PureOne/EVE-AITHRAEL-Robust-Causal-Calibration

EVE–AITHRÆL: Reliable Calibration of Latent Causal Models

Exact Fault Tolerance, Hardware Constraints, and Computational Limits

A 92-page theoretical manuscript with editable LaTeX, exact-arithmetic Python implementations, six worked sensor-design instances, recovery and impossibility certificates, and an explicit claim ledger.

Manuscript: version 2.0 · Hugging Face packaging: 2.0-hf1 · Date: 21 October 2026.

Research prepared for Maciej Nowicki with Eve, OpenAI AI assistant. The manuscript credits Eve with derivation, computational implementation, and internal adversarial review. This packaging preserves the manuscript's attribution.

Start here	Contents
Read the manuscript	92 pages; 11 chapters; two appendices; proofs, examples, figures, and literature discussion.
Resolved-question ledger	Eight questions resolved within the model, with assumptions and proof locations.
Claims and remaining problems	Inherited results, proposed extensions, prior-art boundaries, and unresolved questions.
Reproduce the calculations	Core verification and planner commands, input contract, and implementation limits.
Validation report	Executed checks and corrections made during internal review.

Research summary

Soft interventions can leave a latent causal model identifiable only up to a structured change of coordinates. This work begins after alignment and normalization, when the remaining freedom is represented by a finite family of column spaces $E_j$. It studies how to remove that freedom using calibrated sensing channels whose weights may be constrained by hardware, while allowing some channels to be missing or arbitrarily wrong.

The main theorem characterizes the best attainable channel distance under independently configurable linear sensor-row constraints. Matching constructions and obstruction witnesses give an exact recovery criterion. An observation bridge connects calibrated aligned observations to the residual ambiguity by an inverse-coordinate transformation. Further results cover failure-severity profiles, dense-channel counts, noise margins, sensor selection, and a hardness reduction on a depth-one causal graph.

This is a research-artifact collection hosted as a dataset repository. It contains mathematical documents, programs, rational examples, and verification reports. It has no trained model weights, collected raw observations, or train/validation/test split. The tabular viewer is disabled because the repository contains heterogeneous research artifacts.

Main mathematical results

Constrained sensing and exact fault tolerance

Let $E_j$ be the residual ambiguity space for column $j$. Each sensing row $c_a$ is chosen independently from a prescribed linear space $H_a$. For nonzero $V\le E_j$, define

$${\nu }_j(V)=\mathrm{\#}\{a:\mathrm{\exists }h\in H_a,\mathrm{\exists }v\in V,hv\mathrm{\ne }0\}\mathrm{.}\backslash nu\_j(V)=\backslash \#\backslash \{a:\backslash exists\; h\backslash in\; H\_a,\backslash \; \backslash exists\; v\backslash in\; V,\backslash \; h\; v\backslash ne0\backslash \}.$$

If at least one residual space is nonzero, the optimum channel distance is

$$D^{\ast }=\max \text{\hspace{0.17em}⁣}\{0,\underset{j:E_j\mathrm{\ne }0}{\min }\underset{0\mathrm{\ne }V\le E_j}{\min }[{\nu }_j(V)-\dim V+1\left]\right\}\mathrm{.}D^*=\backslash max\backslash !\backslash left\backslash \{0,\backslash \; \backslash min\_\{j:E\_j\backslash ne0\}\backslash \; \backslash min\_\{0\backslash ne\; V\backslash le\; E\_j\}\; \backslash bigl[\backslash nu\_j(V)-\backslash dim\; V+1\backslash bigr]\backslash right\backslash \}.$$

One common generic choice of the rows attains the optimum simultaneously across all residual columns and surviving channel subsets. For $f$ erased channels with known locations and $t$ arbitrarily corrupted channels with unknown locations, exact uniform recovery is possible precisely when

$$D^{\ast }>f+2t\mathrm{.}D^*>f+2t.$$

For freely designed dense rows, the sharp count for a nonzero residual family is

$$m_{\min }=d_{\ast }+f+2t,d_{\ast }=\underset{j}{\max }\dim E_j\mathrm{.}m\_\{\backslash min\}=d\_*+f+2t,\backslash qquad\; d\_*=\backslash max\_j\backslash dim\; E\_j.$$

An already identified model requires zero additional channels. Positive and normalized-positive dense constructions are included. Hardware coupling between different row choices is outside the central theorem.

Observation bridge and reconstruction

For a compatible reference $B_0$, known sensor matrix $C$, and available aligned mixing response $D$, the discrepancy satisfies

$$Y=D{B}_0-C=CQ,Q=U^{-1}-I\mathrm{.}Y=DB\_0-C=CQ,\backslash qquad\; Q=U^\{-1\}-I.$$

After decoding $Q$, the model is reconstructed by

$$B=B_0(I+Q{)}^{-1}\mathrm{.}B=B\_0(I+Q)^\{-1\}.$$

The bridge is conditional on availability of the aligned response $D$. Estimating and aligning that response from raw samples with finite-sample guarantees remains open in this release.

Computational limit

A depth-one causal star can realize an arbitrary rational kernel as its sole residual ambiguity space. Via the established hardness of rational spark, failure detection is NP-complete, positive uniform robustness certification is coNP-complete, and exact distance computation is NP-hard when the fault budget is part of the input. The causal realization is the proposed specialization; the underlying spark-hardness theorem is credited prior work.

Eight questions resolved in the stated model

ID	Question	Result
R1	Can aligned calibrated observations expose residual freedom linearly?	The exact inverse-coordinate bridge and inverse reconstruction.
R2	What is the optimum robustness under independent linear restrictions on sensing rows?	The exact subspace-cut formula, simultaneous attainment, and obstruction certificates.
R3	How many deletions release a specified number of ambiguity directions?	The per-column deletion hierarchy and surviving ambiguity dimension for shared failure sets.
R4	How many dense channels suffice with erasures and arbitrary corruption?	Exactly $d_*+f+2t$ for a nonzero residual family.
R5	Does a depth-one causal graph guarantee easy certification?	Arbitrary rational-kernel realization gives the stated complexity obstruction.
R6	Can fault-aware selection use a valid submodular-cover guarantee?	A sum over specified scenarios is submodular; direct worst-scenario rank can fail submodularity.
R7	What governs bounded-noise recovery?	A retained-row singular-value margin and propagation through the exact inverse.
R8	What changes when future spaces or subspace labels are unknown?	Ambient injectivity for universal future lines; pairwise-sum injectivity for unknown finite-family membership.

These are model-specific research questions. Their resolution is not a claim to have solved eight independently recognized longstanding open problems. The full ledger records proof locations and originality status.

Exact computational verification

The supplied runner uses integers and fractions.Fraction for rank, kernel, inverse, and decoding equalities. It also extracts the preserved original calibration archive into an isolated temporary directory and reruns its verifier.

Check	Executed scope
Constrained architectures	216
Finite candidate assignments	729
Independent subset-rank comparisons	5,832
Common-design subset-rank comparisons	8,640
Erasure/corruption scenarios	115
Successful exact column decodes	345
Observation-bridge assertions	182 across nine intervention contexts
Submodularity comparisons	768
Greedy-cost instances checked against exhaustive optimum	768
Shared failure sets for ambiguity severity	64
Planner inputs with certificates	Six

All supplied core verification suites pass. Finite checks validate implementations and their declared instances; universal statements rely on the written proofs. The conditioning figure is a floating-point illustration, separate from the exact certificates.

Reproduce

Run from the repository root with Python 3. The original validation used Python 3.12.14. Core verification has no third-party dependencies.

python code/reproduce_all.py
python code/plan_robust_calibration.py examples/star_spark_three.json --output results/my_certificate.json

The transparent planner enumerates channel subsets and accepts at most 16 candidate channels. Its bounded coefficient search can return search_exhausted_not_infeasible; search exhaustion is not an impossibility certificate.

Optional figure regeneration:

python -m pip install -r requirements-figures.txt
python code/plot_results.py

To rebuild the PDF with a suitable TeX installation:

cd source
latexmk -pdf manuscript.tex

Rerunning verifiers rewrites generated reports, including runtime-dependent fields. Release checksums describe the distributed snapshot. See REPRODUCE.md for exact data contracts.

Repository contents and provenance

Path	Description
EVE_AITHRAEL_Manuscript.pdf	Complete manuscript, preserved byte for byte from the source release.
source/	Editable LaTeX chapters and 14-entry BibTeX bibliography.
code/	Exact planner, algebraic primitives, verifiers, runner, and optional plots.
examples/	Six handcrafted mathematical input instances and six planner certificates.
results/	Generated exact verification reports and figure data.
figures/	Three scientific PDF figures.
audits/	Internal proof and literature audits.
data/claims.jsonl	Eight structured claim-ledger records; not an independently validated benchmark.
Original_Calibration_Package.zip	Preserved input used by the legacy verifier.
CITATION.cff, CITATION.bib	Suggested citation and attribution metadata; no DOI has been assigned here.
MANIFEST.sha256	Checksums of the distributed files, excluding the manifest itself.
UPLOAD_GUIDE.md	Manual upload and Windows uploader instructions.
PACKAGING_NOTES.md	Preparation changes and provenance hashes.

The examples are constructed finite mathematical instances. There was no human-subject data collection, observational cohort, or external benchmark collection for this package. AI assistance was used for derivation, implementation, internal review, and release preparation. The original package, reports, code, and proofs provide the provenance chain.

Scientific status and intended use

Status: completed theoretical draft for the stated finite model, with internal review and passing exact implementation checks. External peer review, formal proof-assistant certification, worldwide priority, and empirical sensing superiority remain unestablished.

The framework assumes a known graph, aligned and normalized latent coordinates, known labels and units, a compatible reference, exact trusted calibrations, independently configurable linear sensor-row spaces, and the aligned response operator needed by the observation bridge. A fault affects an entire channel; erasure locations are known and corruption locations are unknown.

The proposed contribution is the combined causal specialization and operational formulation. Rado independent representatives, coding distance, generic cospark, generalized Hamming weights, rational spark hardness, and submodular cover are established foundations credited in the manuscript and literature audit. The finite examples do not establish performance on large, noisy, or physical systems.

Intended uses include proof inspection, reproducible small-instance calibration studies, exact certificate generation, and further work on constrained causal sensing. Open directions include raw-data acquisition and alignment, unreliable trusted calibrations, unknown graph or coordinates, efficient general decoding, optimal conditioning, coupled hardware, and nonlinear extensions. Deployment performance is not evaluated by this collection.

License and citation

No license was specified in the supplied release. This preparation preserves that status and does not assign a new reuse license. See LICENSE_STATUS.md. The citation files offer a suggested joint credit using the names in the source. The manuscript describes preparation roles rather than a formal journal authorship declaration; no journal publication or DOI is asserted.

@misc{nowicki_eve_aithrael_2026,
  author = {Nowicki, Maciej and {Eve (OpenAI AI assistant)}},
  title = {{EVE--AITHRAEL}: Reliable Calibration of Latent Causal Models:
           Exact Fault Tolerance, Hardware Constraints, and Computational Limits},
  year = {2026},
  month = oct,
  note = {Manuscript version 2.0; internally reviewed theoretical research draft.
          Research prepared for Maciej Nowicki with Eve, OpenAI AI assistant}
}

Packaging follows the official dataset-card metadata and viewer configuration documentation. Upload instructions use the current Hugging Face CLI.