Nexa’s algorithms

Symbol definitionsF processes facts, Z calculates structure, E holds supporting material, and A provides the explanation. V denotes versions and U uncertainty. Arrows show the processing order, not evidence of causal validity.

Conditions and scopeAI should not invent calendar calculations or rewrite a recorded casting.

Symbol definitionsx is the raw input; F(x; v_c) transforms it into facts; Z computes structure; E and U are supporting material and uncertainty; q is your question. v_c, v_r, and v_m identify calendar, rule, and language-model versions. Theta denotes internal parameters.

Conditions and scopeThe equations describe dependencies between data and calculations. AI explanations must be based on the supporting material in E and must not change its calculated facts.

Symbol definitionstrace is the audit record. v_c, v_r, and v_m identify calendar, rule, and language-model versions. v_theta and theta_version both denote the parameter version; e and evidence_ids both denote supporting-evidence identifiers.

Conditions and scopeVersion labels and identifiers do not replace the underlying records. Reproduction also depends on retaining and being able to access the inputs, relevant versions, and necessary generation records.

Symbol definitionsx_i is the proportion of part i. S⁴ denotes a simplex with five parts and four independent dimensions. These equations use its strictly positive interior for the logarithms that follow.

Conditions and scopeIf the raw data contain zeros, they need a clearly defined, traceable treatment before taking logarithms.

Symbol definitionsg is the geometric mean; clr is the centered log-ratio; ln is the natural logarithm; d_A is Aitchison distance; the subscript-2 norm is the Euclidean norm. x and y are the two compositions.

Conditions and scopeEvery component of x and y must be positive. A larger distance means a larger difference in relative structure, not an inherently good or bad outcome. Zero replacement and numerical precision need separate records.

Symbol definitionsx^(r) is source r and w_r its weight. Products and powers operate component by component. C is closure, or normalization; z is the vector before closure.

Conditions and scopeSource components must meet the positivity requirement, and the closure denominator must be positive. Weights need a documented basis and version; the combination formula alone cannot determine which source is more credible.

Symbol definitionsH is entropy. ln(5) is the maximum entropy for five equally weighted parts. current and background identify the two states; d_A is the distance defined above.

Conditions and scopeProportions must be positive and sum to one. Entropy can treat zeros by a limit, but Aitchison distance still requires positive parts. Concentration lies between 0 and 1; neither concentration nor shift is inherently a fortune score.

Symbol definitionsz is the structure being assessed, k its category, P_k the Boolean test of necessary conditions, g_k the continuous degree function, and theta its parameters.

Conditions and scopeP_k depends on the selected sources, school, and rule version; a high score cannot redefine it. The score is an internal structural quantity, not an event probability.

Symbol definitionsG is the graph. Here V means the set of nodes, not the version symbol used earlier. E_generate and E_control are generating and controlling edges; A_ij is the directed strength from i to j; z_i and z_j are the participating components.

Conditions and scopeA need not be symmetric. Signals in opposite directions can coexist and do not automatically cancel each other.

Symbol definitionsR is the relationship record. n, d, c, s, and v stand for participants, direction, condition, source, and version. c(z) and path_exists(z) are Boolean tests; AND requires both to be true.

Conditions and scopePairs, complete participant sets, and paths may need different rules. A shared interface must preserve those differences and allow checks of both activating and non-activating examples.

Symbol definitionsI_t is the current interval, starting at s_t. J_j are overlapping cycle intervals; duration measures elapsed time; w_tj is the overlap weight. lcm means least common multiple. The least common multiple of the 60-day and 7-day cycles is 420 days.

Conditions and scopeI_t must have positive duration. The intervals J_j must cover it without gaps or overlaps for the weights to sum to one. Time zones and solar-term boundaries must be aligned first.

Symbol definitionsx_t is the composition in period t; c_t its clr transform; v_t the displacement vector; a_t its length; cos is cosine similarity between vectors; turn_t is the turning indicator.

Conditions and scopeclr requires positive components. Cosine similarity is undefined if either displacement is a zero vector; report it as unavailable or use an explicitly documented treatment. Turning thresholds require calibration.

Symbol definitionseffect_r(t) is the amount of effect r at time t; direction_r is its direction vector; m_t sums absolute amounts; d_t combines their directions.

Conditions and scopeEffects need compatible scales and explicit direction definitions. A near-zero d_t does not mean nothing is happening. Neither m_t nor d_t is an event probability.

Symbol definitionsmu_k(x) is the membership of input x in state k; c is a candidate; state_k is state k; score is the internal score under that state.

Conditions and scopeSumming to one is this model's blending convention, not an automatic property of every fuzzy set. Membership is not an event probability and cannot introduce judgments absent from the underlying rules. Function shapes still need versioning and calibration.

Symbol definitionsf produces a ranking; epsilon_b is perturbation b; D_eta describes allowed input error; B is the number of repeats; K is the number of top positions. The indicator is one when its condition holds and zero otherwise. S_c is the stability rate.

Conditions and scopeB must be a positive integer, K must fit within the candidate count, and perturbed inputs must remain valid. S_c depends on the chosen error model. It is not a career success rate, event probability, or measure of divination accuracy.

Symbol definitionsHere q means completeness of the supporting information, not the user's question. s_raw is the raw internal score, s_0 the neutral reference, and s_display the displayed value.

Conditions and scopeCompleteness and the neutral reference need explicit definitions and compatible score scales. A low q does not mean a job or relationship is unsuitable. With severely limited information, precise rankings may be withheld.

Symbol definitionsN is the sample count, p_i the predicted probability for event i, and y_i the observed outcome, either 0 or 1. L_i is the log-likelihood of observation i under its predicted probability; Log Loss is the negative mean of these values.

Conditions and scopeN must be positive. Direct logarithms require 0<p_i<1; endpoints need limits or documented numerical treatment. Evaluation needs independently held-out data and calibration curves; rare events also require base rates, precision, recall, and PR-AUC. High accuracy does not replace calibration, and internal scores cannot simply be renamed probabilities.

Symbol definitionsI is the set of internal line values; rho_t is the density matrix at step t; P_i projects onto state i; Tr is the matrix trace; p_t(i) is the resulting probability. The symbol ≽0 means positive semidefinite.

Conditions and scopePositive semidefiniteness is a property of the whole Hermitian matrix, not a requirement that every entry be nonnegative. The projectors must form a complete, mutually exclusive set of states. This mathematical representation uses quantum probability without requiring quantum hardware.

Symbol definitionsi and j are source and destination states; T_t is the conditional transition kernel. h_t contains results so far, selective observation states, and filtered context. p_t denotes the internal state distribution given the current history. This is not an identity for unconditional marginal distributions.

Conditions and scopeFor each fixed history, every row of T must be nonnegative and normalized; checking only the sum of the entire matrix is insufficient. This keeps the probabilities at each step valid.

Symbol definitionspi is the specified traditional baseline, T_t the transition kernel, lambda the observation-coupling strength, and y_t the value of line t. With lambda=0, observation coupling is off: both the initial distribution and each transition return to pi, and the six-line joint probability equals the product of the individual baseline probabilities.

Conditions and scopepi must itself be nonnegative and sum to one. Stationarity is not independence: pi T=pi does not replace exact fallback when coupling is off. The new mechanism still needs comparison with the independent baseline and simpler sequence models.

Symbol definitionsy_1 through y_6 are generated line values; y_<t is the preceding sequence; h_(t-1) is the available history; the product symbol multiplies across steps. Step one uses the initial history h_0.

Conditions and scopeEvery conditional distribution must be valid, and history may use only information available before that step. The product is calculated for a specified observation mechanism and context. If history includes additional random information, it must be explicitly conditioned on or included in the joint model; the expression cannot simply be treated as the unconditional joint probability of the line values.

Symbol definitionsy_t is the generated line value; event is its persisted generation record; h_t is updated history. r and request_id both identify the same request. Arrows show the order of generation, storage, display, observation, and update.

Conditions and scopeA retry is not a new draw. Coins are a conditional display; derived hexagrams must be computed deterministically from the six generated lines without rewriting that casting's state.

Symbol definitionsE contains facts, rules, conflicts, scope, and versions. U contains missing information, sensitivity, disagreement, and calibration information. q is the question, s the safety policy, LLM the language model, and A the answer. Unmet conditions also belong in the supporting records.

Conditions and scopeThe supporting package needs to trace back to specific evidence_ids; the presence of fields does not establish that their contents are sufficient. Calculated facts, traditional interpretations, model synthesis, and practical suggestions need to remain distinguishable.

Symbol definitionssupported_claims and checkable_claims count supported and verifiable statements. omitted_required_items and required_items count missing and required items. contradictory_pairs and checked_pairs count contradictory and examined pairs of statements.

Conditions and scopeA zero denominator makes the ratio unavailable, not zero or a perfect score. Definitions must be applied consistently, alongside blinded human review and user research. These ratios measure fidelity to the supplied material, not divination's real-world predictive validity.