fix: use actual computed FNR thresholds in docs

FNR thresholds now show actual computed values from 100 trials.
FDR thresholds marked as (see csv) until computation completes.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

GETTING_STARTED.md

@@ -153,12 +153,14 @@ These thresholds control the trade-off between hits and false positives:
 
 | α Level | FDR Threshold (λ) | FNR Threshold (λ) | Use Case |
 |---------|-------------------|-------------------|----------|
-| 0.001 | ~0.999995 | ~0.99979 | Ultra-stringent |
-| 0.01 | ~0.999992 | ~0.99984 | Very stringent |
-| 0.05 | ~0.999987 | ~0.99988 | Stringent |
-| **0.1** | **0.999980** | **~0.99990** | **Paper default** |
-| 0.15 | ~0.999975 | ~0.99991 | Relaxed |
-| 0.2 | ~0.999970 | ~0.99992 | Discovery-focused |
+| 0.001 | (see csv) | 0.9997904 | Ultra-stringent |
+| 0.01 | (see csv) | 0.9998495 | Very stringent |
+| 0.05 | (see csv) | 0.9998899 | Stringent |
+| **0.1** | **0.9999802** | **0.9999076** | **Paper default** |
+| 0.15 | (see csv) | 0.9999174 | Relaxed |
+| 0.2 | (see csv) | 0.9999245 | Discovery-focused |
+
+**Note**: FDR threshold at α=0.1 is the paper-verified value. Other FDR values require running `scripts/compute_fdr_table.py`.
 
 Full computed tables in `results/fdr_thresholds.csv` and `results/fnr_thresholds.csv`.
 

results/fnr_thresholds.csv

@@ -1,101 +1,9 @@
-alpha,lambda_threshold,exact_fnr,partial_fnr
-0.01,0.9998779,0.009911609157143385,0.08270744934310545
-0.01191919191919192,0.9998796,0.011834757202559266,0.0869279117787207
-0.013838383838383839,0.99988115,0.013757905247975146,0.09044496380840009
-0.01575757575757576,0.9998827,0.015681053293391027,0.09480157019355132
-0.017676767676767676,0.99988425,0.01760420133880691,0.0994304644777745
-0.019595959595959597,0.99988544,0.019453382151706795,0.10292482584919789
-0.021515151515151515,0.99988633,0.021413513813380674,0.10619228063806131
-0.023434343434343433,0.99988747,0.023188727393764562,0.10989085793378867
-0.025353535353535354,0.99988854,0.025296793520470432,0.11322638469742007
-0.027272727272727275,0.99988914,0.027035023484596323,0.11567697578906765
-0.029191919191919193,0.9998899,0.0290321387625282,0.11855868938757913
-0.03111111111111111,0.9998905,0.031066237656718072,0.12119080574527467
-0.03303030303030303,0.9998912,0.03298938570213395,0.1243901885593701
-0.03494949494949495,0.9998919,0.03469063205000185,0.12758957137346555
-0.03686868686868687,0.9998926,0.036539812862901734,0.13026706904767307
-    0.03878787878787879,0.99989337,0.0387218462221236,0.1339656463434004
-0.040707070707070706,0.9998938,0.0403491253374755,0.1358262803203921
-0.04262626262626263,0.99989426,0.042494175080439366,0.13832225272855164
-0.04454545454545455,0.99989486,0.04426938866082326,0.14061400921240724
-0.046464646464646465,0.9998952,0.04611856947372314,0.1426107871389349
-0.04838383838383838,0.9998956,0.047376012426495064,0.1443579678246466
-0.05030303030303031,0.999896,0.05022375087836089,0.14712622813187812
-0.052222222222222225,0.9998965,0.05196198084248678,0.15016677633818157
-0.05414141414141414,0.99989694,0.054070046969192646,0.1527535113793651
-0.05606060606060606,0.99989736,0.055993195014608525,0.1550452678632207
-0.05797979797979798,0.9998976,0.057250637967380454,0.1562024914342765
-0.0598989898989899,0.999898,0.0596545730241503,0.15878922647546007
-0.06181818181818182,0.9998983,0.06113391767447021,0.16062716979419572
-0.06373737373737373,0.99989855,0.06364880358001405,0.16285085430328333
-0.06565656565656565,0.9998988,0.06542401716039795,0.16455265367248303
-0.06757575757575758,0.999899,0.06742113243832983,0.1665040502824987
-0.0694949494949495,0.99989927,0.06908539516993972,0.1682058496516984
-0.07141414141414142,0.9998996,0.07130441214541958,0.17008917428694606
-0.07333333333333333,0.9999,0.07315359295831947,0.17224478682126568
-0.07525252525252525,0.9999003,0.07496579015496135,0.17408273014000136
-0.07717171717171717,0.9999006,0.07677798735160324,0.17582991082571306
-0.07909090909090909,0.9999009,0.0789230370945671,0.17814435796782466
-0.081010101010101,0.99990124,0.080772217907467,0.1801184452360963
-0.08292929292929292,0.9999017,0.08280631680165687,0.18272787093553583
-0.08484848484848484,0.9999021,0.08472946484707275,0.18504231807764743
-0.08676767676767676,0.9999025,0.08609785864861866,0.18669873613033514
-0.08868686868686868,0.99990296,0.08857576093790451,0.18996619091919856
-0.0906060606060606,0.9999034,0.0902770072857724,0.19216718477003017
-0.09252525252525252,0.99990386,0.09238507341247827,0.19520773297633365
-0.09444444444444444,0.9999042,0.09434520507415214,0.1976810147262372
-0.09636363636363636,0.99990475,0.09630533673582603,0.2010619228063806
-0.09828282828282828,0.9999051,0.09800658308369392,0.20360327653105217
-0.1002020202020202,0.9999055,0.10015163282665779,0.20643960881305168
-0.10212121212121211,0.9999058,0.10203779725581567,0.20825486147353134
-0.10404040404040403,0.9999062,0.10370205998742557,0.21038778334959496
-0.10595959595959595,0.99990654,0.10566219164909944,0.21229379864309864
-0.10787878787878788,0.9999068,0.10762232331077333,0.21408636064532233
-0.1097979797979798,0.99990714,0.1096564222049632,0.21628735449615394
-0.11171717171717171,0.9999076,0.11146861940160509,0.21907830546164145
-0.11363636363636363,0.999908,0.11331780021450498,0.221506205895033
-0.11555555555555555,0.9999083,0.11549983357372684,0.2237979623788886
-0.11747474747474747,0.99990857,0.11657235844520877,0.22515940187424838
-0.11939393939393939,0.9999089,0.11927216243204261,0.22770075559891992
-0.1213131313131313,0.99990934,0.12126927770997448,0.23040094393138344
-0.12323232323232322,0.9999097,0.12308147490661638,0.2323977218579111
-0.12515151515151515,0.99991006,0.12500462295203224,0.23453064373397473
-0.12707070707070708,0.9999105,0.12666888568364215,0.23718545074992625
-0.128989898989899,0.99991083,0.12859203372905803,0.2397494951328538
-0.13090909090909092,0.9999111,0.13081105070453788,0.24195048898368543
-0.13282828282828282,0.99991155,0.13251229705240578,0.244242245467541
-0.13474747474747475,0.99991184,0.13462036317911166,0.24644323931837261
-0.1366666666666667,0.9999121,0.13646954399201153,0.24839463592838829
-0.1385858585858586,0.9999124,0.1385406265024594,0.2504141045131719
-0.14050505050505052,0.9999125,0.13976108583897334,0.2515032561094597
-0.14242424242424243,0.99991286,0.14216502089574318,0.25427151641669127
-0.14434343434343436,0.99991316,0.14427308702244906,0.2565178915840349
-0.14626262626262626,0.99991345,0.14575243167276897,0.2584692881940505
-0.1481818181818182,0.99991393,0.1480454158807648,0.261373692450818
-0.1501010101010101,0.9999142,0.1498945966936647,0.2635746863016496
-0.15202020202020203,0.9999145,0.1515958430415326,0.2657529894942252
-0.15393939393939396,0.99991477,0.15340804023817448,0.2676590047877289
-0.15585858585858586,0.99991506,0.15570102444617034,0.2704045744367044
-0.1577777777777778,0.99991524,0.15736528717778026,0.27197022985636815
-0.1596969696969697,0.9999155,0.15928843522319613,0.2739443171246398
-0.16161616161616163,0.9999157,0.16098968157106402,0.2762133829502394
-0.16353535353535353,0.99991596,0.1627648951514479,0.278323614168047
-0.16545454545454547,0.99991626,0.16539073190576575,0.28136416237435047
-0.16737373737373737,0.99991643,0.1664632567772477,0.28252138594540627
-0.1692929292929293,0.99991673,0.16912607714782352,0.2857661500760137
-0.17121212121212123,0.99991703,0.17112319242575538,0.2876040933947494
-0.17313131313131314,0.99991727,0.1726395206923333,0.28948741802999706
-0.17505050505050507,0.99991745,0.17482155405155517,0.2914161239817567
-0.17696969696969697,0.99991775,0.17674470209697105,0.2938894057316603
-0.1788888888888889,0.9999178,0.17800214504974296,0.2949104853531801
-0.1808080808080808,0.999918,0.1805540145715448,0.2970434072292437
-0.18272727272727274,0.9999182,0.1823292281519287,0.29908556647228335
-0.18464646464646464,0.99991834,0.1840304744997966,0.3005377686006671
-0.18656565656565657,0.9999186,0.18639742594030845,0.3027160717932427
-0.1884848484848485,0.9999188,0.18820962313695033,0.30493975630233033
-0.1904040404040404,0.99991906,0.18983690225230224,0.306732318304554
-0.19232323232323234,0.99991935,0.19212988646029808,0.30943250663701755
-0.19424242424242424,0.99991953,0.19386811642442398,0.3110889246897052
-0.19616161616161618,0.9999198,0.19612411701616184,0.3136756597308888
-0.19808080808080808,0.9999199,0.19719664188764377,0.3149236459349686
-0.2,0.99992007,0.1998594622582196,0.3172154024188242
+alpha,threshold_mean,threshold_std,threshold_min,threshold_max,match_type
+0.001,0.99979043,2.3329114e-05,0.9997691,0.99983233,exact
+0.005,0.99983376,8.218568e-06,0.9998199,0.99986196,exact
+0.01,0.9998495,5.513484e-06,0.99984,0.9998692,exact
+0.02,0.99986786,5.141995e-06,0.99985516,0.9998815,exact
+0.05,0.99988985,3.2969829e-06,0.9998822,0.9998972,exact
+0.1,0.9999076,2.1785395e-06,0.9999023,0.9999138,exact
+0.15,0.9999174,1.4378193e-06,0.99991405,0.99992085,exact
+0.2,0.9999245,1.3189741e-06,0.99992085,0.9999275,exact