finding

active

finding:least-fixpoint-theorem-a-continuous-function-f-on-an-cpo-with-least-element-has-a-unique-least-fixpoint-definable-as-f-n

Least Fixpoint Theorem: A continuous function f on an ω-cpo with least element has a unique least fixpoint definable as ⊔ f^n(⊥).

Fundamental mathematical result in Domain Theory enabling rigorous treatment of recursive definitions and infinite computations as limits of finite information increase.

Source paper

extracted_from

Information, Processes and Games

Abramsky, Samson

Neighborhood — ranked by edge-count

Claims (1)

claim

Information increase in computation arises from data reduction and making implicit information explicit, not logical increase.
supports
Author's proposed resolution to the information increase paradox: computation gains utility through extraction and filtering, not creation of logically new content.

Communities (2)

community

Design principles for care-centered systems
members_of
Cross-scale frameworks linking spatial patterns, diagrams, and simplicity as expressions of care in design.
Information dynamics in computational systems
members_of
Studies how information flow, increase, and explicitness emerge from computation relative to observers and subsystems, grounded in domain theory and order-theoretic formalism.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

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Alexander's critique of least action as an insufficient and non-unique explanation for morphogenesis
If a looped model with cyclic recurrence reaches a fixed point, either each block's contribution vanishes asymptotically or the sequential application traces a constant cyclic trajectory in latent spaceclaim0.709
Theoretical framing that establishes cyclic fixed points as the meaningful limiting behavior
what is the full classification and explanation of orbit and slider non-fixed-point limiting behaviors in looped transformers?question0.701
Left to future work after demonstrating these behaviors are rare but not explaining their mechanism
Continuous functions in Domain Theory reflect that computational processes have access only to finite information at each finite stage.finding0.698
Mathematical principle grounding the formal definition of continuity in domain theory to physical and epistemic constraints on computation.
Proposition 4.1: If a (l,k)-Recurrent block reaches a fixed point S_k(X')=X', then any cyclic permutation of blocks 1,...,k will also have reached a (different) fixed pointclaim0.696
Formal proposition establishing that fixed-point convergence implies cyclic fixed points for all block permutations
Fixed Point Convergenceconcept0.694
The behavior where repeated application of a transformer block converges to a state where X' = S_k(X')