Shunyaya Symbolic Mathematical Symbols – Minimal Manifest (1.7)

What this page covers
A single, study-wide manifest that declares guards, weights, division policy, optional gate knobs, display and streaming options, comparison bands, and calibration bookkeeping. Declare once, publish with results, and freeze for reproducibility.

Required keys (declare once per study)

Core guards and weights

gamma      # >= 0 ; weighting exponent for pooling (e.g., w_i = |m_i|^gamma)
eps_a      # alignment clamp margin (recommend 1e-6)
eps_w      # denominator guard for pooling (recommend 1e-12)

Division policy

division_policy  # "strict" | "meadow" | "soft"   (default "strict")
denom_soft_min   # > 0 ; required iff division_policy == "soft"
meadow_div       # boolean alias for "meadow" (compatibility only; prefer division_policy)

Gate controls (optional, alignment-only)

gate_used   # "on" | "off" ; gate applied after each operator
lane_recipe # short string id for gate (e.g., "ZE-lane-v1") ; required iff gate_used == "on"
kappa, mu   # >= 0 ; gate knobs
rho         # in [0,1] ; gate memory knob
Q0          # in [0,1] ; initial memory state for gate

Display and streaming

zero_class_display  # boolean (default true; show m == 0 as (0, +1))
init_U              # default 0.0 ; streaming accumulator init for sums
init_W              # default 0.0 ; streaming accumulator init for sums

Comparisons and bands (global policy)

V_eps     # > 0 ; magnitude normalizer floor used in s_gt
beta_v    # >= 0 ; weight for normalized magnitude delta in s_gt
lambda_u  # >= 0 ; weight for alignment delta (rapidity) in s_gt
beta_u    # >= 0 ; weight for alignment gap in s_eq

# band thresholds (use quantile calibration once; then freeze)
tau_hi    # in (0,1) ; decision band for s_gt (">" / "<")
tau_eq    # in (0,1) ; equality threshold for s_eq ("equal" takes precedence)

Calibration bookkeeping (publish for reproducibility)

alpha_gt    # in (0,1)
alpha_eq    # in (0,1)
ref_size    # integer ; |D_ref| used for calibration
split_seed  # integer ; seed for train/holdout split
policy_gate # "on" | "off" ; gate state used during calibration (must match gate_used)

Compatibility (accepted but not preferred)

meadow_div      # boolean ; synonym for division_policy == "meadow"
gate_used_bool  # boolean ; if provided, map true->"on", false->"off" (avoid in new manifests)
V_unit          # legacy scaler for magnitude scores ; prefer V_eps in s_gt
tau_eq_mag      # legacy magnitude-only tie band ; prefer s_eq + tau_eq
tau_align       # legacy alignment floor ; prefer s_gt weights (beta_v, lambda_u) + bands

Example (minimal JSON, strict division, gate off, pre-calibrated bands)

{
  "gamma": 0.0,
  "eps_a": 1e-6,
  "eps_w": 1e-12,

  "division_policy": "strict",
  "denom_soft_min": null,
  "meadow_div": false,

  "gate_used": "off",
  "lane_recipe": null,
  "kappa": 0.0,
  "mu": 0.0,
  "rho": 0.0,
  "Q0": 0.0,

  "zero_class_display": true,
  "init_U": 0.0,
  "init_W": 0.0,

  "V_eps": 1e-12,
  "beta_v": 1.0,
  "lambda_u": 1.0,
  "beta_u": 1.0,

  "tau_hi": 0.70,
  "tau_eq": 0.80,
  "alpha_gt": 0.05,
  "alpha_eq": 0.10,
  "ref_size": 1000,
  "split_seed": 1729,
  "policy_gate": "off"
}

Notes and guards

- division_policy "strict": require nonzero denominators for division and multiplicative inverse
- division_policy "meadow": totalized inverse on magnitudes (inv_m(0) = 0)
- division_policy "soft": guard tiny denominators with denom_soft_min > 0 ; preserve sign

- gate_used must match policy_gate used during band calibration
- gating never alters magnitudes; apply clamp_a at the end of the alignment path
- publish all numeric knobs actually used in a release; freeze for reproducibility


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