{
  "generatedAt": "2026-09-07T09:39:13.978Z",
  "note": "Two-exit Aether + Grossman-Zhou grail ceiling on homogeneous GBM. Fit on expand IS. Holdout check. Frozen r44. PAPER. Not a search.",
  "cfg": {
    "step": 0.0025,
    "levels": 3,
    "tp": 0.01,
    "lev": 15
  },
  "gbm": {
    "beta": 0.32281545487923546,
    "d": 0.9925187343750002,
    "eN": {
      "k0": 0.7525635781955532,
      "k1": 0.5019117275884166,
      "k2": 0.25105725612112384,
      "total": 1.5055325619050937
    },
    "rWin": 0.042499999999999996,
    "rLose": [
      -0.044906328124999215,
      -0.03246874999999953,
      -0.01999999999999973
    ],
    "rLoseSum": -0.09737507812499847,
    "uLog": 0.04162167469081945,
    "vLog": 0.10244818076390237,
    "needEN": 2.461414191642306,
    "gTilde": -0.039785394235852575,
    "eRdollar": -0.033389944244031994
  },
  "grail": {
    "mu": 0.000043680620645176266,
    "gU": 0.000013910298244332628,
    "gUMo": 0.01021327594942445,
    "gDD": 0.000002086544736649894,
    "gDDMo": 0.0015253831452606281,
    "bStarTotal": 0.6369093679930927,
    "bDDAtPeak": 0.0955364051989639,
    "hoursMo": 730.5,
    "alphaNeedFor30": 25.819511392586882,
    "note": "g_DD*=alpha*g_u on homogeneous GBM from ATM beta, sigma_h, equicorrelation rho. Fee-free continuous relaxation; hourly+fees can only be lower. Not a market estimate."
  },
  "corrFix": {
    "nEff": 3.469300733389236,
    "rho": 0.5196078640043255,
    "sigH": 0.011358104997323598,
    "sigBookEqCorr": 0.12422152053451839,
    "sigBookWrong": 0.09146947032145608,
    "note": "N_eff is Frobenius participation, not variance-effective n. Equicorrelation ρ=sqrt((n/N_eff-1)/(n-1)), not 1-N_eff/n."
  },
  "is": {
    "tpN": 18291,
    "tpByK": [
      10851,
      7272,
      168
    ],
    "abortEvents": 8139,
    "abortEmpty": 10814,
    "abortEod": 2,
    "abortLegs": 15087,
    "allTpResets": 10624,
    "tpInAbortEp": 960,
    "tpInAllTpEp": 17331,
    "tpInEodEp": 0,
    "sumRAbort": -484.04110975157397,
    "sumRAllTp": 1004.6914121253903,
    "sumLogAbort": -501.61772345700325,
    "sumLogAllTp": 943.8956705543259,
    "hoursTp": 36045,
    "hoursAb": 31692,
    "hoursEmpty": 10814,
    "hoursCdAb": 195336,
    "hoursCdEmpty": 259536,
    "ruinAb": 0,
    "uHat": 2.247327681533358,
    "uHatAbortOnly": 0.11795060818282345,
    "meanAbortLegs": 1.8536675267231846,
    "meanRAbort": -0.05947181591738223,
    "meanRAllTp": 0.09456809225577846,
    "meanLogAbort": -0.06163137037191341,
    "meanLogAllTp": 0.08884560152055025,
    "meanHrsTp": 3.3927899096385543,
    "meanHrsAb": 3.893844452635459,
    "meanHrsEmpty": 1,
    "hours": 13152
  },
  "holdoutCheck": {
    "tpN": 11533,
    "tpByK": [
      6909,
      4503,
      121
    ],
    "abortEvents": 6231,
    "abortEmpty": 5361,
    "abortEod": 7,
    "abortLegs": 11646,
    "allTpResets": 6789,
    "tpInAbortEp": 659,
    "tpInAllTpEp": 10874,
    "tpInEodEp": 0,
    "sumRAbort": -377.72207589716027,
    "sumRAllTp": 595.0353999107958,
    "sumLogAbort": -391.29045348090534,
    "sumLogAllTp": 563.7357561405279,
    "hoursTp": 26755,
    "hoursAb": 27012,
    "hoursEmpty": 5361,
    "hoursCdAb": 149544,
    "hoursCdEmpty": 128664,
    "ruinAb": 0,
    "uHat": 1.8509067565398813,
    "uHatAbortOnly": 0.10576151500561708,
    "meanAbortLegs": 1.869041887337506,
    "meanRAbort": -0.06061981638535713,
    "meanRAllTp": 0.08764698776120133,
    "meanLogAbort": -0.06279737658175338,
    "meanLogAllTp": 0.08303664105767092,
    "meanHrsTp": 3.940933863602887,
    "meanHrsAb": 4.335098700048146,
    "meanHrsEmpty": 1,
    "hours": 8136
  },
  "sleeveG": {
    "is": {
      "meanLogTp": 0.08884560152055025,
      "meanLogAb": -0.06163137037191341,
      "jensenTp": 0.09035984916191414,
      "jensenAb": -0.06131366356340372,
      "meanHrsTp": 3.3927899096385543,
      "meanHrsAb": 3.893844452635459,
      "meanHrsEmpty": 1,
      "meanHrsEpLive": 2.6558136389762317,
      "meanHrsEpWithCd": 18.035061027149474,
      "gHour": 0.0008291317530315015,
      "gMo": 0.832499250161022,
      "gHourNonempty": 0.0016811985536232248,
      "gMoNonempty": 2.4147884486654547,
      "ruinAb": 0,
      "nEp": 29577
    },
    "holdoutCheck": {
      "meanLogTp": 0.08303664105767092,
      "meanLogAb": -0.06279737658175338,
      "jensenTp": 0.08401663600698095,
      "jensenAb": -0.0625350003374759,
      "meanHrsTp": 3.940933863602887,
      "meanHrsAb": 4.335098700048146,
      "meanHrsEmpty": 1,
      "meanHrsEpLive": 3.216799956476797,
      "meanHrsEpWithCd": 18.352429138784615,
      "gHour": 0.0005111974490111419,
      "gMo": 0.4527084875784415,
      "gHourNonempty": 0.0008481848137071902,
      "gMoNonempty": 0.8581827730570464,
      "ruinAb": 0,
      "nEp": 18381
    }
  },
  "kpis": {
    "uHatIs": 2.247327681533358,
    "uHatHo": 1.8509067565398813,
    "uHatAbortOnlyIs": 0.11795060818282345,
    "uHatAbortOnlyHo": 0.10576151500561708,
    "abortEventsIs": 8139,
    "abortEventsHo": 6231,
    "abortEmptyIs": 10814,
    "abortEmptyHo": 5361,
    "allTpResetsIs": 10624,
    "allTpResetsHo": 6789,
    "meanAbortLegsIs": 1.8536675267231846,
    "meanAbortLegsHo": 1.869041887337506,
    "tpNIs": 18291,
    "tpNHo": 11533,
    "mixRIs": 0.027748776974567842,
    "mixRHo": 0.01669073149106264,
    "meanLogTpIs": 0.08884560152055025,
    "meanLogAbIs": -0.06163137037191341,
    "meanLogTpHo": 0.08303664105767092,
    "meanLogAbHo": -0.06279737658175338,
    "meanHrsTpIs": 3.3927899096385543,
    "meanHrsAbIs": 3.893844452635459,
    "meanHrsEmptyIs": 1,
    "meanHrsEpWithCdIs": 18.035061027149474,
    "meanHrsEpWithCdHo": 18.352429138784615,
    "gMoSleeveIs": 0.832499250161022,
    "gMoSleeveHo": 0.4527084875784415,
    "eNtot": 1.5055325619050937,
    "needEN": 2.461414191642306,
    "gTilde": -0.039785394235852575,
    "eRdollar": -0.033389944244031994,
    "beta": 0.32281545487923546,
    "rho": 0.5196078640043255,
    "sigBookEqCorr": 0.12422152053451839,
    "sigBookWrong": 0.09146947032145608,
    "meanRAbortIs": -0.05947181591738223,
    "meanRAllTpIs": 0.09456809225577846,
    "meanRAbortHo": -0.06061981638535713,
    "meanRAllTpHo": 0.08764698776120133,
    "gUMo": 0.01021327594942445,
    "gDDMo": 0.0015253831452606281,
    "bStarTotal": 0.6369093679930927,
    "bDDAtPeak": 0.0955364051989639,
    "alphaNeedFor30": 25.819511392586882,
    "verdict": "Grail on this GBM: unconstrained +1.02%/mo; DD15% cushion +0.153%/mo. Need alpha=25.8 for 30% — impossible. Two-exit sleeve g IS +83.2%/mo (with empty+cooldown). AIM no. PAPER."
  }
}