s1209 — Paper 9 look-elsewhere census (frozen Gemini D1386 B1 + A1742 §3 + R3′/R7′/R9′) · headline ceiling C = 6

[1] PRINTED FORMULAS — complexity k_s and the p9-sharp reproduction (absolute, √σ = 445; the ⁶He/¹²C… targets as pinned)
  d      k_s =  1 · value 0.005024999 · residual +0.51958 % (band ±0.52500 %, R5′) 
  3H     k_s =  7 · value 0.018913754 · residual -0.76844 % (band ±0.77500 %, R5′) 
  3He    k_s = 15 · value 0.017360944 · residual +0.09817 % (band ±0.10500 %, R5′) 
  4He    k_s =  0 · value 0.063685638 · residual +0.15709 % (band ±0.16500 %, R5′) 
  6He    k_s =  4 · value 0.065778087 · residual +0.00393 % (band ±0.00395 %, R5′) 
  6Li    k_s =  9 · value 0.071816257 · residual -0.11179 % (band ±0.11500 %, R5′) 
  7Li    k_s = 12 · value 0.088184458 · residual -0.00743 % (band ±0.00745 %, R5′) 
  7Be    k_s = 26 · value 0.084559627 · residual +0.07615 % (band ±0.07650 %, R5′) 
  8Li    k_s = 14 · value 0.092756353 · residual -0.00272 % (band ±0.00275 %, R5′) 
  8B     k_s = 24 · value 0.084798804 · residual -0.00485 % (band ±0.00495 %, R5′) 
  9Be    k_s =  4 · value 0.130476897 · residual -0.17665 % (band ±0.18500 %, R5′) 
  12C    k_s =  3 · value 0.207318153 · residual +0.10291 % (band ±0.10500 %, R5′) 
  16O    k_s =  5 · value 0.287265029 · residual +0.16739 % (band ±0.17500 %, R5′) 
  20Ne   k_s =  5 · value 0.361000665 · residual +0.00029 % (band ±0.00032 %, R5′) 
  24Mg   k_s =  5 · value 0.447158781 · residual +0.36751 % (band ±0.37500 %, R5′) 
  28Si   k_s =  7 · value 0.533316897 · residual +0.33364 % (band ±0.33450 %, R5′) 
  32S    k_s =  7 · value 0.610891290 · residual +0.02445 % (band ±0.02450 %, R5′) 
  40Ca   k_s =  7 · value 0.768412560 · residual -0.03175 % (band ±0.03250 %, R5′) 
  Hoyle  k_s =  3 · value 0.000906208 · residual +6.23352 % (band ±6.25000 %, R5′) 

[2] ENUMERATION (comparator-free) — distinct values per complexity level
  phi      C0 2 · C1 55 · C2 354 · C3 4023 · C4 35598 · C5 346733 · C6 3533935
  silver   C0 2 · C1 55 · C2 358 · C3 4529 · C4 40826 · C5 434845 · C6 4587881
  2+sqrt3  C0 2 · C1 55 · C2 339 · C3 4054 · C4 33880 · C5 332038 · C6 3195611
  silver-leaves/φ-atoms C0 2 · C1 55 · C2 361 · C3 4607 · C4 43145 · C5 472126 · C6 5303576
  LEVEL LOCK (sha256 over every sorted level key array, all units) = 24782558f2b8a61e4af563daf4d3eb61baee8b5864ca9d96257d1d092911d4e1 — printed before any AME target is read

[3] PER-ROW CENSUS — mode ratio (HEADLINE)
  row    k_s  printed-res   band      in?  RANK(≤k)         ACC(≤k)      row-p
  d        1    +0.36193 %  ±0.52500 %  yes   1          0.03030   0.03030
  3H       7    -0.92408 %  ±0.77500 %  NO   ≥2027      ≥1.00000   1.00000
  3He     15    -0.05882 %  ±0.10500 %  yes  ≥504       ≥1.00000   1.00000
  4He     —   (the ratio denominator; scored in the scan only)
  6He      4    -0.15292 %  ±0.00395 %  NO    1          0.16485   1.00000
  6Li      9    -0.26845 %  ±0.11500 %  NO   ≥614       ≥1.00000   1.00000
  7Li     12    -0.16426 %  ±0.00745 %  NO   ≥20        ≥1.00000   1.00000
  7Be     26    -0.08081 %  ±0.07650 %  NO   ≥153       ≥1.00000   1.00000
  8Li     14    -0.15956 %  ±0.00275 %  NO   ≥10        ≥0.99930   1.00000
  8B      24    -0.16169 %  ±0.00495 %  NO   ≥20        ≥1.00000   1.00000
  9Be      4    -0.33322 %  ±0.18500 %  NO    9          0.99810   1.00000
  12C      3    -0.05409 %  ±0.10500 %  yes   1          0.32235   0.32235
  16O      5    +0.01029 %  ±0.17500 %  yes   33         1.00000   1.00000
  20Ne     5    -0.15655 %  ±0.00032 %  NO    0          0.11630   1.00000
  24Mg     5    +0.21009 %  ±0.37500 %  yes   521        1.00000   1.00000
  28Si     7    +0.17627 %  ±0.33450 %  yes  ≥734       ≥1.00000   1.00000
  32S      7    -0.13243 %  ±0.02450 %  NO   ≥110       ≥1.00000   1.00000
  40Ca     7    -0.18854 %  ±0.03250 %  NO   ≥202       ≥1.00000   1.00000
  Hoyle    3    +6.06690 %  ±6.25000 %  yes   11         1.00000   1.00000

[3] PER-ROW CENSUS — mode abs445 (sensitivity i)
  row    k_s  printed-res   band      in?  RANK(≤k)         ACC(≤k)      row-p
  d        1    +0.51958 %  ±0.52500 %  yes   1          0.02875   0.02875
  3H       7    -0.76844 %  ±0.77500 %  yes  ≥1974      ≥1.00000   1.00000
  3He     15    +0.09817 %  ±0.10500 %  yes  ≥491       ≥1.00000   1.00000
  4He      0    +0.15709 %  ±0.16500 %  yes   1          0.00220   0.00220
  6He      4    +0.00393 %  ±0.00395 %  yes   1          0.16170   0.16170
  6Li      9    -0.11179 %  ±0.11500 %  yes  ≥632       ≥1.00000   1.00000
  7Li     12    -0.00743 %  ±0.00745 %  yes  ≥20        ≥1.00000   1.00000
  7Be     26    +0.07615 %  ±0.07650 %  yes  ≥154       ≥1.00000   1.00000
  8Li     14    -0.00272 %  ±0.00275 %  yes  ≥10        ≥0.99955   1.00000
  8B      24    -0.00485 %  ±0.00495 %  yes  ≥18        ≥1.00000   1.00000
  9Be      4    -0.17665 %  ±0.18500 %  yes   12         0.99740   0.99740
  12C      3    +0.10291 %  ±0.10500 %  yes   1          0.32860   0.32860
  16O      5    +0.16739 %  ±0.17500 %  yes   39         1.00000   1.00000
  20Ne     5    +0.00029 %  ±0.00032 %  yes   1          0.11780   0.11780
  24Mg     5    +0.36751 %  ±0.37500 %  yes   522        1.00000   1.00000
  28Si     7    +0.33364 %  ±0.33450 %  yes  ≥731       ≥1.00000   1.00000
  32S      7    +0.02445 %  ±0.02450 %  yes  ≥67        ≥1.00000   1.00000
  40Ca     7    -0.03175 %  ±0.03250 %  yes  ≥85        ≥1.00000   1.00000
  Hoyle    3    +6.23352 %  ±6.25000 %  yes   11         1.00000   1.00000

[4] ε CENSUS (B1 e) — ε ∈ {−φᵏ, 0, φᵏ}, k ∈ [−19, 5] (51 values); frozen bar 1 %; "sharper" = strictly smaller |residual| than printed
  ratio 12C    n= 3 printed -0.05409 % · in 1% bar 31/51 · sharper 11 · best ε = +0.008131 (res 0.00964 %)
  ratio 16O    n= 4 printed +0.01029 % · in 1% bar 33/51 · sharper  8 · best ε = -0.001919 (res 0.00058 %)
  ratio 20Ne   n= 5 printed -0.15655 % · in 1% bar  3/51 · sharper  0 · best ε = -0.381966 (res 0.15655 %)
  ratio 24Mg   n= 6 printed +0.21009 % · in 1% bar 34/51 · sharper 15 · best ε = -0.055728 (res 0.00700 %)
  ratio 28Si   n= 7 printed +0.17627 % · in 1% bar 28/51 · sharper  0 · best ε = +0.381966 (res 0.17627 %)
  ratio 32S    n= 8 printed -0.13243 % · in 1% bar 35/51 · sharper  0 · best ε = +0.236068 (res 0.13243 %)
  ratio 36Ar   n= 9 printed -0.13935 % · in 1% bar 36/51 · sharper  1 · best ε = +0.236068 (res 0.07305 %)  [report tier, unscored]
  ratio 40Ca   n=10 printed -0.18854 % · in 1% bar 37/51 · sharper  2 · best ε = +0.145898 (res 0.07083 %)
  abs445 12C    n= 3 printed +0.10291 % · in 1% bar 31/51 · sharper 12 · best ε = -0.013156 (res 0.00038 %)
  abs445 16O    n= 4 printed +0.16739 % · in 1% bar 33/51 · sharper 14 · best ε = -0.034442 (res 0.02790 %)
  abs445 20Ne   n= 5 printed +0.00029 % · in 1% bar  2/51 · sharper  0 · best ε = -0.381966 (res 0.00029 %)
  abs445 24Mg   n= 6 printed +0.36751 % · in 1% bar 34/51 · sharper 16 · best ε = -0.090170 (res 0.03839 %)
  abs445 28Si   n= 7 printed +0.33364 % · in 1% bar 32/51 · sharper  1 · best ε = +0.236068 (res 0.11270 %)
  abs445 32S    n= 8 printed +0.02445 % · in 1% bar 35/51 · sharper  0 · best ε = +0.236068 (res 0.02445 %)
  abs445 36Ar   n= 9 printed +0.01752 % · in 1% bar 36/51 · sharper  0 · best ε = +0.145898 (res 0.01752 %)  [report tier, unscored]
  abs445 40Ca   n=10 printed -0.03175 % · in 1% bar 36/51 · sharper  0 · best ε = +0.090170 (res 0.03175 %)

[5] VAULT PRICING (B1 f) — 10⁶ targets U[0, 10]; hit = some φ-menu value of complexity ≤ k within the tolerance (relative)
  T5 = φ²      complexity ≤ 1 (57 values) · tolerance 3e-05 · frequency 0.00034 · realized 2.64e-05 vs the sealed 2.617965
  T9 = 7 + φ⁻⁴ complexity ≤ 3 (4434 values) · tolerance 1e-03 · frequency 0.31771 · realized 1.04e-03 vs the sealed 7.138500
  scale caveat (A1742 F2 / H1): implied 𝒯₅ at √σ = 439 / 445 / 451 = 2.9214 / 2.617969 / 2.3226
  with the s732 pin 160.6448 (the sealed object): implied 𝒯₅ = 2.617965; with the AME nα row 160.644824: 2.617969

[6] SCALE SCAN (sensitivity ii) — fraction of √σ ∈ [439, 451] (1201 points) at which the printed value is inside ± its sharp
  d 0.387 · 3H 0.502 · 3He 0.078 · 4He 0.122 · 6He 0.003 · 6Li 0.086 · 7Li 0.006 · 7Be 0.057 · 8Li 0.002 · 8B 0.004 · 9Be 0.137 · 12C 0.077 · 16O 0.130 · 20Ne 0.001 · 24Mg 0.277 · 28Si 0.247 · 32S 0.018 · 40Ca 0.024 · Hoyle 0.505

[7] AGGREGATE (B1 g under R7′)
  A≤4 coefficient complexities in the lane's language: c₁ = 2φ⁻² → 3 · c₃ = ½φ⁻¹ → 7 (φ¹¹ is outside [−19, 5]; built as ½φ⁻¹²·φ⁵·φ⁵·φ) · c₂ = φ³ − ½φ⁻¹ → 9
  A≤4 coefficient ACC (lower bounds where k > ceiling): c1 (³H) 0.96610 · c3 (³He) ≥1.00000 · c2 (⁴He) ≥1.00000
  A≤4 group (absolute 445): d 0.02875 · c1 (³H) 0.96610 · c3 (³He) 1.00000 · c2 (⁴He) 1.00000  → p = 2.778e-02
  ratio  ladder: 16O 0.1765 · 20Ne 1.0000 · 24Mg 0.3137 · family n≥7 1.0000  (family 1/45 at least as good) → p = 5.536e-02
         singles: 6He 1.0000 · 6Li 1.0000 · 7Li 1.0000 · 7Be 1.0000 · 8Li 1.0000 · 8B 1.0000 · 9Be 1.0000 · 12C 0.3224 · Hoyle 1.0000
         AGGREGATE p (product, R7) = 4.957e-04 · Fisher χ² = 15.22 on 22 dof → p = 8.527e-01
  abs445 ladder: 16O 0.2941 · 20Ne 0.0196 · 24Mg 0.3333 · family n≥7 0.0222  (family 1/45 at least as good) → p = 4.272e-05
         singles: 6He 0.1617 · 6Li 1.0000 · 7Li 1.0000 · 7Be 1.0000 · 8Li 1.0000 · 8B 1.0000 · 9Be 0.9974 · 12C 0.3286 · Hoyle 1.0000
         AGGREGATE p (product, R7) = 6.288e-08 · Fisher χ² = 33.16 on 22 dof → p = 5.960e-02

[8] CONTROLS (B1 h)
  alternative irrational (ratio mode, best |residual| per row at ≤ min(k_s, 6), mean over 18 rows): φ 3.270e-04 · 1+√2 2.254e-02 (×68.92) · 2+√3 1.226e-02 (×37.48)
  house extra (not in the verdict): 1+√2 LEAVES with the φ-built atoms B_α, T₃ kept — isolates the leaf menu from the atoms: 5.673e-04 (×1.73)
  random targets (10⁵ log-uniform over the scored range, menu ≤ C6): hit-rate at each row's sharp — d 1.0000 · 3H 1.0000 · 3He 1.0000 · 6He 0.9993 · 6Li 1.0000 · 7Li 1.0000 · 7Be 1.0000 · 8Li 0.9953 · 8B 0.9998 · 9Be 1.0000 · 12C 1.0000 · 16O 1.0000 · 20Ne 0.5631 · 24Mg 1.0000 · 28Si 1.0000 · 32S 1.0000 · 40Ca 1.0000 · Hoyle 1.0000
  shuffled targets (absolute 445): 0 of 342 wrong-nucleus pairs inside the formula's own band
  ⁶He pin sensitivity: with 29.2711 (s1123 "AME") the ratio-mode residual is -0.15633 % (headline pin 29.2701: -0.15292 %)

[9] VERDICT (B1 i, the lane's thresholds; alt-irrational ratio ×68.92)
  ratio  aggregate p (product) 4.957e-04 → CHARGE ANSWERED · Fisher p 8.527e-01 → CHARGE SUSTAINED
  abs445 aggregate p (product) 6.288e-08 → CHARGE ANSWERED · Fisher p 5.960e-02 → CHARGE SUSTAINED

results → s1209_p9_lookelsewhere_census_C6_results.json · sha256 5a08df85572890384cb198b28ec44ce6d994af966fd21d6d2c5eadbb57f79859
s1209: 8 computed + 3 receipt PASS-able, 1 argument, 0 failed
