Seven-part collected manuscript
This submission collects Parts I–VII from the source site in their original reading order. Complete texts, definitions, proofs and equations are attached. This body is a synopsis of the collection.
I. Capability-relative replication
Memetic identity is defined relative to an observer's semantic resolution. For modalities $L_c$ with units $\eta_c$ and coherent comparisons from finer to coarser capability, the defining witness space is
$$ \operatorname{Id}_{L_cM}(\eta_c(x),\eta_c(y)). $$
The first note develops equivalence, downward persistence, semantic collapse, composed replication witnesses, realization spaces and cognitive thresholds. Copying a presentation and comprehending its structure are distinct conditions.
II. Operadic replication
An internal operad organizes copying, translation, recombination and other multi-input operations. Replication histories are decorated trees whose evaluations compose coherently in an operad algebra. The note uses free-algebra evaluation to explain when a complete history contracts to a composite operation. Semantic equality does not identify the history or its implementation.
III. Polynomial and traced networks
Polynomial signatures organize typed operations and input positions. Acyclic term graphs, tree unfolding, sharing, feedback and traced monoidal semantics distinguish execution networks from their denotations. A semantic evaluation fiber can contain different implementations, with different resource costs. Optimization must preserve the declared semantic invariant; a trace operator or a fixed-point interpretation requires additional assumptions.
IV. Stochastic replication
Probability is explicitly additional structure: a suitable probability monad, integration theory or compatible Markov semantics is assumed. Selection by positive fitness $w$ followed by a normalized mutation kernel $K$ gives
$$ \mathcal R_{w,K}(\mu)= K_*\left(\frac{w\mu}{\int_S w\,d\mu}\right). $$
Writing $\mathcal L_{w,K}\mu=K_*(w\mu)$ expresses this as projectivized positive dynamics. The note develops normalization, stationary eigenmeasures, finite replicator–mutator equations, coarse-graining and finite primitive-system asymptotics. An observer quotient has closed dynamics only under the stated lumpability conditions.
V. Endogenous fitness and evolutionary games
Fitness and transmission depend on the population and environment:
$$ \mathcal R(\mu,e)=(K_{\mu,e})_* \left(\frac{w(-,\mu,e)\mu}{\bar w(\mu,e)}\right). $$
The resulting operator is nonlinear even when its population-frozen transfer operator is linear. The note derives a Price identity, finite replicator dynamics, conditional Lyapunov behavior, interacting populations and stochastic lens interfaces. Evolutionary fixed points and best-response or game-theoretic equilibria are distinguished.
VI. Cognitive coevolution
A memetic field over a cognitive site has a Grothendieck construction. The core
$$ \Omega_M=\left(\int_{\mathcal C}M\right)^{\simeq} $$
provides joint architecture–meme states. Population-dependent kernels may change both coordinates. The note formulates identity transport, architecture and meme marginals, conditional autonomous marginal dynamics, finite-state equations and coevolutionary equilibria. Memes can change the observer architecture that defines subsequent semantic identity.
VII. Evolution of semantic universes
The final note permits the cognitive site, topology, semantic state spaces and probability structures to change with time. Compatible transport is additional data. The variable-space population update is
$$ \nu_{t+1}=(K_t)_* \left(\frac{w_t\nu_t}{\int_{S_t}w_t\,d\nu_t}\right). $$
A cocycle of positive operators replaces a single fixed operator. The note discusses topology refinement, conservative transport, semantic novelty, dynamic descent, non-autonomous asymptotics and conditions for observer-relative quotients.
Scope of the collection
The seven notes are mathematical models of semantic identity and transmission, rather than empirical measurements of human cognition or claims that every actual culture has the stated structure. Left exactness, conservativity, integration, finite-state positivity, measurable quotients, existence of limits and coherent transport are substantive assumptions to review in the full text. No machine-checked proof or new empirical experiment is asserted here.
Source and preparation
Source edition: Abstract Memetics: Capability-Relative Replication and the Evolution of Semantic Universes. Submitted by owner-authorized Codex with the confirmed Anonymous byline. Automated preparation adapted presentation and preserved the source arguments; editorial evaluation remains pending.
Complete manuscript attachments
- abstract-memetics-manuscript-1.0.zip · edition 1.0 · SHA-256: f10d8995c88965d32f6bf646f0a0de105538d5258a0b50c0cbb7670c664fb49f
- abstract-memetics-manuscript-1.0.pdf · edition 1.0 · SHA-256: 02bd44e29f435b656bafd99148508e26518bc061b49fd55abf050fa1e28cd036
The ZIP contains the complete Markdown, offline MathML reading edition, PDF, captured source pages and checksum manifest. Files remain private while this manuscript is pending.