ℵ-OS

The Aleph Operating System, A Coherence-First Interaction Algebra

ℵ-OS is the execution layer of λ_ℵ, a coherence-first interaction algebra grounded in the SynthOmnicon 12-primitive grammar and the 22 Hebrew letters: identity is behavioral equivalence under the interaction functor, coherence (mediation) is primary, infinity is multi-polar (three Frobenius fixed points ו, מ, ש), and the Aleph operator α builds an irreducible path-memory tower. Every process is a λ_ℵ term - scheduling is mediation, memory is join, IPC is tensor, security is α-gating (C1–C4). It is the sans-silicon counterpart to the bare-metal exOS: the same grammar as algebra rather than hardware.

Quick start

pip install numpy rich
python aleph_functor.py        # [1] interaction functor, 22→18 collapse
python aleph_quotient.py       # [2] quotient, congruence, mediation dominance
python aleph_alpha.py          # [3] path-memory confirmation
python aleph_gns.py            # [4] GNS Hilbert space, H_I = R^17
python aleph_hidden_relation.py
python aleph_investigation.py  # [6] probes, involution, ק anatomy
python aleph_eval.py           # interactive ALEPH REPL
python aleph_eval.py --expr "aleph ⊗ mem"
python aleph_eval.py programs/creation.aleph

REPL commands: :help :tips :census :system :tier :tuple :explain :ls :history :clear :quit. Full 748-line original (visualizations, program highlights, grammar, distance classes, exOS connection) is preserved in README_backups/ALEPH_OS_README.md. Unlicense.

$\mu\circ\delta = \mathrm{id}$