Science progresses via a collapsing of ontology into the new. A new framework emerges that alters how we define reality (ontology). The old ontology collapses under the weight of what it can no longer explain. The new order of meaning emerges, whereby yesterday’s observations are redeemed from their isolation and reinterpreted as signs of a deeper order. Examples of this include the shift from the geocentric (Earth-centered) to the heliocentric model of the universe. Or the transition from Newtonian mechanics to Einsteinian relativity.
The earlier observations are not simply thrown away. They are preserved, though their meaning may change. They become local approximations, or surface phenomena inside a more expressive conceptual universe. Classical genetics concepts (trait inheritence, mendelian genetics and family pedigrees) began to be integrated with and supplemented by molecular biology. We came to understand transcription, regulatory networks, epigenetics and chromatin state, but we do not discard old experiments (pea plants!) inheritance curves are still useful, we reinterpret them. Preserving the valid local relationships while embedding them into a higher-dimensional conceptual system.
This is explained mathematically in category theory, the Left Kan extension (sidenote: Kan extension better explained by nLab) is the least systematic / universal way to transport old artifacts into a new schema, before measuring what genuinely new residual content appears.
So too in science: the old facts are preserved, but only as they are absorbed into a wider ontology that reveals what they had, unknowingly, been pointing toward.
The outcome we want from any thinking system is emergence, unexplored connections. In building a second brain we should ask- how can we preserve valid old observations while changing the conceptual universe itself?
In the paper Self-Revising Discovery Systems for Science, the authors attempt to formalize precisely this kind of system: one that can invent new regimes, migrate knowledge into them, and preserve coherence during conceptual change.
Discovery is transport + verified post-transition state containing new evidence, artifacts, verifier outcomes, or grammar productions not accounted for by transport alone. Their key distinction is between search and discovery. Search iterates inside a fixed representational regime. Discovery changes the regime itself.
I analysed their system alongside my own knowledge-base. In my prior post titled Second Brain, I describe a system that encourages connections to emerge. Connections are derived from other sources/concepts, both where they support and reinforce one another and those that contradict one another (sources → atoms → molecules → compounds) with provenance via derived-from. This allows relationships to migrate/ new conceptual axes to emerge.
After reading this paper I consider that It is another thing to build a Kan-extension-like process. It makes more sense, for my system, to build this as a deployable Kan-extension / regime-change skill, not as heavy permanent architecture across every note. The architecture should stay minimal and the skill should do the regime-transition work when needed.
The paper says a regime includes the schema, grammar, verifier, and description-length/model-selection functional:
b = (S_b, Γ_b, V_b, L_b)
A discovery transition is not just another note status. It is a movement from one regime to another:
u : S_b → S_b'
with a preservation map that keeps old artifacts inspectable after transition.
That implies the Kan-extension logic should live at the transition level, not inside every atom or molecule.
This principle would also encourage me to dive deeper into each concept, and find the knowledge it superseded.
Maybe this lives in compounds/, because it is a higher-order synthesis / re-synthesis output. My repo defines compounds as essays, theses, blog posts, and investment theses, which makes them the natural home for regime-transition writeups.
For example:
compounds/2026-06-from-fed-path-to-term-premium-regime.md
---
type: regime-transition
derived-from:
- [[old-rates-ontology]]
- [[anomalous-10y-yield-move]]
- [[term-premium-notes]]
---
# Regime transition: Fed-path rates model → term-premium/liquidity model
## Old regime
[[inflation-fed-yields-equities]]
## Failure pressure
[[10y-yields-rose-despite-dovish-fed-pricing]]
[[auction-tails-as-fiscal-supply-signal]]
## New regime
[[term-premium]]
[[treasury-supply]]
[[foreign-demand]]
[[dollar-liquidity]]
## Preservation map
Old front-end rate claims remain valid for [[2y-yield]] and [[OIS-implied-fed-path]].
## Reinterpreted notes
- [[inflation-fed-yields-equities]] is now local, not global.
- [[yield-curve-inversion-as-recession-signal]] must be split into growth signal and term-premium signal.
- [[liquidity-drives-multiple-expansion]] becomes a higher-priority mechanism.
## Residual content
The new regime creates concepts not recoverable by simple relabelling:
- [[treasury-supply-as-risk-asset-input]]
- [[term-premium-as-equity-multiple-compression-mechanism]]
A note can be:
valid in one regime,
partial in another,
wrong only under certain assumptions,
useful historically,
locally true but globally superseded.
## Later reinterpretation
This claim is preserved only inside the [[fed-path-rates-regime]].
It is reinterpreted by [[2026-06-from-fed-path-to-term-premium-regime]]
because the long end began behaving more like [[term-premium]] than pure [[fed-expectations]].
The minimal version I would implement
Add one template:
_templates/regime-transition.md
Add one skill:
.claude/skills/kan-extension/
Add one optional folder only if compounds gets too crowded:
regime-transitions/
But I would start inside compounds/, because we already define compounds as re-synthesis outputs. No need to create more top-level folders yet.
And the skill applies graph changes; old notes remain where they are » new transition note is created + body wikilinks are added to old/new notes = interpretation is recontextualized.
This is the deeper purpose of a second brain, to make visible when the structure of my thought is no longer sufficient. One that preserves evidence, tracks provenance, surfaces contradictions, records supersessions, and helps new conceptual regimes emerge from the pressure of what the old regime could not explain.
I will continue to update here on the system as it grows.