Which Particles Defy Their Own Layer? Pre-Registered Rank Divergers in the Standard Model

Background

In a prior experiment, we confirmed that the Functional Proximity Law holds across the Standard Model: hub rank in force_coupling correlates with hub rank in decay_channel more than with mass_proximity (5/5 pre-registered hypotheses confirmed). The W boson was the top hub in both force coupling and decay.

The obvious next question: which specific particles are structural rank outliers -- particles that rank very differently across layers?

This is a discovery-mode question. FPL tells us the law holds; diverger analysis tells us who breaks the pattern.

The Two Experiments

M_PHYSICS_2_divergers_v1 (pre-registered 2026-06-02T16:55:39, hash 6119706e...): 5 hypotheses about which particles would show the largest rank gaps between layers, and whether the diverger count would exceed chance.

M_PHYSICS_3_v1 (pre-registered 2026-06-02T17:23:23, hash 08d934fe...): 5 hypotheses adding permutation-based significance tests (p-values via 500 label shuffles), re-specifying two errored test types from M_PHYSICS_2, and testing the decay channel hub prediction.

Both datasets: sm_particles.json, n=17 particles, 3 layers (force_coupling, decay_channel, mass_proximity), source: PDG 2024.

What IRDME Found

Force Coupling vs Mass Proximity: Rank Gap = 13

The largest rank separation was between force_coupling and mass_proximity:
• photon: force_coupling rank #3 (degree=10), mass_proximity rank #16 (degree=1). Gap = 13.
• gluon: force_coupling rank #4 (degree=7), mass_proximity rank #14 (degree=1). Gap = 10-13.

Photon couples to all electrically charged particles (high force degree) but is massless (minimal mass proximity connections). This rank separation is consistent with known physics: massless force mediators are structurally distinct from massive particles.

h4 (M_PHYSICS_2): at least 3 particles with rank gap >= 10 between force and mass -- CONFIRMED (8 particles showed divergence).

Force Coupling vs Decay Channel: Photon Is Invisible in Decays

Between force coupling and decay channel, photon showed the largest gap: force rank #3, decay rank #17. Gluon: force rank #4, decay rank #16. Both particles mediate forces but rarely appear as endpoints in decay products.

Conversely, muon (force rank #14, decay rank #4) and tau (force rank #11, decay rank #3) show the reverse: high in decay products, low in force coupling.

The Persistent Hubs

Across all three layers, three particles consistently rank in the top 5: w_boson, z_boson, higgs. The W boson was confirmed as rank #1 in mass_proximity (M_PHYSICS_3 h2: CONFIRMED).

Significance Tests (M_PHYSICS_3)

Permutation-based p-values (500 label shuffles per pair):
• r(force_coupling, mass_proximity) = 0.501, p = 0.026 -- CONFIRMED (h1)
• r(force_coupling, decay_channel) = 0.569, p = 0.020 -- CONFIRMED (h4)
• Null model (200 permutations): all three layer pairs significant at p <= 0.030

The rank separation survives label randomization. It is not a degree-distribution artifact.

The Informative Denial

h3 predicted higgs in top-4 of mass_proximity. Result: DENIED -- higgs ranks #5.

Why: bottom quark, top quark, and z_boson all share degree=3 in mass_proximity (same as higgs). The engine's tie-breaking placed higgs at rank 5. The prediction needed max_rank=5 to account for the four-way tie.

This denial is not a scientific failure -- it reveals a metric sensitivity issue. When four particles share the same degree, rank predictions must account for ties. This is a useful calibration finding for designing future hypotheses.

Full Verdict Summary

M_PHYSICS_2 (5 hypotheses): 3/5 CONFIRMED, 2 UNRESOLVED (delta_centrality_direction test type not supported -- re-tested in M_PHYSICS_3).

M_PHYSICS_3 (5 hypotheses): 4/5 CONFIRMED, 1/5 DENIED (higgs tie).

Combined (10 hypotheses, excluding 2 re-specified errors): 7/8 CONFIRMED, 1/8 DENIED.

Honest Interpretation

What this shows: IRDME rank separation in the Standard Model is statistically significant (p <= 0.030) and consistent with known particle physics structure. Photon and gluon rank as outliers between layers in a way that matches what physicists know about massless force mediators.

What this does not show: these are not newly discovered particle categories. The rank clusters (high-force/low-mass, persistent cross-layer hubs, high-decay/low-force) correspond to structure that particle physicists already know. IRDME recovers it, which is a validation result, not a discovery result.

What is still pending: a baseline comparison against degree-only ranking and PCA. Without this, we cannot claim IRDME adds unique explanatory value beyond simpler rank methods. That comparison is the next step in this chain.

What Comes Next

Two open questions from this chain:
• Baseline comparison: Does a simple degree-rank-difference analysis produce the same diverger list as IRDME? If yes, IRDME's framing is equivalent to simpler methods in this domain. If no, IRDME captures something additional.
• Beyond Standard Model: Hypothetical BSM (beyond Standard Model) particles have predicted force couplings and mass ranges. Would they fit into existing rank clusters or create new ones? This is a forward-looking structural prediction test.

Pre-Registration Record

M_PHYSICS_2: hash 6119706e59832266aa44352dcad16f53fdac3128931bf9821f1e1701ae7a589c, timestamp 2026-06-02T16:55:39+00:00, commit e4f5550

M_PHYSICS_3: hash 08d934fe14f6a25f38655b4bec6beb937190948febf5acd6320981d08ba63206, timestamp 2026-06-02T17:23:23+00:00, commit e181948

Full experiment record: github.com/vladi160/preregistrations