Original multiplier
7modulo 31
CIMMS Systems LLCInteractive mathematics laboratory
Slavin Mirror Analyzer.
Choose an odd prime and a multiplier. The analyzer removes every shift label, then reconstructs the multiplier up to its unavoidable inverse mirror.
Proven resultSᵣ = Sᵤ ⇔ u = r or r⁻¹ (mod p)
Inverse mirror
97 × 9 ≡ 1 (mod 31)Recovered class
{7, 9}Verified from the unlabeled spectrumUnlabeled spectrum Sᵣ
31 values, sorted without shift labels
Parity anchor Dᵣ(0)620
-434-434-310-310-279-279-217-217-186-186-124-124-93-93-62-62-31-319393155155217217248248279279434434620Reflection evidence
Dᵣ(t) = Dᵣ(−t)
1 ↔ 30279 = 279
2 ↔ 29217 = 217
3 ↔ 28434 = 434
4 ↔ 27-31 = -31
5 ↔ 26-217 = -217
6 ↔ 25-124 = -124
7 ↔ 24248 = 248
8 ↔ 23-62 = -62
Modular fingerprint
The anchor reveals the pair.
−24Dᵣ(0)/p mod p= 16r + r⁻¹ mod p= 16What the analyzer proves
The labels disappear. The identity survives.
Reflection pairs every nonzero shift with its negative. That makes the zero-shift value the spectrum’s unique odd-multiplicity anchor. For p > 3, the anchor yields the modular fingerprint r + r⁻¹ ≡ −24Dᵣ(0)/p (mod p). The complete spectrum then verifies the recovered mirror class.
This is an exact theorem demonstration and anomaly detector—not an encryption system or a complete error-correcting code.
Read the published preprint on Zenodo →