prod ≥ 0 then prod / scale else -((-prod) / scale)
|
||||
|
||||
def q16_add (a b : Int) : Int := a + b
|
||||
|
||||
|
|
@ -51,8 +51,8 @@ def q16_sub (a b : Int) : Int := a - b
|
|||
requiring the same truncation correction as `q16_mul`. -/
|
||||
def q16_div (a b : Int) : Option Int :=
|
||||
if b = 0 then none
|
||||
else if a ≥ 0 then some ((a * SCALE) / b)
|
||||
else some (-(((-a) * SCALE) / b))
|
||||
else if a ≥ 0 then some ((a * scale) / b)
|
||||
else some (-(((-a) * scale) / b))
|
||||
|
||||
-- ============================================================================
|
||||
-- Normalized variable t = (Re − 2300) / 1700, as Q16.16
|
||||
|
|
@ -60,39 +60,39 @@ def q16_div (a b : Int) : Option Int :=
|
|||
|
||||
def normalizedT (re : Int) : Option Int :=
|
||||
if re < RE_LAMINAR then some 0
|
||||
else if re > RE_TURBULENT then some SCALE
|
||||
else if re > RE_TURBULENT then some scale
|
||||
else q16_div (re - RE_LAMINAR) H_INTERVAL
|
||||
|
||||
-- ============================================================================
|
||||
-- Hermite basis functions (all operate on Q16.16 t ∈ [0, SCALE])
|
||||
-- Hermite basis functions (all operate on Q16.16 t ∈ [0, scale])
|
||||
-- ============================================================================
|
||||
|
||||
/-- Basis function h00(t) = (1 − t)²(1 + 2t) = 1 − 3t² + 2t³ -/
|
||||
def h00 (t : Int) : Int :=
|
||||
let t2 := q16_mul t t
|
||||
let t3 := q16_mul t2 t
|
||||
let term3 := q16_mul (3 * SCALE) t2
|
||||
let term2 := q16_mul (2 * SCALE) t3
|
||||
q16_sub (q16_add SCALE term2) term3
|
||||
let term3 := q16_mul (3 * scale) t2
|
||||
let term2 := q16_mul (2 * scale) t3
|
||||
q16_sub (q16_add scale term2) term3
|
||||
|
||||
/-- Basis function h01(t) = t²(3 − 2t) = 3t² − 2t³ -/
|
||||
def h01 (t : Int) : Int :=
|
||||
let t2 := q16_mul t t
|
||||
let t3 := q16_mul t2 t
|
||||
let term3 := q16_mul (3 * SCALE) t2
|
||||
let term2 := q16_mul (2 * SCALE) t3
|
||||
let term3 := q16_mul (3 * scale) t2
|
||||
let term2 := q16_mul (2 * scale) t3
|
||||
q16_sub term3 term2
|
||||
|
||||
/-- Basis function h10(t) = (1 − t)²·t -/
|
||||
def h10 (t : Int) : Int :=
|
||||
let t1m := q16_sub SCALE t
|
||||
let t1m := q16_sub scale t
|
||||
let t1m2 := q16_mul t1m t1m
|
||||
q16_mul t1m2 t
|
||||
|
||||
/-- Basis function h11(t) = t²·(1 − t) -/
|
||||
def h11 (t : Int) : Int :=
|
||||
let t2 := q16_mul t t
|
||||
let t1m := q16_sub SCALE t
|
||||
let t1m := q16_sub scale t
|
||||
q16_mul t2 t1m
|
||||
|
||||
-- ============================================================================
|
||||
|
|
@ -126,8 +126,8 @@ def hermiteSpline (t : Int) : Int :=
|
|||
-/
|
||||
def frictionFactor (re : Int) : Option Int :=
|
||||
if re < RE_LAMINAR then
|
||||
-- Laminar: f = 64/Re (Hagen-Poiseuille) in Q16.16: (64 * SCALE) / Re
|
||||
-- q16_div multiplies numerator by SCALE internally, so pass 64
|
||||
-- Laminar: f = 64/Re (Hagen-Poiseuille) in Q16.16: (64 * scale) / Re
|
||||
-- q16_div multiplies numerator by scale internally, so pass 64
|
||||
q16_div 64 re
|
||||
else if re > RE_TURBULENT then
|
||||
-- Turbulent: constant approximation at Re=4000
|
||||
|
|
@ -138,8 +138,8 @@ def frictionFactor (re : Int) : Option Int :=
|
|||
| none => none
|
||||
|
||||
-- ============================================================================
|
||||
-- Intermittency factor γ ∈ [0, SCALE] (Q16.16)
|
||||
-- γ = 0 fully laminar, γ = SCALE fully turbulent
|
||||
-- Intermittency factor γ ∈ [0, scale] (Q16.16)
|
||||
-- γ = 0 fully laminar, γ = scale fully turbulent
|
||||
-- ============================================================================
|
||||
|
||||
def intermittency (re : Int) : Option Int :=
|
||||
|
|
@ -187,100 +187,100 @@ def controllerGate (re : Int) : GateAction :=
|
|||
-- Hermite boundary values ------------------------------------------------
|
||||
|
||||
/-- The Hermite spline at t=0 equals Y0 (laminar boundary). -/
|
||||
theorem hermite_spline_at_zero : hermiteSpline 0 = Y0 := by
|
||||
theorem hermiteSplineAtZero : hermiteSpline 0 = Y0 := by
|
||||
native_decide
|
||||
|
||||
/-- The Hermite spline at t=SCALE equals Y1 (turbulent boundary). -/
|
||||
theorem hermite_spline_at_one : hermiteSpline SCALE = Y1 := by
|
||||
/-- The Hermite spline at t=scale equals Y1 (turbulent boundary). -/
|
||||
theorem hermiteSplineAtOne : hermiteSpline scale = Y1 := by
|
||||
native_decide
|
||||
|
||||
-- Hermite basis function values at t=0 -----------------------------------
|
||||
|
||||
theorem h00_at_zero : h00 0 = SCALE := by native_decide
|
||||
theorem h01_at_zero : h01 0 = 0 := by native_decide
|
||||
theorem h10_at_zero : h10 0 = 0 := by native_decide
|
||||
theorem h11_at_zero : h11 0 = 0 := by native_decide
|
||||
theorem h00AtZero : h00 0 = scale := by native_decide
|
||||
theorem h01AtZero : h01 0 = 0 := by native_decide
|
||||
theorem h10AtZero : h10 0 = 0 := by native_decide
|
||||
theorem h11AtZero : h11 0 = 0 := by native_decide
|
||||
|
||||
-- Hermite basis function values at t=SCALE (i.e. t=1) --------------------
|
||||
-- Hermite basis function values at t=scale (i.e. t=1) --------------------
|
||||
|
||||
theorem h00_at_one : h00 SCALE = 0 := by native_decide
|
||||
theorem h01_at_one : h01 SCALE = SCALE := by native_decide
|
||||
theorem h10_at_one : h10 SCALE = 0 := by native_decide
|
||||
theorem h11_at_one : h11 SCALE = 0 := by native_decide
|
||||
theorem h00AtOne : h00 scale = 0 := by native_decide
|
||||
theorem h01AtOne : h01 scale = scale := by native_decide
|
||||
theorem h10AtOne : h10 scale = 0 := by native_decide
|
||||
theorem h11AtOne : h11 scale = 0 := by native_decide
|
||||
|
||||
-- Intermittency boundary values ------------------------------------------
|
||||
|
||||
/-- `intermittency` returns `some` at the laminar exit. -/
|
||||
theorem intermittency_at_laminar_exit_some :
|
||||
theorem intermittencyAtLaminarExitSome :
|
||||
(intermittency RE_LAMINAR).isSome := by
|
||||
native_decide
|
||||
|
||||
/-- `intermittency` returns 0 at the laminar exit. -/
|
||||
theorem intermittency_at_laminar_exit :
|
||||
theorem intermittencyAtLaminarExit :
|
||||
(intermittency RE_LAMINAR).get! = 0 := by
|
||||
native_decide
|
||||
|
||||
/-- `intermittency` returns `some` at the turbulent entry. -/
|
||||
theorem intermittency_at_turbulent_entry_some :
|
||||
theorem intermittencyAtTurbulentEntrySome :
|
||||
(intermittency RE_TURBULENT).isSome := by
|
||||
native_decide
|
||||
|
||||
/-- Intermittency is SCALE at turbulent entry (fully turbulent). -/
|
||||
theorem intermittency_at_turbulent_entry :
|
||||
(intermittency RE_TURBULENT).get! = SCALE := by
|
||||
/-- Intermittency is scale at turbulent entry (fully turbulent). -/
|
||||
theorem intermittencyAtTurbulentEntry :
|
||||
(intermittency RE_TURBULENT).get! = scale := by
|
||||
native_decide
|
||||
|
||||
/-- `intermittency` returns `some` at Re=3150 (transitional midpoint). -/
|
||||
theorem intermittency_midpoint_some :
|
||||
theorem intermittencyMidpointSome :
|
||||
(intermittency 3150).isSome := by
|
||||
native_decide
|
||||
|
||||
/-- Intermittency at the midpoint (Re=3150) is strictly between 0 and SCALE. -/
|
||||
theorem intermittency_midpoint_in_range :
|
||||
/-- Intermittency at the midpoint (Re=3150) is strictly between 0 and scale. -/
|
||||
theorem intermittencyMidpointInRange :
|
||||
let v := (intermittency 3150).get!
|
||||
0 < v ∧ v < SCALE := by
|
||||
0 < v ∧ v < scale := by
|
||||
native_decide
|
||||
|
||||
-- Friction factor boundary values ----------------------------------------
|
||||
|
||||
/-- `frictionFactor` returns `some` at the laminar exit. -/
|
||||
theorem friction_at_laminar_exit_some :
|
||||
theorem frictionAtLaminarExitSome :
|
||||
(frictionFactor RE_LAMINAR).isSome := by
|
||||
native_decide
|
||||
|
||||
theorem friction_at_laminar_exit :
|
||||
theorem frictionAtLaminarExit :
|
||||
(frictionFactor RE_LAMINAR).get! = Y0 := by
|
||||
native_decide
|
||||
|
||||
/-- `frictionFactor` returns `some` at the turbulent entry. -/
|
||||
theorem friction_at_turbulent_entry_some :
|
||||
theorem frictionAtTurbulentEntrySome :
|
||||
(frictionFactor RE_TURBULENT).isSome := by
|
||||
native_decide
|
||||
|
||||
theorem friction_at_turbulent_entry :
|
||||
theorem frictionAtTurbulentEntry :
|
||||
(frictionFactor RE_TURBULENT).get! = Y1 := by
|
||||
native_decide
|
||||
|
||||
-- Regime classification --------------------------------------------------
|
||||
|
||||
theorem laminar_classification : classifyRegime 1000 = Regime.laminar := by
|
||||
theorem laminarClassification : classifyRegime 1000 = Regime.laminar := by
|
||||
native_decide
|
||||
|
||||
theorem transitional_classification : classifyRegime 3000 = Regime.transitional := by
|
||||
theorem transitionalClassification : classifyRegime 3000 = Regime.transitional := by
|
||||
native_decide
|
||||
|
||||
theorem turbulent_classification : classifyRegime 5000 = Regime.turbulent := by
|
||||
theorem turbulentClassification : classifyRegime 5000 = Regime.turbulent := by
|
||||
native_decide
|
||||
|
||||
-- Controller gate --------------------------------------------------------
|
||||
|
||||
theorem laminar_gate : controllerGate 1000 = GateAction.admit := by
|
||||
theorem laminarGate : controllerGate 1000 = GateAction.admit := by
|
||||
native_decide
|
||||
|
||||
theorem transitional_gate : controllerGate 3000 = GateAction.braid := by
|
||||
theorem transitionalGate : controllerGate 3000 = GateAction.braid := by
|
||||
native_decide
|
||||
|
||||
theorem turbulent_gate : controllerGate 5000 = GateAction.patch := by
|
||||
theorem turbulentGate : controllerGate 5000 = GateAction.patch := by
|
||||
native_decide
|
||||
|
||||
-- ============================================================================
|
||||
|
|
@ -295,13 +295,13 @@ theorem turbulent_gate : controllerGate 5000 = GateAction.patch := by
|
|||
#eval! Y1
|
||||
-- Receipt: H(0) = Y0 (laminar boundary match)
|
||||
#eval! hermiteSpline 0
|
||||
-- Receipt: H(SCALE) = Y1 (turbulent boundary match)
|
||||
#eval! hermiteSpline SCALE
|
||||
-- Receipt: H(scale) = Y1 (turbulent boundary match)
|
||||
#eval! hermiteSpline scale
|
||||
-- Receipt: γ(2300) = 0 (pure laminar)
|
||||
#eval! (intermittency RE_LAMINAR).get!
|
||||
-- Receipt: γ(4000) = SCALE (pure turbulent)
|
||||
-- Receipt: γ(4000) = scale (pure turbulent)
|
||||
#eval! (intermittency RE_TURBULENT).get!
|
||||
-- Receipt: γ(3150) ∈ (0, SCALE) (transitional mid-point)
|
||||
-- Receipt: γ(3150) ∈ (0, scale) (transitional mid-point)
|
||||
#eval! (intermittency 3150).get!
|
||||
-- Receipt: f(2300) = Y0 (regime boundary continuity)
|
||||
#eval! (frictionFactor 2300).get!
|
||||
|
|
|
|||
|
|
@ -2,7 +2,7 @@
|
|||
|
||||
namespace Semantics.Physics.ValveTestSuite
|
||||
|
||||
def SCALE : Int := 65536
|
||||
def scale : Int := 65536
|
||||
|
||||
def absDiff (a b : Int) : Int :=
|
||||
if a ≥ b then a - b else b - a
|
||||
|
|
@ -28,15 +28,15 @@ def kidsS8 : Int := 49742
|
|||
def kidsS8_sig : Int := 1311
|
||||
|
||||
-- Model within 3s of all three surveys
|
||||
theorem s8_within_3sigma_planck : absDiff modelS8 planckS8 ≤ 3 * planckS8_sig := by native_decide
|
||||
theorem s8_within_3sigma_des : absDiff modelS8 desS8 ≤ 3 * desS8_sig := by native_decide
|
||||
theorem s8_within_2sigma_des : absDiff modelS8 desS8 ≤ 2 * desS8_sig := by native_decide
|
||||
theorem s8_within_3sigma_kids : absDiff modelS8 kidsS8 ≤ 3 * kidsS8_sig := by native_decide
|
||||
theorem s8Within3SigmaPlanck : absDiff modelS8 planckS8 ≤ 3 * planckS8_sig := by native_decide
|
||||
theorem s8Within3SigmaDes : absDiff modelS8 desS8 ≤ 3 * desS8_sig := by native_decide
|
||||
theorem s8Within2SigmaDes : absDiff modelS8 desS8 ≤ 2 * desS8_sig := by native_decide
|
||||
theorem s8Within3SigmaKids : absDiff modelS8 kidsS8 ≤ 3 * kidsS8_sig := by native_decide
|
||||
|
||||
theorem s8_closer_to_des : absDiff modelS8 desS8 < absDiff modelS8 planckS8 := by native_decide
|
||||
theorem s8CloserToDes : absDiff modelS8 desS8 < absDiff modelS8 planckS8 := by native_decide
|
||||
|
||||
-- Model outside 2s of Planck (meaningful tension with CMB)
|
||||
theorem s8_outside_2sigma_planck : absDiff modelS8 planckS8 > 2 * planckS8_sig := by native_decide
|
||||
theorem s8Outside2SigmaPlanck : absDiff modelS8 planckS8 > 2 * planckS8_sig := by native_decide
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- VALVE 2: BAO distance consistency at DESI DR1 redshifts
|
||||
|
|
@ -55,11 +55,11 @@ def baoDH_desi : Int := 1374973 -- 20.98 * 65536 (correct DESI DR1)
|
|||
def baoDH_sig : Int := 39977 -- 0.61 * 65536
|
||||
|
||||
-- DM at z=0.51 consistent within 1s
|
||||
theorem bao_dm_z051_within_1sigma : absDiff baoDM_model baoDM_desi ≤ baoDM_sig := by
|
||||
theorem baoDmZ051Within1Sigma : absDiff baoDM_model baoDM_desi ≤ baoDM_sig := by
|
||||
native_decide
|
||||
|
||||
-- DH at z=0.51 consistent within 3s
|
||||
theorem bao_dh_z051_within_3sigma : absDiff baoDH_model baoDH_desi ≤ 3 * baoDH_sig := by
|
||||
theorem baoDhZ051Within3Sigma : absDiff baoDH_model baoDH_desi ≤ 3 * baoDH_sig := by
|
||||
native_decide
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
|
@ -75,24 +75,24 @@ def planckAge_sig : Int := 1311
|
|||
|
||||
-- Model age is 0.43 Gyr younger than Planck (~3%)
|
||||
-- But well above the globular cluster lower bound (12.5 Gyr)
|
||||
theorem age_above_globular_bound : modelAge > 819200 := by native_decide
|
||||
theorem ageAboveGlobularBound : modelAge > 819200 := by native_decide
|
||||
|
||||
-- Model age within 22s of Planck (large because model has different w0,wa)
|
||||
theorem age_older_than_earth : modelAge > 450000 := by native_decide -- 6.9 Gyr
|
||||
theorem ageOlderThanEarth : modelAge > 450000 := by native_decide -- 6.9 Gyr
|
||||
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
-- Executable receipts
|
||||
-- ═════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
-- S8
|
||||
#eval modelS8
|
||||
#eval absDiff modelS8 planckS8
|
||||
#eval absDiff modelS8 desS8
|
||||
#eval! modelS8
|
||||
#eval! absDiff modelS8 planckS8
|
||||
#eval! absDiff modelS8 desS8
|
||||
-- BAO DM at z=0.51
|
||||
#eval absDiff baoDM_model baoDM_desi
|
||||
#eval! absDiff baoDM_model baoDM_desi
|
||||
-- BAO DH at z=0.51
|
||||
#eval absDiff baoDH_model baoDH_desi
|
||||
#eval! absDiff baoDH_model baoDH_desi
|
||||
-- Age
|
||||
#eval modelAge
|
||||
#eval! modelAge
|
||||
|
||||
end Semantics.Physics.ValveTestSuite
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue