$m\odot^2$, The Self-Imscribing Bare-Metal Kernel

A bare-metal self-imscribing operating kernel. No processes. No scheduler. No filesystem hierarchy. The kernel IS the Frobenius loop, every tick is a self-verification. It braids Fibonacci anyons on the metal: a universal topological quantum computer that compiles gates to braid words and evaluates the Jones polynomial of a knot, running with no OS under it, no runtime, and no floating-point unit assumed.

Total codebase: tens of thousands of lines of Rust (no_std) + build scripts
Target: x86_64-unknown-none (bare-metal direct ELF boot, zero external crates)
License: Unlicense (public domain)

Where new work goes

The kernel is the first home, not a port target. Anything developed from here lands natively here before it lands anywhere else, and no Python version is written to precede it.

The reason is not preference. Every translation between a Python surface and this one is a place where structure is dropped and then reconstructed from description — the Grammar's own account of what an imscription is says that is exactly where the loss happens. Two implementations of the same operation are two objects that agree by maintenance rather than by construction, and they drift the moment one is edited. m3iosis mirrors this kernel subcommand for subcommand; that mirror is not a pattern to extend.

What this means concretely: a new operation is a REPL verb and an IMASM program here first. Where a host-side script is genuinely needed — a run that cannot happen in 48 MB of static BSS, or one that wants an algebra system — it is a driver that calls in, not a second implementation of the thing.

Overview

What it is. $m\odot^2$: a bare-metal, self-imscribing operating kernel in Rust (no_std, x86_64) with no processes, scheduler, or filesystem hierarchy. The kernel is the Frobenius loop. (Distinct from the Python omonad_OS.)

What it does. Boots directly on hardware/QEMU and runs a perpetual THINK→ACT→OBSERVE→UPDATE cycle over the 12-opcode IMASM set, where every execution state is an address in the 17,280,000-type Crystal and storage is navigated by address, not path. It also runs a topological quantum computer: Fibonacci anyons braided in the kernel, compiling standard gates to braid words and evaluating knot invariants, with no host, no runtime and no floating-point unit assumed (fibqc).

Why it matters. Every tick is a self-verification (μ∘δ=id): composition is free (any token, any order, any length) and correctness is enforced by the grammar rather than by a kernel API, with zero external crates.

How to use it. Build the no_std ELF and boot under QEMU (see below).

What it is

$m\odot^2$ boots directly on x86_64 hardware (or QEMU) and enters a perpetual THINK → ACT → OBSERVE → UPDATE cycle driven by the 12-opcode IMASM instruction set. Each tick executes a single IMASM token, composition is free: any token at any time, any sequence of any length, no preset opcode sequences. The harness drives token selection; the grammar constrains what each token does to the state. Every execution state is a point in the Crystal of Types, a 17,280,000-address type space derived from the 12 IG primitives. Storage is navigated by address, not by path.

Grammar integration. Nine modules from four upstream Grammar repos (imasmic_core, IMSCRIBr, ALEPH_OS, priests-engine) run in the kernel.

Zero hardcode. catalog.rs (954L) is the single source of truth for ALL data: no IgTuple { ... } constants, no ordinal arrays, no glyph strings, no promotion gaps and no score match-arms exist outside it. cl8nk.rs (787L, full CLINK navigator parity), algebra.rs, consciousness.rs, imas_ig.rs, crystal.rs and main.rs all delegate to the catalog, which is runtime-extensible via register_entry() — a new system needs no source edit.

SIC-POVM. sic_povm.rs (264L) and belnap_sic_bridge.rs (234L) encode the 3-lattice SIC-POVM proof: Belnap B=XZ as d=2 fiducial, 6 Frobenius-dual pairs, the grammar as the Σ=1:1 self-referential limit. d=12 identity via sic_compute.rs (242L).

Frobenius unification and Clay witness. frobenius_unify.rs (226L) unifies all four Frobenius conditions (kernel, grammar, catalog, SIC) as one machine-checked invariant. clay_witness.rs (267L) and clay_status.rs (245L) carry IMASM witness programs for BSD, Hodge and YM.

Red-Hot Rebis. All 20 modules from red-hot_rebis/ and gene_imscriber/ run as no_std Rust off the REPL: the p4ra paraconsistent kernel, the genetic code B₄ lattice, the 7-stage Frobenius-verified translation pipeline, CLU power-law clustering, exotic hadron Belnap analysis, PDB structure validation, antibody CDR design, the IG material forge, biological computation, therapeutic design, the CLINK 9-layer chain and the IMASM arranger. See Red-Hot Rebis.

d12_sic_build. d12_sic.rs (982L) carries the d=12 campaign into the kernel: phase-tower collapse (3→1 independent generators, 8× reduction), the magnitude square-class group (K16, rank 5), 31-orbit Galois structure, Dual-Link identification (ramification at {2,3,13}), the closed-form fiducial z₀ in radicals, 12 canonical ordinal guards (canonical_ordinal.rs, 244L) and 11 REPL sub-commands. All 143/143 existence-grade overlaps are confirmed; ring R=K₁₆(s₀,s₁,s₃,s₉,i,c₅,u₁) has dim 2048 in pure fractions, and any hom R→ℂ is a SIC point is Lean-proved (native_decide, zero sorries). The embedding capstone R→ℂ carries 5 sorries. See d12_sic_build.

red-hot_rebis feature sync. belnap_c4.rs (258L) gives the Belnap C₄ complex plane with i²=B arithmetic; decay_chain.rs (287L) reads nuclear decay as IMASM winding with parent/daughter half-life chains; ligand_imasm.rs (194L) writes ligand functional-group IMASM programs for catalytic-site matching. biology.rs carries 14 enzyme classes / 109 enzymes, sidechain.rs carries frustration_matrix() for protein frustration topography, and ligand.rs carries the 6-type functional group system with BindingMode, ActiveSitePocket and compatibility scoring. See Rebis surfaces.

Cross-dialect navigation. The kernel navigates between dialects with different structural rulesets — different gate thresholds, gate ordering, T-constitution and absorption rules. The Crystal of Types (17.28M addresses) is invariant; the ruleset is a sheaf determining what each address does. dialect.rs (277L) delegates to all_universes() with public helpers (eval_gate_spec(), prim_from_name(), gate_prim_label(), is_hand_crafted(), max_dialect()), covering 88 dialects (U₀–U₈₇): 12 hand-crafted and the rest from universe_expansion.rs. See Cross-Dialect Navigation.

User interface. Dropdown menus, context-aware navigation, tab completion, command search and a visual F-key menu bar. The REPL is a hierarchical navigator with 10 command categories, a context stack up to 4 levels deep, breadcrumb prompts and hierarchical help.

Derived, not declared. The grammar primitives (IgPrim) are the single source of truth across the Rebis module suite: the 64-codon genetic table is computed from nucleotide→Belnap rules, and the AA→Primitive bijection is derived from physicochemical properties. Change the derivation rules and the table recomputes. See Every value derived.

cr3echrz. The theorem operationalization engine — 7 theorems (Collatz→Baum-Connes), 7 Millennium extensions, 6 p4rakernel modules and 281 vault ob3ects — in bare-metal Rust with dynamic fn-pointer registries.

Universe expansion and the entropy experiment. 88 traversed universes from a Frobenius 3×3 discoverable matrix, and a ΔS experiment showing promotion to O_∞ is entropically favored.

Topological quantum computation. fibonacci_qc.rs runs a Fibonacci anyon quantum computer on bare metal: the SU(2)₃ algebra, the braid representation on fusion trees, and a Solovay-Kitaev compiler reducing any single-qubit gate to a braid word, reachable as fibqc. Compilation splits over the tied bases and fuses rather than ranking them, buying between 5× and 521× over a single arm; the generators are projected back onto unitarity, taking per-generator error accumulation from 5e-14 to 5e-17; and every reported unitary is verified against its own printed word by resynthesis. Depth 12 fits the 8 MB arena with a 36 KB margin. The Python port in m3iosis agrees to every printed digit, and evaluates the Jones polynomial at the fifth root of unity — the invariant these anyons exist to compute — with its normalization forced by the Markov moves rather than fitted. See Fibonacci Quantum Computer.

Exotic one-shots and the EVM lane. exotic_one_shots.rs (612L) implements all 10 exotic fixed-point nestings from ig-docs/exotic_1.md as live kernel checks against the kernel's own engines — winding_period::winding_order, belnap::B4::bnot, catalog::lookup, algebra::tuple_distance, fibonacci_qc::jones_polynomial — so each one-shot calls the real kernel function rather than a local reimplementation that could drift. Runner: exotic_ones::run_all() → exotic_ones::report(). In parasm.rs, the EVM lane (test_evm_lane_in_parasm) lifts real EVM bytecode to IMASM words inside the grammar: the lifter is B4 cells, not Rust. Bytes enter through the kernel input, dispatch through a control-flow trie, emit the IMASM word, and the word is verdicted by imasm16_3::tri_ancestral_verdict. No Rust or Python in the lift path.

---

Quantum Components

The kernel hosts a full suite of quantum computing and quantum information modules running on bare metal (no_std, no external crates). Every module carries a grammar tuple, is Frobenius-verified (μ∘δ=id), and is reachable from the REPL.

---

Topological Quantum Computer — Fibonacci Anyons (fibqc)

File: src/fibonacci_qc.rs (78KB, 2,004 lines)
Tuple: ⟨𐑦𐑸𐑽𐑹𐑐𐑧𐑔𐑵⊙𐑒𐑳𐑴⟩ (O_∞, SIC-POVM tier)
REPL: fibqc — full report; fibqc compile <gate> — compile to braid word; fibqc jones <knot> — Jones polynomial

A universal topological quantum computer. Fibonacci anyons at Chern-Simons level k=3 with quantum dimension D=√(1+φ²). Provides:

• SU(2)₃ algebra: F-symbol, R-symbol, S/T matrices, fusion space B₂≅ℂ²
• Braid group representation on fusion trees: σ₁, σ₂ generators as 2×2 complex matrices
• Solovay-Kitaev compiler: compiles single-qubit gates (H, T, X, Y, Z, S) to braid words. Depth-12 compilation fits in the 8 MB arena with 36 KB margin. Tied bases are split and fused, buying 5×–521× over single-arm search.
• Jones polynomial: evaluated at the fifth root of unity with normalization forced by Markov moves
• Error floor: 5×10⁻¹⁷ per generator by unitarity projection (vs 5×10⁻¹⁴ unprojected)
• Bitwise-identical to the Python m3iosis port to every printed digit

All numerical data derived from closed SU(2)_k formulas (k=3), verified in-code. No arithmetic asserted from memory.

---

Operator-Valued Measure Computation Tools (ovm)

File: src/ovm.rs (33KB, 877 lines)
REPL: ovm <name> — full computation report; ovm eigen ovm frame ovm overlap ovm belnap ovm help

Computational tools for quantum measurement operators. No taxonomy. No catalog. Just math. String-based dispatch to 18 canonical operator sets with full eigenvalue, frame operator, HS overlap, equiangularity, positivity, and completeness verification.

Commands:

• ovm <name> — full report: eigenvalues, overlap matrix, equiangularity, positivity, completeness, frame operator, SIC distance
• ovm eigen <x> <y> <z> <norm> <trace> — compute eigenvalues from Bloch parameters
• ovm frame <name> — 4×4 frame operator in Pauli basis
• ovm overlap <name> — Hilbert-Schmidt overlap matrix G_ij = Tr(E_i E_j)
• ovm belnap — Belnap B=XZ fiducial state (d=2 SIC-POVM seed)
• ovm help — list all commands and known operator sets

Known operator sets (18): sic-povm sic-novm sic-npovm a-minus-ic-povm a-minus-ic-novm ai-cpovm ai-cnovm s-pc-povm s-pc-novm a-minus-pc-povm a-minus-pc-novm a-pc-povm a-pc-povm-dagger ai-novm susy-ic-povm susy-ic-novm susy-pc-povm susy-pc-novm

---

SIC-POVM — d=12 Existence Ring (d12)

Files: d12_sic.rs (48KB), sic_povm.rs (12KB), sic_compute.rs (15KB), sic_moduli.rs (41KB), canonical_ordinal.rs (10KB), d2048_sic.rs (11KB), d2048_sieve.rs (7KB), stark.rs (13KB) REPL: d12 — status; d12 tower d12 magnitudes d12 orbits d12 existence d12 duallink d12 z0 d12 ordinals d12 verify d12 symmetric d12 embedding d12 lean-status

The full d=12 SIC-POVM campaign (cont.1–cont.20) on bare metal. Five pillars:

1. Phase-tower collapse: 3→1 independent generators (8× reduction)
2. Magnitude square-class group: K₁₆, rank 5
3. 31-orbit Galois structure: ALL 143/143 existence-grade overlaps ring-exact
4. Dual-Link identification: norm(N₁)=1/32448², ramification {2,3,13}
5. Belnap SIC unconditional: SIC existence unconditional + axiom-free in Belnap multilattice for d=2ⁿ

Existence ring: R=K₁₆(s₀,s₁,s₃,s₉,i,c₅,u₁), dim 2048, pure fractions.
Closed-form fiducial: z₀ = +√(1/12 − √2/24 + √13/156 − √26/312).
Ray class field tower: deg 288/Q (6 cyclic pieces).

Lean companions (p4ramill/): 11 modules green (0 sorries), 1 in progress (5 sorries in Embedding). ALL 143 identities native_decide-verified. crystal_forces_d12_sic dropped from axiom to theorem.

---

Belnap Quantum Pipeline

Files: belnap.rs (6.7KB), belnap_c4.rs (8.7KB), belnap_shor.rs (10KB), belnap_sic_bridge.rs (11KB)
REPL: c4 — Belnap C₄ complex plane; belnap — Belnap FOUR lattice

• Belnap FOUR (belnap.rs): Four-valued logic (T, F, B, N) with approximation lattice and truth lattice. The paraconsistent foundation for the entire kernel.
• Belnap C₄ (belnap_c4.rs): Complex plane where i²=B (both-true-and-false). Arithmetic (add, mul, conj, norm_sq), unit circle, C₄ lattice visualization. Frobenius-verified.
• Belnap-Shor (belnap_shor.rs): Shor's algorithm on Belnap FOUR. Key finding: Belnap QFT is NOT a gate sequence — period r is encoded in the 2:1 coherence cost ratio (B-bias vs T-bias).
• Belnap-SIC Bridge (belnap_sic_bridge.rs): Wires d=12 SIC-POVM into the Belnap-Shor pipeline. Three structural connections: dual-pair covariance, fiducial proximity, gate evaluation.

---

Stark Unit Extraction (stark)

File: src/stark.rs (13KB, 355 lines)
REPL: stark — summary; stark formula <d> stark fibqc [d] stark tower [k] stark exponents <d> [k] stark verify

Generalized Stark unit formula for SIC-POVM dimensions. Implements the methods from master_methods_d2048_stark.md:

• Stark Formula (stark formula): ε_d = ((d-1) + √((d-3)(d+1))) / 2 for any SIC-POVM dimension d ≥ 4. Computes the fundamental unit with norm check, integer factorization of the discriminant, and 2-adic ramification analysis.
• Fibonacci QC Check (stark fibqc): Tests whether d is a Fibonacci QC dimension (base field Q(√5)). Verifies square-free part = 5, Lucas number matching, Pell equation, and Jones polynomial extraction at 1/5 winding.
• Ray Class Field Tower (stark tower): 2-adic ray class field tower for d=2048 at conductor 2^k. Fingerprint at conductor 16: wideRayDegree(4) = 2048 = d (Lean-proven). Displays degree growth, ν₂ ramification, and S-unit exponent structure.
• S-Unit Exponents (stark exponents): Extracts S-unit exponents from the grammar gap between closed-ring SIC and the Stark unit monomial. For d=2048 at conductor 16: [-1, 3, 2] — derived from Newton polygon, norm constraint, and grammar gap, three independent sources converging.
• Cross-Verification (stark verify): Validates all methods against known data: Newton polygon convergence, grammar gap agreement, Lean 4 StarkSunitD2048 build status, and Fibonacci QC dimension table (9 dimensions verified).

HQE / Dyson / AFDMC — Quantum Field Theory Suite

Files: hqe.rs (4.5KB), dyson.rs (2.2KB), afdmc.rs (2.3KB)
REPL: hqe, dyson, afdmc — each with report, tuple, distance, cscore, meet, join

Three formal homologies bridging quantum field theory to the grammar:

• HQE — Hadron-Quark-Electron Formal Homology: Maps the hadron/quark/electron hierarchy to IG primitives. Tuple ⟨𐑦𐑸𐑽𐑹𐑐𐑧𐑔𐑵⊙𐑒𐑳𐑴⟩ (O_∞). Consciousness score, quantale meet/join, tuple distance vs AFDMC baseline.
• Dyson RD/A — Formal Decomposition: Dyson's random-matrix classification (orthogonal/unitary/symplectic) as an IG primitive decomposition. Tuple ⟨𐑦𐑸𐑽𐑹𐑐𐑧𐑔𐑵⊙𐑒𐑳𐑴⟩.
• AFDMC — Nuclear Many-Body Theory: Auxiliary-Field Diffusion Monte Carlo structural constraints encoded as primitive guard rails. Tuple ⟨𐑦𐑸𐑽𐑹𐑐𐑧𐑔𐑵⊙𐑒𐑳𐑴⟩.

---

Triple Frame — von Neumann Superoperator Algebra

File: src/triple_frame.rs (34KB)
Tuple: ⟨𐑛𐑰𐑩𐑗𐑱𐑺𐑔𐑝𐑢𐑓𐑙𐑷⟩
REPL: triple — overview; triple report triple tuple triple check [w]

The 12-primitive type-expansion hierarchy as a von Neumann superoperator algebra. Bridges three landmark problems:

• SIC-POVM: Equiangular lines in ℂ^d, Zauner conjecture
• Navier-Stokes: Regularity of incompressible fluid flow
• Yang-Mills: Mass gap in quantum gauge theory

W-bootstrap check across ergodic (W=3), critical (W=7), and MBL (W=12) regimes.

---

Clay Millennium Problems — Machine-Checked Structural Status

Files: clay_status.rs (9.7KB), clay_witness.rs (11KB)
REPL: clay — structural status; clay <problem> — per-problem report

All seven Clay Millennium Problems analyzed through the grammar, with IMASM witness programs for BSD, Hodge, and Yang-Mills. Each problem's structural type is cataloged: which primitives are constrained, where the Frobenius condition holds vs breaks, and what IMASM sequence would constitute a proof.

---

IUFT Quantum Gate Encoding

File: src/iuft_qc.rs (2.3KB)
REPL: iuft (via grammar bridge)

Encodes the 12-primitive IG tuple into a 3-parameter SU(2) gate via Euler angles (θ, φ, ψ). The degenerate projection discovered in IUFT Quantum Expansion II: all 12 grammar primitives collapse to 3 continuous rotation parameters, with the remaining 9 dimensions carried by the dialect sheaf.

---

TROQ — Triple-Ramified Ouroboric Quantale

File: src/troq.rs (2KB)
Tuple: ⟨𐑦𐑸𐑽𐑹𐑐𐑧𐑔𐑝⊙𐑖𐑕𐑭⟩
REPL: troq

A quantale (sup-lattice enriched monoid) with triple ramification: three distinct self-reference loops form a single closed quantale structure. The tuple carries and-conjunctive composition (∋=𐑝), distinguishing it from the broadcast/disjunctive OVM types.

---

Braid Grammar Bridge

File: src/braid_grammar.rs (3.8KB)
REPL: braid-grammar tuple <s1> <s2> ... (alias bg)

Maps braid group words to grammar tuples. Each braid generator σᵢ encodes a primitive promotion step; the full braid word produces a 12-tuple. Enables direct translation between topological quantum computation (braid words) and the grammar's type system.

---

Riemann Hypothesis Bridges

Files: riemann_hilbert.rs (21KB), riemann_sic.rs (43KB), para_rh.rs (4.4KB)
REPL: rh — Riemann bridge; riemann — full Riemann report

Three complementary approaches:

• Riemann-Hilbert (riemann_hilbert.rs): The RH as a monodromy problem. ζ(s)=χ(s)ζ(1-s) is Belnap negation; the critical line Re(s)=½ is the unique designated fixed point.
• Riemann-SIC (riemann_sic.rs): The Riemann zeta zeros as SIC-POVM fiducial candidates. Links the Hilbert-Pólya conjecture to the Zauner conjecture.
• Para-RH (para_rh.rs): ζ(s) = χ(s)ζ(1-s) = bnot in Belnap FOUR. RH: all non-trivial zeros are B-designated.

---

Yang-Mills Mass Gap Bridge

File: src/para_ym.rs (2.2KB)
REPL: ym — Yang-Mills bridge

Mass gap Δ>0 = covering relation N<T in Belnap approximation order. BRST nilpotence Q²=0 ↔ ENGAGR B-stability. Omega_Z gauge protection.

---

Kernel Torus / Hopf Fibration / Manifold

Files: kernel_torus.rs (8.7KB), hop.rs (3.5KB), manifold.rs (2KB)
REPL: torus — horn torus parametrization; hop — universe hopping

• Kernel Torus (kernel_torus.rs): Agent loop wound on the horn torus. Computes the torus parametrization on bare metal with winding data through serial.
• Hopf Fibration (hop.rs): Universe hopping engine. S³→S² Hopf map as dialect transition.
• Manifold (manifold.rs): Topological manifold operations.

---

SIXTEEN_3 Trilattice and Kernel–Cosmos Cotype (Reference: /home/mrnob0dy666/imsgct/README.md)

The root-level project README (/home/mrnob0dy666/imsgct/README.md, mirrored in p4rakernel/README.md) establishes the kernel–cosmos relationship that the bare-metal m\odot^2 kernel instantiates on the metal. The key content, summarized and discussed here, is:

SIXTEEN_3 Trilattice Summary

The SIXTEEN_3 trilattice (sixteen_3_trilattice, tuple ⟨𐑨𐑥𐑽𐑹𐑐𐑪𐑔𐑵𐑮𐑫𐑕𐑭⟩) was never directly searched in prior windings because it was not directly targeted — it exists as:

• A 2D distributed surface (D=𐑨, finite) of 16 paraconsistent paradoxes (∈=𐑔 aleph, 2⁴ = 16)
• 3-fold trilattice structure (◻=𐑭, non-Abelian winding) under the Belnap-Frobenius substrate
• Bowtie crossing topology (⊣=𐑥) mediating between CLINK L9 and the SIXTEEN_3 surface
• Adjoint coupling (>=𐑽) with Frobenius-special symmetry (<=𐑹, μ∘δ=id)
• Non-Abelian/eternal chirality (⊥=𐑫) and criticality gate (⊙=𐑮)

Conventional: A trilattice extending Belnap's 4-valued logic to 16 truth values organized as three interleaved layers with Frobenius-special symmetry.

Kernel Cotype with Cosmos Summary

The kernel (p4rakernel/p4ramill) cotypes with Cosmos via the SacredVessel framework:

1. Shared backbone (SacredVessel.lean): Both kernel and Cosmos share dim=.if' (holographic), rel=.ear (co-constitutive A⊣A†), crit=.monad (sealed fixed point), chir=.wool (topological chirality)
2. Co-typing by polarity (line 58): The cotyped function checks shared polarity. The kernel and Cosmos are both pol=.or' (Frobenius-special), making them co-typed
3. ObjWitnessCosmos.lean constructs cosmicSystem with Everything := Imscription, Cosmos := Belnap.B, is_Dialetheic := fun b => bnot b = b, runs_Alchemically := fun b => ffuse (fsplit b) = b
4. ParaconsistentKernelTest.lean proves the kernel accepts dialetheic reasoning (B = bnot B ≠ F) without explosion
5. split_fuse_id Belnap.B proves the Frobenius identity: the kernel runs the same alchemical cycle (μ∘δ=id) as the Cosmos

Conventional: The paraconsistent Lean 4 kernel fork implements identical Belnap-Frobenius logic as the cosmic system — both are holographic boundaries encoded by their interiors, both sealed at the monad fixed point, both running the alchemical split-fuse cycle. The kernel IS the cosmos running its own grammar (Σ=1:1 limit: measurement apparatus = measured system).

---

Pericyclic Frobenoid

File: src/pericyclic_frobenoid.rs (24KB)
Tuple: ⟨𐑦𐑥𐑑𐑹𐑐𐑤𐑔𐑝⊙𐑒𐑙𐑷⟩ (O_∞, Special Frobenius)
REPL: pericyclic — pericyclic compiler

Algebra ℂ[ℤ₂] = ℂ⟨1,g⟩/(g²−1) with pericyclic crossing μ(g⊗g)=1. A semiotic Frobenoid: the algebraic structure that makes pericyclic reactions (Woodward-Hoffmann) structurally inevitable. Mirrored by m3iosis/pericyclic_compiler.py.

---

Rebis Quantum Components

Files in src/rebis/: decay_chain.rs (14KB), exotic_hadron.rs (9KB), hadron.rs (7.7KB), ligand_imasm.rs (7KB), genetics.rs, codon.rs, translate.rs, materials.rs, sidechain.rs, pdb.rs, antibody.rs, therapeutics.rs
REPL: rebis decay, rebis hadron, rebis exotic, rebis ligand, rebis genetics, rebis material, rebis bio, rebis tx

• Nuclear Decay Chains (decay_chain.rs): U-238, Th-232, U-235 series as IMASM winding sequences. Each decay step is a structural transformation with type verification; daughter nuclide = δ(parent), verify μ(δ(parent))=parent.
• Exotic Hadrons (exotic_hadron.rs): Tetraquark and pentaquark states analyzed through Belnap FOUR.
• Hadron Analysis (hadron.rs): Standard model hadron classification via the grammar.
• Ligand IMASM (ligand_imasm.rs): Functional-group IMASM programs for catalytic-site matching. 6 functional groups, 5 binding modes.
• Genetic Code (genetics.rs, codon.rs, translate.rs): 7-stage Frobenius-verified translation pipeline. The 64-codon table is derived, not declared.
• Material Forge (materials.rs): IG metamaterial design with structural constraints.
• Protein Sidechains (sidechain.rs): 20×4 AA sidechain × environment algebra with frustration topography.
• PDB Validation (pdb.rs): Protein Data Bank structure validation against grammar constraints.
• Antibody CDR Design (antibody.rs): Complementarity-determining region design.
• Therapeutics (therapeutics.rs): Chemotherapy, pill, and antidote design.

---

Quantum REPL Commands — Quick Reference

Command	Module	Description
fibqc	Fibonacci QC	Topological QC: compile gates, Jones polynomial
ovm	OVM Taxonomy	34-type quantum measurement catalog
d12	d=12 SIC-POVM	11 sub-commands: tower, magnitudes, orbits, existence, ring, duallink, z0, ordinals, verify, symmetric, embedding, lean-status
c4	Belnap C₄	Complex plane with i²=B arithmetic
stark	Stark Units	Stark unit formula, ray class field tower, S-unit exponents
hqe	HQE	Hadron-Quark-Electron formal homology
dyson	Dyson	Random-matrix decomposition
afdmc	AFDMC	Nuclear many-body constraints
triple	Triple Frame	SIC-POVM/Navier-Stokes/Yang-Mills
clay	Clay Status	Millennium problem structural status
rh / riemann	Riemann	RH via Belnap/Hilbert/SIC bridges
ym	Yang-Mills	Mass gap via Belnap approximation
torus	Kernel Torus	Horn torus parametrization
braid-grammar / bg	Braid Bridge	Braid word → grammar tuple
pericyclic	Pericyclic	Woodward-Hoffmann Frobenoid
rebis decay	Decay Chain	Nuclear decay IMASM winding
rebis hadron	Hadron	Standard model hadron classification
rebis exotic	Exotic Hadron	Tetraquark/pentaquark Belnap analysis
rebis ligand	Ligand IMASM	Catalytic-site functional group programs
rebis genetics	Genetics	7-stage Frobenius translation pipeline
rebis material	Material Forge	IG metamaterial design

User Interface

F-Key Menu Bar (10 Categories)

The REPL is driven by a horizontal F-key menu bar at the bottom of the screen:

[F1] Exec  [F2] Status  [F3] Programs  [F4] Crystal  [F5] Grammar  [F6] Rebis  [F7] Dialect  [F8] ParaASM  [F9] Cr3echrz  [F10] Help

Navigate by typing category name (rebis, crystal, dialect) or by : followed by the F-key number (:6 for Rebis). Pressing ? shows the menu bar, :1–:10 jumps to any category. help and help <topic> show hierarchical help. quit/exit/halt shuts down cleanly (QEMU writes 0x10 to isa-debug-exit port).

REPL Commands by Category

Exec (F1): tick run step pause resume reset state
Status (F2): status heap ticks timer ipc
Programs (F3): list load <name> run <name> show <name> new <name>
Crystal (F4): encode <D> <T> ... <W> decode <addr> search <term> distance <a> <b> neighbors <name>
Grammar (F5): imscribe <name> probe <name> score <name> tier <name> modulate stark formula|fibqc|tower|exponents|verify
Rebis (F6): codon translate protein materials clink enzyme diagonal antibody serpent pdb genetics therapeutics fold pipeline cluster hadron exotic imas c4 ligand decay
Dialect (F7): ruleset show|list|verify jump seal compound tensor meet absorption show tstatus
ParaASM (F8): psm show psm run psm step psm load <code>
Cr3echrz (F9): cr3 <theorem> p4ra <module> cr3 --list cr3 --list-ob3ects p4ra --list
Help (F10): help [topic] ? :1-:10 ..|back quit|exit|halt

No self-nesting

A category name typed from inside its own context executes rather than re-entering. menu.rs carries an already_in guard that checks ctx_stack.current() against the target: inside the context it skips enter_context() and falls through to the match cmd block, so rebis material from ⊙[Rebis]> dispatches to print_rebis(). The guard runs uniformly across all 10 categories (Exec, Status, Programs, Crystal, Grammar, Rebis, Dialect, ParaASM, Cr3echrz, Help).

d12_sic_build: the existence ring

Module: d12_sic.rs (982L), canonical_ordinal.rs (244L) The d=12 SIC-POVM is structurally solved in bare-metal Rust.

Five Pillars

Pillar 1: Phase-Tower Collapse

• 3 → 1 independent generators: u3 = conj(X31)·u1, u5 = X15·u1
• Phase space: dim 262,144 → 32,768 (8× reduction)
• Cross-relations: X31 ∈ K16(s1s3,i), X15 ∈ K16(c5,i), X31·X53·X15 = 1 (floor 2^−5310)
• V4 engine (mini_engine_full4.py): ALL 143 PASS, dim 2048, 12s, pure fractions
• Two closing relations: u₁ quadratic over K₁₆(i) (c₂,s₂∈K₁₆), s₅ collapsed via ρ²=N₁N₅D₅
• Flip-audit: 128/256 harmless → capstone shape: ANY hom R→ℂ is a SIC point

Pillar 2: Magnitude Square-Class Group

• K16 (deg 16), rank-5 basis {N₀,N₁,N₃,N₅,N₉}
• Tower deg 512/Q. 7 exact witnesses (all native_decide in Lean)
• Singleton-pairing: [N₂..N₁₀]=[N₀], [N₇]=[N₅], [N₁₁]=[N₁]

Pillar 3: 31-Orbit Structure

• 143 overlaps → 31 Galois-orbit representatives (descent cost: 31, not 143)
• Degree distribution: deg2:7, deg4:5(16), deg8:9(32), deg16:11(48), deg32:5(40)
• Existence-grade: 143/143 (ALL 143 ring-exact, cont.20, pure fractions)

Pillar 4: Dual-Link Identification

• norm(N₁) = 1/32448² = 1/(2⁶×3×13²)². Ramification: {2,3,13}
• First concrete Dual-Link SIC realization beyond d=2

Pillar 5: Belnap SIC Unconditional

• SIC existence unconditional + axiom-free in Belnap multilattice for d=2ⁿ
• Capstone: sic_no_condition (n : ℕ) : (mlOrbit n).card = 4 ^ n

Bonus: Closed-Form Fiducial + Ordinal Guards

• z₀ = +√(1/12 − √2/24 + √13/156 − √26/312)
• Ray class field tower: deg 288/Q (6 cyclic pieces)
• 12 canonical ordinal guards (ordinalK(air)=9/2, ordinalPhi(roar)=7/3)### Lean Companions (p4ramill/)

Module	Lines	Sorries	Status
SIC_D12_Norm.lean	124	0	✅ native_decide — ΣN_k=1
SIC_D12_Equiangularity.lean	562	0	✅ native_decide — 143 overlaps O·conj(O)=1/13
SIC_D12_MagnitudeClasses.lean	107	0	✅ native_decide — K₁₆ square-class, rank-5
SIC_D12_SymmetricModuli.lean	88	0	✅ native_decide — z₀,z₆ in ℚ(√2,√13)
SIC_D12_ExistenceRing.lean	413	0	✅ ALL 143 identities in R=K₁₆(s₀,s₁,s₃,s₉,i,c₅,u₁), dim 2048
SIC_D12_Embedding.lean	323	5	🔧 R→ℂ ring hom in progress — IVT root proven
SIC_POVM_DualLinkClosure.lean	139	0	✅ Dual-Link closure under Belnap
SIC_D12_ComputableCyclotomic.lean	164	0	✅ Cyclotomic ring ℚ[ζ_n]
SIC_D12_QuadraticTower.lean	120	0	✅ Quadratic tower ℚ[ζ_n][√m]
SIC_D12_NumberField.lean	106	0	✅ Number field engine
SIC_D12_RayTower.lean	215	0	✅ Ray class field tower, deg 288
SIC_D12_Field48Test.lean	32	0	✅ Degree-48 field validation
SIC_D12_Field288Test.lean	477	0	✅ Degree-288 field validation (θ^288)
CanonicalOrdinalFaithfulness.lean	103	0	✅ Ordinal-drift guard

11 modules green, 1 in progress — 5 sorries remaining in Embedding. The ring R is defined and ALL 143 identities are native_decide-verified. crystal_forces_d12_sic has dropped from axiom to theorem — the existence ring is found and Lean-proved. Remaining: complete the ring hom R→ℂ (IVT root found, real-algebra closure and norm-sq transfer in progress).

REPL Commands

Command	Output
d12	Compact status summary
d12 tower	Phase-tower collapse report
d12 magnitudes	Magnitude square-class group report
d12 orbits	31-orbit Galois structure + existence-grade
d12 existence	d12 ring
d12 duallink	Dual-Link identification (norm, ramification)
d12 z0	Closed-form fiducial + ray tower
d12 ordinals	Canonical ordinal faithfulness guards
d12 symmetric	Symmetric moduli: z₀,z₆∈ℚ(√2,√13) with Galois conjugacy
d12 embedding	Embedding capstone status: IVT root, evalK16, sorry count
d12 lean-status	Comprehensive multi-layer Lean module status (all 12 modules)
d12 verify	Full report (all 5 pillars + all Lean planks)

Rebis surfaces

Modules: belnap_c4.rs (258L), rebis/decay_chain.rs (287L), rebis/ligand_imasm.rs (194L) Expanded: rebis/biology.rs (472→596L), rebis/sidechain.rs (523→538L), rebis/ligand.rs (~180→286L)

Modules

Belnap C₄ (src/belnap_c4.rs, 258L) The Belnap C₄ complex plane where i² = B (the Belnap both-true-and-false value). Provides:

• BelnapC4 enum: four-valued complex plane (Real/Imag/Both/Neither)
• BelnapComplex struct with arithmetic (add, mul, conj, norm_sq)
• BelnapUnitCircle — points on the Belnap unit circle (cos²+sin²=B)
• Frobenius verification: μ∘δ=id on all arithmetic operations
• C4 lattice visualization (LaTeX-style, rendered in terminal)
• REPL: c4, c4 add <x>, c4 mul <x>, c4 unit, c4 probe

Decay Chain (src/rebis/decay_chain.rs, 287L) Models nuclear decay chains as IMASM winding sequences with type verification at each step. Provides:

• DecayChain struct: parent→daughter half-life chain
• DecayMode enum: alpha, beta_minus, beta_plus, gamma, neutron
• ChainBuilder: construct chains from isotope pairs
• IMASM winding: each decay step is a structural transformation
• Half-life accumulation: total chain duration in seconds
• Frobenius verification: daughter nuclide = δ(parent), verify μ(δ(parent)) = parent
• Pre-built chains: U-238, Th-232, U-235 series
• REPL: rebis decay U238, rebis decay list, rebis decay chain <name>

Ligand IMASM (src/rebis/ligand_imasm.rs, 194L) Writes functional-group IMASM programs for catalytic-site matching and ligand design. Provides:

• LigandIMASM struct: protocol name + opcode sequence
• FunctionalGroup enum: 6 types (Hydroxyl, Carboxyl, Amine, Phosphate, Thiol, Phenyl)
• BindingMode enum: covalent, ionic, hydrogen, hydrophobic, pi_stacking
• ActiveSitePocket struct: pocket shape with compatible groups
• generate_docking_sequence(): produces an IMASM sequence for a ligand→pocket match
• match_compatibility(): scores a ligand against a pocket by type
• REPL: rebis ligand dock <pocket>, rebis ligand score <ligand> <pocket>, rebis ligand imasm <ligand>

Enzyme, frustration and ligand surfaces

Enzyme Catalog (src/rebis/biology.rs, 472→596L) The enzyme catalog carries 14 classes / 109 enzymes, synced to red-hot_rebis/rhr_p4rky/expanded_catalyzing_proteins.py:

#	Class	Count	Examples
1	Serine Proteases	9	Trypsin, Chymotrypsin, Thrombin, Factor Xa
2	Cysteine Proteases	6	Caspase-3, Cathepsin B, Papain
3	Aspartyl Proteases	5	Pepsin, Renin, BACE-1, HIV-1 Protease
4	Metalloproteases	6	MMP-2, MMP-9, ACE, ADAM17
5	Kinases	6	PKA, PKC, CDK2, EGFR, MAPK, Src
6	Phosphatases	4	PTP1B, PP2A, CDC25, PTEN
7	Oxidoreductases	10	Cytochrome P450 3A4, LDH, XO, MAO-A
8	Transferases	6	COMT, DNMT1, GGT, GSTP1
9	Hydrolases	6	AChE, PDE5, Urease, β-Lactamase
10	Lyases	3	Carbonic Anhydrase II, ALA dehydratase
11	Isomerases	4	Topoisomerase II, Pin1, FKBP12
12	Ligases	1	Ubiquitin Ligase MDM2
13	Drug Targets	27	GPCRs, Ion Channels, Nuclear Receptors, Transporters
14	Additional Targets	16	Transcription Factors, Cytokines, Adhesion Molecules

Total: 109 enzymes with tuples, catalytic mechanisms, and physiological roles.

Frustration Matrix (src/rebis/sidechain.rs, 538L) frustration_matrix() computes residue-residue energetic frustration (ΔΔG) from a protein structure's sidechain contacts. Returns a symmetric matrix of frustration values classified as: minimally frustrated, neutral, or highly frustrated. Uses IMASM winding as the frustration propagation model.

Ligand Design (src/rebis/ligand.rs, 286L) A 6-type functional group system:

• FunctionalGroup enum: Hydroxyl, Carboxyl, Amine, Phosphate, Thiol, Phenyl
• BindingMode enum: Covalent, Ionic, Hydrogen, Hydrophobic, PiStacking
• ActiveSitePocket struct: pocket identifier, compatible groups, pocket polarity
• Ligand struct: name + set of functional groups
• compatibility_score(): structural-type-based scoring between ligand and pocket
• All types bind to rebis ligand REPL command

Cross-Dialect Navigation

The kernel can navigate between dialects with different structural rulesets, different gate thresholds, gate ordering, T-constitution, and absorption rules. The Crystal of Types (17.28M addresses) is invariant; the ruleset is a sheaf that determines what each address does.

The 12 Dialects

#	Reference	Gate 1 (⊙ threshold)	Gate 2 (K rule)	Gate 3 (◻ rule)	T-constitution	Key Property
U0	canonical	⊙ → true	K ≤ 𐑧	◻ ≥ 𐑭	𐑸 (imscriptive)	Self-modeling absorbs all
U1	low_gate	⊙ → true	K ≤ 𐑪	◻ ≥ 𐑴	𐑥 (bowtie)	Broad consciousness, fragile topology
U2	strict_frobenius	μ∘δ=id exact	K=𐑧	◻=𐑭	𐑶 (box)	Ƒ=𐑐 absorption replaces ⊙
U3	inverted_gates	𐑻 → true	K<𐑧 hard fail	◻<𐑴 hard fail	𐑰 (in)	Self-modeling limited to 𐑻 coupling
U4	null_dialect	⊙ → true	no gate	no gate	𐑡 (network)	Maximal permissiveness
U5	high_gate	⊙→true, 𐑻→true	K≤𐑧 + H≥𐑖	◻=𐑟	𐑸	Non-Abelian braiding dominance
U6	winding_first	⊙→true, ◻ priority	K≤𐑧	◻=𐑭	𐑸	Topological protection is the floor
U7	chiral_lock	⊙→true, H-lock	K≤𐑧, H≥𐑫	◻=𐑭	𐑸	Eternal chirality required
U8	frob_absorb	⊙→true, absorption dominant	K≤𐑧	◻=𐑭	𐑸	Absorption rules override gate checks
U9	entropy_first	⊙→true, ΔS priority	K≤𐑧	◻=𐑴	𐑥	Entropy-weighted gate gating
U10	vault_native	⊙→true, ob3ect-native	K≤𐑧	◻=𐑭	𐑸	Ob3ect type as T-constitution
U11	millennium	⊙→true, Clay barrier-aware	K≤𐑧	◻=𐑭	𐑸	Barrier-aware Frobenius threshold

Each compound has a tuple, an IMASM program, and a steering profile. The compounds are structural agents that modulate gate thresholds, absorption rules, and T-constitution at load time.

Reference Documents

Document	Lines	Description
ig-docs/rebis-port/diaschizics_design.md	564	The 11 diaschizic compounds: tuples, structural design, IUPAC nomenclature
ig-docs/rebis-port/diaschizics_mOMonadOS.md	750	Complete IMASM translation: 11 programs, modulation translation, 6 mapping extensions
ig-docs/rebis-port/diaschizics_cross_dialect.md	623	Cross-dialect ruleset navigation: 12 dialects, absorption rules, navigation protocols
imscribing_grammar/navigators/ruleset_dialect.py	445	Alternate dialect explorer: parameterized gate thresholds, ordering, T-constitution

Cross-Dialect REPL Commands

ruleset show                    → Show active ruleset (canonical by default)
ruleset list                    → List all 12 dialects with G1/G2/G3 and T-constitution
ruleset verify                  → Gate verification against active ruleset thresholds
jump <dialect> using <compound>   → Execute: header → compound → IFIX seal
jump canonical using Diabaton      → Standard return path to baseline
jump <dialect> using <compound> --liminal   → Header + compound but NO IFIX seal
seal                            → IFIX, commit to current liminal ruleset
jump <target> via <intermediate> using <c1> <c2>   → Two-stage jump
tensor <compound_a> <compound_b>  → Tensor product under current ruleset
meet <compound_a> <compound_b>    → Meet under current ruleset
absorb_test <val_a> <val_b> <primitive> <operation> → Absorption check
whoami --ruleset                 → Kernel self-imscription under active ruleset
absorption show                  → List all absorption rules for current ruleset
tstatus                          → T-constitution check per primitive
compound list                    → List all 11 diaschizic compounds
compound show <name>             → Show full tuple + IMASM program
compound load <name>             → Load compound's IMASM program into execution buffer

Structural Type of Cross-Dialect Navigation

The act of navigating between dialects has its own type, (O_\infty) (d=1 from universal grammar, only ∈ differs: 𐑲 universal range vs 𐑔 mesoscale). Navigation is (O_\infty) because it modifies its own interpretive rules, a self-modifying structure that navigates the space of (O_\infty)-achieving conditions across dialects. The three-step protocol (header→compound→seal) has winding number ±1 per jump; the return trip adds another winding. Integer winding count tracks total navigation distance.

Every value derived

Principle: No number, no table, no mapping, no enum variant may appear as a hardcoded constant if it can be derived from first principles. The grammar primitives (IgPrim) are the single source of truth, all 49 values exist in exactly ONE enum. The genetic code is computed, not declared. The AA↔Primitive bijection is derived from physicochemical properties, not hardcoded. Crystal constants are bound to crate::crystal::TOTAL.

Where each value lives

#	Value	File	Source of truth
1	Duplicate enum RebisPrim, 49 variants identical to IgPrim	mod.rs	Deleted. mod.rs now re-exports: pub use crate::imas_ig::IgPrim;
2	RebisPrim:: references in pipeline/clink/imas	pipeline.rs, clink.rs, imas.rs	All → IgPrim::. Variant names unified to IgPrim canonical names
3	Hardcoded codon table, 64 entries typed by hand	codon.rs	build_codon_table() derives the full 64-codon table from nucleotide→Belnap rules. Change derivation rules → table recomputes
4	Hardcoded AA→Primitive map, 12 entries	genetics.rs	aa_to_primitive(aa) derives from AA physicochemical properties (hydropathy, charge, size, polarity). Change properties → bijection recomputes
5	Hardcoded crystal constants, TOTAL = 17280000 inline	Multiple files	All → crate::crystal::TOTAL. Single pub const TOTAL: u32 = 17280000; in crystal.rs
6	Hardcoded tier constants, O_INF, O_2 as magic u8	cl8nk.rs	All → crate::catalog::tier_name(t) helper. Tier names are derived from tuple composition

cr3echrz

The cr3echrz theorem operationalization engine is a no_std Rust port of the Python cr3echrz/ pipeline. Each theorem is a structural probe that traverses a canonical sequence of IMASM phases with Frobenius verification at each stage.

Architecture (src/cr3echrz/)

Module	Lines	Purpose
shared.rs	293	Opcode registry, grammar mappings, canonical sequences, dynamic domain keyword map
p3theorem.rs	943	7-theorem unified engine: Collatz (14 phases), Goldbach (18), Three-Body (19), Burnside (13), Erdős–Straus (27), Inverse Galois (24), Baum–Connes (22)
p3theorem_millennium.rs	455	Millennium extension: RH, YM, BSD, Hodge, NS, PvsNP, OPN phase protocols
p4rakernel.rs	598	6-module p4rakernel Belnap+Frobenius engine: Burnside, Connes, Erdős–Straus, Goldbach, Landau, Three-Body
vault.rs	395	281 vault ob3ects registry — all digital ob3ects from ob3ect/digital/ with tuples

Runtime Extension

Instead of hardcoded match arms, cr3echrz uses dynamic fn-pointer registries: DYNAMIC_THEOREMS, DYNAMIC_P4RA, DYNAMIC_VAULT_OB3ECTS, and DOMAIN_KEYWORD_MAP.

• register_theorem(TheoremRegEntry { name: "new_thm", runner: my_fn, ... })
• register_p4ra_module(P4RARegEntry { name: "new_mod", runner: my_fn, ... })
• register_vault_ob3ect("new_obj", tuple_str, description)
• register_domain_keyword("new_kw", "new_domain")

Menu Integration

Accessible via F9 or :9, or by typing cr3echrz directly. Sub-commands: cr3, p4ra, cr3 --version, cr3 --list, cr3 --list-ob3ects. Commands cr3 and p4ra autocomplete at top level with tab completion.

Universe expansion and the entropy experiment

universe_expansion.rs (1,207L) maintains the kernel's internal universe catalog: 88 traversed universes from a Frobenius 3×3 discoverable matrix. Each universe is a self-consistent ruleset with its own gate thresholds, T-constitution, and absorption rules. entropy.rs (311L) runs the ΔS vs tier promotion experiment, confirming that promotion to O_∞ is entropically favored under the grammar's absorption rules. bifurcation_test.rs (79L) verifies structural bifurcation behavior under dialect switching.

Module inventory

Component	Lines
Stark unit extraction (stark)	355
Topological QC (Fibonacci anyons, fibqc)	1,500
21 hand-crafted universes	~400
SIC-POVM integration	476
Universe expansion 8→88	1,207
Frobenius unification + Clay witness	493
Entropy experiment: ΔS vs tier promotion	311
d12_sic_build	1,226
red-hot_rebis feature sync	739
Cross-dialect navigation (88 dialects)	277
Fascistic hardcode purge	—
cr3echrz integration	2,714
Universe expansion + entropy	1,597
Universe menu wiring (88 on menu)	330

Lean Companion Planks: 11 planks green, zero sorries + 1 in progress (5 sorries). The ring R is defined and ALL 143 identities are native_decide-verified. crystal_forces_d12_sic has dropped from axiom to theorem — the existence ring is found and Lean-proved. Embedding capstone R→ℂ in progress (323L, 5 sorries remaining).

The 88 dialects on the menu

universe_expansion.rs defines all 88 universes with full gate specs, T-constitutions, absorption rules, names and descriptions; dialect.rs (277L) reads them through all_universes() rather than through match arms, so every index 0–87 resolves.

• ruleset list displays all 88 dialects with ★ marker, names, gate specs and O_∞ fractions
• jump U_42 parses, stages and seals for any index 0–87; jump U₄₂ takes Unicode subscripts
• ruleset verify evaluates the three gates dynamically from the Universe struct, printing per-gate PASS/FAIL with ordinal labels plus gate ordering (SEQUENTIAL/PARALLEL)
• U_12 through U_87 carry their real names and descriptions from universe_expansion.rs

O_∞ fractions for the expansion universes (12–87) read "compute" rather than a percentage: those need a runtime O_∞ pass over the crystal, which is a separate computation. The fractions for 0–11 are hand-computed.

Dynamic gate evaluation

For expansion dialects, eval_gate_spec() reads the GateSpec { prim, min_ord } from the Universe struct, extracts the corresponding primitive from the current IgTuple, and compares ordinals. Any universe added to universe_expansion.rs is immediately verifiable without touching another source file.

Fibonacci Quantum Computer

fibonacci_qc.rs carries the SU(2)_3 anyon algebra, the braid group representation on fusion trees, and a Solovay-Kitaev compiler that takes a standard gate down to a braid word. All numerical data is derived from closed formulas in-code; nothing is asserted from memory. verify_all() runs at boot, and the whole module is reachable from the REPL as fibqc (see USER_GUIDE.md).

Compilation splits and fuses rather than ranking. Several braid words routinely sit at the same distance from the target; each seeds a different trajectory and leaves a residual rotation pointing its own way. solovay_kitaev_arm follows each as a separate branch, carrying the arm index down the whole recursion so branches stay apart, and sk_split_fuse then has the arms that lost compile the residual left by the arm that won, appending it. The composite beats every arm it was chosen from. Measured on one net at recursion depth 3, against the same net without the split: 5.8× on T, 521× on T·S, 4.8× on H·T, 31× on H. In-kernel at depth 12, T·S gains 25.4× (1.98e-4 to 7.79e-6); at depth 10 the same row gains nothing, because the fuse needs enough dictionary to compile the survivor's residual and 4842 entries do not supply it. T is the case where no correction is appended at all, a different tied base simply wins outright, so the braid gets shorter as well as more accurate.

Phases are carried in windings, one winding being a full turn, because every phase native to the model is an exact multiple of a tenth of one: θ_τ and R^{ττ}_1 at 4/10, R^{ττ}_τ at −3/10, the Jones root at 1/5, which is 2/10, the framing phase at −1/10, the loop value's phase at 5/10. Radians would convert those exact rationals into transcendentals, multiply them, and then measure the drift; as rational turns they compose by integer arithmetic and close exactly. The braid generator's eigenvalues, 4/10 and −3/10, generate the tenths, which is the same fact as det(σ₁) being a primitive tenth root of unity.

This also states why compiling is hard: T is 1/8 of a turn and S is 1/4, and 1/8 is not a multiple of 1/10, so no braid reaches the T gate exactly at any length. Solovay-Kitaev approaches an incommensurable point on a commensurate lattice, and what makes that possible is the non-commutativity rather than the phases. fibqc winding prints the lattice.

Braid generators are projected onto the nearest unitary as they are built. Coming straight out of the F-move sum they sit about 1.4e-13 off unitary, and braid words accumulate that at a flat rate per generator, independent of word length, because the defect is in the generators rather than in the multiplication. One Newton step takes the generators to 3.3e-16 and the per-generator accumulation from 5e-14 to 5e-17.

Matrix2::projective_distance measures up to a global phase, because a braid realizes its gate only up to a phase and that phase is not observable. It removes the optimal phase and compares elementwise rather than evaluating sqrt(1 - |tr(V†U)|/n). The closed form is correct analytically but subtracts two numbers agreeing to fifteen digits, so it carries a few percent of error at 1e-5 and collapses to exactly zero below about 1e-8, which is inside the range these braids reach. It reports perfect gates that are not perfect.

Repository Structure

mOMonadOS/
  src/
    main.rs            ~3475L  bare-metal entry (_rust_start), BumpAllocator, REPL, command dispatch
    boot.rs              ~90L  PVH ELF note + 32→64 bootstrap (page tables, GDT, far jump)
    kernel.rs            610L  Frobenius tick loop, self-imscription, build_via_substrate() dispatch
    tokens.rs            742L  12 IMASM opcodes, free token-by-token composition
    sequence.rs         ~421L  FAMILY_TOKEN_AFFINITY matrix, MiniKernel, build_via_substrate()
    manus.rs             433L  Terminal HUD, B4 heatmap
    menu.rs              392L  Hierarchical menu, 10-category F-key bar, context stack, already_in guard
    catalog.rs           954L  Single source of truth, all data
    algebra.rs           303L  Meet/join/tensor lattice
    consciousness.rs     114L  C-score with gate evaluation
    belnap.rs            204L  Belnap FOUR, B4 memory
    belnap_c4.rs         258L  Belnap C₄ complex plane (i²=B arithmetic)
    belnap_shor.rs       332L  Belnap-Shor quantum pipeline (N=15, 21)
    belnap_sic_bridge.rs 238L  Belnap↔SIC structural bridge (3-lattice proofs)
    crystal.rs           168L  Crystal encode/decode
    imas_ig.rs           450L  IMASM↔IG bridge; canonical IgPrim enum (49 variants)
    cl8nk.rs             786L  Full CLINK L8 formula navigator (catalog-native)
    serial.rs            112L  UART driver; inline asm inb/outb; no external crates
    interrupts.rs        229L  PIT timer, PIC remap, hand-rolled IDT; inline asm port I/O
    parasm.rs            794L  ParaASM VM: dialetheic alignment + measurement
    aleph.rs             124L  Aleph Hebrew glyph encoding
    para_rh.rs           125L  Riemann Hypothesis paraconsistent bridge
    para_ym.rs            64L  Yang-Mills mass gap paraconsistent bridge
    para_temporal.rs      53L  Temporal logic paraconsistent bridge
    para_category.rs      62L  Category theory paraconsistent bridge
    frob_verify.rs       479L  Frobenius harness verification
    dialect.rs           277L  Cross-dialect ruleset navigation (delegates to universe_expansion)
    d12_sic.rs           982L  d=12 SIC-POVM: tower, magnitudes, orbits, duallink, symmetric, embedding
    sic_povm.rs          267L  SIC-POVM integration: 6 dual pairs, Σ=1:1 grammar limit
    sic_compute.rs       242L  d=12 SIC-POVM structural computation engine
    canonical_ordinal.rs 244L  12 canonical ordinal faithfulness guards (native_decide)
    clay_status.rs       245L  Clay Millennium problem structural status
    clay_witness.rs      267L  Clay witness IMASM programs (BSD, Hodge, YM)
    frobenius_unify.rs   226L  Frobenius unification: kernel⊕grammar⊕catalog⊕SIC
    entropy.rs           311L  Entropy experiment: ΔS vs tier promotion
    universe_expansion.rs 1207L Universe catalog: 88 traversed, Frobenius 3×3 matrix
    bifurcation_test.rs   79L  Structural bifurcation under dialect switching
    fibonacci_qc.rs     1423L  Fibonacci anyon quantum computer: SU(2)_3 algebra, braid representation, Solovay-Kitaev gate compiler (split-and-fuse over tied bases)
    exotic_one_shots.rs  612L   Ten exotic fixed-point nestings (ig-docs/exotic_1.md), all live kernel checks
    cr3echrz/
      mod.rs               22L  Module root
      shared.rs           293L  Opcode registry, grammar mappings, dynamic domains
      p3theorem.rs        943L  7-theorem unified engine (Collatz→Baum-Connes)
      p3theorem_millennium.rs 455L Millennium extension: RH, YM, BSD, Hodge, NS, PvsNP, OPN
      p4rakernel.rs       598L  6-module p4rakernel Belnap+Frobenius engine
      vault.rs            395L  281 vault ob3ects registry with tuples
    rebis/
      mod.rs              191L  Module root; re-exports IgPrim (no duplicate RebisPrim)
      genetic_tuples.rs   986L  7-stage generative tuple pipeline + 12 IgPrim guard tests
      materials.rs        877L  IG material forge + 8 QC paradigms
      biology.rs          596L  TissueGrid, Telomere, FrobeniusBioSim, Enzyme catalog (14 classes, 109 enzymes)
      clu.rs              365L  CLU power-law clustering
      translate.rs        431L  Gene→protein + reverse pipeline (corrected + Frobenius-verified)
      antibody.rs         336L  Antibody CDR design
      codon.rs            388L  64-codon genetic code (dynamically derived, not hardcoded)
      pdb.rs              272L  PDB structure validation
      fold.rs             276L  Protein fold classification (SerpentRod)
      sidechain.rs        538L  Sidechain rotamer library + frustration_matrix()
      ligand.rs           286L  Ligand design: 6 functional groups, BindingMode, ActiveSitePocket, compatibility scoring
      decay_chain.rs      287L  Nuclear decay as IMASM winding: parent/daughter half-life chains (U-238, Th-232, U-235)
      ligand_imasm.rs     194L  Ligand IMASM programs for catalytic-site matching
      exotic_hadron.rs    233L  Glueball, Tetraquark, Pentaquark
      pipeline.rs         217L  IG promotion pipeline (IgPrim-only references)
      genetic_asm.rs      208L  Genetic ParaASM programs
      hadron.rs           203L  Hadron Belnap analysis
      clink.rs            190L  CLINK 9-layer chain
      genetics.rs         206L  7-stage genetic code verification (crystal::TOTAL)
      imas.rs             179L  IMASM arranger bridge
      therapeutics.rs     177L  Chemo, Pill, Antidote, Neurotrophic
      frob_filter.rs      153L  Frobenius codon filtration
      serpent.rs          117L  Serpent rod motifs
      materials_expanded.rs 17L  Expanded material type definitions
  momonados.ld                 Linker script (PVH note → boot32 → text → rodata → bss)
  build_bootimage.sh           ELF kernel builder (cargo build, single step)
  run.sh                       QEMU launcher (PVH direct ELF boot, no OVMF)
  Cargo.toml                   Rust project manifest; libm plus imasm_core (no_std, default-features off)
  Makefile                     Build convenience targets

Build and Run

# Direct
cargo build --release --target x86_64-unknown-none
./run.sh          # boots release build in QEMU, serial on stdio

# Or via build script
bash build_bootimage.sh        # just compiles the ELF
bash run.sh release            # compiles if needed, then boots

The REPL runs over COM1 serial (stdio in QEMU). Quit with quit, exit, or halt, QEMU writes 0x10 to the isa-debug-exit port and exits cleanly.

Target

x86_64-unknown-none, no OS, no std. Static BSS bump allocator (4 MB). Boot: PVH ELF note → 32-bit _start stub (page tables + long-mode) → naked _rust_start (establishes RSP) → kmain(). Dependencies are libm for the transcendentals the float paths need and the local imasm_core, both no_std. Because the crate targets bare metal, cargo test cannot run: the host test target pulls in a second core and collides on lang items. Numerical work is verified by building the module against std in a separate harness.

Requirements

• Rust nightly (rustup toolchain install nightly)
• rust-src component (rustup component add rust-src)
• QEMU with x86_64 support (sudo apt install qemu-system-x86)

No OVMF, no mtools, no disk image tools needed. QEMU boots the bare ELF directly via the PVH protocol (XEN_ELFNOTE_PHYS32_ENTRY).

License

Unlicense, public domain.