{
  "slug": "2026-09-09-crystallization-pathways",
  "assembly_states": {
    "experimental_conditions": 39,
    "simulation_conditions_in_table": 10,
    "experimental_transitions": {
      "Aggregate -> Aggregate": 3,
      "Aggregate -> Polycrystal": 13,
      "Aggregate -> Single crystal": 6,
      "Crystal -> Single crystal": 2,
      "Gas -> Gas": 15
    },
    "limits": "Author state classifications at selected conditions; not a continuous equilibrium phase diagram, independent repeats or directly measured nucleation barriers. Initial snapshots are about5min; absence of visible blobs does not exclude shorter unresolved precursors."
  },
  "published_md": {
    "energy_points": {
      "direct": 10000,
      "two_step": 20000
    },
    "timestamp_reversal_source_rows": {
      "direct": [
        4187
      ],
      "two_step": []
    },
    "histogram_sums_before_rounding_normalization": {
      "crystal": 0.999,
      "blob": 0.9980000000000001,
      "intermediate": 0.9980000000000001
    },
    "limits": "These are original author simulations, not rerun MD. Direct-path source row4187 reverses the time label and has a short overlapping range; values are preserved and the plotted line breaks there, without an invented cause or correction. Two paths differ in density, Debye length and surface potentials. MD steps are not experimental minutes. Histograms are not a matched time-series or proof of a third thermodynamic phase."
  },
  "salt_diffusion": {
    "D_m2_s": 1.61e-09,
    "length_m": 0.05,
    "initial_concentration_mM": 4.5,
    "boundary": "open end c=0; closed end no flux; uniform initial interior, no advection",
    "source_nodes": 901,
    "positive_time_fields": 672,
    "source_field_horizon_h": 168.0,
    "compared_values": 605472,
    "maximum_absolute_difference_mM": 0.018630298321907546,
    "rms_difference_mM": 0.003042854261549514,
    "series64_vs128_max_mM": 3.7836400679225335e-12,
    "mass_balance_checks": [
      {
        "time_s": 900.0,
        "integral_relative_error": 1.1102230246251565e-16
      },
      {
        "time_s": 3600.0,
        "integral_relative_error": 1.1102230246251565e-16
      },
      {
        "time_s": 86400.0,
        "integral_relative_error": 2.220446049250313e-16
      },
      {
        "time_s": 345600.0,
        "integral_relative_error": 0.0
      }
    ],
    "experimental_points": {
      "microscopic": 175,
      "growth_end": 19,
      "macroscopic": 92
    },
    "limits": "Source field spans168h although Methods describe96h; plot uses96h and full positive-time field comparison uses168h. t=0 source values near the opening are not the analytic uniform step and are excluded. No cause of the residual numerical difference is inferred. Experimental origins are unshifted, including a nonzero front at t=0; no refit of D or threshold, no nucleation-rate or particle-growth model."
  },
  "kinetic_example": {
    "state_free_energies_kBT": {
      "D": 0,
      "A": -10,
      "B": -12
    },
    "symmetric_transition_state_energies_kBT": {
      "D_M": 3,
      "D_A": 9,
      "D_B": 7,
      "M_A": 2,
      "M_B": 8
    },
    "rate_rule": "k_ij=exp[-(barrier_ij-G_i)]; chosen common attempt frequency=1",
    "cases": [
      {
        "case": "direct_only",
        "intermediate_free_energy": null,
        "mean_first_arrival_time": 965.9112815574425,
        "eventual_first_A_probability": 0.11920292202211756,
        "eventual_first_B_probability": 0.8807970779778824,
        "crystallized_by_1000": 0.6448772482300984,
        "mean_time_integral_relative_check": 0.0,
        "rates": {
          "D_M": 0.0,
          "M_D": 0.0,
          "D_A": 0.00012340980408667956,
          "D_B": 0.0009118819655545162,
          "M_A": 0.01831563888873418,
          "M_B": 4.5399929762484854e-05
        }
      },
      {
        "case": "productive",
        "intermediate_free_energy": -2,
        "mean_first_arrival_time": 79.65524736194824,
        "eventual_first_A_probability": 0.9732508053720721,
        "eventual_first_B_probability": 0.026749194627927905,
        "crystallized_by_1000": 0.9999997731159692,
        "mean_time_integral_relative_check": 5.551115123125783e-16,
        "rates": {
          "D_M": 0.049787068367863944,
          "M_D": 0.006737946999085467,
          "D_A": 0.00012340980408667956,
          "D_B": 0.0009118819655545162,
          "M_A": 0.01831563888873418,
          "M_B": 4.5399929762484854e-05
        }
      },
      {
        "case": "deep_intermediate",
        "intermediate_free_energy": -8,
        "mean_first_arrival_time": 21391.401848613106,
        "eventual_first_A_probability": 0.9732508053720724,
        "eventual_first_B_probability": 0.026749194627927905,
        "crystallized_by_1000": 0.06341062062925548,
        "mean_time_integral_relative_check": 3.3306690738754696e-15,
        "rates": {
          "D_M": 0.049787068367863944,
          "M_D": 1.670170079024566e-05,
          "D_A": 0.00012340980408667956,
          "D_B": 0.0009118819655545162,
          "M_A": 4.5399929762484854e-05,
          "M_B": 1.1253517471925912e-07
        }
      }
    ],
    "limits": "Coarse-state free energies are chosen, not experimental pair-well Eb. Reverse rates can satisfy detailed balance before making A/B absorbing for the first-arrival observable. No spatial critical nucleus, growth, MD, experimental fitting or prediction of final equilibrium. Lowering M with absolute saddles fixed slows exits but leaves relative exits unchanged."
  },
  "a2c": {
    "rows": [
      {
        "material": "SiO2",
        "RSS_unique_candidates": 24,
        "A2C_unique_candidates": 4,
        "supplied_count_ratio": 6.0,
        "recomputed_count_ratio": 6.0,
        "RSS_found_target": true,
        "precision_ratio_if_both_found_target": 6.0
      },
      {
        "material": "TiO2",
        "RSS_unique_candidates": 25,
        "A2C_unique_candidates": 7,
        "supplied_count_ratio": 3.5714,
        "recomputed_count_ratio": 3.5714285714285716,
        "RSS_found_target": true,
        "precision_ratio_if_both_found_target": 3.5714285714285716
      },
      {
        "material": "GeTe",
        "RSS_unique_candidates": 23,
        "A2C_unique_candidates": 10,
        "supplied_count_ratio": 2.3,
        "recomputed_count_ratio": 2.3,
        "RSS_found_target": true,
        "precision_ratio_if_both_found_target": 2.3
      },
      {
        "material": "BiBO3",
        "RSS_unique_candidates": 9,
        "A2C_unique_candidates": 5,
        "supplied_count_ratio": 1.8,
        "recomputed_count_ratio": 1.8,
        "RSS_found_target": true,
        "precision_ratio_if_both_found_target": 1.8
      },
      {
        "material": "VO2",
        "RSS_unique_candidates": 23,
        "A2C_unique_candidates": 13,
        "supplied_count_ratio": 1.7692,
        "recomputed_count_ratio": 1.7692307692307692,
        "RSS_found_target": true,
        "precision_ratio_if_both_found_target": 1.7692307692307692
      },
      {
        "material": "Al2O3",
        "RSS_unique_candidates": 15,
        "A2C_unique_candidates": 12,
        "supplied_count_ratio": 1.25,
        "recomputed_count_ratio": 1.25,
        "RSS_found_target": true,
        "precision_ratio_if_both_found_target": 1.25
      },
      {
        "material": "Mn2C",
        "RSS_unique_candidates": 21,
        "A2C_unique_candidates": 24,
        "supplied_count_ratio": 0.875,
        "recomputed_count_ratio": 0.875,
        "RSS_found_target": false,
        "precision_ratio_if_both_found_target": null
      }
    ],
    "limits": "Author precision counts one known target divided by unique low-energy candidates; this is not per-trajectory success probability, runtime acceleration or nucleation-rate ratio. Mn2C RSS did not find target under reported settings; supplied21/24=.875 cannot be interpreted as the stated precision ratio, so preserved but not used as a finite comparable value. Full GNN/MQMD/RSS not rerun."
  }
}