Why this page. A redox bridge that maps n, F, and DeltaE (optionally via Nernst with Q and T) into e_redox, then assigns symmetric, bounded alignments with the same RSI skeleton.
Meta description. Shunyaya Symbolic Mathematical Chemistry: map redox data (n, F, DeltaE, optional Q) to e_redox and bounded alignments; sign tracks DeltaE, while E_unit and c set scale without changing direction.
Definitions (ASCII)
• Net electrons transferred: n (positive integer)
• Faraday constant: F (C/mol)
• Standard cell potential: DeltaE_std (V)
• Nonstandard (Nernst) potential (optional): DeltaE = DeltaE_std – ( R * T / ( n * F ) ) * ln( Q )
• Potential scale (declare once): E_unit > 0 (energy per mol; use J/mol or kJ/mol consistently)
• Study slope: c > 0 (as in §4.2)
Contrast (replace e only; rest unchanged)
standard-state lens:
e_redox = ( n * F * DeltaE_std ) / E_unit
nonstandard composition (Nernst lens):
e_redox = ( n * F * ( DeltaE_std – ( R * T / ( n * F ) ) * ln( Q ) ) ) / E_unit
which simplifies to:
e_redox = ( n * F * DeltaE ) / E_unit
Alignment assignment (same bounded, symmetric map)
a_r = tanh( -c * e_redox )
a_p = tanh( +c * e_redox )
Then clamp both so |a| <= 1 – eps_a.
RSI skeleton (unchanged, guarded)
U_r = sum_r |m_r|^gamma * atanh_safe( a_r , eps_a )
V_p = sum_p |m_p|^gamma * atanh_safe( a_p , eps_a )
W_r = sum_r |m_r|^gamma
W_r_safe = max( W_r , eps_w )
RSI_redox = tanh( ( V_p – U_r ) / W_r_safe )
Condition-aware use (optional)
RSI_env_redox = g_t * RSI_redox # g_t from the unified calm gate (§5)
Minimal algorithm (per reaction, fixed T)
INPUT: {reactants}, {products}; gamma; E_unit; c; n; F; eps_a; eps_w; (optionally DeltaE_std or E0_cathode, E0_anode or Q, T)
STEP 1: choose data path
A) have DeltaE_std:
e_redox = ( n * F * DeltaE_std ) / E_unit
B) have half-cell E0 values:
DeltaE_std = E0_cathode – E0_anode
e_redox = ( n * F * DeltaE_std ) / E_unit
C) have Q, T (Nernst):
DeltaE = DeltaE_std – ( R * T / ( n * F ) ) * ln( Q )
e_redox = ( n * F * DeltaE ) / E_unit
STEP 2: a_r = tanh( -c * e_redox ); a_p = tanh( +c * e_redox )
a_r = clamp_a( a_r , eps_a )
a_p = clamp_a( a_p , eps_a )
STEP 3: U_r, V_p, W_r as above; W_r_safe = max( W_r , eps_w )
RSI_redox = tanh( ( V_p – U_r ) / W_r_safe )
OPTIONAL STEP 4: RSI_env_redox = g_t * RSI_redox
OUTPUT: RSI_redox in ( -1 , +1 ); sign( RSI_redox ) = sign( e_redox )
Sign sanity (why direction is preserved)
• Galvanic (spontaneous-as-written): DeltaE_std > 0 ⇒ e_redox > 0 ⇒ RSI_redox > 0.
• If DeltaE_std < 0, then e_redox < 0 ⇒ RSI_redox < 0.
• If DeltaE_std = 0, then e_redox = 0 ⇒ RSI_redox = 0.
Equivalence note (thermo link, optional)
DeltaG_std = – n * F * DeltaE_std. If you set G_unit = E_unit and use the same T, then e_G (from §4.13) equals e_redox. Choose one lens; do not double-count.
Guards and policy
• Electron balance: ensure the reaction is electron-balanced (the n used matches the net electrons transferred in the skeleton).
• Units: keep R, T, F, DeltaE, E_unit consistent; convert kJ <-> J as needed before forming e_redox.
• Scale: choose E_unit near a typical | n * F * DeltaE | for your study (see §4.4A); publish its value.
• Monotonicity: c > 0 preserves “larger DeltaE ⇒ larger e_redox ⇒ larger RSI_redox”.
• Idempotence: if no redox data, skip this bridge and use e from §4.1.
• Safety: observation-only; no rates or hazards or operational cell design are implied.
Manifest additions (diffs from §4.12)
• use_Redox # boolean: when true, set e := e_redox
• E_unit # energy-per-mol scale used by redox lens
• n # electrons transferred (positive integer)
• F # Faraday constant value used
• data_path # one of {“DeltaE_std”, “E0_cathode,E0_anode”, “DeltaE_Q_T”}
• R, T # constants if using Q (publish values)
Result. The redox bridge swaps in an electrochemistry-derived contrast e_redox while keeping the same bounded alignment map and RSI engine. Directionality follows classical electrochemistry (sign of DeltaE), magnitudes remain transparent via E_unit and c, electron balance is explicit, and collapse to classical stoichiometry is unchanged.
Navigation
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