3. Mathematical Framework

This section states the evaluation mathematics explicitly so that dataset comparisons, threshold decisions, and RAG policy recommendations can be reproduced without relying on spreadsheet implementation details.

3.1 Atomic-fact notation

For each atomic fact i, let $y_{i} \in \{ C,P,U,X,M,N,V\}$ , denoting Correct, Partially correct, Unsupported, Contradicted, Missing, Not applicable, and Unverifiable. The quantitative counts are defined as TP = number of correct facts, PARTIAL = number of partially correct facts, FP = unsupported plus contradicted extracted facts, and FN = missing PDF-supported facts. Unverifiable and not-applicable facts are reported separately and excluded from the main precision-recall denominators.

This definition treats extraction as a directed information-recovery problem. FP measures information introduced without support; FN measures supported source information not represented by the extraction. The direction matters because a missing fact and an unsupported fact have different consequences in RAG: the former creates false negative retrieval, while the latter creates false positive evidence.

3.2 Strict precision, recall, and F1

$P_{s} = \frac{\text{TP}}{\text{TP} + \text{PARTIAL} + \text{FP}}$	(1)

Strict precision credits only fully correct facts while retaining partial facts in the predicted-fact denominator.

$R_{s} = \frac{\text{TP}}{\text{TP} + \text{PARTIAL} + \text{FN}}$	(2)

Strict recall credits only fully correct facts and measures the fraction of relevant PDF facts recovered exactly.

$F_{1,s} = \frac{2P_{s}R_{s}}{P_{s} + R_{s}}$	(3)

The harmonic mean penalizes systems that achieve a high value on only one of precision or recall.

The strict definitions are intentionally conservative. Partially correct facts contribute to neither strict true positives nor false positives alone; they remain in the denominators because the extractor produced an imperfect representation that cannot be counted as exact recovery.

3.3 Partial-credit metrics

The evaluation assigns a fixed partial-credit coefficient $\alpha = 0.5$ . Let WTP denote weighted true positives.

$\text{WTP} = \text{TP} + \alpha \cdot \text{PARTIAL},\quad\quad\alpha = 0.5$	(4)

$P_{\text{w}} = \frac{\text{WTP}}{\text{TP} + \text{PARTIAL} + \text{FP}}$	(5)

$R_{\text{w}} = \frac{\text{WTP}}{\text{TP} + \text{PARTIAL} + \text{FN}}$	(6)

$F_{1,w} = \frac{2P_{\text{w}}R_{\text{w}}}{P_{\text{w}} + R_{\text{w}}}$	(7)

The coefficient alpha is an operational convention rather than an empirically calibrated utility value. It makes partial facts comparable across reports, but it does not imply that every partial fact is exactly half as useful as a correct fact. Sensitivity analysis with alternative alpha values would be appropriate when the downstream application assigns different costs to omitted dates, truncated responsibilities, or imprecise titles.

3.4 Completeness, unsupported content, and schema quality

$C = \frac{\text{TP} + \text{PARTIAL}}{\text{TP} + \text{PARTIAL} + \text{FN}}$	(8)

Completeness asks whether relevant PDF facts were represented at least partially, irrespective of exactness.

$U = \frac{\text{FP}}{\text{TP} + \text{PARTIAL} + \text{FP}}$	(9)

Unsupported rate measures the proportion of extracted facts that are not supported or are contradicted by the PDF.

$A_{\text{exact}} = \frac{\text{TP}}{\text{TP} + \text{PARTIAL} + \text{FP} + \text{FN}}$	(10)

$C_{\text{schema}} = \frac{N_{\text{pop,app}}}{N_{\text{app}}}$	(11)

Fields that are genuinely not applicable are excluded from the denominator.

$S_{\text{pipeline}} = \frac{N_{\text{eval,match}}}{N_{\text{PDF}}}$	(12)

$R_{\text{critical}} = \frac{N_{\text{critical}}}{N_{\text{eval}}}$	(13)

Schema completeness and factual completeness measure different constructs. A schema can be fully populated with incorrect or generic values, while a sparse schema can contain only correct facts. This distinction is empirically visible in the weak dataset-level correlation between schema completeness and weighted F1.

3.5 Document outcomes and aggregation

Table 5. Operational document-outcome thresholds.

Outcome	Operational rule
Successful	Evaluable; no critical unsupported/contradicted claim; weighted F1 >= 0.90; completeness >= 0.90; unsupported rate <= 0.05.
Partially successful	Evaluable and not successful; weighted F1 >= 0.60 or completeness >= 0.60.
Failed	Not evaluable, unmatched, weighted F1 < 0.60, major unsupported content, or critical schema/pipeline failure.

Note. These are fixed research thresholds from prompt2(5), not universal scientific or legal standards.

Pooled metrics are micro-aggregated from atomic-fact counts, so large datasets and fact-rich documents contribute more weight. Dataset summaries are also examined using macro statistics because micro-aggregation can conceal occupational heterogeneity. Let $m_{j}$ be a metric for dataset j and $J$ be the number of datasets.

$\overline{m} = \frac{1}{J}\sum_{j = 1}^{J}m_{j}$	(14)

No formal confidence intervals were included in the source reports. Because facts within a CV are not independent and documents are clustered by occupational dataset, naive binomial intervals would be inappropriate. A defensible uncertainty analysis should bootstrap at the document level within dataset and then aggregate across datasets.

3.6 Field-aligned RAG scoring

For a job criterion $q_{k}$ , let $t\left( q_{k} \right)$ be its required evidentiary type. For candidate evidence $e_{i}$ , let $T\left( e_{i} \right)$ be a set of compatible semantic roles rather than a single exclusive label. For example, a work-history sentence that explicitly names Python may have both experience and skill roles. A field-aligned score can combine lexical, embedding, cross-encoder, recency, evidence-quality, and source-verification terms while penalizing only genuinely incompatible evidence.

$S\left( q_{k},e_{i} \right) = w_{l}L + w_{s}E + w_{r}R + w_{q}Q - \lambda\,\mathbf{1}\left\lbrack t\left( q_{k} \right) \notin T\left( e_{i} \right) \right\rbrack$	(15)

Here L is lexical matching, E is semantic similarity, R is a reranker score, Q is an evidence-quality or source-verification score, $\mathbf{1}\lbrack \cdot \rbrack$ is an indicator function, and $\lambda$ is a mismatch penalty. The penalty is activated when the criterion type is not a member of the evidence-role set. Mandatory criteria may therefore be supported by explicit skills or skill-bearing experience, but not by unrelated hobbies, metadata, or merely topically similar text.

$S_{\text{cand}}(c) = \sum_{k}^{}\beta_{k}\max_{e_{i} \in c}S\left( q_{k},e_{i} \right) - \sum_{k}^{}\gamma_{k}U_{k}$	(16)

The term $U_{k}$ represents uncertainty, such as an empty structured field with no completed source fallback. The coefficients $\beta_{k}$ encode criterion importance; $\gamma_{k}$ prevents uncertainty from being silently interpreted as evidence of absence. The system should expose each max-scoring evidence item and its source excerpt.

3.7 Latency, throughput, and memory model

The source reports do not contain timing telemetry. Speed must therefore be discussed analytically and measured in a follow-up benchmark. End-to-end extraction time for one document can be decomposed as follows:

$T_{\text{doc}} = T_{\text{pdf}} + T_{\text{prefill}} + T_{\text{decode}} + T_{\text{parse}} + T_{\text{validate}} + T_{\text{I/O}}$	(17)

$T_{\text{pdf}}$ is PDF decoding and text extraction; $T_{\text{prefill}}$ is prompt processing; $T_{\text{decode}}$ is model token generation; $T_{\text{parse}}$ is XML/JSON parsing; $T_{\text{validate}}$ is schema and evidence validation; and $T_{\text{I/O}}$ is storage and transport. Reasoning tokens increase $T_{\text{decode}}$ and can also increase memory pressure through longer sequences.

$\Theta_{\text{docs}} = \frac{N_{\text{completed}}}{T_{\text{wall}}}$	(18)

$M_{\text{weights}} \approx \frac{N_{\text{parameters}}\, b_{\text{w}}}{8} + M_{\text{quant}}$	(19)

$M_{\text{KV}} \approx \frac{2L_{\text{ctx}}\, n_{\ell}\, n_{\text{KV}}\, d_{\text{h}}\, b_{\text{KV}}}{8}\quad\text{per active sequence}$	(20)

The lower-bound raw storage for 25.2 billion parameters at 4 bits is approximately 12.6 GB before quantization metadata, tensors stored at higher precision, vision components, runtime buffers, and KV cache. In Equation (19), $N_{\text{parameters}}$ is the total parameter count and $b_{\text{w}}$ is the storage width in bits per parameter. In Equation (20), $L_{\text{ctx}}$ is sequence length, $n_{\ell}$ is the number of layers, $n_{\text{KV}}$ is the number of key-value heads, $d_{\text{h}}$ is the head dimension, and $b_{\text{KV}}$ is the KV-cache storage width in bits. Although only approximately 3.8 billion parameters are active per token, all expert weights generally need to be resident for efficient routing [4].