sa-sv-duality

S_A / S_V Entropy Duality -- GenesisAeon Package 36

Standalone foundational module implementing the duality between Action Entropy (S_A) and Volume Entropy (S_V) -- the mathematical core underlying diffusive routing (P30), the unified GenesisAeon Lagrangian, and the AFET field equations.

The Duality

S_A  =  integral of sigma_s(H,Gamma) dt    (entropy produced along a path)
S_V  =  -integral p(H) ln p(H) dH          (Shannon entropy of state distribution)

S_A * S_V = const  (along the optimal UTAC trajectory)

Lagrangian interpretation:

L = T - V + Phi(H) + Gamma(C,R,E,P)
         ^^^^^^^^^^   ^^^^^^^^^^^^^
         S_A coupling  S_V coupling

The variational principle delta(S_A - lambda * S_V) = 0 reproduces the UTAC ODE -- this is the deepest formulation of the GenesisAeon dynamics.

Installation

pip install sa-sv-duality
# or
uv tool install sa-sv-duality

Usage

CLI

# Run a full S_A/S_V cycle (Gamma = 0.251, sigma = 2.2)
sav run

# Custom parameters
sav run --gamma 0.46 --sigma 2.2 --duration 20

# Show S_A, S_V for all 16 Q4 states
sav q4-map

# Find the optimal entropy path through Q4 state space
sav route 0 15 --lambda 1.0

# Run benchmarks
sav benchmark
sav benchmark --fast

Python API

from sa_sv_duality import SAVDuality, ActionEntropy, VolumeEntropy, Q4SAVMap

# Full Diamond interface
system = SAVDuality(gamma=0.251, sigma=2.2)
result = system.run_cycle(duration_years=10.0)
print(result["S_A"], result["S_V"], result["duality_constant"])

# CREP state
print(system.get_crep_state())  # {"C": ..., "R": ..., "E": ..., "P": ..., "Gamma": 0.251}

# Q4 entropy map
q4 = system.q4_entropy_map()   # {0: (S_A, S_V), ..., 15: (S_A, S_V)}

# Optimal path through Q4 space (= diffusive routing from P30)
path = system.optimal_path(start=0, end=15)

# Zenodo-compatible record
record = system.to_zenodo_record()

# Lower-level components
ae = ActionEntropy()
t, H = ae.generate_trajectory(H0=0.1, T=10.0)
S_A = ae.integrate(H.tolist(), times=t.tolist())

sv = VolumeEntropy()
S_V = sv.from_trajectory(H.tolist())
print(S_A * S_V)   # duality constant

Module Structure

src/sa_sv_duality/
  __init__.py           -- public API
  constants.py          -- Phi, sigma_UTAC, Gamma_universal, Q4 constants
  action_entropy.py     -- S_A = integral sigma_s(H,Gamma) dt
  volume_entropy.py     -- S_V = -integral p*ln(p) + Q4 discrete entropies
  duality_relation.py   -- S_A * S_V conservation + hyperbola geometry
  lagrangian_bridge.py  -- Phi(H) = S_A coupling, Gamma = S_V coupling
  variational.py        -- delta(S_A - lambda*S_V) = 0 solver
  q4_sav_map.py         -- (S_A, S_V) for all 16 Q4 states
  network_routing.py    -- SAV-optimal routing via modified Dijkstra
  system.py             -- Diamond interface (run_cycle, CREP/UTAC state)
  cli.py                -- `sav` CLI
  benchmark.py          -- Package 36 benchmark targets

Q4 State Entropy Map

Each of the 16 Q4 states (4-bit encoding of C/R/E/P activation) carries a characteristic (S_A, S_V) pair:

S_V ordering: monotone non-decreasing with number of active bits. S_A ordering: depends on effective Gamma of each state.

Benchmark Targets (from Feldtheorie Preprint)

Connection to Other Packages

Development

git clone https://github.com/GenesisAeon/sa-sv-duality.git
cd sa-sv-duality
uv sync --dev
uv run pytest

Citation

Reference: Johann Roemer * MOR Research Collective * Mai 2026 DOI: 10.5281/zenodo.17472834 UTAC v1.0: 10.5281/zenodo.17472834