Appendix: The Evidence Ledger

The book argues that a claim should be governed by its provenance, its evidential support, and an explicit statement of what it does not establish. This appendix applies that discipline to the book itself.

Every original empirical number produced for this book is listed here with three things: where it was measured, what its provenance status is, and what it does not establish.

Two facts are visible immediately from the ledger:

1. The Empirical Core: Every original experimental number produced for this book comes from Chapters 5 through 7 and traces to two sources: one 10,000-row HaluEval summarization run, and one three-domain hard-negative table. Chapter 8 interprets those results; it does not add new original model-performance measurements.
2. The Architectural Derivation: Chapters 9 through 15 contain no original empirical model-performance measurements. The consistency and sensitivity axes, the abstention router, the policy engine, the recovery loop, and the memory architecture are derived from the earlier results and from first principles. The runnable demonstrations in those chapters are deterministic tests of architectural invariants under a perfect structured oracle. They establish that the types hold. They establish nothing about the accuracy of a real verifier or model.

A reader who finishes Chapter 15 should not believe the architecture has been validated. It has been reasoned through. The experiments that would validate it are listed in Table B.

    flowchart TD
    A[Raw Data: HaluEval 10k Run] --> B[Feature Extraction: Geometry, Entailment, Structure]
    B --> C[Measured Results: Chapters 5-7]
    C --> D[Interpretation & Ceilings: Chapter 8]
    D --> E[Derived Architecture: Chapters 9-15]
    E --> F[Owed Experiments: Table B]
    F -.->|Future Validation| E
  

The appendix separates measured results from derived architecture: Chapters 9 through 15 consume earlier evidence but still owe direct validation experiments.

A. What the book measured

All Hallucination Energy results trace to the Certum implementation and the config-preserved summarization run 20260216_225831.

A.1 — HaluEval summarization (Chapter 5 §16, §18; Chapter 6)

Run configuration (recorded in the run’s config.json): HaluEval summarization, $N = 10,000$ rows; embedding model sentence-transformers/all-MiniLM-L6-v2; NLI model MoritzLaurer/deberta-v3-base-mnli-fever-anli; geometry rank $r = 32$, $top\_k = 1000$; run seed 1337; sentence-decomposed pipeline; 70/30 stratified row split plus 5-fold stratified cross-validation; modeling seed 42. Re-running the modeling stage reproduces every value below.

A.2 — Hard-negative separation, three domains (Chapter 5 §20; Chapter 6 §5; Chapter 7 §12; Chapter 8 §15)

Negative construction: hard_mined_v2 — for each claim, shortlist the 16 evidence sets with the highest centroid similarity, exclude the claim’s own evidence and any set sharing its source page, and select the most similar remaining mismatch. Selection is by similarity, not energy: this is a semantic-neighbour hard negative (difficulty Level 3), not a metric-aware adversary. Recorded in adversarial_consolidated.csv (rerank_by_energy: false). Seed 1337.

    flowchart LR
    subgraph Factual Domains
        W[Wikipedia / FEVEROUS] -->|Separation +1.92| P[PubMed]
        P -->|Separation +2.11| S[Success: Thresholding Works]
    end
    subgraph Relational Domain
        C[CaseHOLD] -->|Separation -0.40| F[Failure: Energy Inverts]
    end
  

What these do not establish:

• Wikipedia / PubMed: an operating point at any other false-acceptance budget; behaviour under a metric-aware adversary or a larger search budget $K$; that the strict-threshold supported acceptance (6.7% for Wikipedia) is usable in production.
• CaseHOLD: that legal language is intractable for embeddings, or that role binding is the only missing variable. Chapter 8 §15 states the bounded reading: under this representation, evidence construction, rank, and hard-negative regime, containment energy does not preserve the ordering required to separate supported from structurally similar legal alternatives. The detector inverts on this task; a threshold cannot fix a sign flip.
• Note: The standardized separation is a distributional quantity (a Cohen-style ratio). It is not an operating point.

A.3 — The negative result (Chapter 5 §22)

The search for a second scalar that would recover the missing separation under hard adversarial overlap — participation ratio, projection ratios, leave-one-out sensitivity, similarity margins, adaptive monotone combinations, gap-width tuning — did not reliably succeed. This is reported as a negative result, not omitted.

B. What the book owes

These experiments are named in the chapters as not yet run. They are not fabricated in prose.

C. The runnable demonstrations (Chapters 12–15)

These are deterministic scripts, standard library only. They exercise the architecture’s type discipline. They are not model-quality experiments.

    flowchart TD
    V[Diagnostic Vector: H, C, S, E, A] --> C1[Consumed as Settled Object from Ch 12]
    C1 --> C2[Axes & Independence: NOT VALIDATED in Book]
    C2 --> C3[Requires: Perturbation-Fidelity Experiment]
  

The diagnostic reliability vector $(H, C, S, E, A, \dots)$ is consumed as a settled object from Chapter 12 onward. Its axes, their combination rule, and their statistical independence are not validated anywhere in the book (Chapter 9 §18 says so explicitly). The perturbation experiment in Table B is what would validate it.

D. External results the argument leans on

The book cites primary sources for its research claims. The load-bearing ones:

Full citations are in each chapter’s Research roots.

E. The honest summary

• Measured: that a bundle of geometry-derived features separates supported from unsupported summary sentences on one HaluEval run at roughly $0.71$ AUC, rising to about $0.73\text{–}0.75$ with entailment and structural features; that this signal survives semantic-neighbour hard negatives in two factual domains; that it inverts on a relation-heavy legal task; that retained rank barely matters for the bundle on this workload.
• Derived, not measured: everything about consistency, sensitivity, abstention routing, policy, recovery, and memory governance — Chapters 9 through 15.
• Owed: the isolated-scalar baseline, the simple-proximity baselines, dependency-correct splits, cross-embedder transfer, the energy-aware adversary, the coordinate-vs-scalar test, the perturbation-fidelity experiment, and the contamination metrics.

The destination of the book is a method, not a validated system. This appendix is the book keeping its own score.