Structural address conditions task-relevant information in explicit H&E measurements

Controlled evidence at tissue-boundary and nucleus-relative scales

Manuscript status: methods-paper draft, version 1, revised 1 September 2026; post-result covariance sensitivity added without redefining an endpoint
Author list and affiliations: to be finalized
Keywords: computational pathology; histology; structural address; interpretable measurement; spatial context; morphology; H&E; spatial transcriptomics

Abstract

Computational pathology routinely uses spatial context, tissue compartments, and cellular neighborhoods, but the held-out discriminative value added by structural position is often entangled with new pixels, learned representations, or increased feature dimension. We developed a controlled structural-address assay for explicit hematoxylin-and-eosin (H&E) measurements. Within each experiment, representations used the same eligible image region and elementary distribution operators while positional identity was preserved, pooled, randomized, or shifted; ordered and randomized arms were also equal-dimensional and count-matched. We first analyzed 2,168 EBHI-Seg colorectal biopsy patches using five distance compartments defined relative to the official foreground annotation. Under a numerically stable shrinkage-LDA readout, the primary 5/15-pixel ordered representation (304 classifier axes) achieved 85.3% exact accuracy, against 81.3–82.0% for twenty equal-dimensional, count-matched random partitions; ordered address exceeded the strongest random replicate by 3.32 percentage points (accession-bootstrap 95% interval, 1.65–5.13), ruling out increased feature dimension as the explanation. It also exceeded a deliberately lower-dimensional monolithic pooled baseline (81.0%), and every disclosed scale exceeded that baseline across ten alternative grouped-fold partitions. In a post-result fixed-grid sensitivity analysis, the ordered-over-random advantage stayed positive at every covariance-shrinkage setting from 0 to 1 and under analytic automatic shrinkage (at least 2.49 points; every grouped-bootstrap interval above zero), while absolute accuracy was not shrinkage-invariant. We then tested nucleus-relative address in a prespecified bounded pilot of the public STHELAR H&E–Xenium resource. Across 17,492 high-confidence cells under leave-one-slide-out evaluation of 11 slides (breast, pancreatic, and skin), ordered radial summaries exceeded count-matched random partitions by a mean 0.0537 slide macro-F1 (11/11 positive; exact two-sided sign-flip p=0.0009766; slide-bootstrap 95% interval, 0.0336–0.0735). Post-result controls showed that ordered address also exceeded a contiguous shifted anchor by 0.0532 macro-F1 on every slide and that addressed context remained informative after target-nucleus pixels were removed. These results do not introduce spatial or compartmental pathology, and they do not establish clinical grading, training-free cell typing, or a universal spatial law. They provide a controlled, interpretable demonstration that fixed H&E summaries can change in task-relevant usefulness when their declared structural address is retained.

Introduction

Histology is spatial by construction. Pathologists read boundaries, compartments, interfaces, neighborhoods, gradients, and the relation of local marks to larger tissue architecture. Computational pathology reflects this reality through tumor–stroma analyses, cell graphs, spatial statistics, multi-scale classifiers, and context-aware whole-slide models. The broad proposition that location matters is therefore neither controversial nor new.

A narrower measurement question remains useful: if the eligible image region and elementary summary operators are held constant, how much task-relevant information is lost when structural position is forgotten? Many spatial models cannot isolate that question cleanly. Adding context may add pixels. Adding graph edges may add learned capacity. Splitting a region into several parts may increase dimensionality. A performance gain can therefore reflect more content, more parameters, more feature slots, or biologically meaningful positional identity.

Parallax Pathology is a versioned family of deterministic, named H&E measurements. Its explicit summaries make a matched ablation possible. We define structural address as the position of a measurement relative to a declared biological or annotation-derived anchor. The assay compares the same summary family under representations that preserve meaningful address, pool it away, or destroy it while retaining matched feature dimension and occupancy. A further shifted-anchor control preserves contiguity and hierarchy while breaking correspondence to the intended anchor.

Throughout this manuscript, task-relevant information is an operational term: discriminative information measured by held-out performance under the specified supervised readout. It does not denote Shannon information, mutual information, a representation-independent intrinsic quantity, or a readout-independent property. Likewise, external-data corroboration means a concordant representation contrast in a different public dataset; it does not mean independent-team, institution-shift, prospective, or clinical external validation.

We report two experiments discovered sequentially rather than constructed as a single retrospective demonstration. EBHI-Seg provides a tissue-scale, annotation-relative experiment around a foreground boundary. STHELAR provides a cell-scale experiment around a nucleus linked to independently derived Xenium cell metadata. The tasks, labels, datasets, and anchors differ. Their common element is the controlled representation contrast.

The contribution is not a new spatial classifier and not the claim that compartments are novel. It is an explicit assay for asking whether named H&E summaries use structural address, together with cross-dataset mechanistic corroboration at two reference scales.

Materials and methods

General assay

For an image region and declared anchor, a fixed family of scalar image fields is summarized either over a pooled support or separately within ordered distance compartments. The pooled arms deliberately collapse address and are therefore lower-dimensional than their compartmental counterparts. The primary negative control allocates the same eligible pixels to compartments with the same counts but randomizes their positional identity. Ordered and randomized arms therefore match feature count, compartment occupancy, missingness structure, and source support. In STHELAR, a second control toroidally shifts the full contiguous compartment map away from the target nucleus, preserving compartment shapes, hierarchy, dimension, counts, and window support while breaking correspondence to the target nucleus.

The assay tests operational task-relevant information under a specified readout, not Shannon information, measurement invariance, or an intrinsic property of a representation. Its endpoint is whether a fixed supervised readout performs differently when address is preserved or disrupted. The image measurements are deterministic, but the downstream LDA and logistic-regression readouts are trained inside the evaluation design; neither experiment is a training-free classifier.

EBHI-Seg tissue-boundary experiment

The stable EBHI analysis used 2,168 annotated patches from the conventional five-class pathway: Normal, Polyp, Low-grade intraepithelial neoplasia, High-grade intraepithelial neoplasia, and Adenocarcinoma. The source EBHI-Seg publication describes 2,228 image–mask pairs across six categories; this analysis excluded Serrated adenoma and retained the 2,168 conventional-pathway pairs that passed the frozen analysis inputs. Case-like accession groups were derived from filenames and kept intact across five-fold stratified grouped evaluation. These are accession-like proxies, not verified patient identifiers.

The official foreground annotation defined the structural anchor. The primary 5/15-pixel representation separated three inward compartments (0–5 pixels, 5–15 pixels, and deeper than 15 pixels) and two outward compartments (0–5 pixels and 5–15 pixels). Within every compartment, 45 fixed summaries were calculated from RGB, CIELAB, hematoxylin/eosin deconvolution, and gradient image fields using the mean, standard deviation, and 10th, 50th, and 90th percentiles. The ordered compartment block therefore contained 225 axes; adding the shared 79-axis image frame produced a 304-axis classifier input. Each count-matched random arm was also 304-dimensional. The monolithic official-mask pooled baseline contained 154 axes rather than only the 45 pooled content summaries, because it also retained the shared image frame and mask-derived terms. Thus dimensionality is controlled by the ordered-versus-random comparison, not by the deliberately lower-dimensional ordered-versus-pooled comparison. Random controls reassigned pixels separately within the foreground interior and the exterior neighborhood while preserving all five compartment counts and missingness.

The fixed downstream model used training-fold median imputation, training-fold standardization, uniform-prior linear discriminant analysis with analytic automatic covariance shrinkage, and the previously declared ordinal readout. The 5/15-pixel definition remained primary. Two sensitivity scales, 3/10 and 8/24 pixels, were disclosed without selecting a replacement winner. Twenty deterministic SHA-256-seeded count-matched randomizations were evaluated. Paired differences were summarized with accession-group bootstrap intervals, and the complete comparison was repeated across ten alternative grouped-fold seeds.

An earlier legacy V6 analysis used an ill-conditioned 304-axis LDA. Machine-scale feature perturbations changed 136 of 2,168 predictions. V6.1 therefore superseded the numerical headline with the stable shrinkage analysis while preserving the scientific mechanism claim.

After the manuscript result was assembled, V6.2 tested whether the ordered-versus-random contrast depended on the covariance regularizer. It reused the frozen primary 5/15 features, all twenty archived random representations, the same 348 accession-like groups, and the same five grouped folds. Only LDA covariance shrinkage varied over a fixed grid: analytic auto and numeric values 0, 0.01, 0.05, 0.10, 0.25, 0.50, 0.75, 0.90, and 1.00. Median imputation, standardization, uniform priors, Ridge α=10, and ordinal penalty 0.8 remained fixed. At every setting we compared ordered address both with archived random replicate 09, the strongest adversary under auto, and with the strongest of all twenty random arms at that setting. Five-thousand-sample accession-group bootstrap intervals were computed separately for each contrast. This was a post-result sensitivity analysis, not model selection and not a replacement primary endpoint.

STHELAR nucleus-relative experiment

STHELAR links H&E imagery to co-registered Xenium-derived nuclear maps and broad cell labels. We froze the public 20× patch release at repository revision a01e22cdb7368edf595edf6150d0ac57deb5e548. The executable release contained 154,814 patches from 27 slides and 13 tissues. The bounded pilot selected the 11 slides in tissues represented by at least three slides: four breast, three pancreatic, and four skin slides. Four spatially separated 32-row blocks per slide yielded 1,408 acquired candidate patches. Images, nuclear maps, metadata, source rows, and hashes were retained locally.

Eligible target cells required a central 96×96-pixel window, at least six target-nucleus pixels, RNA-depth quantile at least 0.02, and, only for the primary analysis, final-label confidence at least 0.60. Stable cell IDs were deduplicated before evaluation, and deterministic class caps were applied within slide. The primary outcome comprised five broad categories: Epithelial, Fibroblast/Myofibroblast, Blood vessel, Myeloid, and T/NK. These categories are RNA-derived and curated through the STHELAR pipeline; they are not manual pathology gold-standard labels.

Nine image fields, RGB, CIELAB, hematoxylin, eosin, and gradient, were summarized by mean, standard deviation, and the 10th, 50th, and 90th percentiles. The ordered arm distinguished the target nucleus, 0–8-pixel perinuclear field, 8–24-pixel near field, and greater-than-24-pixel far field. Its address-summary block therefore contained 180 axes, versus 45 for pooled summaries. Seven shared target-geometry and tissue covariates yielded actual classifier inputs of 187 axes for ordered, randomized, and shifted arms and 52 axes for the pooled arm. The randomized arm retained the four ordered compartment counts but assigned the identical window pixels deterministically at random. Shared covariates were identical across primary arms; ordered-versus-random and ordered-versus-shifted are the dimension-matched tests.

A fixed balanced multinomial logistic regression used training-fold median imputation and standardization, C=1, and no hyperparameter tuning. Outer evaluation left one slide out. Macro-F1 was primary; balanced accuracy, per-class F1, and log loss were supporting metrics. The independent inferential unit was the slide. Primary paired slide deltas used an exact two-sided sign-flip test and slide-cluster bootstrap intervals.

The three-arm protocol was frozen before outcome extraction. After the primary summary was sealed and hashed, a dated amendment added five mechanistic controls: a contiguous shifted radial map, target nucleus only, target nucleus plus pooled context, ordered context only, and pooled context only. These are explicitly post-result controls, not retrospectively prespecified primary endpoints.

Reproducibility and numerical environment

The EBHI V6.1 robustness archive separately regenerated features and required stable predictions under shrinkage covariance. STHELAR initially showed 61–73 near-boundary prediction changes under multithreaded numerical libraries. OpenMP, OpenBLAS, MKL, Accelerate, and NumExpr were then fixed to one thread. Two independent complete evaluations matched exactly for predictions, contrasts, and final results. Modeling was closed after a descriptive tissue-stratified summary; no additional feature selection, threshold adjustment, or hyperparameter optimization is authorized under STHELAR V1.

The twenty EBHI randomizations, ten alternative grouped-fold seeds, and STHELAR tissue-stratified closeout are sensitivity analyses within their respective datasets, not independent dataset replications. Their purpose is to probe design and numerical stability rather than multiply the number of external validation cohorts.

Results

Ordered tissue-boundary address exceeded dimension-matched and pooled controls

Under the stable shrinkage readout, ordered distance compartments achieved 86.1%, 85.3%, and 84.5% exact accuracy at 3/10-, 5/15-, and 8/24-pixel scales. The decisive comparison holds feature dimension fixed. The primary 5/15 ordered representation (304 classifier axes) was tested against twenty equal-dimensional, count-matched random partitions, also 304 axes, which ranged from 81.3% to 82.0%. Ordered 5/15 address exceeded every replicate on all five recorded endpoints; against the strongest random replicate the advantage was 3.32 points (95% accession-bootstrap interval, 1.65–5.13), with a corresponding ordinal-correlation advantage of 0.051 (0.032–0.077). Because the arms match in dimension, occupancy, and support, this contrast rules out increased feature dimension as the explanation for the gain.

Ordered address also exceeded a deliberately lower-dimensional baseline, a 154-axis annotation-assisted monolithic pooled arm (81.0% exact accuracy; the arm labeled “oracle” in the frozen register), by 4.38 points at the 5/15 scale (95% interval, 2.22–6.63); that comparison establishes benefit over monolithic pooling but does not itself control dimension. Every ordered scale improved exact accuracy, adjacent accuracy, quadratic kappa, and ordinal correlation with paired intervals above zero, and each exceeded the pooled baseline across ten alternative grouped-fold seeds.

The V6.2 sensitivity harness exactly reproduced the archived automatic-shrinkage predictions: zero disagreements for the ordered arm and zero total disagreements across all twenty random arms. Ordered-minus-random-replicate-09 exact-accuracy differences ranged from 2.49 to 8.26 points across the ten shrinkage settings. Against the strongest random arm recomputed separately at each setting, differences ranged from 2.49 to 8.03 points; all ten accession-group bootstrap intervals excluded zero. The smallest conservative contrast occurred at numeric shrinkage 0.50: +2.49 points, with a 95% interval of +0.95 to +4.11. Strong shrinkage reduced absolute performance in both arms, ordered accuracy fell to 61.7% at shrinkage 1.00, so the analysis supports stability of the representation contrast, not invariance of the classifier’s absolute accuracy and not selection of a replacement shrinkage value.

These results localize information within the annotation frame. They do not show that the foreground bands correspond to validated cell types or histologic compartments, and they do not establish automatic localization.

Nucleus-relative address improved broad STHELAR cell discrimination

The sealed primary STHELAR analysis included 17,492 high-confidence cells across 11 slides. Overall macro-F1 was 0.3427 for pooled summaries, 0.3936 for ordered radial summaries, and 0.3420 for count-matched random partitions. Ordered-minus-random mean slide macro-F1 was 0.0537, with all 11 slides positive, an exact two-sided sign-flip p=0.0009766 (the unanimity floor for 11 slides, 2/2¹¹), and a slide-cluster bootstrap interval of 0.0336–0.0735. Ordered-minus-pooled mean slide macro-F1 was 0.0586, again with all slides positive.

All five reported classes improved in macro-F1 under the ordered representation relative to both pooled and randomized controls. Log loss did not improve over pooled summaries, so the result is a discrimination gain rather than evidence of better probability calibration.

The post-freeze tissue closeout showed positive ordered-minus-random deltas within all represented tissue groups: mean 0.0491 across four breast slides, 0.0556 across three pancreatic slides, and 0.0610 across four skin slides. Every individual slide was positive. This rules out a result produced by only one represented tissue family, but it does not test unseen tissues or institutions.

Mechanism controls separated meaningful address from contiguity and nuclear isolation

In the deterministic amended analysis, full ordered address exceeded the contiguous shifted-anchor control by a mean 0.0532 slide macro-F1; all 11 slides were positive and the exact sign-flip p=0.0009766. Thus a contiguous hierarchical partition was not sufficient when it no longer corresponded to the target nucleus.

After target-nucleus pixels were removed entirely, ordered context exceeded pooled context by 0.0360 macro-F1 on all 11 slides (p=0.0009766). Full ordered address also exceeded target nucleus plus pooled context by 0.0155 on 9 of 11 slides (p=0.00684). The effect therefore cannot be reduced to isolating nuclear pixels; surrounding H&E context carries additional information when its address relative to the nucleus is retained.

Cross-dataset synthesis

EBHI and STHELAR are not literal replications. They differ in tissue, task, label provenance, anchor, scale, classifier, and inferential grouping. Their common result is a representation contrast. In each dataset, fixed explicit H&E summaries supported better held-out discrimination when declared positional identity was retained than when it was pooled or deliberately disrupted. EBHI demonstrates this internally around an annotation boundary; STHELAR supplies external-data corroboration around a transcriptomically linked nucleus, not independent-team or clinical external validation.

Discussion

Principal finding

The experiments support a bounded proposition: an explicit histologic measurement is not fully characterized by its scalar value or regional distribution. Its task-relevant value under a specified supervised readout can depend on its address relative to a declared structure. Pooling can erase this address while retaining the same eligible image region and summary operators.

The random controls matter because ordered compartment representations are higher-dimensional than monolithic pooling. Preserving compartment counts while randomizing identity tests whether gains arise from additional feature slots or occupancy alone. The shifted STHELAR control is stronger: it preserves contiguity, hierarchy, dimension, and counts, and changes only correspondence to the intended nucleus. The context-only comparison further shows that addressed information exists outside the target nucleus itself.

Relationship to prior art

The broad scientific territory is established. Contextual nuclear classifiers, SuperCRF, multi-class spatial context models, cell graphs, spatially aware multiple-instance learning, tumor-boundary reconstruction, and point–object spatial statistics all demonstrate the importance of context and tissue organization. Computational tissue shuffling provides a particularly close conceptual predecessor by preserving the same cells and their content while generating randomized spatial nulls. Recent coordinate-permutation work likewise asks whether nominally spatial whole-slide models actually use position.

The contribution here is therefore not “location matters” and not “Parallax introduces compartments.” A targeted adversarial audit found no exact predecessor for the complete combination: a fixed, named H&E summary family; a shared eligible image region and summary operators; ordered distance address relative to a biological or annotation-derived anchor; pooled and equal-dimensional count-matched random alternatives; a contiguous shifted-anchor control; grouped unit-level inference; deterministic chronology; and concordant experiments at tissue-boundary and nucleus-relative scales. This supports the phrase controlled structural-address assay, while not proving absolute priority.

Interpretation and practical implications

The EBHI sequence also separates segmentation overlap from downstream structural information. Improving automatic mask Dice from 0.756 to 0.829 did not improve the locked grading endpoint: every V5-versus-V4 downstream interval crossed zero. Preserving annotation-relative distance, by contrast, produced the positive V6/V6.1 representation result. Within this fixed pipeline, overlap was therefore not a sufficient surrogate for retained task-relevant structure. This does not show that Dice is generally irrelevant, nor does it prove that lower-overlap masks are preferable; it shows that better pixel agreement and better measurement utility are distinct endpoints.

At the cell scale, the STHELAR result suggests that broad RNA-derived identity is reflected not only in the target nucleus but also in the organization of its immediate H&E field. The assay does not assign biological meaning to individual image summaries. It identifies where informative distributions reside and provides an interpretable route for later mechanistic annotation.

The design can be reused for tumor interior versus invasive front, epithelial boundary versus surrounding stroma, immune gradients around tumor regions, gland wall versus lumen, and other declared reference geometries. Each application should prespecify the anchor, distance coordinate, eligible support, randomization logic, grouping unit, and biological interpretation boundary.

The affirmative result is not merely that context helps; the fixed summaries become more useful specifically when correspondence to the declared reference structure is preserved. The recurrence at a tissue boundary and around a nucleus is scientifically suggestive because the datasets, tasks, anchors, and readouts differ. It supports a cross-scale structural-address hypothesis: explicit morphology may carry more task-relevant information when indexed by meaningful position. Two experiments do not establish scale invariance or a universal law. They justify a frozen assay and a new external test.

Deterministic measurement as an audit layer

The broader programme suggests an audit role for named, versioned measurements. The useful property is not immunity from bias; these experiments themselves expose annotation convention, site signal, segmentation-target mismatch, and supervised-readout dependence. The useful property is that a fixed measurement and a matched ablation hold still long enough to ask what changed, which nuisance channel survives, and which interpretation fails.

That role is not yet externally validated. The present harness has primarily audited its own claims, and several important corrections came from provenance review, statistical controls, and version discipline rather than from the named measurements alone. A domain-level auditor contribution requires an outward-facing test on an open pathology model whose claimed spatial mechanism matters independently of Parallax.

Limitations

EBHI is an internal annotation-assisted benchmark. Its accession-like groups are not verified patients, its official masks may encode annotation convention, and its distance bands are not validated biological compartments. The stable result depends on a supervised shrinkage readout and does not establish an automatic 85% system. V6.2 was added after the primary result was known. Its fixed-grid analysis makes dependence on the single automatic-shrinkage choice less plausible, but it remains an internal sensitivity analysis, not independent confirmation. The decline in absolute accuracy under heavy shrinkage also prevents language implying readout invariance.

STHELAR is a bounded 120 MB pilot rather than the full 17.6 GB release. Although the cell count is large, the independent inference unit is 11 slides. The represented tissues are limited to breast, pancreatic, and skin material, and the readout learns across the same tissue families it evaluates. Labels are broad, RNA-derived, and curated rather than manual pathology ground truth. The primary random control was prespecified; the shifted and context-decomposition controls were added after the primary result and must remain labeled accordingly.

The pooled comparisons answer whether retaining address improves over collapsing it, but they do not by themselves separate address from increased feature dimension. That separation rests on the equal-dimensional, count-matched random controls and, in STHELAR, the equal-dimensional contiguous shifted-anchor control. The twenty EBHI randomizations and ten fold seeds are repeated perturbations of one dataset, not twenty or ten independent studies.

Across both datasets, positive supervised discrimination does not prove that the measured axes correspond to pathologists’ causal or diagnostic reasoning. No prospective, clinical, independent-team, or institution-shift validation is presented. A general statement that sampling geometry conditions histologic information remains an organizing hypothesis, not a universal law.

Next decisive test

A complementary outward-facing audit should reproduce an open spatial or foundation-model result, freeze the nuisance and mechanism hypotheses before evaluation, and compare observed embeddings or predictions against deterministic color, edge, texture, compartment, and shifted-coordinate controls under patient- and site-separated inference. Its objective should be neutral, identify what the model uses and whether the advertised spatial interpretation survives, not to presume that the external model is confounded. Such a study would test the audit role; it would not replace biological replication of the structural-address assay.

Conclusion

Across two public histology resources and two structural reference geometries, fixed explicit H&E summaries supported better held-out discrimination when their declared distance-relative identity was retained than when their address was pooled, randomized, or shifted. The result is best understood as a controlled measurement finding: structural address conditions task-relevant information under specified supervised readouts. It is not a statement about Shannon information, a new theory of spatial pathology, or a universal law. This is not a training-free classifier. Its value is that the mechanism is declared, falsifiable, traceable to named measurements, and portable to other reference geometries.

Data and code availability

The EBHI complete verification record, stable V6.1 robustness appendix, V6.2 covariance-sensitivity archive, STHELAR protocol and result archive, prior-art audit, and synchronized master claim ledger are preserved in the Parallax Pathology project. Public source data are available from the EBHI-Seg Figshare release and the STHELAR 20× Hugging Face/BioStudies releases. Exact local paths and SHA-256 hashes are recorded in SOURCE_INDEX.csv and the experiment manifests. The manuscript HTML is self-contained; its figures are embedded from the frozen source reports.

Ethics statement

This study reanalyzes publicly released, de-identified images and metadata and involved no new tissue collection or participant recruitment. The EBHI-Seg source publication reports its dataset-origin ethics certification; STHELAR provenance and ethics remain governed by its source release. No claim of institutional-review exemption is made here, and submission-specific wording should be confirmed against the target journal's requirements.

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