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 :math:`p_{if}`, Conditional Fate Affinity
(CFA) is

.. math::

   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
---------------------

.. math::

   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
-----------------------

.. math::

   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
-------------------

.. math::

   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:

.. list-table::
   :header-rows: 1

   * - 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