Demonstrating Utility as a Structural Law Beyond Operator Control
Abstract
This article presents the culmination of a systematic research program spanning four experimental chambers (XLIV–XLVII) and two complete research axes. Through pre-registered experiments with decisive falsification criteria, we establish that worldline-local utility is not controllable through operator-level mechanisms (Axis II falsified) but is instead a structural admissibility property of grammar–topology classes (Axis III confirmed). We demonstrate that utility emerges only in structures with irreversible convergence of independent histories—specifically, directed acyclic graphs (DAGs)—while remaining inadmissible in tree-based structures. This finding elevates a previously empirical observation (worldline commitment) to a structural theorem with precise mathematical conditions.
1. Introduction: A Complete Methodological Cycle
Most theoretical frameworks encounter negative results and move on. UNNS treats them differently: negative results become decisive when they exhaust an entire explanatory class. This article documents such an exhaustion, followed by a principled reframing that led to a positive structural discovery.
The research arc proceeded in three phases:
2. The Experimental Arc: Four Chambers, Two Axes
Chamber XLIV
Established that utility can occur under generative asymmetry (k ≥ 2). Branch-local, non-ensemble, requires irreversible branching.
Chamber XLV
ε-κ-t Sweep. Tested static asymmetry, coherence regulation, and temporal κ injection. No utility transitions observed.
Chamber XLVI
Temporal–Generative Alignment Test. Pre-registered binary test: does γ timing matter? 160 runs, all timing windows tested.
Chamber XLVII
Structural Admissibility Test. All operators disabled. 3 grammars × 3 topologies × 50 seeds. Topology dominates admissibility.
Methodological Innovation: Axes as Units of Falsifiable Inquiry
An Axis in UNNS is not a parameter or variable—it's an explanatory assumption that defines what kinds of answers are admissible. Each Axis is explored through multiple pre-registered chambers designed to either identify a robust invariant or falsify the assumption itself.
3. Axis II: Operator Control Hypothesis Falsified
What Was Tested
Axis II investigated whether worldline-local utility could be controlled through operator-level intervention. Across Chambers XLV and XLVI, we systematically tested:
- Static asymmetry (ε): Does parametric bias create utility boundaries?
- Coherence regulation (κ): Does history smoothing enable utility?
- Temporal coherence (κ(t)): Does injection timing matter?
- Generative alignment (γ(t)): Does temporal coordination of generation with coherence admit utility?
Results: Complete Falsification
Swept ε ∈ [0.02–0.18], κ ∈ {0, 2, 4, 6}, temporal injection times {0, 40, 80, 120, 160, 200}.
Result: κ stabilizes dynamics but does not generate utility. ε produces no utility transitions. Temporal injection produces no admissibility windows.
Single control variable: γ_injection_time ∈ {0, 20, 40, 60, 80, 120, 160, 200}. All other parameters frozen.
Total runs: 160 (8 points × 20 seeds). Falsifiers pre-registered.
Result: Utility frequency = 0 for all timing configurations. Falsifier F3 (No Emergence) triggered.
Axis II Closure Statement
G° ≠ f(ε), G° ≠ f(κ), G° ≠ f(γ), G° ≠ f(timing)
Operator-level control of utility is falsified under preregistered tests. Utility does not emerge from operator timing or alignment alone. This result strengthens earlier chambers by excluding operator-driven explanations for utility emergence.
Scientific Significance
This is not a "negative result" in the usual sense. It is a methodological closure: an entire class of explanations has been systematically exhausted. Any future claim that utility can be "tuned" or "controlled" through operators must now provide extraordinary evidence to overcome this pre-registered falsification.
4. Axis III: Structural Admissibility Confirmed
The Methodological Shift
After Axis II closure, further operator exploration would constitute tuning rather than inquiry. The only remaining honest question was structural:
Is utility admissible at all, independent of operators? Does the substrate architecture itself permit or forbid utility?
Chamber XLVII Experimental Design
All operators disabled: ε = 0, κ = 0, γ = 0. No operator code paths active.
Independent variables: Grammar (G1: Reference, G2: Pruned, G3: Enriched) ×
Topology (T1: Balanced Tree, T2: Asymmetric Tree, T3: DAG)
Execution: 9 structures × 50 seeds = 450 simulations. Fixed depth 400, no early stopping.
Empirical Results: Topology Dominance
Utility Frequency by Structure (450 Total Simulations)
Complete Results Table
| Grammar | Topology | Ufreq | Seeds w/ Utility | Admissibility |
|---|---|---|---|---|
| G1 (Reference) | T1 (Balanced Tree) | 0.000 | 0/50 | ❌ Inadmissible |
| G1 (Reference) | T2 (Asymmetric Tree) | 0.000 | 0/50 | ❌ Inadmissible |
| G1 (Reference) | T3 (DAG) | 0.120 | 6/50 | ✅ Admissible |
| G2 (Pruned) | T1 (Balanced Tree) | 0.000 | 0/50 | ❌ Inadmissible |
| G2 (Pruned) | T2 (Asymmetric Tree) | 0.000 | 0/50 | ❌ Inadmissible |
| G2 (Pruned) | T3 (DAG) | 0.200 | 10/50 | ✅ Admissible |
| G3 (Enriched) | T1 (Balanced Tree) | 0.000 | 0/50 | ❌ Inadmissible |
| G3 (Enriched) | T2 (Asymmetric Tree) | 0.000 | 0/50 | ❌ Inadmissible |
| G3 (Enriched) | T3 (DAG) | 0.100 | 5/50 | ✅ Admissible |
- All DAG structures admit utility (3/3 grammars)
- No tree structures admit utility (6/6 combinations: all grammars × both tree types)
- Grammar variations modulate frequency (10-20%) but not admissibility
- This correlation is too clean to be noise—it indicates a fundamental structural constraint
5. The Structural Irreversibility Theorem
From Empirical Result to Mathematical Principle
The Chamber XLVII results are not merely statistical. The 100% topology correlation—DAGs admissible, trees inadmissible—points to an underlying structural principle. We formalize this as a theorem.
Theorem: Structural Irreversibility Criterion
Worldline-local utility is admissible if and only if the underlying grammar–topology structure is structurally irreversible.
A structure is structurally irreversible if there exist histories h₁, h₂ and time t such that h₁(t) ≠ h₂(t), but h₁(t') = h₂(t') for all t' > t, and no inverse operation can recover the prior distinction.
What This Means: Trees vs. DAGs
❌ Tree Structures (Inadmissible)
- Single parent per node — strict hierarchy
- Histories diverge but never converge
- Separability preserved — you can trace back each history independently
- Irreversible in time but reversible in structure
- Result: No worldline commitment possible
✅ DAG Structures (Admissible)
- Multiple parents possible — convergence allowed
- Independent histories can merge
- Separability destroyed — cannot recover individual pasts after merge
- Structurally irreversible — merging is final
- Result: Worldline commitment enforced by structure
Why This Distinction Matters
Process irreversibility (time's arrow, branching evolution) is insufficient. Trees are irreversible processes but preserve structural separability.
Structural irreversibility (unavoidable history merging) is necessary. DAGs enforce irreversible convergence—once histories merge, they cannot be un-merged.
Core insight: Utility does not arise from making a process irreversible. It arises only in structures where irreversibility is unavoidable.
6. Implications and Theoretical Consolidation
What We Now Know
The complete Axis II→III research arc has established five decisive results:
Operator-level mechanisms (ε, κ, γ, timing) are insufficient to induce or stabilize utility. This has been systematically falsified across 160+ pre-registered experiments.
Grammar variations modulate frequency but not admissibility. Topology determines permission. DAG = admissible (100%), Tree = inadmissible (100%).
Utility requires structures where independent histories can merge irreversibly, destroying separability. This elevates "worldline commitment" from metaphor to mathematical condition.
In tree structures, histories remain separable and ensemble descriptions remain valid. Structural irreversibility breaks ensemble reducibility—utility vanishes when you average.
The Structural Irreversibility Theorem was not invented—it was extracted. It names the invariant that survived an exhaustive falsification program.
Why Cycles Are Excluded
A natural objection: what about cyclic structures? The answer is precise and formal.
Cycles permit histories to re-separate after merging. Once you allow return paths, merges are no longer final. Worldline commitment is destroyed. DAGs are therefore maximal: adding cycles negates the very condition that admits utility.
Relation to Prior UNNS Work
Importantly, these results do not replace or reinterpret earlier findings. They complete them:
- Chamber XLIV existence proof remains valid — utility can occur under generative asymmetry
- Earlier worldline-local results are strengthened — structural irreversibility explains why ensemble descriptions fail
- No prior chamber is invalidated — they are properly contextualized as existence proofs, not control mechanisms
- Theoretical claims are now precise — "worldline commitment" is no longer vague; it's a topological fact
7. Conclusion: From Questions to Laws
Most research programs end with open questions. This one ends with a structural law:
UNNS Proposition: Structural Irreversibility of Utility
Worldline-local utility is admissible if and only if the underlying grammar–topology structure enforces irreversible convergence of histories.
Directed acyclic graph (DAG) structures admit utility; tree-based and cyclic structures do not. This is a property of topology, not dynamics. No operator-level mechanisms are required or permitted.
Status: Empirically supported by Chamber XLVII (450 simulations, 100% topology correlation). Derived after closure of Axis II. Independent of operator assumptions.
What Makes This Result Rare
This research arc achieved something most theoretical programs never reach: a place where further tuning is no longer meaningful, because the constraint is structural.
- Hypothesis generation (Axis II: operator control)
- Pre-registered falsification (Chambers XLV–XLVI: systematic negatives)
- Principled reframing (Axis III: structural admissibility)
- Positive discovery (Chamber XLVII: topology dominance)
- Theoretical consolidation (Structural Irreversibility Theorem)
This is not just a result—it's a cleanly closed research arc.
Looking Forward
The Structural Irreversibility Criterion opens new questions while closing others:
- Closed: Can utility be controlled through operators? (No, falsified)
- Closed: Is utility an emergent phase? (No, it's a structural permission property)
- Open: What other structures beyond DAGs admit utility?
- Open: Can the convergence requirement be formalized categorically?
- Open: Do physical systems with DAG-like causal structures exhibit analogous properties?
The transition from "How can utility emerge?" to "Utility is not something that emerges—it is something that structure either permits or forbids" represents a qualitative shift in how UNNS frames fundamental questions about recursive substrates and physical observability.
Epilogue: What Is Closed / What Remains Open What is closed.
The Axis II program is conclusively closed: worldline-local utility cannot be induced, stabilized, timed, or controlled through operator-level mechanisms, including asymmetry, coherence regulation, generative bias, or temporal alignment. These hypotheses have been preregistered, systematically tested, and falsified. More broadly, any explanation that treats utility as an emergent phase, a tunable outcome, or a consequence of process irreversibility is no longer viable within the UNNS framework.The question “how to produce utility” is therefore resolved in the negative. What remains open. Axis III establishes structural irreversibility as a necessary and sufficient condition for admissibility, but it does not exhaust the space of structural questions.
Open directions include the classification of admissible DAG subclasses, the minimal structural conditions for persistence and robustness, the interaction between structural admissibility and external observational constraints, and whether analogous admissibility criteria appear in non-UNNS substrates. Future axes, if any, must operate at the level of structural taxonomy and comparative universality, not control or tuning.
Terminal takeaway.
Worldline-local utility is not something a system can be made to do;
it is something a structure either permits or forbids.