Spatial Displacement Theory · Section Paper VI · Prepared for Submission
The Engine: laws.hpp as Single Source of Truth, the Provenance Schema, and the Benchmark Ledger
Melbourne, Australia · July 2026 · Atlas Chapter Five — The Engine
Abstract. The framework's numerical claims are not a manuscript's — they compile. A single header, Engine/include/sdt/laws.hpp, is the source of truth: every constant, force law, and derivation flows through namespace sdt::laws, whose sub-namespaces mirror the Six Laws, with bridge (the k-hierarchy and koppa), atomic, nuclear, and coulomb_identity carrying the domain functions. Whitelist discipline is structural — a quantity absent from sdt::laws::measured is not an admissible input — and every load-bearing constant carries a machine-readable provenance block: provenance status, correspondence status, input dependency, certification class A–F, delete-test assertion, risk flag. The benchmark executable self-reports PASS/FAIL against measured values within stated tolerances, with IDENTITY and CALIBRATED rows labelled as such rather than counted as predictions; the audited ledger stands at 46/57 earned passes, 11 identities, 2 calibrated, 0 failures, 11 pending. The suite now also carries the nuclear closure schedule as a compile-time proof — a static_assert that the deuteron-tier/triton-belt alternation rebuilds every measured magic number — and suite row B38 tallies the parity-lock predicate at 7/7 mono-isotopic grips and 12/12 combined checks.
Keywords: single source of truth · whitelist discipline · provenance blocks · certification classes · benchmark ledger · compile-time closure proof
1. Architecture
Header-only C++20, constexpr-heavy, zero external dependencies. Downstream headers (cosmology, magnetosphere, neutrino, state28d) and every benchmark and investigation tool include laws.hpp and may not redefine what it exposes. Orbital mechanics computes without G, nuclear structure without quark degrees of freedom, cosmological observables without a dark sector — not as a stylistic choice but because those symbols do not exist in the namespace.
2. The provenance schema
| Field | Content |
|---|---|
| provenance_status | SDT-derived · SDT-posited · calibrated · observed-input · unresolved |
| correspondence_status | known-match · internal-only · novel · measured |
| input_dependency | primitive-whitelist · measured-observable · calibrated-target · definitional-identity |
| class | A (axiom) · B (whitelist derivation) · C (derived, passes delete-test) · D (computed/observed correlation) · E (calibrated) · F (definitional identity) · X (observed input conditioning a chain) |
| circularity_assertion | the delete-test statement — what vanishes if the matched target is removed |
| risk_flag | load-bearing caveats, stated at the definition site |
The schema keeps the register at the point of use: Peff is class E with "fails delete-test" on its own definition line; the coupling identity kee² = αℏc is class F with the tautology named; the koppa-per-baryon constant carries its ℓP-convention disclosure. A reader auditing the framework audits the header.
3. The benchmark ledger
The suite (benchmarks_suite.cpp, B01 and up) compares SDT-derived values to measured constants within stated tolerances and prints its own report. Ledger discipline: identity rows (z·k² = 1 among them) are labelled IDENTITY and carry no evidential weight; calibrated rows name their anchor; a historical fabricated row (a Lamb-interval literal with no derivation behind it) was deleted with authorization and its retraction is part of the record. Two structural rows are new with the closure-schedule canon change:
Equation (3) is a compile-time proof that the deuteron-tier/triton-belt alternation rebuilds the measured closure sequence: if the schedule and the sequence ever disagree, the header fails to compile. As of 2026-07-30 the capacities themselves are DERIVED from two closed forms — tier F(n) = (n+1)(n+2), belt B(n) = 2(n+1) — with the forward prediction closure(7) = 184; the descent onset n = 3 remains read from the data, and the provenance block says so at the definition site.
4. Build and reproduction
Windows/MSVC is the primary environment (UTF-8 sources require /utf-8); GCC and Clang build unmodified. Investigation tools compile standalone against the header. Reports under ATOMICUS/reports/ are generated outputs — the tool is the source; regeneration, not hand-editing, is the change mechanism.
5. Certification
| Item | Value | Status |
|---|---|---|
| Single-source discipline | one header | STRUCTURAL — no constant defined twice |
| Whitelist enforcement | sdt::laws::measured | STRUCTURAL — absent ⟹ inadmissible |
| Benchmark ledger | eq. (2) | AUDITED — identities and calibrations labelled; one retraction on record |
| Closure-schedule proof | eq. (3) | COMPILE-TIME — arithmetic of the alternation; capacities [measured, schedule-named] |
| Parity-lock tally | eq. (4) | SUITE ROW B38 — exact |
Methodological declaration. The engine contains no gravitational constant, no weighed mass as a fundamental, no wavefunction, no metric tensor, no quark field, and no dark-sector parameter — such symbols are absent from the namespace, so their import is a compile error, not a policy. Certification labels live at definition sites; the benchmark report separates earned passes from identities and calibrations. The header is the audit surface.
References
- Engine/include/sdt/laws.hpp (v6.0, Six-Law framework) and downstream headers.
- Benchmarks/benchmarks_suite.cpp; Benchmarks/nuclear_grammar_output.txt; Benchmarks/CMakeLists.txt.
- Audits/ — the provenance and correspondence audit set (formulations census, contamination audit, paradox census).
- Section Papers II and IV of this series (the laws the engine encodes; the schedule it proves).