E47 Validation Scope
What is validated
The software validates the finite-dimensional algebraic construction of the E47 spectral kernel on $V_2^{\otimes 3}$.
Validated properties include:
- Carrier dimension: $125$
- SU(2) Casimir spectrum and multiplicities
- Kernel operator: $K = (C - 6I)(C - 30I)$
- Kernel dimension: $47$
- Decomposition: $5V_2 \oplus 2V_5$
- Hermiticity of projector
- Projector idempotence: $P^2 = P$
- Projector rank: $47$
- Kernel annihilation: $KP = 0$
- Discrete dephasing channel contraction
- Continuous semigroup: $S(t) = \exp(-tK^2)$
- Semigroup composition law
- K² spectral gap: $11664$
- Asymptotic convergence to $P_{47}$
- QuTiP reconstruction where available
What is not validated
This repository does not, by itself, establish:
- A physical realization of $E_{47}$
- Experimental evidence for a new field or particle
- Equivalence to a physical quantum error-correcting device
- Claims about cosmology, gravity, consciousness, biology, or UAP phenomena
- Uniqueness of the $47/125$ ratio outside this representation
- Derivation of measured physical constants
- Scalability beyond the tested finite-dimensional construction
- Hardware performance claims
- Global PDE regularity results
- Operational feasibility or resource requirements
Evidence classes
Claims in this package are categorized as follows:
- E0: Exact mathematical identities and symbolic proofs
- E1: Deterministic machine reconstruction (floating-point arithmetic)
- E2: Numerical or simulation evidence (QuTiP, Monte Carlo)
- E3: External independent replication by other research groups
- H0: Proposed hardware protocol (blueprint phase)
- H1: Completed hardware test with experimental data
The current package primarily supports E0 and E1 claims, with limited E2 coverage through QuTiP and numerical validation.
Numerical interpretation
Residuals below tolerance (typically $10^{-10}$ to $10^{-13}$) indicate agreement with the finite-dimensional model and implementation precision.
They are not substitutes for proof where an exact theorem has not been supplied. Numerical validation addresses:
- Floating-point fidelity of constructions
- Spectrum alignment with theory
- Operator property consistency
It does not address:
- Existence of infinite-dimensional generalizations
- Physical realizability
- Uniqueness beyond the finite-dimensional setting
Failure behavior
Validation functions return structured certificates with detailed status fields.
validate_* functions return certificate objects without raising exceptionsrequire_* functions raise aggregated exceptions when validation fails- The certificate-generation script exits with code
0 for valid results, 1 for invalid results with --allow-invalid, and 2 for validation failure without that flag
Invalid certificates are faithfully serialized and recorded (for audit and debugging) unless explicitly rejected by require_* guards.
Certificate reproducibility
Certificates include:
- Python version and implementation (CPython, PyPy, etc.)
- NumPy, SciPy, and QuTiP versions
- Operating system and architecture
- Repository commit SHA
- Generation timestamp (UTC)
- Numerical tolerance thresholds
This enables bit-for-bit reproduction of the certificate and identification of any deviations caused by environment changes.
Relationship to peer review
This validation package provides:
- Executable specifications of the E47 algebra
- Automated detection of construction errors
- Detailed numerical residuals for human review
- Reproducible artifact generation
It does not replace:
- Mathematical peer review of novel theorems
- Experimental validation for physical claims
- Independent verification by other researchers
- Domain-expert certification of impact
Scope document updated: 2026-07-21
Validation package: src/e47/
Repository: https://github.com/nicholaskouns-create/E47-Kartekeya