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"81256006217701144379925098514861/12500000000000000000000000000000" }, "scope": "Frozen restricted medium at one hour, zero chemical stocks/floors; independent of editable numerical scenarios." }, "bypass": { "route": { "R_HCYSTRDX": 1, "R_TRDRy": 1, "R_LHCYSTIN": -1, "R_GTHP": 1, "R_ESTRONEDHy": -1 }, "chemical_net": { "M_h2o2_c": "-1", "M_h2o_c": "2", "M_estrone_c": "1", "M_estradiol_c": "-1" }, "auxiliary_net": { "M_enzyme_HCYSTRDX_fwd_pc": "-427350427350427/100000000000000", "M_enzyme_HCYSTRDX_rev_pc": "427350427350427/100000000000000", "M_enzyme_TRDRy_fwd_pc": "-427350427350427/100000000000000", "M_enzyme_TRDRy_rev_pc": "427350427350427/100000000000000", "M_enzyme_GTHP_fwd_pc": "-427350427350427/100000000000000", "M_enzyme_GTHP_rev_pc": "427350427350427/100000000000000", "M_enzyme_ESTRONEDHy_fwd_pc": "427350427350427/100000000000000", "M_enzyme_ESTRONEDHy_rev_pc": "-427350427350427/100000000000000" }, "scope": "Chemical cancellation only; surviving enzyme-allocation terms prevent calling this a standalone feasible cycle." }, "symbolic": { "adjoint": "a*(1 - exp((T - t)*(-a - b)))/(a + b)", "attaining_state": "C*b/(a + b) + (-C*b/(a + b) + g0)*exp(t*(-a - b))", "finite_time_bound": "C*T*a*b/(a + b) + a*(1 - exp(T*(-a - b)))*(-C*b/(a + b) + g0)/(a + b)", "oxidized_start": "C*T**2*a**3*b/(2*a**2 + 4*a*b + 2*b**2) + C*T**2*a**2*b**2/(a**2 + 2*a*b + b**2) + C*T**2*a*b**3/(2*a**2 + 4*a*b + 2*b**2) - C*T*a**2*b/(a**2 + 2*a*b + b**2) - C*T*a*b**2/(a**2 + 2*a*b + b**2) + C*T*a*b/(a + b)", "paired_cancellation": "(Cs-rD)prime = -k(Cs-rD) exactly" }, "numerical_lp": { "baseline": { "finished": true, "status": 0, "M": 1.0, "Q": 6.500480497416092, "peroxide_import": 1000.0, "peroxide_export": 0.0, "peroxide_other_consumption": 0.0, "peroxide_internal_production": 0.0, "terminal_peroxide": 993.4995195025839, "minimum_floor_slack": -1.942890293094024e-16, "max_auxiliary_residual": 2.9103830456733704e-11, "peroxide_terms": { "R_CAT": -3.240607645343328, "R_H2O2t": 1000.0, 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0.0, "terminal_peroxide": 0.0, "minimum_floor_slack": -4.440892098500626e-16, "max_auxiliary_residual": 2.9103830456733704e-11, "peroxide_terms": { "R_CAT": -3.240607645343328, "R_H2O2t": 6.500480487416092, "R_GTHP": -3.259872842072764 }, "scope": "Floating-point integrated relaxation; no trajectory or exact feasibility claim." }, "GTHOx_sensitivity": [ { "fraction": 0.0, "result": { "finished": true, "status": 0, "M": 1.0, "Q": 4.301079713928063, "peroxide_import": 1000.0, "peroxide_export": 0.0, "peroxide_other_consumption": 0.0, "peroxide_internal_production": 0.0, "terminal_peroxide": 995.6989202860719, "minimum_floor_slack": -3.3306690738754696e-16, "max_auxiliary_residual": 2.9103830456733704e-11, "peroxide_terms": { "R_CAT": -3.240607645343328, "R_H2O2t": 1000.0, "R_GTHP": -1.0604720685847355 }, "scope": "Floating-point integrated relaxation; no trajectory or exact feasibility claim." } }, { "fraction": 0.5, "result": { "finished": true, "status": 0, "M": 1.0, "Q": 5.400780105672078, "peroxide_import": 1000.0, "peroxide_export": 0.0, "peroxide_other_consumption": 0.0, "peroxide_internal_production": 0.0, "terminal_peroxide": 994.5992198943279, "minimum_floor_slack": -4.440892098500626e-16, "max_auxiliary_residual": 2.9103830456733704e-11, "peroxide_terms": { "R_CAT": -3.240607645343328, "R_H2O2t": 1000.0, "R_GTHP": -2.1601724603287504 }, "scope": "Floating-point integrated relaxation; no trajectory or exact feasibility claim." } }, { "fraction": 1.0, "result": { "finished": true, "status": 0, "M": 1.0, "Q": 6.500480497416092, "peroxide_import": 1000.0, "peroxide_export": 0.0, "peroxide_other_consumption": 0.0, "peroxide_internal_production": 0.0, "terminal_peroxide": 993.4995195025839, "minimum_floor_slack": -1.942890293094024e-16, "max_auxiliary_residual": 2.9103830456733704e-11, "peroxide_terms": { "R_CAT": -3.240607645343328, "R_H2O2t": 1000.0, "R_GTHP": -3.259872852072764 }, "scope": "Floating-point integrated relaxation; no trajectory or exact feasibility claim." } } ], "scope": "Fresh floating-point LPs on the configured medium; intermediate-burden and damage constraints absent. Absolute-flux parsimony mixes source column scales and is a declared selection rule." }, "carrier": [ { "theta": 0.0, "turnover_at_one_hour": 0.45550823741508084, "solver_error": 1.9204526857663495e-11, "total_needed_for_witness_GTHP": 7.156561388474144 }, { "theta": 0.3333333333333333, "turnover_at_one_hour": 0.6666666666666666, "solver_error": 3.1086244689504383e-15, "total_needed_for_witness_GTHP": 4.889808996025022 }, { "theta": 1.0, "turnover_at_one_hour": 1.088983525169838, "solver_error": 2.8173463562097822e-11, "total_needed_for_witness_GTHP": 2.9935004420826945 } ], "paired": { "identity_solver_error": 7.7982065249671e-12, "synthetic_rejection": { "rejected": true, "minimum_numerator_margin": "2/25", "common_r": [ "0", "1/20" ] }, "inference": { "status": "bounded", "K_lower": 0.6539264674066638, "K_upper": 0.7339691750802005, "z_lower": "12/25", "z_upper": "13/25" }, "raw_error_bound": "200/9603" }, "scope": "Conditional mathematical model. Exact source verification, numerical LPs, illustrative kinetic envelopes and synthetic signal tests are distinct. No clinical threshold, donor fit or Lean replay." }