Research note · v0.2 · May 2026
Seven findings from the means-test.
Forty-four retention substrates were laid out against eleven axes and means-tested against the published record. Most cells are empty. The ones that are full reveal a coherent set of structural relationships. These are the seven that justify the table.
Finding 01
The Landauer-ratio axis partitions everything.
Log₁₀(Eᵂ / k_B T · ln 2) places every substrate on the energy-efficiency line. The partition is clean and the indictment is immediate.
Biology sits five orders below current AI inference per bit. SRAM also sits at the synapse level. The waste is not in the substrate. The waste is in the abstraction layer that turns "I want a fact" into "spin up seven hundred watts of silicon and run attention across one hundred thousand tokens."
Finding 02
Capacity failure is often a first-order phase transition.
Amit, Gutfreund and Sompolinsky proved it for Hopfield: at α_c ≈ 0.138, all retrieval collapses to a spin glass in a first-order transition. DRAM cliffs at missed refresh. Flash has a hard endurance wall. Cowan's four-plus-or-minus-one is a discontinuity, not a soft taper.
Episodic memory does not phase-transition because the CLS architecture separates the fast hippocampus from the slow neocortex — interference in one is buffered by the other. The axis must distinguish phase-transition substrates from graceful-degradation substrates. That distinction predicts where catastrophic forgetting lives.
Finding 03
τ_information / τ_substrate is the recurring trick.
The same pattern appears across substrates that share nothing else:
The ratio ρ is the axis. When ρ ≫ 1, an active refresh process is mandatory. Lose the refresh and the information is gone in one τ_substrate, regardless of substrate. This was hidden in v0.1 as a binary "refresh required?" column. The honest axis is the ratio.
Finding 04
Forgetting is multi-exponential, not single-decay.
Murre and Dros (2015) replicated Ebbinghaus. A single exponential is the textbook simplification. A power law fits better. A summed exponential fits best (ΔAIC = 1.6). There is a twenty-four-hour upward boost from sleep-driven consolidation.
This is what the CLS framework predicts: hippocampal τ plus neocortical τ produces the observed shape. A single τ axis is insufficient. The honest treatment is a spectrum, or equivalently the number of consolidation tiers — which is why the cascade has eight.
Finding 05
The quantum corner is structurally empty.
Trapped-ion ¹⁷¹Yb⁺ at T₂ > 1 hour, capacity = 1 qubit. NV centers at T₂ ≈ 1 s, capacity = 1 qubit. They occupy (high τ, very low C, low T_operating) — a region nothing classical or biological enters.
This is structural, not coincidental: anything classical or biological with high τ must have high capacity to be useful at the scale of its substrate. Quantum systems trade capacity for coherence by their nature. The table predicts the trade-off as a constraint, not a contingency.
Finding 06
Verifiability converges on five regimes across substrates.
The axis is discrete, narrow, and recurs everywhere:
Vedic recitation and the adaptive immune system arrive at the same axis position by entirely different mechanisms. This is the strongest evidence that V is a real axis, not a construct.
Finding 07
Reconsolidation is not unique to brains.
Recall as a write event recurs on far more substrates than the cognitive literature catalogs:
Recall is a write event on most substrates that hold information at all. The "free read" model is the exception, not the rule. The cascade treats this as the default and audits where recall costs nothing versus where it pays its share.
The Kepler step
Eᵂ · τ_half ≥ k(substrate).
With log₁₀(Eᵂ / k_B T · ln 2) and log₁₀(τ_half) populated for the working substrates, the candidate relation is an envelope on the (log E, log τ) plane. Energy-time uncertainty applied to information: the longer you want to remember a bit, the more energy you must commit to writing it. The constant k depends on substrate class — silicon, biological, molecular, quantum — and is testable as cells fill.
This is the F = ma move. The table is the data the formula is fitted to. Until it is fitted, the structure is a hypothesis. Once fitted, the empties at well-attested intersections become predictions.