Canonical laboratories of From Bell to Tsirelson without Hilbert-space formalism: a deterministic nonlocal apparatus of the Vector System (SV) with a ternary alphabet, uniqueness of the coupled factual angular correlator, and a structural derivation of the quantum bound

Reproducible laboratory set — From Bell to Tsirelson without Hilbert-space formalism in the Vectorial System SV

A set of six canonical Python laboratories that verify, by deterministic computation, the structural articulation of the CHSH-SV apparatus of From Bell to Tsirelson without Hilbert-space formalism (Lloret Egea, 2026) on the canonical cell SV(3, 9) and the family SV(b, b²) for b ∈ {3, 4, 5, 7, 9, 11}. Each laboratory checks a specific doctrinal section of the canonical document and returns a deterministic numerical verdict together with structured diagnostic output keyed to the unified error catalogue (codes E-01 through E-09) under a strict no-silent-passes policy.

Package content (laboratorios.zip): eight files under the root folder laboratorios/ comprising the E-01 to E-09 error catalogue (CATALOGO-DE-ERRORES.md), the aggregated runner runner.py, and the six canonical laboratories LAB-01 through LAB-06.

Catalogue of the six laboratories: factual saturation |S_SV| = 2√2 on the family of cells SV(b, b²) (Theorem 11.2.1, §11.2); separable factorization on the regime R₀ — cardinality |R₀(Q)| = 260 on SV(3, 9) under the SV ternary encoding (0 ↦ 0, 1 ↦ +1, U ↦ −1), modular shadow T(v; Q) ≡ 0 (mod 2) over 𝔽₂, and bound |X(v)| ≤ 2 (Lemma 7.4.1, §13.9); strict monotonicity over the fine sweep [χ_min, 1] (Postulate 11.1.1, §11.1); equivalence with the quantum correlator C_SV(δ) = E_QM(α, β) (Theorem 10.2.1, §10.2); uniqueness of the coupled factual angular correlator under the axiom system A1–A9 (§§9–10); and A9 faithfulness via the kernel test (Lemma 9.4.1, §9.4).

Canonical aptitude: the six laboratories are APT (exit code 0, all verifications within operational tolerance) on the canonical structural-articulation input; the aggregated runner's global verdict is |S_SV|_sat = 2√2 with saturation of the Tsirelson bound on R₂★ and CHSH ≤ 2 on R₀ (APT).

Deterministic nature: each laboratory is strictly deterministic. Same input produces same output to IEEE 754 machine precision (operational tolerance |·| < 1e-14, and exact for combinatorial verifications). The single use of a pseudorandom generator (LAB-04) is fixed by np.random.seed(42) to guarantee cross-platform reproducibility. The set does not use opaque inference, sampling, probability, or inductive learning. Compliant with the constitutive prohibitions P.1, P.2, and P.4 of the Vectorial System SV corpus.

Dependencies: only the Python standard library (version ≥ 3.10) and NumPy. No further external dependencies.

Reproducibility: terminal execution via python runner.py from the laboratorios/ folder. Human-readable output to console; the runner returns exit code 0 if the six laboratories pass all verifications and exit code 1 otherwise.

Subordination clause: the laboratory set is subordinated to the canonical document From Bell to Tsirelson without Hilbert-space formalism: a nonlocal deterministic apparatus of the Vectorial System SV (Lloret Egea, 2026). Its sole function is to verify and check, by deterministic computation, the statements of the canonical document. It does not introduce new doctrinal content. In case of discrepancy between the laboratory set and the canonical document, the canonical document prevails.

Cryptographic integrity and authenticity

Alongside the laboratorios.zip file, two integrity and authenticity files are published, enabling independent verification by third parties of the deposit's provenance and date of existence:

1. laboratorios_zip_signed.csig — Author's digital signature on laboratorios.zip in DER PKCS#7 Signed Data format (standard CMS signature). It enables cryptographic verification that laboratorios.zip has been signed by Juan Antonio Lloret Egea on 2026-05-04 at 06:25:17 UTC, under the qualified personal certificate issued by AC FNMT Usuarios (FNMT-RCM, Spain) within the eIDAS framework. The .csig file contains the author's digital signature and full certificate chain (AC RAIZ FNMT-RCM → AC FNMT Usuarios → signer); verification is performed by third parties using OpenSSL or any other PKCS#7-compatible tool.
2. laboratorios_zip.ots — OpenTimestamps timestamp of laboratorios.zip with cryptographic anchoring verifiable on the Bitcoin blockchain through the calendar servers alice.btc.calendar.opentimestamps.org, bob.btc.calendar.opentimestamps.org, and finney.calendar.eternitywall.com. It demonstrates irrefutably that laboratorios.zip exists in its exact content as of the timestamping date, with no possibility of retrospective alteration. Verification is performed by third parties using the OpenTimestamps client (https://opentimestamps.org).

SHA-256 of laboratorios.zip: 7a34823d351529c152d8744879f2256d38f8a11444fac1535ea28be8a53f8335

Any subsequent modification of the laboratorios.zip file would invalidate both the digital signature and the timestamp, ensuring the structural integrity of the deposit.

Author: Juan Antonio Lloret Egea (Instituto Tecnológico Virtual de la Inteligencia Artificial para el Español, ITVIA) — ORCID 0000-0002-6634-3351

Publisher: IA eñ™ — La Biblia de la IA™ (ITVIA) — ISSN 2695-6411

License: CC BY-NC-ND 4.0 — Protected by CEDRO (https://www.cedro.org/english?lng=en)

© 2026 Juan Antonio Lloret Egea. All rights reserved.