Hydrogen Null Result

Status: null-result Domain: physics Source: → debunked Aug 2025 paper (with Grok)

What We Know

• Smooth functions of n (like hydrogen ΔE(n) = 13.6(2n+1)/[n²(n+1)²]) CANNOT encode prime structure
• Primality requires multiplicative structure (factorisation) — smooth functions only see n as a real number
• Old Aug 2025 hydrogen paper was cherry-picked — properly debunked with null models (Apr 28, 2026)
• Critical methodological lesson: Don’t look for primes in existing simple physics. BUILD prime-ratio physics (v3/v4 boards) and measure what happens.
• Any smooth function evaluated at prime indices will show “patterns” that are artifacts of the function’s smoothness, not prime structure

The Parameter–Function Distinction (6 Jun 2026)

Hydrogen’s smooth energy function encodes no primes — but its constants are deeply prime-structured:

• α = 1/137 (137 is prime, the 33rd prime, 33=3×11)
• mₚ/mₑ ≈ 1836 = 2² × 3³ × 17

The prime structure is in the parameters, not the function. The smooth function is the shadow; the constants are the sunlight. This refines the null result: it’s not that hydrogen lacks prime structure — it’s that the structure lives in the coupling constants and mass ratios, not in the functional form E(n). See [[natural-units-prime-ladder]].

What We Don’t Know

• Q-HN-01: Are there ANY existing physical systems (not smooth) that naturally encode prime structure? (Nuclear binding energy may be one — see sopfr)

Relationships

• [[sopfr-binding-energy]] — nature: contradicts (partially) — sopfr IS multiplicative and DOES correlate with physics; hydrogen is smooth and doesn’t
• [[prime-composite-duality]] — nature: supports — confirms that primes live in multiplicative structure, not additive/smooth structure
• [[v3-experimental-proof]] — nature: supports — the lesson “build, don’t find” directly motivated the v3 experimental programme
• [[square-root-problem]] — nature: analogous-to — both are about what mathematical structure CAN’T do

Bridging Potential

• The null result IS the bridge: it tells us WHERE NOT to look, which is as valuable as knowing where to look
• Sharpens methodology for all future investigations

Key Evidence

• Null model comparison showing smooth functions produce identical “patterns” at prime indices
• Debunking analysis (Apr 28, 2026)