logs/analysis_n40.log

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Kronecker S_40 Analysis
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Loading partitions...
  37338 partitions of 40
Computing centralizer orders...

--- Phase 1: Character Table Statistics ---
  Identity class index: 37337
  Row 0/37338 (0%) [0s]
  Row 5000/37338 (13%) [60s]
  Row 10000/37338 (26%) [117s]
  Row 15000/37338 (40%) [172s]
  Row 20000/37338 (53%) [227s]
  Row 25000/37338 (66%) [281s]
  Row 30000/37338 (80%) [337s]
  Row 35000/37338 (93%) [395s]
  Nonzero entries: 891,693,627 / 1,394,126,244 (64.0%)
  Max |χ|: 58965081685061803130880
  Σ dim² = 40!: True

--- Phase 2: Hook Kronecker Coefficients ---
  Found 40 hook partitions
  Loading 40 character table rows...
  Scanning row 5000/37338...
  Scanning row 10000/37338...
  Scanning row 15000/37338...
  Scanning row 20000/37338...
  Scanning row 25000/37338...
  Scanning row 30000/37338...
  Scanning row 35000/37338...
  Computing 11480 hook triples...
    Hook row 0/40 (0%) [27s]
    Hook row 5/40 (12%) [138s]
    Hook row 10/40 (25%) [223s]
    Hook row 15/40 (37%) [284s]
    Hook row 20/40 (50%) [325s]
    Hook row 25/40 (62%) [350s]
    Hook row 30/40 (75%) [363s]
    Hook row 35/40 (87%) [367s]
  Hook Kronecker: 3969/11480 nonzero (34.6%), max=1, 368.0s

--- Phase 3: Near-Rectangular Kronecker Coefficients ---
  Found 40 near-rectangular partitions:
    (40^1) -> index 0
    (20^2) -> index 2087
    (14^1,13^2) -> index 9203
    (10^4) -> index 20410
    (8^5) -> index 27589
    (7^4,6^2) -> index 30915
    (6^5,5^2) -> index 33651
    (5^8) -> index 35591
    (5^4,4^5) -> index 35675
    (4^10) -> index 36706
    (4^7,3^4) -> index 36721
    (4^4,3^8) -> index 36814
    (4^1,3^12) -> index 37057
    (3^12,2^2) -> index 37185
    (3^10,2^5) -> index 37192
    (3^8,2^8) -> index 37205
    (3^6,2^11) -> index 37224
    (3^4,2^14) -> index 37249
    (3^2,2^17) -> index 37280
    (2^20) -> index 37317
    (2^19,1^2) -> index 37318
    (2^18,1^4) -> index 37319
    (2^17,1^6) -> index 37320
    (2^16,1^8) -> index 37321
    (2^15,1^10) -> index 37322
    (2^14,1^12) -> index 37323
    (2^13,1^14) -> index 37324
    (2^12,1^16) -> index 37325
    (2^11,1^18) -> index 37326
    (2^10,1^20) -> index 37327
    (2^9,1^22) -> index 37328
    (2^8,1^24) -> index 37329
    (2^7,1^26) -> index 37330
    (2^6,1^28) -> index 37331
    (2^5,1^30) -> index 37332
    (2^4,1^32) -> index 37333
    (2^3,1^34) -> index 37334
    (2^2,1^36) -> index 37335
    (2^1,1^38) -> index 37336
    (1^40) -> index 37337
  Loading 40 character table rows...
  Scanning row 5000/37338...
  Scanning row 10000/37338...
  Scanning row 15000/37338...
  Scanning row 20000/37338...
  Scanning row 25000/37338...
  Scanning row 30000/37338...
  Scanning row 35000/37338...
  Computing 11480 near-rectangular triples...
  Near-rect Kronecker: 1156/11480 nonzero (10.1%), max=105927325, 304.3s

--- Phase 4: Random Sample (nonzero fraction estimate) ---
  Sampling 1000 random triples from 37338 partitions...
  Loading 2889 unique character table rows...
  Scanning row 5000/37338...
  Scanning row 10000/37338...
  Scanning row 15000/37338...
  Scanning row 20000/37338...
  Scanning row 25000/37338...
  Scanning row 30000/37338...
  Scanning row 35000/37338...
    Sample 0/1000 (0%) [0s]
    Sample 100/1000 (10%) [2s]
    Sample 200/1000 (20%) [3s]
    Sample 300/1000 (30%) [5s]
    Sample 400/1000 (40%) [7s]
    Sample 500/1000 (50%) [9s]
    Sample 600/1000 (60%) [10s]
    Sample 700/1000 (70%) [12s]
    Sample 800/1000 (80%) [14s]
    Sample 900/1000 (90%) [16s]
  Sample: 949/1000 nonzero = 94.9% (95% CI: [93.4%, 96.1%])
  Max sampled |g| = 1300912596785734847, time = 17.3s

--- Phase 5: Cross-n Trend Summary ---
  n=20: 79.5% nonzero, max g = 6,408,361
  n=30: 89.9% nonzero, max g = 24,233,221,539,853
  n=40: ~94.9% nonzero (sampled), max g (hooks) = 1

Results saved: scripts/experiments/kronecker-coefficients/results/analysis_n40.json

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S_40 Analysis Complete
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