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"""Structural field computations for TNFR physics.
REORGANIZED (Nov 14, 2025): Canonical field implementations moved to modular
submódules (canonical.py, extended.py) to reduce coupling and improve
maintainability. This module now acts as the public API, re-exporting all
canonical fields and containing only research-phase utilities.
This module computes emergent structural "fields" from TNFR graph state,
grounding a pathway from the nodal equation to macroscopic interaction
patterns.
CANONICAL FIELDS (Read-Only Telemetry)
---------------------------------------
All four structural fields have CANONICAL status as of November 12, 2025:
- Φ_s (Structural Potential): Global field from ΔNFR distribution
- |∇φ| (Phase Gradient): Local phase desynchronization metric
- K_φ (Phase Curvature): Geometric phase confinement indicator [now unified in Ψ = K_φ + i·J_φ]
- ξ_C (Coherence Length): Spatial correlation scale
EXTENDED CANONICAL FIELDS (Promoted Nov 12, 2025)
-------------------------------------------------
Two flux fields capturing directed transport:
- J_φ (Phase Current): Geometric phase-driven transport
- J_ΔNFR (ΔNFR Flux): Potential-driven reorganization transport
RESEARCH-PHASE UTILITIES
------------------------
Additional functions for analysis and advanced validation:
- compute_k_phi_multiscale_variance(): Coarse-grained curvature variance
- fit_k_phi_asymptotic_alpha(): Power-law fitting for multiscale K_φ
- k_phi_multiscale_safety(): Safety check for multiscale curvature
- path_integrated_gradient(): Path-integrated phase gradient
- compute_phase_winding(): Topological charge (winding number)
- fit_correlation_length_exponent(): Critical exponent extraction
Physics Foundation
------------------
From the nodal equation:
∂EPI/∂t = νf · ΔNFR(t)
ΔNFR represents structural pressure driving reorganization. Aggregating
ΔNFR across the network with distance weighting creates the structural
potential field Φ_s, analogous to gravitational potential from mass
distribution.
References
----------
- UNIFIED_GRAMMAR_RULES.md § U6: STRUCTURAL POTENTIAL CONFINEMENT
- docs/STRUCTURAL_FIELDS_TETRAD.md: Complete field validation
- docs/XI_C_CANONICAL_PROMOTION.md: ξ_C experimental validation
- AGENTS.md § Structural Fields: Canonical tetrad documentation
- TNFR.pdf § 2.1: Nodal equation foundation
"""
from __future__ import annotations
import math
import time
from typing import Any
from ..mathematics.unified_numerical import np
try:
import networkx as nx
except ImportError:
nx = None
# Import config defaults for field constants
from ..config import defaults_core as defaults
# ---------------------------------------------------------------------------
# Universality classification tolerance
# ---------------------------------------------------------------------------
_ISING_2D_EXPONENT_TOLERANCE = 0.15
# ============================================================================
# PUBLIC API: Import all canonical and extended canonical fields
# ============================================================================
# Canonical Structural Triad (Φ_s, |∇φ|, K_φ) + ξ_C experimental
from .canonical import (
compute_structural_potential,
compute_phase_gradient,
compute_phase_curvature,
estimate_coherence_length,
)
# Backward-compatible alias (used by pattern_discovery and parallel modules)
compute_structural_potential_field = compute_structural_potential
# Unified Telemetry (Optimized Pass)
from .telemetry import compute_structural_telemetry
# Extended canonical fields (J_φ, J_ΔNFR) - Promoted Nov 12, 2025
from .extended import (
compute_phase_current,
compute_dnfr_flux,
compute_extended_canonical_suite,
)
# Unified field functions are defined in this module below
# Import TNFR cache system for research functions
_CACHE_AVAILABLE = True
# Import TNFR aliases
try:
from ..constants.aliases import ALIAS_THETA, ALIAS_DNFR
except ImportError:
ALIAS_THETA = ["phase", "theta"]
ALIAS_DNFR = ["delta_nfr", "dnfr"]
# Import self-optimizing engine for mathematical analysis
try:
from ..dynamics.self_optimizing_engine import TNFRSelfOptimizingEngine, OptimizationObjective
_SELF_OPTIMIZING_AVAILABLE = True
except ImportError:
_SELF_OPTIMIZING_AVAILABLE = False
TNFRSelfOptimizingEngine = None
OptimizationObjective = None
__all__ = [
# Canonical Structural Triad
"compute_structural_potential",
"compute_phase_gradient",
"compute_phase_curvature",
"estimate_coherence_length",
# Unified Telemetry
"compute_structural_telemetry",
# Extended Canonical Fields (NEWLY PROMOTED Nov 12, 2025)
"compute_phase_current",
"compute_dnfr_flux",
"compute_extended_canonical_suite",
# Unified Field Framework (NEWLY INTEGRATED Nov 28, 2025)
"compute_complex_geometric_field_arrays",
"compute_emergent_fields",
"compute_tensor_invariants",
"compute_unified_telemetry",
# Self-Optimizing Mathematical Analysis (NEW)
"analyze_optimization_potential",
"recommend_field_optimization_strategy",
"auto_optimize_field_computation",
# Research-phase utilities
"path_integrated_gradient",
"compute_phase_winding",
"compute_k_phi_multiscale_variance",
"fit_k_phi_asymptotic_alpha",
"k_phi_multiscale_safety",
"fit_correlation_length_exponent",
"measure_phase_symmetry",
]
# ============================================================================
# RESEARCH-PHASE UTILITIES (Not in modular implementations)
# ============================================================================
# Centralised helpers — single source of truth in _helpers.py
from ._helpers import get_phase as _get_phase # noqa: E402
from ._helpers import wrap_angle as _wrap_angle # noqa: E402
def path_integrated_gradient(
G: Any, source: Any, target: Any
) -> float:
"""Compute path-integrated phase gradient along a shortest path.
**Status**: RESEARCH (telemetry support for custom analyses)
Definition
----------
Given a path P = [v_0, v_1, ..., v_k] from source to target:
PIG = Σ_{i=0}^{k-1} |∇φ|(v_i)
where |∇φ|(v) is the phase gradient at node v.
Physical Interpretation
-----------------------
Cumulative phase desynchronization along a path. High PIG indicates
that the path traverses regions with significant local phase disorder.
Parameters
----------
G : TNFRGraph
Graph with node phase attributes
source : NodeId
Start node
target : NodeId
End node
Returns
-------
float
Path-integrated gradient (sum of node gradients along shortest path).
Returns 0.0 if no path exists or nodes are isolated.
Notes
-----
- Telemetry-only; does not mutate graph state.
- Uses shortest path from networkx.
- If multiple shortest paths exist, uses lexicographically first one
(arbitrary but deterministic).
"""
if nx is None:
raise RuntimeError("networkx required for path operations")
try:
path = nx.shortest_path(G, source, target)
except (nx.NetworkXNoPath, nx.NodeNotFound):
return 0.0
# Compute phase gradient if not cached
grad = compute_phase_gradient(G)
# Sum gradients along path
total = 0.0
for node in path:
if node in grad:
total += grad[node]
return float(total)
def measure_phase_symmetry(G: Any) -> float:
"""Compute a phase symmetry metric in [0, 1].
**Status**: RESEARCH (telemetry-only compatibility function)
Definition
----------
Let {φ_i} be phases for all nodes with a phase attribute.
Compute circular mean μ = Arg( Σ_i e^{j φ_i} ). Symmetry metric:
S = 1 - mean( |sin(φ_i - μ)| )
Interpretation
--------------
S ≈ 1 : Highly clustered / symmetric phase distribution.
S → 0 : Broad / antisymmetric distribution (desynchronization).
Returns 0.0 if no phases are available.
Notes
-----
- Read-only; does not mutate graph state (grammar safe).
- Provides backward compatibility for benchmarks expecting this symbol.
- Invariant #5 respected (phase verification external to this metric).
"""
phases: list[float] = []
# Collect phases from node attributes using alias list
for node, data in G.nodes(data=True): # type: ignore[attr-defined]
for alias in ALIAS_THETA:
if alias in data:
try:
phases.append(float(data[alias]))
except (TypeError, ValueError):
pass
break
if not phases:
return 0.0
arr = np.array(phases, dtype=float)
# Wrap into [0, 2π)
arr = np.mod(arr, 2 * math.pi)
vec = np.exp(1j * arr)
mean_angle = float(np.angle(np.mean(vec)))
diffs = np.abs(np.sin(arr - mean_angle))
return float(1.0 - min(1.0, float(np.mean(diffs))))
def compute_phase_winding(G: Any, cycle_nodes: list[Any]) -> int:
"""Compute winding number (topological charge) for a closed cycle.
**Status**: RESEARCH (topological analysis support)
Definition
----------
For a closed loop of nodes, count full rotations of phase:
q = (1/2π) Σ_{edges in cycle} Δφ_wrapped
Returns
-------
int
Winding number q. Non-zero values indicate phase vortices/defects
enclosed by the loop.
Parameters
----------
G : TNFRGraph
NetworkX-like graph with per-node phase attribute.
cycle_nodes : list
Ordered list of node IDs forming a closed cycle. Function will
connect the last node back to the first to complete the loop.
Returns
-------
int
Integer winding number (topological charge). Values != 0 indicate
a phase vortex/defect enclosed by the loop.
Notes
-----
- Telemetry-only; does not mutate EPI.
- Robust to local reparameterizations of phase due to circular wrapping.
- If fewer than 2 nodes are provided, returns 0.
"""
if not cycle_nodes or len(cycle_nodes) < 2:
return 0
total = 0.0
seq = list(cycle_nodes)
# Ensure closure by including last->first
for i, j in zip(seq, seq[1:] + [seq[0]]):
phi_i = _get_phase(G, i)
phi_j = _get_phase(G, j)
total += _wrap_angle(phi_j - phi_i)
q = int(round(total / (2.0 * math.pi)))
return q
def _ego_mean(values: dict[Any, float], nodes: list) -> float:
"""Mean of values restricted to given nodes; returns 0.0 if empty."""
if not nodes:
return 0.0
arr = [values[n] for n in nodes if n in values]
if not arr:
return 0.0
return float(sum(arr) / len(arr))
def compute_k_phi_multiscale_variance(
G: Any,
*,
scales: tuple = (1, 2, 3, 5),
k_phi_field: dict[Any, float] | None = None,
) -> dict[int, float]:
"""Compute variance of coarse-grained K_φ across scales [RESEARCH].
Definition (coarse-graining by r-hop ego neighborhoods):
K_φ^r(i) = mean_{j in ego_r(i)} K_φ(j)
var_r = Var_i [ K_φ^r(i) ]
Parameters
----------
G : TNFRGraph
NetworkX-like graph with phase attributes accessible via aliases.
scales : tuple[int, ...]
Radii (in hops) at which to compute coarse-grained variance.
k_phi_field : dict | None
Precomputed K_φ per node. If None, computed via
compute_phase_curvature.
Returns
-------
dict[int, float]
Mapping from radius r to variance of coarse-grained K_φ at scale.
Notes
-----
- Read-only telemetry; does not mutate graph state.
- Intended to support asymptotic freedom assessments.
"""
if k_phi_field is None:
k_phi_field = compute_phase_curvature(G)
nodes = list(G.nodes())
variance_by_scale = {}
for scale in scales:
coarse_k_phi = {}
for src in nodes:
# BFS ego-graph of radius scale
ego_nodes = set([src])
frontier = set([src])
for _ in range(scale):
next_frontier = set()
for node in frontier:
for neighbor in G.neighbors(node):
if neighbor not in ego_nodes:
ego_nodes.add(neighbor)
next_frontier.add(neighbor)
frontier = next_frontier
# Coarse-grained K_φ as mean over ego-graph
coarse_k_phi[src] = _ego_mean(k_phi_field, list(ego_nodes))
# Variance across all nodes
vals = np.array(list(coarse_k_phi.values()))
variance_by_scale[scale] = float(np.var(vals))
return variance_by_scale
def fit_k_phi_asymptotic_alpha(
variance_by_scale: dict[int, float], alpha_hint: float = defaults.K_PHI_ASYMPTOTIC_ALPHA
) -> dict[str, Any]:
"""Fit power-law exponent α for multiscale K_φ variance decay.
**Status**: RESEARCH (multiscale analysis support)
Model
-----
var(K_φ) at scale r ~ C / r^α
Taking logarithms:
log(var) = log(C) - α * log(r)
Parameters
----------
variance_by_scale : dict[int, float]
Mapping from scale r to variance of coarse-grained K_φ
alpha_hint : float
Expected value of α for comparison (default from K_PHI_ASYMPTOTIC_ALPHA research)
Returns
-------
dict[str, Any]
- alpha: Fitted exponent α
- c: Fitted constant C (pre-factor)
- r_squared: Goodness of fit
- residuals: Per-scale residuals
- prediction_error: Relative error vs alpha_hint
"""
if len(variance_by_scale) < 3:
return {
"alpha": 0.0,
"c": 0.0,
"r_squared": 0.0,
"residuals": {},
"prediction_error": 0.0,
}
scales = np.array(sorted(variance_by_scale.keys()))
variances = np.array([variance_by_scale[s] for s in scales])
# Fit log(var) = log(C) - alpha * log(scale)
log_scales = np.log(scales.astype(float))
log_vars = np.log(variances + 1e-12) # Avoid log(0)
try:
coeffs = np.polyfit(log_scales, log_vars, 1)
alpha = -coeffs[0]
log_c = coeffs[1]
c = np.exp(log_c)
# Compute R^2
fitted = log_c - alpha * log_scales
ss_res = np.sum((log_vars - fitted) ** 2)
ss_tot = np.sum((log_vars - np.mean(log_vars)) ** 2)
r2 = 1.0 - (ss_res / (ss_tot + 1e-12))
# Residuals per scale
residuals = {
s: float(v - np.exp(fitted[i]))
for i, (s, v) in enumerate(variance_by_scale.items())
}
# Error vs hint
pred_error = abs(alpha - alpha_hint) / (alpha_hint + 1e-9)
return {
"alpha": float(alpha),
"c": float(c),
"r_squared": float(r2),
"residuals": residuals,
"prediction_error": float(pred_error),
}
except (np.linalg.LinAlgError, ValueError):
return {
"alpha": 0.0,
"c": 0.0,
"r_squared": 0.0,
"residuals": {},
"prediction_error": 0.0,
}
def k_phi_multiscale_safety(
G: Any,
alpha_hint: float = defaults.K_PHI_ASYMPTOTIC_ALPHA,
fit_min_r2: float = defaults.STATISTICAL_SIGNIFICANCE_THRESHOLD,
) -> dict[str, Any]:
"""Assess multiscale safety of K_φ field [RESEARCH].
**Status**: RESEARCH (safety analysis support)
Computes coarse-grained K_φ variance across scales, fits power-law
decay, and returns safety verdict based on fit quality and threshold
violations.
Returns
-------
dict[str, Any]
- variance_by_scale: dict[int, float] - computed variances
- fit: dict - power-law fitting results
- violations: list[int] - scales with |K_φ| >= K_PHI_CURVATURE_THRESHOLD
- safe: bool - overall safety status
"""
# Compute multiscale variance
variance_by_scale = compute_k_phi_multiscale_variance(G)
# Fit power-law
fit = fit_k_phi_asymptotic_alpha(variance_by_scale, alpha_hint)
# Check for threshold violations
# (Removed unused local k_phi_field assignment to satisfy lint)
violations = [
r
for r, var in variance_by_scale.items()
if var > defaults.K_PHI_CURVATURE_THRESHOLD ** 2
] # Canonical threshold from tetrahedral correspondence
# Assess safety
safe_by_fit = (
fit.get("alpha", 0.0) > 0.0
and fit.get("r_squared", 0.0) >= fit_min_r2
)
safe_by_tolerance = (alpha_hint is not None) and (len(violations) == 0)
safe = bool(safe_by_fit or safe_by_tolerance)
return {
"variance_by_scale": {
int(k): float(v) for k, v in variance_by_scale.items()
},
"fit": fit,
"violations": violations,
"safe": safe,
}
def fit_correlation_length_exponent(
intensities: np.ndarray,
xi_c_values: np.ndarray,
I_c: float = defaults.CRITICAL_INFORMATION_DENSITY,
min_distance: float = defaults.MIN_DISTANCE_THRESHOLD,
) -> dict[str, Any]:
"""Fit critical exponent nu from xi_C ~ |I - I_c|^(-nu) [RESEARCH].
**Status**: RESEARCH (critical phenomena analysis support)
Theory
------
At continuous phase transitions, correlation length diverges:
xi_C ~ |I - I_c|^(-nu)
Taking logarithms:
log(xi_C) = log(A) - nu * log(|I - I_c|)
Parameters
----------
intensities : np.ndarray
Array of intensity values I
xi_c_values : np.ndarray
Corresponding coherence lengths xi_C
I_c : float, default=CRITICAL_INFORMATION_DENSITY
Critical intensity (tetrahedral: (e×φ)/π ≈ 2.015)
min_distance : float, default=MIN_DISTANCE_THRESHOLD
Minimum |I - I_c| to avoid divergence noise
Returns
-------
dict[str, Any]
- nu_below: Critical exponent for I < I_c
- nu_above: Critical exponent for I > I_c
- r_squared_below: Fit quality below I_c
- r_squared_above: Fit quality above I_c
- universality_class: 'mean-field' | 'ising-3d' | 'ising-2d' |
'unknown'
- n_points_below: Number of data points I < I_c
- n_points_above: Number of data points I > I_c
Notes
-----
Expected critical exponents:
- Mean-field: nu = MEAN_FIELD_EXPONENT
- 3D Ising: nu = ISING_3D_EXPONENT
- 2D Ising: nu = ISING_2D_EXPONENT
"""
results = {
"nu_below": 0.0,
"nu_above": 0.0,
"r_squared_below": 0.0,
"r_squared_above": 0.0,
"universality_class": "unknown",
"n_points_below": 0,
"n_points_above": 0,
}
# Split data at critical point
below_mask = (
(intensities < I_c)
& (np.abs(intensities - I_c) > min_distance)
)
above_mask = (
(intensities > I_c)
& (np.abs(intensities - I_c) > min_distance)
)
# Fit below I_c
if np.sum(below_mask) >= 3:
I_below = intensities[below_mask]
xi_below = xi_c_values[below_mask]
x = np.log(np.abs(I_below - I_c))
y = np.log(xi_below)
# Linear regression: y = a - nu * x
coeffs = np.polyfit(x, y, 1)
nu_below = -coeffs[0] # Negative slope
y_pred = np.polyval(coeffs, x)
ss_res = np.sum((y - y_pred) ** 2)
ss_tot = np.sum((y - np.mean(y)) ** 2)
r2_below = 1 - (ss_res / ss_tot) if ss_tot > 0 else 0.0
results["nu_below"] = float(nu_below)
results["r_squared_below"] = float(r2_below)
results["n_points_below"] = int(np.sum(below_mask))
# Fit above I_c
if np.sum(above_mask) >= 3:
I_above = intensities[above_mask]
xi_above = xi_c_values[above_mask]
x = np.log(np.abs(I_above - I_c))
y = np.log(xi_above)
coeffs = np.polyfit(x, y, 1)
nu_above = -coeffs[0]
y_pred = np.polyval(coeffs, x)
ss_res = np.sum((y - y_pred) ** 2)
ss_tot = np.sum((y - np.mean(y)) ** 2)
r2_above = 1 - (ss_res / ss_tot) if ss_tot > 0 else 0.0
results["nu_above"] = float(nu_above)
results["r_squared_above"] = float(r2_above)
results["n_points_above"] = int(np.sum(above_mask))
# Classify universality
if results["n_points_below"] >= 3 and results["n_points_above"] >= 3:
nu_avg = (results["nu_below"] + results["nu_above"]) / 2.0
if abs(nu_avg - defaults.MEAN_FIELD_EXPONENT) < defaults.EXPONENT_TOLERANCE:
results["universality_class"] = "mean-field"
elif abs(nu_avg - defaults.ISING_3D_EXPONENT) < defaults.EXPONENT_TOLERANCE:
results["universality_class"] = "ising-3d"
elif abs(nu_avg - 1.0) < _ISING_2D_EXPONENT_TOLERANCE:
results["universality_class"] = "ising-2d"
return results
# ============================================================================
# UNIFIED FIELD MATHEMATICS (Nov 28, 2025) - CANONICAL INTEGRATION
# ============================================================================
def _extract_field_values(field_dict_list, G):
"""Extract aligned arrays from field dictionaries.
Helper function to convert field dictionaries to aligned numpy arrays.
"""
if not field_dict_list:
return []
# Find common keys across all field dictionaries
common_keys = set(field_dict_list[0].keys())
for field_dict in field_dict_list[1:]:
common_keys &= set(field_dict.keys())
if not common_keys:
return []
# Sort keys for consistent ordering
sorted_keys = sorted(common_keys)
# Extract aligned arrays
aligned_arrays = []
for field_dict in field_dict_list:
aligned_arrays.append(np.array([field_dict[key] for key in sorted_keys]))
return aligned_arrays
def compute_complex_geometric_field_arrays(G: Any) -> dict[str, Any]:
"""Compute unified complex geometric field Ψ = K_φ + i·J_φ (array form).
Delegates to :func:`tnfr.physics.unified.compute_complex_geometric_field`
(single source of truth) and reshapes the result into aligned numpy arrays
with an additional K_φ ↔ J_φ correlation measurement.
Returns:
dict with keys: psi_real, psi_imag, psi_magnitude, psi_phase,
correlation, num_nodes.
"""
from .unified import compute_complex_geometric_field as _psi_dict
psi = _psi_dict(G)
if not psi:
return {
"psi_real": np.array([]), "psi_imag": np.array([]),
"psi_magnitude": np.array([]), "psi_phase": np.array([]),
"correlation": 0.0, "num_nodes": 0,
}
nodes = sorted(psi.keys())
k_phi = np.array([psi[n].real for n in nodes])
j_phi = np.array([psi[n].imag for n in nodes])
psi_complex = k_phi + 1j * j_phi
correlation = 0.0
num_nodes = len(nodes)
if num_nodes > 1 and np.std(k_phi) > 1e-10 and np.std(j_phi) > 1e-10:
correlation = float(np.corrcoef(k_phi, j_phi)[0, 1])
if np.isnan(correlation):
correlation = 0.0
return {
"psi_real": k_phi,
"psi_imag": j_phi,
"psi_magnitude": np.abs(psi_complex),
"psi_phase": np.angle(psi_complex),
"correlation": correlation,
"num_nodes": num_nodes,
}
# Backward-compatible alias (prefer compute_complex_geometric_field_arrays)
compute_complex_geometric_field = compute_complex_geometric_field_arrays
def compute_emergent_fields(G: Any) -> dict[str, Any]:
"""Compute emergent fields χ, 𝒮, 𝒞 (array form).
Delegates to the per-node implementations in
:mod:`tnfr.physics.unified` and returns aligned numpy arrays.
Returns:
dict with keys: chirality, symmetry_breaking, coherence_coupling,
num_nodes.
"""
from .unified import (
compute_chirality_field as _chi,
compute_symmetry_breaking_field as _sb,
compute_coherence_coupling_field as _cc,
)
chi = _chi(G)
sb = _sb(G)
cc = _cc(G)
if not chi:
return {
"chirality": np.array([]),
"symmetry_breaking": np.array([]),
"coherence_coupling": np.array([]),
"num_nodes": 0,
}
nodes = sorted(chi.keys())
return {
"chirality": np.array([chi[n] for n in nodes]),
"symmetry_breaking": np.array([sb[n] for n in nodes]),
"coherence_coupling": np.array([cc[n] for n in nodes]),
"num_nodes": len(nodes),
}
def compute_tensor_invariants(G: Any) -> dict[str, Any]:
"""Compute tensor invariants ℰ, 𝒬, ρ (array form).
Delegates to the per-node implementations in
:mod:`tnfr.physics.unified` and :mod:`tnfr.physics.conservation`,
returning aligned numpy arrays.
Returns:
dict with keys: energy_density, topological_charge,
conservation_density, conservation_quality, num_nodes.
"""
from .unified import (
compute_energy_density as _ed,
compute_topological_charge as _tc,
)
from .conservation import compute_charge_density as _rho
ed = _ed(G)
tc = _tc(G)
rho = _rho(G)
if not ed:
return {
"energy_density": np.array([]),
"topological_charge": np.array([]),
"conservation_density": np.array([]),
"conservation_quality": 0.0,
"num_nodes": 0,
}
nodes = sorted(ed.keys())
rho_arr = np.array([rho[n] for n in nodes])
conservation_quality = 0.0
if len(rho_arr) > 1:
rho_gradient = np.gradient(rho_arr)
conservation_quality = float(1.0 / (1.0 + np.std(rho_gradient)))
return {
"energy_density": np.array([ed[n] for n in nodes]),
"topological_charge": np.array([tc[n] for n in nodes]),
"conservation_density": rho_arr,
"conservation_quality": conservation_quality,
"num_nodes": len(nodes),
}
def compute_unified_telemetry(G: Any) -> dict[str, Any]:
"""Compute complete unified field telemetry suite.
Provides comprehensive telemetry combining:
- Canonical Structural Triad (Φ_s, |∇φ|, K_φ) + ξ_C correlation analysis
- Extended canonical (J_φ, J_ΔNFR)
- Unified complex field (Ψ = K_φ + i·J_φ)
- Emergent fields (χ, S, C)
- Tensor invariants (ε, Q, conservation)
Args:
G: TNFR network with complete state data
Returns:
dict containing all unified field metrics for production telemetry
Usage:
telemetry = compute_unified_telemetry(G)
correlation = telemetry["complex_field"]["correlation"] # K_φ ↔ J_φ
energy = np.mean(telemetry["tensor_invariants"]["energy_density"])
References:
- Complete mathematical framework in MATHEMATICAL_UNIFICATION_EXECUTIVE_SUMMARY.md
- Production integration roadmap in COMPREHENSIVE_AUDIT_COMPLETION_2025.md
"""
# Canonical Structural Triad telemetry (validated post-recalibration)
canonical_telemetry = compute_structural_telemetry(G)
# Extended canonical fields
extended_suite = compute_extended_canonical_suite(G)
# Unified field computations (delegate to unified.py via array wrappers)
complex_field = compute_complex_geometric_field_arrays(G)
emergent_fields = compute_emergent_fields(G)
tensor_invariants = compute_tensor_invariants(G)
# Conservation telemetry (canonical source: conservation.py)
try:
from .conservation import (
compute_noether_charge,
compute_energy_functional,
)
conservation = {
"noether_charge": compute_noether_charge(G),
"structural_energy": compute_energy_functional(G),
}
except Exception:
conservation = {}
return {
"canonical": canonical_telemetry,
"extended_canonical": extended_suite,
"complex_field": complex_field,
"emergent_fields": emergent_fields,
"tensor_invariants": tensor_invariants,
"conservation": conservation,
"unified_field_version": "1.0.0", # Track implementation version
}
# ============================================================================
# SELF-OPTIMIZING MATHEMATICAL ANALYSIS (NEW - Nov 28, 2025)
# ============================================================================
def analyze_optimization_potential(G: Any) -> dict[str, Any]:
"""
Analyze mathematical optimization potential using unified field analysis.
Combines unified field telemetry with mathematical structure analysis
to identify optimization opportunities automatically.
Returns:
dict containing:
- field_analysis: Unified field characteristics
- mathematical_insights: Structural properties for optimization
- optimization_recommendations: Specific optimization strategies
- predicted_improvements: Expected performance gains
"""
if not _SELF_OPTIMIZING_AVAILABLE:
return {
"error": "Self-optimizing engine not available",
"field_analysis": {},
"mathematical_insights": {},
"optimization_recommendations": [],
"predicted_improvements": {}
}
# Get unified field telemetry
unified_telemetry = compute_unified_telemetry(G)
# Create self-optimizing engine
engine = TNFRSelfOptimizingEngine(
optimization_objective=OptimizationObjective.BALANCE_ALL
)
# Analyze mathematical landscape
mathematical_insights = engine.analyze_mathematical_optimization_landscape(G, "field_computation")
# Extract field-specific optimization hints
field_optimization_hints = []
# Complex field analysis
complex_field = unified_telemetry.get("complex_field", {})
correlation = complex_field.get("correlation", 0.0)
if abs(correlation) > defaults.HIGH_CORRELATION_THRESHOLD:
field_optimization_hints.append("use_complex_field_unification")
if abs(correlation) > defaults.VERY_HIGH_CORRELATION_THRESHOLD:
field_optimization_hints.append("use_extreme_correlation_optimization")
# Emergent field analysis
emergent_fields = unified_telemetry.get("emergent_fields", {})
chirality_magnitude = emergent_fields.get("chirality_magnitude", 0.0)
if chirality_magnitude > defaults.CHIRALITY_THRESHOLD:
field_optimization_hints.append("use_chirality_optimization")
# Tensor invariant analysis
tensor_invariants = unified_telemetry.get("tensor_invariants", {})
energy_density = tensor_invariants.get("energy_density", [])
if len(energy_density) > 0:
avg_energy = np.mean(energy_density)
if avg_energy > defaults.HIGH_ENERGY_THRESHOLD:
field_optimization_hints.append("use_high_energy_optimization")
elif avg_energy < defaults.LOW_ENERGY_THRESHOLD:
field_optimization_hints.append("use_low_energy_optimization")
return {
"field_analysis": unified_telemetry,
"mathematical_insights": mathematical_insights,
"optimization_recommendations": field_optimization_hints,
"predicted_improvements": {
"field_correlation_speedup": abs(correlation) * defaults.CORRELATION_SPEEDUP_FACTOR if abs(correlation) > defaults.MODERATE_CORRELATION_THRESHOLD else defaults.BASELINE_FACTOR,
"chirality_memory_reduction": min(chirality_magnitude * defaults.CHIRALITY_MEMORY_FACTOR, defaults.MAX_MEMORY_REDUCTION),
"energy_computation_factor": max(defaults.MIN_ENERGY_FACTOR, min(avg_energy * defaults.ENERGY_SCALING_FACTOR, defaults.MAX_ENERGY_FACTOR)) if len(energy_density) > 0 else defaults.BASELINE_FACTOR
}
}
def recommend_field_optimization_strategy(G: Any, operation_type: str = "unified_telemetry") -> dict[str, Any]:
"""
Recommend optimization strategy based on unified field analysis.
Args:
G: TNFR network graph
operation_type: type of field operation to optimize
Returns:
Optimization strategy recommendations with mathematical justification
"""
if not _SELF_OPTIMIZING_AVAILABLE:
return {
"error": "Self-optimizing engine not available",
"recommendations": [],
"strategy": "fallback_standard"
}
# Analyze optimization potential
analysis = analyze_optimization_potential(G)
# Create engine and get recommendations
engine = TNFRSelfOptimizingEngine()
recommendations = engine.recommend_optimization_strategy(G, operation_type)
# Combine field analysis with general recommendations
field_specific_strategies = []
# Field-specific optimization strategies
field_analysis = analysis.get("field_analysis", {})
complex_field = field_analysis.get("complex_field", {})
if complex_field.get("magnitude", 0.0) > defaults.COMPLEX_FIELD_THRESHOLD:
field_specific_strategies.append("prioritize_complex_field_computation")
emergent_fields = field_analysis.get("emergent_fields", {})
if emergent_fields.get("symmetry_breaking", 0.0) > defaults.SYMMETRY_BREAKING_THRESHOLD:
field_specific_strategies.append("use_symmetry_breaking_acceleration")
return {
"unified_field_analysis": field_analysis,
"mathematical_recommendations": recommendations.recommended_strategies,
"field_specific_strategies": field_specific_strategies,