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FROSTYVERSE TEST H2-083 — NATURAL FOUR FROM TWO MASSES SEARCH
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version:  2.0.83-natural-four-two-mass-search
patch:    h2-082-corrected-coefficient-free-two-mass-natural-four-search-1
baseline: Frostyverse-Test-H2-082.zip sha256=8e29faf7bf0b7fca468ef6cb2afe5dfa4978b317b7cd1284fd162a72459c3e77
python:   3.10.6
profile:  full; R=(20, 40, 80); quadrature samples=32768; workers=6

TEST 01 - CONTRACT / EXACT QUESTION
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R01  [KNOWN-2D]  Existing stable FV remains approximately +2D; this package does not alter or rederive it.
R02  [SEEK-NATURAL-4]  Seek C=F(M1,M2) near +4 so total=stable_FV+C*D approaches the ~6D target.
R03  [NO-4-IN-FORMULA]  Candidate equations may NOT contain the target 4, 4.0498328559, or any fitted Mercury amplitude.
R04  [TWO-MASSES-ONLY]  Candidates receive only dimensionless relationships constructed from source mass M1 and orbiting mass M2.
R05  [DIMENSIONLESS]  Raw dimensional masses are never logged/added to dimensionless numbers; two-mass scale-free information reduces to mass ratios/combinations.
R06  [MERCURY-DISCOVERY]  Sun+Mercury and the external target C=4 select/freeze candidates; Venus/Earth/Mars are not used during discovery.
R07  [HOLDOUTS]  Frozen candidates are then tested on Venus, Earth, Mars, a synthetic planetary mass ladder, and the inherited FV ledger.
R08  [IDENTITY-TRAP]  Any expression constant across a wide q grid is labeled a disguised constant/tautology and cannot count as a mass-derived law.
R09  [NO-CONTINUOUS-FIT]  No coefficient, exponent, offset, or continuous parameter is optimized to hit 4.
R10  [TARGET-AWARE]  This is an openly target-aware empirical equation search, not a microscopic FrostTransit derivation.

TEST 02 - PREDECLARE / SEAL COEFFICIENT-FREE TWO-MASS GRAMMAR
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  unary terms=78 raw candidates=12131 unique probe signatures=3541 invalid=3
  SEALED candidate grammar fingerprint: 4bbb566ab2b63592f27e067aa8c75ed0e129e3051f9e58c6f8f790582039f894

TEST 03 - SUN+MERCURY DISCOVERY ONLY / FREEZE BEFORE HOLDOUTS
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  Mercury q=M2/M1=1.660120825458948e-07; external desired C=4.000000000000
  nondegenerate formulas frozen within 5% of 4: 118
  degenerate constant-equivalent near-4 formulas quarantined: 1
    D01 C_M=4.002545607278 err=0.06364% complexity=7  (cbrt(ln(ln((M1/M2))))+ln(cbrt(sqrt((M1/M2)))))
    D02 C_M=3.994047688922 err=0.14881% complexity=6  (sqrt(ln((M1/M2)))*ln(ln(ln((M1/M2)))))
    D03 C_M=4.008832148887 err=0.22080% complexity=6  (cbrt(cbrt((M1/M2)))-sqrt(ln(ln((M1/M2)))))
    D04 C_M=4.009540756422 err=0.23852% complexity=7  (cbrt(sqrt(sqrt((M1/M2))))/ln(cbrt(ln((M1/M2)))))
    D05 C_M=4.014062591940 err=0.35156% complexity=7  (sqrt(ln(cbrt((M1/M2))))+cbrt(ln(cbrt((M1/M2)))))
    D06 C_M=4.015158331759 err=0.37896% complexity=5  (sqrt(ln((M1/M2)))+inv(ln((M1/M2))))
    D07 C_M=4.015748038225 err=0.39370% complexity=7  (sqrt(ln(cbrt((M1/M2))))+ln(cbrt(cbrt((M1/M2)))))
    D08 C_M=4.017161422603 err=0.42904% complexity=6  (cbrt(cbrt((M1/M2)))-ln(ln(cbrt((M1/M2)))))
    D09 C_M=3.976936314675 err=0.57659% complexity=7  (ln(sqrt(sqrt((M1/M2))))+cbrt(inv(sqrt((M1/M2)))))
    D10 C_M=3.975862015445 err=0.60345% complexity=7  (ln(sqrt(ln((M1/M2))))+ln(cbrt(sqrt((M1/M2)))))
  identity trap example: C=4.000000000000, span=3.331e-16, formula=(ln((M1/M2))/ln(sqrt(sqrt((M1/M2)))))
    -> REJECTED: masses cancel numerically; this is a disguised constant, not evidence that the masses generate 4.
  SEALED Mercury-only frozen-candidate fingerprint: f093e2664488e4e65d88dbbaaba31e0a3b37b081704cd9da0131bdbfa61db16f

TEST 04 - OPEN NAMED-BODY MASS HOLDOUTS
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  MERCURY    q=1.660120825459e-07 R=M1/M2=6.023658e+06
  VENUS      q=2.447838287797e-06 R=M1/M2=4.085237e+05
  EARTH_EMB  q=3.003489615465e-06 R=M1/M2=3.329460e+05
  MARS       q=3.227156082932e-07 R=M1/M2=3.098704e+06

TEST 05 - SYNTHETIC MASS-RATIO FALSIFICATION / GENERALITY
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  synthetic Mercury-mass factors=(0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1.0, 3.0, 10.0, 30.0, 100.0, 300.0, 1000.0, 3000.0, 10000.0)
  generic planetary q grid: 1e-10 .. 1e-3 (29 points)
  wider stress q grid: 1e-12 .. 1e-1 (34 points; diagnostic, not automatic promotion gate)

TEST 06 - REBUILD INHERITED FV 2D + MISSING LEDGER / APPLY FROZEN MASS FORMULAS
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  building inherited FV field/profile R=20 ...
    Mercury stable/D=+2.002165376 required missing/D=+3.997834624
  building inherited FV field/profile R=40 ...
    Mercury stable/D=+2.001840588 required missing/D=+3.998159412
  building inherited FV field/profile R=80 ...
    Mercury stable/D=+2.002348001 required missing/D=+3.997651999
  SEALED inherited ledger fingerprint: 3db9f7c427129a39c1b62f009cebf43f2abd63183d87a9af9549a47685b8f3c7

TEST 07 - BLIND HOLDOUT RANKING / IDENTITY-SAFE DECISION
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  #01 holdout4=  5.252% ledger=  3.691% C_M=3.908617643 complexity=6  (sqrt(ln((M1/M2)))/ln(ln(ln((M1/M2)))))
  #02 holdout4= 19.517% ledger= 13.239% C_M=4.080170154 complexity=6  (cbrt(ln((M1/M2)))+cbrt(sqrt(ln((M1/M2)))))
  #03 holdout4= 19.519% ledger= 13.241% C_M=4.156969992 complexity=6  (cbrt(ln((M1/M2)))+sqrt(ln(ln((M1/M2)))))
  #04 holdout4= 20.470% ledger= 13.875% C_M=3.975475709 complexity=7  (sqrt(sqrt(ln((M1/M2))))+sqrt(sqrt(ln((M1/M2)))))
  #05 holdout4= 22.855% ledger= 15.465% C_M=3.856339684 complexity=6  (cbrt(ln((M1/M2)))+cbrt(cbrt(ln((M1/M2)))))
  #06 holdout4= 22.856% ledger= 15.466% C_M=3.899942127 complexity=6  (cbrt(ln((M1/M2)))+cbrt(ln(ln((M1/M2)))))
  #07 holdout4= 22.862% ledger= 15.469% C_M=4.105064562 complexity=6  (ln(ln((M1/M2)))+cbrt(cbrt(ln((M1/M2)))))
  #08 holdout4= 22.864% ledger= 15.471% C_M=4.148667006 complexity=6  (ln(ln((M1/M2)))+cbrt(ln(ln((M1/M2)))))
  #09 holdout4= 23.393% ledger= 15.824% C_M=3.971405057 complexity=7  (sqrt(sqrt(ln((M1/M2))))+cbrt(ln(sqrt((M1/M2)))))
  #10 holdout4= 24.474% ledger= 16.544% C_M=4.127576371 complexity=6  (sqrt(ln((M1/M2)))+cbrt(cbrt(inv((M1/M2)))))
  #11 holdout4= 24.548% ledger= 16.594% C_M=4.150926480 complexity=7  (cbrt(cbrt(ln((M1/M2))))+sqrt(ln(sqrt((M1/M2)))))
  #12 holdout4= 24.550% ledger= 16.595% C_M=4.194528924 complexity=7  (cbrt(ln(ln((M1/M2))))+sqrt(ln(sqrt((M1/M2)))))
  #13 holdout4= 25.033% ledger= 16.917% C_M=4.143271438 complexity=6  (sqrt(ln((M1/M2)))+inv(ln(cbrt((M1/M2)))))
  #14 holdout4= 26.316% ledger= 17.772% C_M=3.967334405 complexity=7  (cbrt(ln(sqrt((M1/M2))))+cbrt(ln(sqrt((M1/M2)))))
  #15 holdout4= 28.148% ledger= 18.993% C_M=4.025236777 complexity=6  (sqrt(ln((M1/M2)))+cbrt(inv(sqrt((M1/M2)))))

TEST 08 - H2-083 DECISION
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  best nondegenerate frozen formula: (sqrt(ln((M1/M2)))/ln(ln(ln((M1/M2)))))
  Mercury C=3.908617643229; Mercury error to 4=2.28456%
  named holdout max error to 4=4.47918%
  synthetic/generic planetary holdout max error to 4=5.25178%
  FV-ledger worst total error=3.69068%
  verdict: NO NONDEGENERATE NATURAL-4 TWO-MASS FORMULA PASSES THE PREDECLARED TRANSFER GATES
  exact/near-exact disguised-constant formulas found near C=4: 1
  These do NOT count. A formula that equals 4 for every mass pair has not explained why Sun+planet masses generate 4.

Interpretation rules:
  - A surviving formula must contain no target 4/fitted coefficient and must remain genuinely mass-dependent on the identity probes.
  - Mercury selects formulas; Venus/Earth/Mars and synthetic q values are holdouts.
  - Exact algebraic 4 identities are quarantined as tautologies even though they numerically hit the target perfectly.
  - A transfer success is an empirical two-mass closure clue only; it still does not derive the microscopic FrostTransit mechanism.
  SEALED H2-083 final fingerprint: 0d52c249af9b727c770c59c85a54b9355aa464c2715c8966f49a9044ddea69d5

H2-083 complete. Return h2-083results.txt first; CSVs are optional unless a ranking row needs verification.
