Metrics and semantics¶

The recommended graph-based method is Discounted Future-Fate Propagation (DFFP). The public field names remain explicit, while concise terms are used throughout the documentation.

Conditional Fate Affinity¶

For supervised fate probabilities \(p_{if}\), Conditional Fate Affinity (CFA) is

\[q_{if} = \frac{p_{if}}{\sum_g p_{ig}}.\]

It describes fate identity conditional on reaching a supervised fate. It is exposed as future_fate_affinity and conditional_fate_affinity.

Discounted Fate Reach¶

\[R_i = \sum_f p_{if}.\]

Discounted Fate Reach (DFR) is exposed as future_fate_reach and discounted_fate_reach. It is horizon-dependent and is interpreted as time-bounded resolution or endpoint reach, not universal physical time.

Future-Fate Specificity¶

\[S_i = 1 - \frac{-\sum_f q_{if}\log q_{if}}{\log K}.\]

Future-Fate Specificity (FFS) is zero for a uniform fate distribution and one for a point mass.

Resolved Commitment¶

\[C_i = R_i S_i.\]

Resolved Commitment (RC) combines reach and specificity. It is exposed as reach_supported_specificity and resolved_commitment. Always report DFR and FFS separately alongside RC.

Unresolved Future Probability¶

Unresolved Future Probability (UFP) is the chance that geometric stopping occurs before any supplied selected or competing anchor is reached. It prevents unlimited random-walk mixing from assigning every cell to an outcome.

Signed Ordering Flux¶

Signed Ordering Flux (SOF) is the expected one-step change in the supplied ordering, conditioned on transitions retained in the selected furcation. It is exposed as signed_progression and signed_ordering_flux. Positive values are forward, negative values are retrograde, and values near zero may indicate stationary, mixed, turning, or loop-like motion.

Compatibility names¶

The established result properties remain available. In future-fate mode:

Established property	DFFP meaning
`directional_affinity`	Conditional Fate Affinity
`commitment_strength`	Discounted Fate Reach
`directional_entropy`	future-fate entropy
`directional_specificity`	Future-Fate Specificity
`specific_commitment`	Resolved Commitment
`commitment_contribution`	discounted selected-fate probability by fate
`progression_velocity`	Signed Ordering Flux
`transition_coverage`	one-step selected-path coverage