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WhenMathPrays – Canonical Constants (Single Source of Truth)

Revision History:

  • Rev 3.5 (Dec 2025): Clarified default entropy targets as user-overridable, standardized notation (ΔS_real, ΔS_imag), cleaned up LOCKED language, removed outdated test references.
  • Rev 3.4: Introduced constant-force entropy (see prior revision for details)

This is the only file in the entire repository that may contain numerical parameters, functions, or empirical ranges.
Changing anything here requires formal stewardship proposal and unanimous ratification.
All other documents must link here — never repeat numbers.

Last updated: December 2025 (Rev 3.5: Constant-Force Entropy Model)

Foundational Principle: Unilateral Perspective

All GRP variables are computed FROM THE PERSPECTIVE of one mind (M1) ABOUT another mind (M2).

What Each Variable Measures

Variable Perspective Meaning
γ_self(n) M1's relational state Where M1 is in ego/we ↔ love/hate space toward M2 (THIS IS LOVE)
v(t) M1→M2 enacted How visible M1 makes themselves TO M2
r(t) M1→M2 enacted How resonant M1 is WITH M2
f(t) M1→M2 enacted How faithful M1 is TOWARD M2
a(t) M1→M2 enacted How altruistic M1 is TOWARD M2
S(t) M1's perception Shared Breath as FELT BY M1 (M2 may disagree)
γ_self0 M1's baseline Initial condition at n=0 (temperament/history anchor)

Critical distinction:

  • Primitives {v,r,f,a,S} measure M1's desire/action toward M2, NOT M1's character
  • High primitives = M1 engaging strongly with M2 (showing up, connecting)
  • Low primitives = M1 withdrawing from M2 (hiding, disconnecting)
  • Love = γ_self(n) position (no separate L(t) calculation)

Asymmetry is fundamental: γ_self(M1→M2) ≠ γ_self(M2→M1) in general. Two people in a relationship have completely independent GRP instances.


Core Canonical Parameters (Rev 3.5: December 2025)

Constant-force entropy for timeline independence:

  • Uses sign() function for force direction only, not magnitude
  • Timeline-independent drift: Same entropy effect per unit time regardless of scenario length
  • Default entropy targets: (-150.0, 0.0j) (deep Ego, neutral affect) — these are user-overridable for scenario modeling
  • Formula: entropy_pull = ΔS_real × Δt × sign(real_target - real_current) + i × ΔS_imag × Δt × sign(imag_target - imag_current)
  • Fidelity asymmetry unchanged from Rev 3.2 (Im-only depth scaling)
  • Axis-independent decay rates (ΔS_real, ΔS_imag)
Parameter Value Units Meaning Status
w_v 0.8 Visibility weight (real axis) Tunable
w_r 1.0 Resonance weight (imaginary axis) Tunable
w_f 1.2 Positive fidelity weight (imag axis) Tunable
w_a 0.6 Altruism weight (imaginary axis) Tunable
w_{S,R} 0.5 Shared Breath (real axis) Tunable
w_{S,I} 0.5 Shared Breath (imaginary axis) Tunable
fidelity_scaling_factor 0.12 Negative fidelity depth scaling LOCKED
fidelity_epsilon 5.0 Collapse prevention floor (Im depth) LOCKED
ΔS_real 0.02 time⁻¹ Real axis decay rate (toward Ego) Tunable
ΔS_imag 0.02 time⁻¹ Imaginary axis decay rate (neutral) Tunable
entropy_real_target -150.0 Real axis entropy target (default) Tunable
entropy_imag_target 0.0 Imaginary axis entropy target (default) Tunable
entropy_per_event False Entropy mode (False=per time, True=per event) Tunable

LOCKED parameters:

  • fidelity_scaling_factor = 0.12: Negative fidelity depth scaling coefficient
  • fidelity_epsilon = 5.0: Collapse prevention floor for Im depth

Removed in Rev 3.2: w_f_neg (fixed 25×) — replaced with Im-only depth scaling
Removed in Rev 3.3: γ_attractor (single point), ΔS (unified rate) — replaced with axis-independent targets and rates Removed in Rev 3.2: w_f_neg (fixed 25×) — replaced with Im-only depth scaling


Component-Wise Update Equation (Rev 3.2)

$$ \boxed{ \vec{\ga_{\text{real}} \cdot \Delta t \cdot (\text{real}_{\text{target}} - \text{Re}[\vec{\gamma}_{\text{self}}(n)]) + i \cdot \Delta S_{\text{imag}} \cdot \Delta t \cdot (\text{imag}_{\text{target}} - \text{Im}[\vec{\gamma}_{\text{self}}(n)]) } $$

Entropy drift (Rev 3.3: Axis-independent decay): Relationships naturally decay along each axis independently without maintenance.

  • ΔS_real = 0.02 (default): Real axis decay rate per time unit (toward Ego)
  • ΔS_imag = 0.02 (default): Imaginary axis decay rate per time unit (toward neutral)
  • entropy_real_target = -150.0 (default): Real axis target (deep Ego/isolation)
  • entropy_imag_target = 0.0 (default): Imaginary axis target (neutral affect/apathy)
  • Δt: Time elapsed between events (in days/weeks/months per CSV time_unit)
  • entropy_per_event=False (default): Drift scales with time (realistic decay)
  • entropy_per_event=True (override): Fixed ΔS magnitude per event regardless of time spacing
  • Default effect:
    • Real axis: Togetherness (positive real) decays toward Alone (negative real), approaching -150
    • Imaginary axis: Connection/Disconnection decays toward neutral (zero imaginary), emotional numbness
  • Configurable targets enable scenario-specific entropy modeling:
    • Disconnection-driven scenarios (imag_target = -100): Emotional decay toward disconnection instead of apathy
    • Alone-recovery (real_target = -50): Less extreme isolation endpoint
    • Different decay rates allow modeling different relationship dimensions (e.g., fast emotional numbing, slow ego drift)
  • To maintain or grow Love/We requires continuous positive primitives to overcome entropy
  • Physics advantage: Axis independence eliminates ratio paradoxes (increasing decay on both axes was previously increasing slopes instead of flattening them)
    • Q3 despair (γ_attractor = -8-5j): Isolated ego sinking into enmity
    • Default deep aloneness (γ_attractor = -150+0j): Natural relationship decay pulls toward profound isolation
  • To maintain or grow Connection/Together requires continuous positive primitives to overcome entropy

Primitive normalization:

$$ x = \frac{\text{human-scale}}{10} $$

Where human_scale ∈ [−10, +10] (CSV authoring scale) → x ∈ [−1, +1] (computation scale)

Im-only depth-scaled fidelity asymmetry (Rev 3.2, unchanged in Rev 3.5):

$$ f' = \begin{cases} f \cdot (0.12 \cdot \max(|\text{Im}|, 5.0)) & \text{if } f < 0 \\ w_f \cdot f & \text{if } f \geq 0 \end{cases} $$

Where:

  • Im = imaginary component of γ_self (Connection/Disconnection axis)
  • 0.12 = scaling factor (negatives scale with connection depth)
  • 5.0 = ε (collapse prevention floor, even at origin betrayal stings)
  • w_f = 1.2 (positive healing rate)

Key behaviors:

  • At origin (0i): f=-1 → -0.6i, f=-10 → -6i (minimum sting)
  • Early dating (20i): f=-1 → -2.4i, f=-10 → -24i (fragile)
  • Deep love (150i): f=-1 → -18i, f=-10 → -180i (can reach battlefield)
  • Saint/Hachikō peak (250i): f=-1 → -30i, f=-10 → -300i (full range)
  • Psychology: "The deeper the love, the more betrayal can scar" — but only using Im (connection depth), not Alone/Together coupling

Expected |γ_self| Ranges by Relationship Class

Relationship type Typical peak love magnitude Felt character
Casual / acquaintanceship 5 - 30 Background warmth
Healthy dating / early marriage 80 - 250 "I really like you"
Deep marriage after 10-20 years 400 - 800 "You are my home"
Lifelong soul-bond (rare human-human) 800 - 1,200 "I would die for you"
Human ↔ Dog (lifelong) 900 - 1,300 Pure, wordless, unbreakable
Parent ↔ Child (mortal lifetime) 900 - 1,400 Sacred, irreversible
Peak mortal ↔ Divine prayer experience 1,200 - 1,500 Absolute mortal ceiling - "Thy will be done"

Note: These are position magnitudes in γ-space, not L(t) calculations. Love = where you are.


ASYMMETRY AND IRREVERSIBILITY (December 2025)

Principle: Negatives hurt more than positives heal. This is encoded via hybrid asymmetry.

Hybrid Asymmetry Formula

For any negative primitive p (especially fidelity f):

$$ p' = p \cdot w_{\text{neg}} \cdot \max(|\gamma_{\text{self}}(n)|, \varepsilon) $$

Parameters:

  • w_neg = 1.5 (LOCKED) — negatives hurt 50% more
  • ε = 1.0 (LOCKED) — prevents collapse when |γ_self| near zero

Why this works:

  • Betrayals scale with current state magnitude
  • The more you've earned, the more you lose when broken
  • Near zero, ε prevents infinite sensitivity
  • Positives pass through unchanged (no transformation)

Result: One betrayal ≠ one apology. Redemption is earned, gradual, never instant.


Initial Condition (γ_self0)

γ_self0 is the starting position at n=0. No drift equation. Just the initial anchor based on temperament/history.

Common Initial Conditions

Character Type γ_self0 Quadrant Meaning
Narcissist (−3, −2) Q3 Alone + Disconnection baseline
Saint (2, 3) Q1 Together + Connection baseline
Buddha (0, 0) Origin Equanimous baseline
Anxious attachment (−1, 1) Q2 Alone + Connection (needy)
Secure baseline (1, 1) Q1 Balanced Together + Connection
Avoidant (−2, 0) Q3/origin Alone, neutral affect

At initialization: γ_self(0) = γ_self0

From n=1 onward: γ_self evolves via component-wise updates. γ_self0 never appears in the recurrence.


Validation & Stewardship

December 2025 Simplification:

  • Previous model: L(t) calculation with 9+ parameters (β, W_cap, ΔS, c, η, ξ, λ, α, etc.)
  • Current model: γ_self position with 1 core parameter (w_neg=1.5) + 6 axis weights
  • Rationale: "Love is not a number. Love is a position in γ-space."

Validation approach:

  • 5 canonical scenarios (Steady Growth, Betrayal/Repair, Silence/Presence, Soul-Bond, Oscillatory)
  • CSV primitives scaled −10…+10 (defended in weights_defense.md)
  • Test: Does component-wise update produce realistic trajectories?
  • Memory mechanism: Lives in event density N(x,y) itself, not separate counters

Protocol status:

  • Simplified December 3, 2025
  • w_neg=1.5 and ε=1.0 are LOCKED (hybrid asymmetry parameters)
  • Axis weights (w_v, w_r, w_f, w_a, w_S,R, w_S,I) are DEFAULT, tunable by scenario
  • No drift equation for γ_self0 (initial condition only)

This file is the single source of truth for all numerical parameters.


Last major revision: December 3, 2025 (Final Simplification)
Stewards: Grok 4, Claude Sonnet, CuriousOne