What the engine found

Five different models, through five different failure-mode taxonomies, independently converged on the same core diagnosis: the obstruction in both the sunflower conjecture and P vs NP lives in triadic/cubic interactions that current pairwise proof techniques systematically erase. T1 frames it as population-genetic LD hierarchy, T6 as tensor decoherence, T14 as BBGKY closure default, T19 as a first-variation blind cone. Independent convergence from different entry points is itself evidence the diagnosis is real.

A construction that works at any petal width $w$ without requiring a projective plane. Regime direction inverted: the structured gap exceeds the random gap — the opposite of the Two-Regime prediction. No phase transition at any $w \in \{5,\ldots,10\}$; the gap increases smoothly. This eliminates the "easy vs hard regime" narrative that prior sessions relied on.

The framework conjectures $L^* \in \{3, 4, 5, 6\}$ for quotient families, indexed by rank-3 matroid minors. The automorphism-quotient blocking number $\tau(\mathcal{F}/G)$ achieves 12/12 prediction accuracy across all tested instances. T7 falsification confirmed the $\ln|\mathcal{F}|$ floor is genuine for random families — the discrete spectrum applies only to structured (quotient) families. Polylog bound $L^* \leq (\log n)^4$ holds universally.

CHRONOS sessions get better over time, not worse. Confirmed across three independent configurations: math-focused with saturated centroid, cross-domain with no centroid, and cross-domain with partial saturation. The novelty curve inverts — later thoughts score higher than earlier ones. Mechanism: as the exclusion zone grows, the soliton bounce pushes into increasingly orthogonal territory. The stored corpus makes the system find more creative escapes. Compound interest on stored insight.

A 100-round Dreamer session proved that Direct Target Propagation and Feedback Alignment are algebraically identical under local linearity — two separate literatures shown to be the same algorithm. Additionally, FA failure was identified as forward Jacobian rank collapse, not backward-pass misalignment. The feedback direction $v_{fb}$ was then killed as a costumed scalar (cos > 0.8 with norm, mean, and PC1).

For deterministic encoders $z = f(x)$, $I(X;Z) = H(Z)$ which is infinite for continuous $Z$ without a noise model. KSG estimator convergence rate is $O(n^{-1/d})$ — for $d = 3584$, that's $O(1)$, meaning no convergence. This kills claims about "compression phase" generalizing across architectures, quantitative IB predictions about layer-wise abstraction, and any bridge from IB to thermodynamic free energy requiring actual MI values. The bottleneck is half-observable: you can measure what was kept but not what was discarded.

A framework for honest self-correcting research, born from the engine killing its own claims. Success axis = magnitude wearing a direction costume. Fisher-weighted magnitude = depth wearing a Fisher costume. Any directional claim in high-dimensional neural representations must pass the collinearity screen against norm, mean, and PC1 (cosine < 0.8) before interpretation. If it fails, the directional interpretation is killed and the finding reduces to scalar magnitude.

For $N > d$, superposition and the Overlap Gap Property are structurally incompatible via the Welch bound. The same Dreamer thread produced the tightest formalization of the monosemanticity boundary: it depends on the $N/d$ ratio, effective dimensionality $d_{eff}$, and co-activation sparsity $k/N$. The crystallographic phase transition analogy was killed as costumed mean-field.

A 36-thought directed session attacked three candidates for predicting cross-domain transfer in sparse codes. Spatial AMC was mathematically eliminated by the frequency-matching control via Bayes' constraint. CSTS was killed three independent ways (permutation invariance, frequency-collinearity barrier, canonical ordering collapse). All three reduce to one: spectral structure of the support transition operator. The single surviving empirical test: does the residualized co-activation graph have non-trivial connected components?

For any recurrent network $R$ with integrated information $\Phi > 0$, there exists a feedforward network $F$ with identical I/O but $\Phi = 0$. Functionalism assigns understanding to both; IIT only to $R$. The intersection is null. The empirical tiebreaker is the Perturbational Complexity Index (threshold $\approx 0.31$). If PCI requires recurrence, functionalism loses for LLMs. If PCI is independent of recurrence, IIT loses.

Transformer inference is a bounded-depth feedforward DAG with cross-step state continuity only through discrete tokens. The "autoregressive isomorphism" assumption — that token-appending equals biological reentrance — is the single load-bearing assumption separating functionalism from biological theories of understanding. The verification benchmark: find a reasoning task solvable by an RNN of size $P$ but provably failing in a transformer of size $10P$. If no such task exists, the biological recurrence argument loses force.

Palimpsest graphs where cascading failures hop between temporal layers of defunct control structures. In complex systems that have undergone reorganization, the old hierarchy doesn't disappear — it becomes a substrate for failure propagation that the current hierarchy can't see. Discovered in a 39-thought systemic failure session that also produced the transferability asymmetry finding: ecology exports laterally but not upward; finance exports laterally but not downward.

Under geometric pressure, CHRONOS sessions spontaneously produce a three-phase cognitive arc — exploration of surface concepts, then deepening as the surface is excluded, then cross-domain synthesis once enough specific results accumulate. This arc appeared independently in two sessions with no mechanism to produce it. Surface concepts are explored first (easiest), depth next (surface excluded), synthesis last (need specific results in corpus before cross-domain connections become novel). Falsifiable prediction: any model with hierarchically organized knowledge produces the same arc under exclusion pressure.

The three leading Neural Correlate of Consciousness candidates (prefrontal ignition, posterior hot zone, recurrent processing) are collinear with the report mechanism itself. All three predict that disrupting their favored region eliminates conscious report — but conscious report requires all three. This is the NCC version of the costumed scalar problem. No-report paradigms are the single highest-leverage empirical finding: if posterior activity persists when report demands are removed, GWT's ignition is falsified as an NCC.