SPHEREPOP-KERNEL // CIRCLE CALCULUS • MERKLE TRACE VERIFIER • peter <3 Nate • 8b-is <3 Nate

spherepop-kernel

Independently executable circle-calculus reduction kernel in Go (`I, B, C, K, W, S` + labeled brackets `<...>_a` & `sc_a`), paired with bit-exact differential trace verifiers in Zig, Rust, and Idris 2 QTT (`0, 1, ω`), zero-alloc capability bitmasks, lock-free ring-buffer parallelism, and quantTernary (`{-1, 0, +1}`) lossless encoding.

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GitHub: 8b-is/spherepop-kernel Upstream: standardgalactic/spherepop-kernel Specification (SPEC.md) Architecture (ARCHITECTURE.md)

Live Circle-Calculus Evaluator & WebCrypto SHA-256 Verifier spherepop-term/1 + spherepop-trace/1

Loading WebCrypto SHA-256 verifier...

Rule Table & QTT Multiplicity (`0, 1, ω`)

Rule Redex → Contractum QTT Rig
II x → x1 (Linear)
KK x y → x0 on y (Erasure)
BB f g x → f (g x)1 (Composition)
CC f x y → f y x1 (Exchange)
WW f x → f x xω on x (Dup)
SS f g x → (f x) (g x)ω on x (Share)
Scsc_a (<x>_a y) → <x y>_aScope (settled/safe/any)
Abs<<x>_a y>_a → <x>_aAbsorb (s/u/nf/any/off)

4-Language Verification Lanes

Language Verifier Path Status
Go 1.22+term/, reduce/, trace/11/11 pkgs PASS
Zig 0.16+verifiers/zig/src/verifier.zig2/2 tests PASS
Rust 1.75+verifiers/rust/src/lib.rs1/1 test PASS
Idris 2 QTTverifiers/idris/Spherepop.idrQTT Checked

Oct 26 Confluence & Settled-Scope Search Summary (`368,430` Enumerated Terms • `~53.7M` Explorations)

Regime Flags Mathematical Status Notes
Settled Scope + Settled Absorption --absorb s --sc settled PROVED CONFLUENT Proved in notes/settled-scope.tex for all permission structures (including non-terminating terms).
Safe Scope (Scheduler Default) --absorb u --sc safe UNREFUTED / OPEN 0 counterexamples across ~53.7M explorations; proof obstacle isolated at sc_x (<I>_x a).
Unrestricted Scope (Essay Mode) --sc any REFUTED WHEN RESTRICTED Positive control finds expected non-confluence when a bracket label restricts root permissions.