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Add example demonstrating ZHIR bifurcation detection
Co-authored-by: fermga <203334638+fermga@users.noreply.github.com>
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‎examples/zhir_bifurcation_detection_example.py‎

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#!/usr/bin/env python3
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"""Example demonstrating ZHIR bifurcation potential detection.
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This example shows how ZHIR (Mutation) detects when structural acceleration
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∂²EPI/∂t² exceeds the bifurcation threshold τ, according to AGENTS.md §U4a.
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The detection is conservative (Option B) - it sets telemetry flags and logs
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information but does not create structural variants. This enables validation
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of grammar U4a requirement: "If {OZ, ZHIR}, include {THOL, IL}".
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"""
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from tnfr.structural import create_nfr, run_sequence
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from tnfr.operators.definitions import Emission, Dissonance, Mutation, Coherence, Silence
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from tnfr.alias import get_attr
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from tnfr.constants.aliases import ALIAS_EPI
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def example_zhir_bifurcation_detection():
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"""Demonstrate ZHIR bifurcation potential detection."""
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print("=" * 70)
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print("ZHIR Bifurcation Potential Detection Example")
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print("=" * 70)
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# Create a node with evolving EPI
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G, node = create_nfr("evolving_system", epi=0.3, vf=1.0, theta=0.5)
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# Build EPI history showing high acceleration
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# This simulates a system undergoing rapid structural reorganization
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# d²EPI/dt² = 0.60 - 2*0.40 + 0.30 = 0.60 - 0.80 + 0.30 = 0.10
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G.nodes[node]["epi_history"] = [0.30, 0.40, 0.60]
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G.nodes[node]["glyph_history"] = []
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# Configure bifurcation threshold
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# Default is 0.5, but we'll use 0.05 to demonstrate detection
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G.graph["BIFURCATION_THRESHOLD_TAU"] = 0.05
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print(f"\nInitial state:")
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print(f" Node: {node}")
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print(f" EPI: {get_attr(G.nodes[node], ALIAS_EPI, 0.0):.3f}")
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print(f" EPI history: {G.nodes[node]['epi_history']}")
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print(f" Bifurcation threshold τ: {G.graph['BIFURCATION_THRESHOLD_TAU']}")
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# Calculate acceleration manually for demonstration
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history = G.nodes[node]["epi_history"]
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d2_epi_manual = abs(history[-1] - 2*history[-2] + history[-3])
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print(f" Computed ∂²EPI/∂t²: {d2_epi_manual:.3f}")
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print(f" Will trigger detection: {d2_epi_manual > G.graph['BIFURCATION_THRESHOLD_TAU']}")
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# Apply canonical OZ → ZHIR sequence
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# OZ (Dissonance) destabilizes, ZHIR (Mutation) transforms
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print(f"\nApplying OZ → ZHIR sequence...")
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run_sequence(G, node, [Dissonance(), Mutation()])
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# Check bifurcation detection
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print(f"\nAfter ZHIR:")
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if G.nodes[node].get("_zhir_bifurcation_potential"):
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print(f" ✓ Bifurcation potential DETECTED")
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print(f" ∂²EPI/∂t²: {G.nodes[node]['_zhir_d2epi']:.3f}")
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print(f" Threshold τ: {G.nodes[node]['_zhir_tau']:.3f}")
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print(f" Detection suggests: Apply THOL for controlled bifurcation")
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print(f" or IL for stabilization")
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else:
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print(f" ✗ No bifurcation potential detected")
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# Check graph-level events
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events = G.graph.get("zhir_bifurcation_events", [])
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print(f"\n Bifurcation events recorded: {len(events)}")
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if events:
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event = events[0]
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print(f" - Node: {event['node']}")
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print(f" - ∂²EPI/∂t²: {event['d2_epi']:.3f}")
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print(f" - Timestamp: {event['timestamp']}")
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# Verify no structural changes (Option B - detection only)
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print(f"\n Structural integrity (Option B):")
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print(f" - No new nodes created")
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print(f" - No new edges created")
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print(f" - Telemetry flags set for grammar validation")
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print(f"\n" + "=" * 70)
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print("Example complete!")
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print("=" * 70)
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def example_zhir_no_bifurcation():
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"""Demonstrate ZHIR with low acceleration (no bifurcation)."""
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print("\n" + "=" * 70)
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print("ZHIR with Low Acceleration (No Bifurcation)")
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print("=" * 70)
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# Create a node with low acceleration
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G, node = create_nfr("stable_system", epi=0.5, vf=1.0, theta=0.5)
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# Nearly linear EPI progression (low acceleration)
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# d²EPI/dt² = 0.50 - 2*0.49 + 0.48 = 0.50 - 0.98 + 0.48 = 0.00
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G.nodes[node]["epi_history"] = [0.48, 0.49, 0.50]
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G.nodes[node]["glyph_history"] = []
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G.graph["BIFURCATION_THRESHOLD_TAU"] = 0.05
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print(f"\nInitial state:")
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print(f" Node: {node}")
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print(f" EPI history: {G.nodes[node]['epi_history']}")
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history = G.nodes[node]["epi_history"]
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d2_epi_manual = abs(history[-1] - 2*history[-2] + history[-3])
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print(f" Computed ∂²EPI/∂t²: {d2_epi_manual:.3f}")
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print(f" Threshold τ: {G.graph['BIFURCATION_THRESHOLD_TAU']}")
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print(f" Will trigger detection: {d2_epi_manual > G.graph['BIFURCATION_THRESHOLD_TAU']}")
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# Apply ZHIR
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print(f"\nApplying ZHIR...")
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Mutation()(G, node)
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print(f"\nAfter ZHIR:")
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if G.nodes[node].get("_zhir_bifurcation_potential"):
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print(f" ✓ Bifurcation potential detected")
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else:
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print(f" ✗ No bifurcation potential detected (acceleration too low)")
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print(f"\n System remains in stable regime")
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print(f" No bifurcation handlers required")
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print(f"\n" + "=" * 70)
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def example_grammar_u4a_validation():
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"""Demonstrate Grammar U4a validation with bifurcation detection."""
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print("\n" + "=" * 70)
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print("Grammar U4a Validation Support")
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print("=" * 70)
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print("\nGrammar U4a: If {OZ, ZHIR}, include {THOL, IL}")
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print("When ZHIR detects bifurcation potential, grammar validators")
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print("can check that THOL or IL is present in the sequence.")
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# Example 1: Valid sequence with stabilizer
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G1, node1 = create_nfr("system1", epi=0.5, vf=1.0)
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G1.nodes[node1]["epi_history"] = [0.30, 0.40, 0.60] # High acceleration
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G1.nodes[node1]["glyph_history"] = []
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G1.graph["BIFURCATION_THRESHOLD_TAU"] = 0.05
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print(f"\nExample 1: OZ → ZHIR → IL (with stabilizer)")
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run_sequence(G1, node1, [Dissonance(), Mutation(), Coherence()])
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if G1.nodes[node1].get("_zhir_bifurcation_potential"):
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print(f" ✓ Bifurcation detected")
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print(f" ✓ IL (Coherence) present - Grammar U4a satisfied")
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# Example 2: Would violate U4a (no stabilizer)
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G2, node2 = create_nfr("system2", epi=0.5, vf=1.0)
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G2.nodes[node2]["epi_history"] = [0.30, 0.40, 0.60] # High acceleration
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G2.nodes[node2]["glyph_history"] = []
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G2.graph["BIFURCATION_THRESHOLD_TAU"] = 0.05
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print(f"\nExample 2: OZ → ZHIR (no stabilizer)")
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run_sequence(G2, node2, [Dissonance(), Mutation()])
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if G2.nodes[node2].get("_zhir_bifurcation_potential"):
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print(f" ⚠ Bifurcation detected")
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print(f" ⚠ No THOL/IL present - Grammar U4a should flag this")
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print(f" ⚠ Uncontrolled bifurcation risk")
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print(f"\n" + "=" * 70)
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if __name__ == "__main__":
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example_zhir_bifurcation_detection()
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example_zhir_no_bifurcation()
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example_grammar_u4a_validation()

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