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Jaehong Oh

χONN

ONN Research Status — 2026

Current, audited status of the ONN / ORTSF programme: the central higher-order question resolved to a scoped No-Go boundary, one modest positive survived, control results were narrowed to model-level certificates, and the programme moved to ULR.

updated 437 words2 min read

Rewritten 2026-07-10 against the authoritative record in onn_ws/ONN. An earlier AI-generated version attributed settled results and numbers to the papers that are not present in the source; those are removed here.

Bottom line

The ONN / ORTSF programme's central question — is measured higher-order relational structure a usable discriminative resource beyond pairwise? — resolved to a rigorous negative / boundary result, not a positive framework. onn_ws/ONN is now archived; live work continues under ULR.

What is settled

  1. The Two Ceilings (No-Go), proven. Under a complete-pairwise observation contract, on consistent, complete, finite-π1\pi_1 scenes, every admissible measured higher-order readout is pairwise-measurable, exact/zero, label-injected, or noise — so a Bayes-optimal pairwise decoder gains no information from it. Witness: the coker⁡δ1\operatorname{coker}\delta_1 area datum is analytically reconstructible from pairwise positions to the noise floor (residual 0.050≈σ0.050 \approx \sigma). Scope: does not broadly refute higher-order/sheaf networks — each escape violates a named hypothesis (incompleteness, dynamics, external sensor, infinite-cd topology, bounded capacity).
  2. A modest, non-higher-order positive. The direction of the measured curvature field carries signal beyond magnitude (E1b Q-weak =+0.115/+0.120= +0.115/+0.120 AUROC, pass-fraction 1.01.0; selection-corrected single-arm ≈+0.08\approx +0.08–0.100.10).
  3. ORTSF control results (standard, narrowly scoped). For a constructed linear plant with integrating-controller model, a phase-margin gate Δtmax⁡=φPM/ωc\Delta t_{\max} = \varphi_{\mathrm{PM}}/\omega_c is implemented and tested in a guarded pipeline. Separately, the scalar single-mode recurrence et+1=ρet−Kcet−de_{t+1}=\rho e_t-K_c e_{t-d} is stable for every integer delay when ρ+∣Kc∣<1\rho+|K_c|<1. Neither result establishes coupled multimode or deployed PD controller stability; those mappings remain open. See the certificate page.
  4. Methodology finding. A learner is neither necessary nor sufficient to judge an information / reconstructibility claim — decide analytically (false positive Ew2E_{w_2}, false negative PcokerP_{\mathrm{coker}}).

What was refuted / did not survive audit

  • The higher-order loop advantage (the once-headlined "loop beats edge +0.165+0.165") does not survive (E1b Q-strong +0.045/+0.073+0.045/+0.073, Holm p=0.22p = 0.22, GRAY).
  • "Topology preservation" as stated (Betti preserved, a "CSR →1.0\to 1.0" metric): the real result is conditional harmonic-subspace preservation only (hard anchor); the soft-anchor version is refuted for dim⁡H>0\dim H > 0. See the canonical audit.
  • A cohomological Lyapunov certificate: no such object exists. See the audit.
  • The original paper's 7–8 grand theorems: 0 of 8 survive as written.
  • Every legacy number — CSR = 1.0, τ_max = 177 μs, "3M-node", 99.75%, topology-loss 11.68 → 1.15, c_J ≤ 0.7 — is not present in the source and has been removed.

Where it is going

The live programme is ULR (Unified Latent Representation). The published ONN + ORTSF paper remains the paper of record for the original framing; this page is the current, audited status.