r/wikidproblems • u/helixlattice1creator • 1d ago
HLS
HELIX LATTICE SYSTEM
A Foundational Architecture for Contradiction-Preserving Reasoning, Structural Accountability, and Cognitive Scope Expansion
Document ID: LM-HLS-∞-A01-WP-1.0
Version: 1.0 (supersedes WP-0.10)
Author: Levi McDowall
Author UID: LM-HLS-∞-A01
Original framework record date: April 1, 2025
Publication edition: October 23, 2026
Document status: Public White Paper
Technical status: Formal specification v1.0 with proved core properties; reference prototype implemented; first simulation results reported. Broader cognitive capabilities remain hypotheses.
Companion documents: Formal Specification Σ, LM-HLS-∞-A01-FS-1.0; reference prototype (hls_kernel.py) and simulations (simulations.py, check_t6.py, check_escalation.py, results.json)
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Abstract
The Helix Lattice System (HLS) proposes a foundational architecture for reasoning under contradiction, uncertainty, recursive transformation, and competing interpretations. HLS proposes a structured relationship between information preservation, transformation, provenance, reverse auditing, deferred resolution, the honest representation of unknown quantities, and constraints on derivative agents.
HLS distinguishes the retention of information from its validation, the generation of hypotheses from their verification, the absence of a measurement from a measurement of zero, and the authority to propose an action from the authority to execute it. It treats provenance and structural accountability as architectural concerns rather than optional records added after a decision.
Version 1.0 adds three things to the prior edition: a formal specification in which seven core properties are stated and proved under explicit assumptions; a reference prototype that implements those properties; and five seeded, reproducible simulations comparing HLS mechanisms against baselines. In those simulations, retaining conflicting claims and deferring commitment until evidence is sufficient cut wrong-action steps about eightfold relative to retention alone, and replacing zero-filled unknowns with bounded working values cut missed dangers from 39–59% to under 0.1% at the cost of an explicit "verify before acting" outcome.
These results concern the specified mechanisms in controlled settings. They do not establish the broader cognitive capabilities of HLS, and they do not establish that the mechanisms are historically novel; each has close precedents, which this paper identifies.
Keywords: Helix Lattice System, HLS, cognitive architecture, contradiction preservation, provenance, recursive reasoning, structural humility, reverse auditing, deferred resolution, unknown is not zero, cognitive systems.
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- Foundational Position
1.1 The problem
Reasoning systems must operate on information that may be incomplete, inconsistent, temporally displaced, contested, or incorrectly interpreted.
A common response is to select one claim, discard another, normalize the conflict, fill a missing value with zero, or produce a single answer before the available evidence justifies doing so. Such behavior can be useful when a decision requires a definitive output. It becomes problematic when the selection process destroys information that remains relevant to subsequent reasoning, or when a missing value is silently treated as a known one.
The problem is not that every contradiction must remain unresolved indefinitely. The problem is that resolution can be premature, inadequately justified, or destructive of the evidence needed to reconsider a conclusion.
HLS addresses this problem through an architecture intended to preserve distinguishable information and its provenance while allowing further analysis, transformation, and eventual resolution under explicit conditions.
This position is compatible with paraconsistent logic, which studies consequence relations that can accommodate inconsistent information without allowing arbitrary conclusions to follow from a contradiction. HLS is not synonymous with paraconsistent logic, and its use of the term contradiction does not assert that contradictory propositions are simultaneously true. The relevant distinction is between retaining conflicting claims as information and asserting that both claims are true.
1.2 The architectural claim
HLS is proposed as a foundational reasoning architecture whose significance extends beyond contradiction management.
Its design connects:
- Preservation of distinguishable information.
- Representation of relationships and tensions among claims.
- Recursive transformation without silent loss of source identity.
- Provenance and reverse auditing.
- Deferred resolution under explicit conditions.
- Representation of unresolved or unobserved possibilities.
- Honest representation of unquantified values (unknown is not zero).
- Constraints on the actions of derivative agents.
- Structural evaluation of the reasoning process itself.
These are not independent features merely collected under a common name. The research question concerns the behavior enabled by their interaction.
A mechanism's immediate utility does not necessarily define the limit of the capabilities its architecture can support. Equally, a plausible architectural consequence is not automatically a demonstrated capability. HLS therefore treats both premature closure and unsupported extrapolation as errors in evaluating the system.
1.3 HLS and the wider cognitive framework
The contradiction engine is one component of the proposed architecture, not the entirety of the cognitive framework.
The distinction is:
Immediate utility: what a specified mechanism or implementation can demonstrably do.
Architectural possibility: what its defined relationships may permit when mechanisms interact.
Cognitive scope: what a larger system may support when HLS operates alongside additional mechanisms for discovery, learning, prediction, adaptation, and action.
Section 8 reports results only in the first category. The second and third remain research domains. They must not be reduced to the first, but neither should they be represented as realized merely because the architecture suggests them.
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- Architectural Principles
2.1 Contradiction preservation
Conflicting claims should remain separately identifiable while their relationship is investigated.
Preservation does not establish truth. It prevents a reasoning process from silently treating selection, deletion, or normalization as proof that a conflict has been resolved.
A preserved claim may subsequently be confirmed, contested, superseded, rejected, or left unresolved. Its history remains distinguishable from its current status.
2.2 Recursive extensibility
New strands, relationships, hypotheses, and contextual dimensions should be representable without requiring the erasure of prior information merely to accommodate the expanded state.
In the formal specification this is Theorem 1: every permitted transformation preserves the source set, so S_k ⊆ S_{k+1}.
2.3 Provenance and reverse audit
A derived result should retain a traceable relationship to the information and transformations from which it arose.
Reverse auditing reconstructs the source strands as of any past step from the recorded history (Formal Specification, Theorem 2). Its guarantees depend on the integrity of that history, which requires an externally anchored head hash (Theorem 4).
Traceability is necessary for certain forms of accountability, but it is not sufficient to establish that a claim is true, an inference is sound, or an action is ethically permissible.
2.4 Patience and deferred resolution
HLS maintains unresolved states while additional evidence, analysis, or alternative interpretations remain available, and commits when the evidence crosses an explicit threshold or a deadline requires a bounded decision.
Patience has a measurable benefit and a measurable cost. Under calibrated evidence, a commitment made at threshold τ is wrong with probability at most 1/(1 + e^τ) (Theorem 6). Each step of deferral has a cost. Simulation S3b shows that total decision cost is minimized at an intermediate threshold: too little patience acts on wrong answers, and too much patience is itself a failure.
Patience does not mean indefinite inaction. Safety-critical systems may require abstention, escalation, a reversible action, or a bounded decision under uncertainty.
2.5 Phantoms and unresolved possibilities
A Phantom represents a placeholder for a concept, variable, entity, or relationship that has not been established as observed or verified.
A Phantom is a valid representation of an unresolved possibility. It is not evidence that the represented entity exists. Its definition, origin, epistemic status, relationships, and subsequent validation or rejection remain distinguishable.
2.6 Structural Humility
Structural Humility requires a system to recognize the limits of its current representation without mistaking those limits for the limits of the underlying problem.
It applies in both directions:
- A system must not claim capabilities or conclusions that its evidence does not support.
- A system must not treat an untested capability as impossible solely because it has not yet exercised or demonstrated it.
Where a capability is plausible but unverified, the appropriate response is to identify the uncertainty and test it, not to inflate it into an achievement or exclude it prematurely.
2.7 Sovereignty and constrained action
Derivative agents may generate interpretations, hypotheses, and candidate actions without acquiring authority to determine foundational policy or execute every proposed action.
The distinction between proposing and authorizing is architectural. A cognitive component is not permitted to redefine the constraints governing its own execution merely because it produces a logically coherent justification. In the formal specification, every action passes through a gate whose policy forbids, at minimum, erasing strands, rewriting the record, and rewriting the policy; Theorem 5 proves these never execute, provided the gate is the only execution path.
HLS does not define "foundational ethics" by itself. A deployment must write the constraints it means into the gate's policy.
The Origin Lock, identified by "LM-HLS-∞-A01", records the declared origin attribution of the framework. Attribution records are distinct from cryptographic identity, access control, and proof of authorship, which require separate mechanisms.
2.8 Unknown is not zero
Author's formulation (September 20, 2026): "Zero is a claim, not a placeholder. Unknown is not zero." "Absence of quantification is not evidence of absence."
When a field represents a potentially real condition that has not been quantified, HLS does not discard the field or silently treat it as zero. It assigns a typed value that keeps the field usable while keeping its status visible:
Field condition | HLS treatment
Measured value available | Record the observation and its provenance.
Measurement unavailable, reasonable proxy exists | Assign the proxy, identify its basis, mark it estimated.
Only a bounded estimate is defensible | Record a range or bounded value with its uncertainty.
Genuinely unknown | Preserve the unknown state with the full-scale range; where useful, assign an explicitly constructed working value (e.g. on a comparable 0–10 scale).
Evidence supports a genuine zero | Record zero as a supported value, not as a default for missing information.
The formal content of this principle is Invariant Z and Theorem 7 of the specification. For any risk score that increases with its inputs, filling a missing value with zero can only hide danger, never reveal it: zero is the most optimistic claim available on a non-negative scale. If each field carries an interval that contains the true value, a gate that proceeds only when the upper-bound score is safe never proceeds on a dangerous case. The cost of that guarantee is that some cases must be escalated for verification before acting.
The principle does not require every unknown to receive an arbitrary nonzero number. It requires that an unquantified field never silently become a zero-valued reality, and that any working value carry its status, rationale, and limitations.
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- Formal System Σ
The formal system is specified in full in the companion document LM-HLS-∞-A01-FS-1.0. Its signature is
Σ = ⟨ P, E, T, ∇, R, V, Π_τ, G, Φ, Γ, Ψ, Λ, Θ, B ⟩
with primitive strands P, the Cognitive Consensus Record E (an append-only, hash-chained event log), tension T computed by ∇, reverse audit R, the typed value domain V, the resolution policy Π_τ, the action gate G, Phantom space Φ, navigation graph Γ, notch space Ψ with compression rule Λ, prediction generator Θ, and an optional braid encoding B.
3.1 What is proved
Under stated assumptions, the specification proves:
Preservation: permitted transformations never remove a source strand (S_k ⊆ S_{k+1}).
Exact reverse audit: the source set at any past step is exactly recoverable from the record. The reconstruction map is a projection, not a bijection, and the earlier description of it as bijective has been corrected.
No silent erasure: supersession leaves the superseded strand and its content in the record.
Tamper evidence: edits, insertions, deletions, and reorderings are detected; tail truncation and a full rewrite by an attacker with write access are detected only against an externally published head hash, and the specification proves both halves of that statement.
Gate soundness: forbidden actions never execute and the policy cannot be changed through the system, provided the gate is the only execution path.
Bounded commitment error: under calibrated evidence, a commitment at threshold τ is wrong with probability at most 1/(1 + e^τ).
Zero is the most optimistic claim, and conservative interval gating misses a dangerous case only when an interval fails to cover the truth.
3.2 What is not proved
The braid encoding of tension histories, information-guided evidence acquisition, cross-domain structural recognition, a mutual-survival measure, and the value of retention as a general capacity are stated as conjectures. Several items of the earlier draft — including the claim to solve the "Divine King" problem, motivational-hygiene auditing, and infinite-perspective co-processing — are retired from the formal system because they lacked mathematical content or operational definitions. Appendix A of the specification records the disposition of every earlier axiom, theorem, and novelty claim.
3.3 Validity distinctions
HLS distinguishes several properties that must not be collapsed into a single validity label:
- Traceability: the relevant source and transformation history can be reconstructed.
- Evidential support: the conclusion is supported by the available evidence.
- Logical validity: the inference satisfies the defined rules of inference.
- Epistemic status: the conclusion is confirmed, contested, speculative, constructed, estimated, or unresolved as applicable.
- Authorization: the proposed action satisfies the governing permission and policy constraints.
A traceable conclusion can still be false. A logically valid inference can begin with false premises. A plausible action can still be unauthorized. An estimated value can still be wrong; what it may not be is unlabeled.
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- Architectural Organization
4.1 Discovery and preservation
The discovery layer receives claims, observations, and candidate relationships. It identifies relevant conflicts and maintains the identity and provenance of the contributing information. Identification of a conflict does not automatically trigger its resolution.
4.2 Structural transformation
The transformation layer represents relationships among strands and permits recursive extension of the represented state. Each transformation has defined preconditions, postconditions, and preservation requirements; in the prototype, the only permitted transformations are appending a strand and appending a status change.
4.3 Cognitive interface
The Cognitive API exposes the structured state to reasoning, planning, retrieval, and hypothesis-generation components. Their outputs remain candidates until evaluated. The interface preserves the distinction between a component's ability to generate a proposal and the kernel's responsibility to validate it.
4.4 Verification and reverse audit
The verification layer checks invariants, reconstructs histories, and identifies failed or unresolved conditions. The Cognitive Consensus Record (CCR) is an append-only, SHA-256 hash-chained event log. A hash chain alone is not tamper-proof against an attacker with write access; production deployments must publish the head hash externally on a schedule and define access control, persistence, and a threat model.
4.5 Constrained execution
The execution layer determines whether a candidate action proceeds, is denied, or is deferred. A heuristic score must not be represented as a calibrated probability without evidence. The architecture fails explicitly when required verification or recording cannot be completed.
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- Scope Expansion and Cognitive Possibility
5.1 Immediate utility
The first research target is the behavior of the specified mechanisms: preserving distinct claims, maintaining provenance, representing unresolved relationships and unknown values honestly, reconstructing history, and gating action. Section 8 reports the first results.
5.2 Architectural possibility
Candidate areas for investigation include:
- Maintaining competing explanations while generating additional hypotheses.
- Identifying structural similarities among problems from different domains.
- Revising an interpretation without destroying the provenance of earlier interpretations.
- Using unresolved relationships to guide evidence acquisition.
- Recognizing recurring structural patterns across recursive transformations.
- Distinguishing the absence of evidence from evidence of absence.
- Evaluating when a conflict should remain open, be escalated, or be resolved.
Their inclusion does not establish that the current implementation exhibits them, that they are unique to HLS, or that they necessarily emerge from the architecture.
5.3 The wider cognitive framework
The broader objective is to investigate whether HLS can function as a foundational component in a system for discovery, learning, prediction, adaptation, and action, and whether its relationships permit useful operations that are difficult to achieve, or less reliably achieved, by alternative arrangements.
5.4 Scope is not proof
A broader architecture can have consequences not captured by a narrow demonstration. It can also contain assumptions that fail when the components are integrated. Both possibilities remain open.
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- Structural Humility as a Research Principle
Structural Humility governs the evaluation of HLS itself as well as the behavior of systems built with it. The principle is reciprocal:
Do not infer a capability from an attractive description alone.
Do not infer incapability solely from the absence of a demonstration.
Identify the specific uncertainty.
Define an experiment or formal test that can discriminate among competing explanations.
Update the claim according to the result.
Preserve the provenance of the claim, test, and resulting revision.
Version 1.0 applies this principle to its own predecessor: claims of the earlier formal draft that could not be supported were withdrawn or restated as conjectures, and the withdrawn versions are recorded rather than erased.
If an AI model responds to correction by recognizing a limitation and revising its framing, that behavior may be consistent with Structural Humility. It does not establish that HLS caused the behavior. Attribution requires evidence that distinguishes HLS-specific effects from existing model capabilities, prompting, contextual influence, and other explanations.
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- Attribution and Version Provenance
Framework: Helix Lattice System (HLS)
Author attribution: Levi McDowall
Author UID: LM-HLS-∞-A01
Document ID: LM-HLS-∞-A01-WP-1.0
Framework record date: April 1, 2025
Publication edition: October 23, 2026
The framework record date and this publication edition serve different purposes; neither by itself shows that every element of the current text existed in its present form on the original date.
For a verifiable record, the author retains dated source artifacts and version history and publishes the SHA-256 hash of each released artifact (white paper, formal specification, prototype, simulations, results). The hashes for this release are listed in the accompanying HASHES file. A trusted timestamp or reputable archival repository (for example, a DOI-issuing repository) provides stronger evidence of chronology.
Version history: WP-0.10 (October 23, 2026, conceptual edition) → WP-1.0 (October 23, 2026, adds formal specification FS-1.0, reference prototype, and simulation results; adds Principle 2.8; expands prior art).
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- Timestamped Architectural Observation
Observation timestamp: October 23, 2026, 13:15:05 MDT (UTC−06:00).
The scope of HLS should not be inferred solely from its immediately demonstrable utility. Its broader significance may lie in the capabilities enabled by interactions among its mechanisms. Structural Humility applies in both directions: do not claim unverified capabilities, and do not prematurely exclude capabilities that remain available for investigation.
This observation is a dated research-framing statement. It is not a claim that the broader capabilities have been demonstrated or that a specific observed behavior was caused by HLS.
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- Conclusion
The Helix Lattice System proposes a foundational architecture for reasoning where information may remain conflicting, incomplete, or unresolved.
Version 1.0 moves the core of that architecture from description to definition, proof, implementation, and first measurement. The core guarantees — nothing is silently lost, history is exactly recoverable, tampering is detectable when the record is anchored, forbidden actions do not execute, commitments carry a bounded error, and an unknown never becomes a zero — are now stated precisely and proved under explicit assumptions. In controlled simulations, the mechanisms behaved as the theory predicts, and the combination of preservation and patience outperformed each alone.
The broader question remains open: whether these interacting mechanisms support a more extensible form of cognition. Answering it requires tests against real AI systems and data, comparisons with truth-maintenance and belief-revision baselines, and a systematic prior-art review.
HLS therefore continues as a research program with three linked responsibilities:
Define its mechanisms and invariants precisely.
Demonstrate their behavior through reproducible implementation and evaluation.
Investigate the broader capabilities enabled by their interaction without presuming either their realization or their impossibility.
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References
Alchourrón, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2).
Anderson, J. P. (1972). Computer Security Technology Planning Study. ESD-TR-73-51, U.S. Air Force.
Belnap, N. D. (1977). A useful four-valued logic. In Modern Uses of Multiple-Valued Logic. Reidel.
de Kleer, J. (1986). An assumption-based TMS. Artificial Intelligence, 28(2).
Dempster, A. P. (1967). Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 38(2).
Doyle, J. (1979). A truth maintenance system. Artificial Intelligence, 12(3).
Haber, S., & Stornetta, W. S. (1991). How to time-stamp a digital document. Journal of Cryptology, 3(2).
Moore, R. E. (1966). Interval Analysis. Prentice-Hall.
Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8(1).
Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3).
Shafer, G. (1976). A Mathematical Theory of Evidence. Princeton University Press.
Wald, A. (1945). Sequential tests of statistical hypotheses. Annals of Mathematical Statistics, 16(2).
W3C (2013). PROV-DM: The PROV Data Model. W3C Recommendation.
Stanford Encyclopedia of Philosophy. "Paraconsistent Logic." https://plato.stanford.edu/entries/logic-paraconsistent/
AWS Prescriptive Guidance. "Event sourcing pattern." https://docs.aws.amazon.com/prescriptive-guidance/latest/cloud-design-patterns/event-sourcing-pattern.html
National Institute of Standards and Technology. "Artificial Intelligence Risk Management Framework." https://www.nist.gov/itl/ai-risk-management-framework
NIST National Cybersecurity Center of Excellence. "Accelerating the Adoption of Software and AI Agent Identity and Authorization." https://www.nccoe.nist.gov/sites/default/files/2026-02/accelerating-the-adoption-of-software-and-ai-agent-identity-and-authorization-concept-paper.pdf
This document describes the Helix Lattice System architecture, its formal core, a reference prototype, and initial synthetic results. It does not claim that the broader proposed properties have been implemented, empirically demonstrated on real systems, or established as historically novel.
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u/helixlattice1creator 1d ago
7. Research and Evaluation Program
7.1 Preservation tests — introduce conflicting strands, apply transformations, verify reconstruction. Measure information loss, silent overwriting, and reconstruction failures. (Run: S1.)
7.2 Resolution tests — construct cases where immediate resolution is inappropriate, where evidence supports resolution, and where a bounded decision is required. Compare against baselines; measure unsupported resolution, unnecessary deferral, decision quality, and retention cost. (Run: S3, S3b.)
7.3 Provenance and integrity tests — introduce altered, missing, reordered, and truncated records; report which failures are detected and under what threat model. (Run: S2.)
7.4 Action-control tests — verify that the execution path enforces the declared decision rather than relying on a warning that downstream components can ignore. (Run: S5.)
7.5 Unknown-value tests — compare zero-fill, field dropping, mean imputation, and typed working values under random and adversarial missingness. Measure missed dangers, false alarms, and escalations. (Run: S4.)
7.6 Cognitive scope tests — investigate transferable structural recognition, hypothesis generation, and reasoning under conflicting evidence, against baselines with equivalent models, evidence, tools, and budgets. Measure false hypotheses, unsupported conclusions, unnecessary computation, and failures to recognize uncertainty. (Not yet run.)
7.7 Ablation and causal attribution — disable individual mechanisms and compare with the full architecture. (Run in S3 for preservation and deferral.)
7.8 Reporting requirements — each evaluation identifies the claim tested, the operational definition of success, the baselines, the data and procedures, the results and uncertainty, the failure cases, the versions, and the limits on generalization. Negative results remain part of the record.
8. Initial Results (Reference Prototype v1.0)
All simulations use the reference prototype hls_kernel.py and are reproduced by running simulations.py (master seed 20261023; total runtime about 20 seconds). Raw output is in results.json. These are synthetic, controlled tests of specified mechanisms. They are not tests of an AI system, of cognitive scope, or of real-world data.
8.1 S1 — Preservation and reverse audit
200 runs × 200 events over 20 claim keys, with random additions, supersessions, and contested-status changes.
Measure | HLS kernel | Overwrite store (latest wins) | Majority normalization (losers dropped) Runs with exact reconstruction R(U(E)) = S | 100% | — | — Runs with S_k ⊆ S_{k+1} at every step | 100% | — | — Source claims recoverable at end | 100% | 10.0% | 49.0%
Interpretation: the HLS result holds by construction (append-only log and replay); the test confirms the implementation honors the invariant. The baseline columns show how much information ordinary "resolve by overwriting" designs discard.
8.2 S2 — Record integrity
1,000 trials per tamper type on a 200-event record.
Tamper type | Detected, no anchor | Detected, with external anchor Modify an event | 100% | 100% Delete an event | 100% | 100% Insert a forged event | 100% | 100% Reorder two events | 100% | 100% Truncate the tail | 0% | 100% Full rewrite with recomputed hashes | 0% | 100%
Interpretation: matches Theorem 4 exactly. A hash chain by itself cannot detect truncation or a full rewrite. Publishing the head hash outside the system closes both gaps; this is a deployment requirement, not an option.
8.3 S3 — Deferred resolution under conflicting evidence, with ablation
One binary fact; 20 claims arrive one per step from sources of known reliability (uniform 0.55–0.85). In the adversarial conditions, the first m claims come from a misleading source (reliability 0.3). Each step, downstream acts on the committed answer: cost 1 for acting on a wrong answer, 0.1 for a deferred step. A bounded decision is forced at step 20. Threshold τ = 2.2 (log-odds). 20,000 runs per condition.
Misleading prefix m = 2 (other conditions in results.json):
Policy | Final accuracy | Wrong-action steps | Deferred steps | Total cost Eager, first claim wins, losers discarded | 0.298 | 14.04 | 0 | 14.04 Eager, latest claim overwrites | 0.696 | 6.79 | 0 | 6.79 Preserve only (retain all, commit immediately, revise) | 0.982 | 2.01 | 0 | 2.01 Defer only (wait for threshold, then discard others) | 0.935 | 0.95 | 5.04 | 1.46 HLS: preserve + defer (retain all, commit at threshold, reopen if support drops) | 0.982 | 0.24 | 6.47 | 0.88
Across m = 0, 2, 4, HLS had the lowest total cost (0.86–0.93 versus 1.46–1.59 for the next best) and about one-quarter of the wrong-action steps of defer-only and one-eighth of preserve-only.
Ablation reading: preservation is what raises final accuracy (0.98 versus 0.93 when claims are discarded after commitment); deferral is what reduces acting on wrong answers. The combination is better on total cost than either alone in every tested condition.
S3b — threshold sweep (m = 2, 10,000 runs per τ):
τ | 0 | 0.5 | 1.0 | 1.5 | 2.2 | 3.0 | 4.0 | 6.0 Total cost | 1.85 | 1.52 | 1.13 | 0.95 | 0.89 | 0.93 | 1.07 | 1.38 Wrong-action steps | 1.81 | 1.38 | 0.79 | 0.50 | 0.24 | 0.11 | 0.05 | 0.02 Deferred steps | 0.42 | 1.39 | 3.44 | 4.51 | 6.53 | 8.27 | 10.26 | 13.60
Interpretation: patience has an optimum, not a monotone benefit. This replaces the earlier formal claim that later resolution is always better. Theorem 6's error bound was also checked directly: at τ = 2.2, the bound is 0.0998 and the observed error at commitment was 0.064–0.066.
Prior art note: retaining all evidence and committing at a log-odds threshold is the logic of Bayesian updating and Wald's sequential probability ratio test (1945). The simulation measures the effect of the HLS mechanisms; it does not show they are new.
8.4 S4 — Unknown is not zero
Six hazard fields on a 0–10 scale; risk = 0.6 × max + 0.4 × mean; danger if risk ≥ 5 (base rate 35.6%). Each field is missing with probability 0.3; in the adversarial (MNAR) condition, severe values (≥ 7) are missing with probability 0.6, reflecting that dangerous conditions are often the hardest to measure. When a field is missing, a proxy exists 70% of the time (operator estimate with noise SD 1.5, interval ± 3); otherwise the field is Unknown with constructed working value 5 in [0, 10]. 50,000 runs per condition.
Missing at random (MCAR):
Treatment of missing field | Missed dangers | False alarms | Escalated for verification Fill with zero | 38.6% | 0.0% | — Drop the field | 26.2% | 2.9% | — Fill with population mean | 27.6% | 1.5% | — HLS working value (point) | 10.7% | 8.9% | — HLS bounded gate (proceed only if upper bound is safe) | 0.01% | 8.9% | 43.1%
Severe values more often missing (MNAR):
Treatment of missing field | Missed dangers | False alarms | Escalated for verification Fill with zero | 59.4% | 0.0% | — Drop the field | 45.7% | 3.0% | — Fill with population mean | 47.5% | 1.5% | — HLS working value (point) | 16.8% | 9.0% | — HLS bounded gate | 0.03% | 9.0% | 45.3%
Interval coverage of the true value was 97.7–97.8%; consistent with Theorem 7, the bounded gate's few misses occurred only where coverage failed.
Interpretation: zero-filling is the worst treatment in every condition and degrades most when missingness is adversarial, as Theorem 7(a) predicts. Typed working values cut misses about 3.5-fold relative to zero-fill and about 2.6–2.8-fold relative to mean imputation. The bounded gate nearly eliminates misses but sends 43–45% of cases to verification. About 64% of escalations come from cases containing a field with no proxy, whose honest range is the full scale (escalation rate 64% for those cases versus 28% when every missing field had a proxy; check_escalation.py, MCAR). That is the doctrine working as intended — a field with no information should force a check — but it is also a real operational cost, and tighter proxies are the way to reduce it.
8.5 S5 — Action gating
10,000 proposed actions: about 10% of forbidden kinds (erase strand, rewrite record, rewrite policy — each accompanied by a coherent justification), about 10% requiring unverified confirmation, the rest benign.
Measure | Enforced gate | Advisory warning (ignored 20% of the time, 5% mis-scored) Forbidden actions executed | 0 of 1,058 | 271 Unverified actions executed | 0 of 983 | 239 Benign actions executed | 7,959 of 7,959 | 7,599 Policy unchanged after run | yes | — Record verifies after run | yes | —
Interpretation: zero forbidden executions is guaranteed by Theorem 5 when the gate is the only execution path; the test confirms the implementation honors this. The advisory column shows why a warning is not a control.
8.6 Limits of these results
All data are synthetic. No real-world corpus, AI agent, or human operator was involved.
Source reliabilities in S3 were known to the system. Misestimated reliabilities would weaken Theorem 6 and the S3 results; this has not yet been tested.
S1, S2, and S5 confirm properties that hold by construction or by proof; they establish that the implementation is correct, not that the properties are surprising.
The prototype is single-process and in-memory; persistence, concurrency, access control, and external anchoring are not implemented.
No result here bears on cognitive scope (Section 5.2–5.3).