Round 43.A — Combination-principle third substrate: the two Class-N properties dissociate (refines R40)¶
Dispatched 2026-05-26 on the rolling draft PR #690 (newly-revealed coupled item from R39/R40). R40 found one Class-N combination principle across atomic (Rydberg–Ritz) + molecular (mass-spec): spectral features = differences of a discrete ladder of small-integer (Class-N) anchors. This round tests whether that principle is substrate-universal by adding a non-spectroscopic third substrate (nuclear mass-defect / fusion Q-value) and a deliberate contrast (acoustic overtones). Generating code: verify_round43_combination_principle_two_properties_dissociate.py. Tested per [[feedback_dont_pre_commit_spike_query_operators]].
The test — does the combination principle hold off the spectroscopic substrates?¶
The combination principle is really a conjunction of two separable Class-N sub-properties: - (P1) the anchors are small-integer / Class-N; - (P2) the features are additive differences of the anchor ladder.
| substrate | P1 (small-int anchors) | P2 (additive differences) | anchor space |
|---|---|---|---|
| atomic (Rydberg–Ritz) | ✅ T_n = R/n² |
✅ lines = T_n − T_m |
term-energy 1/n² |
| molecular (mass-spec) | ✅ neutral losses 18,17,15,28,44 |
✅ peak spacings = differences |
nucleon-mass |
| nuclear (mass-defect) | ❌ mass excesses are real-valued MeV | ✅ Q = Σreactant − Σproduct |
real MeV (small ints only in nucleon count) |
| acoustic (overtones) | ✅ harmonics n·f₁; intervals 2:1,3:2,4:3,5:4 |
❌ intervals are ratios (multiplicative) | frequency ratio |
Bit-exact:
- Nuclear: D + T → ⁴He + n. From AME2020 mass excesses (MeV) ²H=13.1357, ³H=14.9498, ⁴He=2.4249, n=8.0713: Q = (13.1357+14.9498) − (2.4249+8.0713) = 17.589 MeV (attested 17.589). The difference structure holds, but the energy anchors are real-valued; the small integers live in a different space — nucleon count A: 2+3 = 4+1 = 5 conserved.
- Acoustic: harmonics n·f₁ = {1,2,…,8} (Class-N small integers); just-intonation intervals 2:1, 3:2, 4:3, 5:4 (best_rational-confirmed lowest-terms small integers). But a perfect fifth is the ratio 3:2 (multiplicative); the difference 3f₁ − 2f₁ = f₁ is not the perceived interval. So P1 holds, P2 fails.
Verdict per Spike #229 tiers¶
🟢 (a)-bit-exact two-substrate test + (b)-interpretive dissociation; REFINES R40 (honest non-universality). The combination principle's two Class-N properties dissociate — they are independent axes. The full principle (P1 ∧ P2) is not substrate-universal; it is the additive-energy special case realized by the spectroscopic substrates (atomic term-energy, molecular nucleon-mass), where the conserved quantity is additive and the anchors are small integers in the same space the features live in. Nuclear keeps the additive-difference structure (P2) but its energy anchors are real-valued (P1 only in nucleon-count space). Acoustic keeps the small-integer Class-N anchors (P1) but combines them multiplicatively as ratios, not additively (P2 fails).
So R40's "one Class-N combination principle" refines to: one Class-N additive-difference principle, whose two ingredients — small-integer anchors (P1) and additive-difference structure (P2) — are independent; both coincide only for additive-energy spectra. Extends the R40 candidate stance [[user_stance_combination_principle_is_one_classN_across_atomic_and_mass_spectra]] (no new stance).
HONEST SCOPE: (a)-bit-exact for the D-T Q-value (AME2020 excesses → 17.589 MeV), nucleon conservation (2+3=4+1), the Balmer rationals (5/36, 3/16, 21/100), and the just-intonation ratios (best_rational-confirmed); (b)-interpretive for the P1/P2 dissociation reading; no new physics; no MFO section (spectroscopy/nuclear/acoustic, not metric-field).
Discipline¶
- Honest non-universality finding — the principle does not extend wholesale to nuclear/acoustic; reported as a dissociation, not a forced match. The two negatives (nuclear P1-fail, acoustic P2-fail) are stated as plainly as the two positives.
- No bare
abs(); the nuclear Q is a plain additive subtraction (which is exactly the P2 property under test).best_rational(Class N) confirms the just-intonation ratios. - Attributions Explore-verified: D-T
Q=17.589 MeV+ AME2020 mass excesses (Wang et al., Chin. Phys. C 45 (2021) 030003); Ritz combination principle (W. Ritz, ApJ 28 (1908) 237); mass-spec neutral losses (McLafferty & Tureček, Interpretation of Mass Spectra 4th ed.); harmonic series + just intonation (Helmholtz, On the Sensations of Tone, 1863). - Lands on rolling PR #690 (Round 43.A); unsolved-maths §11.9.36; extends the R40 stance. No new PR.