On this page
Binary waveform spectrum and correlation contract audit
First dossier, 9 October 2026 Australia/Brisbane. Initial decision: Prototype diagnostics; defer new sequence generator. Buyer demand, commercial novelty and profitability remain unvalidated.
Research finding
The latest family 076 manuscript claims uniformly ultraflat real sign polynomials through all sufficiently large lengths and unbounded binary merit factors. The selected formal scope supports asymptotically minimal upper maxima and finite-Lp flatness, explicitly without an effective convergence rate or signing algorithm. Family 179 separately rules out long binary Barker sequences beyond the stated finite length set and classifies real circulant Hadamard orders.
Problem and buyer
Radar and communication R&D teams optimize binary codes under spectral and autocorrelation constraints. A design review can confuse a low aperiodic peak, high integrated merit factor, zero periodic correlation and uniform spectral flatness, although these are different objectives.
What the finding could enable
A waveform design contract framework can record the exact objective, calculate finite correlations, compare sampled spectra and keep existential new targets separate from executable design rules. A new high-merit-factor generator would be valuable if the construction becomes effective and works at relevant finite lengths; that capability has not been extracted here.
Technical and commercial limits
No improved signing algorithm, finite convergence rate or hardware result follows from the inspected formal statements. Sampled frequencies cannot certify the full unit circle. Pulse shaping, Doppler, bandwidth, power and hardware quantization create additional objectives. The latest uniform two-sided flatness result does not inherit the older selected formal badge.
Minimal architecture
Binary sequence import -> exact integer aperiodic/periodic correlations -> integrated merit factor -> sampled spectrum and endpoint checks -> objective/constraint manifest -> waveform simulator connector -> source-linked report. The local audit_binary_waveform.py prototype implements the finite diagnostics with bounded computational budgets; it does not generate new improved codes.
Existing alternatives and differentiation
SciPy already provides direct and FFT correlation routines, including matched-filter examples. A standalone correlation calculator has weak differentiation. The proposed value is objective consistency, exact finite evidence and a bridge to an effective new construction if one becomes available. SciPy correlation API.
Monetization hypothesis
Hypothesis: AUD 6,000–15,000 for an R&D code-assessment integration. At a hypothetical AUD 9,000 fee, 35 specialist hours costed at AUD 180/hour consume AUD 6,300 before simulator access, sales and overhead. Higher-value licensing would require demonstrated waveform improvement on a buyer’s full constraints, which is absent.
Validation experiment
The prototype checks a known length-13 Barker sequence, an order-four zero-periodic-correlation sequence and an all-ones sequence with exact merit factor 4/7. Compare candidate families under the same pulse and Doppler model; sampled spectral plots must remain labeled as samples. Require an effective construction before testing a new-theorem performance advantage.
Conditions to reject or defer
Reject if current design tools already catch objective mismatches or buyers will pay only for a better code, not a review. Defer a new waveform generator until finite construction, runtime and full-system improvement are demonstrated.
Next concrete action
Read the latest construction for effective choices and relevant finite length thresholds. Integrate the existing finite diagnostic with one public waveform model first.
Pinned research sources
- Family 076: Ultraflat real Littlewood polynomials.
- Family 076: selected formal scope; no independent check run here.
- Family 179: The circulant Hadamard conjecture.
- Family 179: selected formal scope; no independent check run here.