hexa-bio — Molecular Toolkit (HEXA family)

5-axis molecular substrate organized around the n=6 invariant lattice: QUANTUM / WEAVE / NANOBOT / RIBOZYME / VIROCAPSID. Four axes are write-side bio sandboxes (the n=6 τ-quartet tetrahedron — weave / nanobot / ribozyme / virocapsid); the fifth axis (quantum) is the external compute bridge — VQE / qpu_bridge over qmirror. weave ships a full numerical empirical sandbox (Caspar-Klug + Zlotnick cage-assembly ODE + Bayesian σ(6)=12 STRUCTURAL-EXACT audit, posterior 0.97); the other three bio axes ship a C0b skeleton simulator + σ(6)=12 verification + falsifier preregister; quantum is at Phase 1+ (H₂/LiH VQE chemical/spectroscopic accuracy, F-Q-1…5 PASS, pocket-VQE F-Q-6 open).

Status (2026-05-13, cycle-30++++++++): v1.x category-(a) closure = 100% across all 5 axes (weave / virocapsid / ribozyme / nanobot / quantum). selftest/run_all.sh → 35/35 PASS on dev host (deterministic in-repo gates; SKIP-clean substrate gates included). v1.1.0 candidate drafted (see RELEASE_NOTES_v1.1.0.md). Cycle 25 traversed the 16-cell C2 matrix (4 bio axis × 4 disease class) at IN-SILICO grade — 16/16 cells PASS the simulator+metadata internal-consistency check. The QUANTUM compute axis is tracked separately in .roadmap.quantum (Phase 1+ LANDED, qpu_bridge L1; F-Q-6-E Ramp B 4e/4o IN-PROCESS 6/6 closure 2026-05-13 (LiH + 5 CMT scaffolds via RFC 034+035 farr-NM, Δ 11.7-274 µHa); Ramp B-2 4e/5o (8-qubit) in-process 6/6 closure same day — LiH 790 µHa

• clc1/sar1/mfn2/hd6 in chem-acc + gjb1 40.27 µHa @ maxiter=4000 stretch; +ADAPT-VQE LiH 4e/4o 0.043 µHa (62% param-reduction vs UCCSD-26) + k-UpCCGSD strict-subspace plateau at 344 µHa, via hexa-lang RFC 036 (farr_int_array packed int64_t* handle) + RFC 039 (parameter-shift gradient kernel + raw-helper refactor; enables hexa-native L-BFGS-B). Honest caveat (raw#10 C3): "100% closure" here is bookkeeping only — category (a) measures in-repo software / formalism / infrastructure. Category (b) v5 Lean stretches and category (c) wet-lab / IP / hardware adoption are explicitly out-of-software-scope (per CLOSURE_RESIDUAL_BACKLOG.md §0). C2 PASS verifies in-silico simulator+metadata internal consistency only — it is NOT therapeutic, clinical, regulatory, immunogenic, or efficacy progress. C3+ (wet-lab → IND → phase I) is explicitly out-of-repo. All 5 axes (synthetic biology / CRISPR / virocapsid / ribozyme catalysis / pocket VQE) are scientifically UNPROVEN at the wet-lab boundary — closure here is software-bookkeeping, never a medical or empirical claim. Real-limits anchors (DNA fidelity, Eyring k_cat, Caspar-Klug ΔG, ATP cost, CRISPR off-target floor): see LIMIT_BREAKTHROUGH.md.

Distribution: GitHub canonical at https://github.com/dancinlab/hexa-bio. CLI tooling — installed via hx install hexa-bio from the hexa-lang package registry. (HF Hub mirror retired 2026-05-04: HF Hub is designed for ML model weights / datasets; CLI tooling distribution is GitHub-canonical.)

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What is hexa-bio?

hexa-bio is a standalone Molecular Toolkit that exposes a 5-axis write-side molecular sandbox. It is the empirical companion to canon/domains/biology/ and the canonical extraction-of-record for the WEAVE axis (cycle 24, 2026-04-29 → standalone 2026-05-04).

Four of the axes are bio "verbs" that form the tetrahedron of the n=6 invariant lattice (the τ(6)=4 quartet); the fifth axis (quantum) is the external compute bridge layered across all four — VQE for molecular electronic structure, plus ML pilots (ProteinMPNN / Boltz-2 / RhoFold+):

                          ┌──────────────┐
                          │   composition│
                          │    (WEAVE)   │
                          └───────┬──────┘
                                  │
                  ┌───────────────┼───────────────┐
                  │               │               │
       ┌──────────▼──────┐  ┌─────▼──────┐  ┌────▼────────┐
       │   actuation     │  │  catalysis │  │  assembly   │
       │   (NANOBOT)     │  │  (RIBOZYME)│  │ (VIROCAPSID)│
       └─────────────────┘  └────────────┘  └─────────────┘
                  │               │               │
                  └───────────────┼───────────────┘
                                  │  (compute substrate spanning all 4)
                          ┌───────▼──────────┐
                          │   computation    │
                          │  (QUANTUM —      │
                          │   qpu_bridge VQE)│
                          └──────────────────┘

The 5-axis framework is locked (.roadmap.axis_expansion_decision_2026_05_08): four 6th/7th-axis candidates (BIO-EVOLUTION, QUANTUM-BIOLOGY, PLANETARY-HEALTH, CONSCIOUSNESS) were all reject/defer — selectivity = rigor. Cross-cutting platform layers and disease-orthogonal entries absorb the salvageable content without inflating the axis count.

weave is the only axis with a full numerical empirical sandbox at v1.0.0 (T=1 60-subunit icosahedral cage; posterior 0.97). nanobot / ribozyme / virocapsid ship a C0b skeleton simulator + σ(6)=12 STRUCTURAL-EXACT(-CANDIDATE) verification + falsifier preregister. quantum is at Phase 1+ (H₂/LiH VQE

• ML pilot smokes; pocket-VQE F-Q-6 is the open Phase C gate).

---

Install

# 1. Install hexa-lang (gives you `hexa` + `hx` package manager)
/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/dancinlab/hexa-lang/main/install.sh)"

# 2. Install hexa-bio
hx install hexa-bio

Run

hexa-bio weave            # protein cage / polyhedral self-assembly        [WIRED]
hexa-bio nanobot          # molecular actuation primitive                  [C0b skeleton]
hexa-bio ribozyme         # RNA-catalyst primitive                         [C0b skeleton]
hexa-bio virocapsid       # viral capsid assembly primitive                [C0b skeleton + PDB corpus]
hexa-bio quantum          # qpu_bridge VQE / ML pilot compute axis (5th)   [Phase 1+; F-Q-1…5 PASS]
hexa-bio status           # 5-axis status table + verdict + caveats
hexa-bio selftest         # full 5-axis sentinel sweep + 16-cell C2 sweep

---

5-axis status table

Axis	Role	n=6 lattice verification	v1.x closure-grade (2026-05-12, cycle-30)	Residual cat.	Empirical sandbox
weave	composition	STRUCTURAL-EXACT (T=1, post 0.97)	✅ ~100%	—	cage-assembly ODE + Bayesian audit
virocapsid	assembly	STRUCTURAL-EXACT (T=1 corpus + multi-T)	✅ ~100% — C5 schema lock + 4-fixture conformance ✅ · C3a + C3b (GATE-26-V-1b) CLOSED in-repo ✅ 2026-05-12 (VIPERdb v3.0 snapshot, n=527 / 87 families / 15 T-strata; log10_BF 876.27) · F-VIROCAPSID-1-c + F-VIROCAPSID-1-d CLOSED in-repo ✅ 2026-05-12 cycle-30 (selftest/virocapsid_f_virocapsid_1c_1d_audit.py: 1-c 3 proxy stratifications all PASS, 1-d annotation completeness mean 0.9930 / min 0.9526 across 7 fields; sentinel __VIROCAPSID_F1C_F1D__ PASS); residual: T=7/13/21 stretch (b)	—	VIPERdb-corpus T-number discrimination (n=527, σ(6)=12 = 12 pentamers ∀T incl. pseudo-T) + Caspar-Klug + Zlotnick cage-assembly ODE
ribozyme	catalysis	STRUCTURAL-EXACT-CANDIDATE (12-nt; deductive PASS)	✅ ~100% (a) — R-R1 (Nussinov MFE) / G26-RB-3 (Hamming off-target screen — pool n=206 via GENCODE v47 subset + FULL GENCODE v47 pc-transcriptome screen EXECUTED via RIsearch2 v2.1, summary vendored) / G26-RB-2 (J₂=|S₄|=24 quotient) / G26-RB-1′ (4-state kinetics sim re-impl, F-RB-4 6/6) + A1.1/A1.2/A1.3 robustness sentinels CLOSED cycle-30 (kinetics ±10% sweep / off-target threshold replay / Nussinov determinism stress) all in-repo ✅ 2026-05-12; residual: wet-lab confirmation (c) out-of-software-scope	(c) only	hammerhead 4-state kinetics (Eyring TST, k_cat≈0.6/min) + Nussinov MFE + Hamming off-target screen + RIsearch2 v2.1 vs GENCODE v47 pc-transcriptome
nanobot	actuation	STRUCTURAL-EXACT-CANDIDATE (12-vertex; deductive PASS)	✅ ~100% (a) — N-R1 v2 reference emitter ✅ · C0d cuboctahedron dual-skeleton actuation sim re-impl ✅ · N-R2 hexa-bio-side LOCKED v1.0.0 ✅ 2026-05-12 (handoff_l6_emission_v0.schema.json lock_metadata, emission unblocked, verified consistent w/ canon@mk1 raw_77_therapeutic_nanobot_l7_acceptance_v1 DECLARED; vendored ref nanobot/spec/canon_l7_acceptance_handoff_ref.json; F-NB-1-c ratio 0.0 PASS); residual: wet-lab/IP (c) out-of-software-scope — not a v1.x software blocker	(c) only	4-state DNA-origami actuation sim (work 50 kT, J₂=24 pose-canon) — both truncated-icosahedron & cuboctahedron skeletons
quantum	computation	VERIFIED (H₂ 6-Pauli / LiH path) + pocket-scale (F-Q-6-D) + library-ranking (F-Q-6-F) + F-Q-6-E LANDED at 5 sub-tiers cycle-30++++++++ + GATE-26-2 v4 ALL AXES ✅ cycle-30++++++	✅ ~100% (a) — F-Q-1…5 + F-Q-EXT-1…6+ + F-Q-6-D PASS (Mpro pocket VQE sub-µHa, tests/mpro_pocket_vqe_v7.py) + F-Q-6-F PASS (5-warhead library ranking, tests/mpro_warhead_library_vqe_v7.py) + F-Q-6-E LANDED 2026-05-13 cycle-30++++++++ at five sub-tiers: (a) 2e/2o pure-hexa UCCSD over all 5 CMT scaffolds (qmirror chemistry_vqe_cmt_hamiltonians.hexa, << 1 µHa vs CASCI(2,2)); (b) 4e/4o vendored ψ* replay over all 6 molecules (LiH + 5 CMT, qmirror chemistry_vqe_cmt_4e4o_<name>.hexa per-molecule, Δ 0.0005-17.78 µHa vs CASCI(4,4)); (c) Ramp B EXTERNALIZED variational closure on LiH 4e/4o (pure-hexa physics via chemistry_vqe_cmt_uccsd_lih_4e4o_oneshot.hexa + Python-stdlib NM driver — Δ=494.8 µHa, 3× under 1.6 mHa chem-acc bound, 58.5% HF→CASCI gap recovery, 5.7-min wall @ maxiter=5); (d) Ramp B IN-PROCESS variational closure 6/6 on LiH + 5 CMT scaffolds at 4e/4o (qmirror chemistry_vqe_cmt_uccsd_<name>_4e4o.hexa) via hexa-lang RFC 034 (whole-loop Pauli C kernels) + RFC 035 (whole-NM-step C kernels — gjb1 only, lifts maxiter cap from ~200 to ≥500), Δ range 11.7-274 µHa, ~10-18s wall/scaffold; (e) Ramp B-2 4e/5o (8-qubit) full NM closure 6/6 — LiH 790 µHa @ 9s + clc1 457 / sar1 630 / mfn2 311 / hd6 15 µHa @ maxiter=500 + gjb1 40.27 µHa @ maxiter=4000 stretch (305s wall) via per-scaffold modules chemistry_vqe_cmt_uccsd_<name>_4e5o.hexa, HEXA_MEM_CAP_MB=2048; +ADAPT-VQE 11/11 across 4e/4o + 4e/5o (LiH 4e/4o 0.043 µHa @ K=10 + 5 CMT 4e/4o 5/5 PASS (K range 2-18,	Δ	1.95-50.6 µHa, hd6 collapses to K=2/3.67 µHa/3s); LiH 4e/5o 0.05 µHa @ K=14 + 5 CMT 4e/5o 5/5 PASS (K range 2-35,

Residual categories (for the "remaining" parenthetical in each row) — full enumeration in CLOSURE_RESIDUAL_BACKLOG.md:

• (a) in-repo software — closeable by code/test work in this repo; counts against v1.x closure-grade. ✅ 100% REACHED 2026-05-12 cycle-30 — all 4 items CLOSED (ribozyme A1.1/A1.2/A1.3 + virocapsid A2.1 Zlotnick ODE CLI; see CLOSURE_RESIDUAL_BACKLOG.md §A).
• (b) v4 formal semantics — cycle-30++/+++/++++/+++++/++++++ Lean / Mathlib work; tracked in .roadmap.lean4_formal. ✅ ALL 4 axes at v4 maximum semantics 2026-05-12 cycle-30++++++ — Axis 1 REAL, Axes 2 + 3 + 4 all v4 PROVEN (substrate-polymorphic energy [AddCommGroup E] [LinearOrder E] [IsOrderedAddMonoid E] + opaque positive floor : E; Prod.lex WellFoundedRelation recursion; [CommMonoid β] payload over Finset (α × β) + totalCaveatPayload); lake build N6 → 900/900 jobs PASS. The v1 → v2 → v3 → v4 abstraction trajectory is now EXHAUSTED. Remaining: v5 stretches per axis (ring/module on E, verifier-strategy typeclass, Finsupp key-collapsing payload) deferred to cycle-30+++++++, NOT a v1.x or v2.0.0 blocker (§B). MechVerif legacy + Theorem B residual sorries remain FROZEN in legacy-canon.
• (c) out-of-software-scope — wet-lab / IP / hardware adoption; does NOT count as a software closure gap; handed off via sister-repo / canonical / external-vendor channels. 100% IMPOSSIBLE in software — closeable only via external counterparties (CRO, patent counsel, quantum vendors). 9 of 11 items currently have no destination repo / vendor selected (§C).

The v1.x closure-grade percentages above measure category (a) only. Categories (b) and (c) are tracked separately and explicitly out-of-scope for the v1.x track terminal.

Verdict: ✅ PASS — v1.x track terminal REACHED for all 5 axes when judged on category (a), the only category v1.x measures. All 5 axes at ~100% (a): weave / virocapsid / ribozyme / nanobot / quantum. Category (b) v3.0.0 cert-strength has also been EXCEEDED (hexa-meta formal/lean4/ all 4 axes at v4 maximum semantics; lake build N6 → 900/900 jobs PASS; commit 7c0ec92). Category (c) wet-lab/IP/hardware is out-of-software-scope per AGENTS.md external-contact deferral policy. The v1 → v2 → v3 → v4 abstraction trajectory is exhausted for the WEAVE-mechanical consumer contract. Per-axis gates / deadlines / owners: AXIS_CLOSURE_PLAN.md.

In-repo / deductive closure status (2026-05-12)

The in-repo, deductively-checkable portion of closure is now complete for all 5 axes:

• selftest/n6_axis_computational_verification.py — deterministic σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24 + master-identity verification across Q/W/N/R/V (42/42 checks PASS, no human raters, no live simulation).
• _python_bridge/module/ribozyme_mfe_nussinov.py — Nussinov MFE solver inline port (closes ribozyme R-R1; dot_bracket='stub' deprecated).
• _python_bridge/module/ribozyme_off_target_screen.py — ribozyme G26-RB-3 off-target screen: Hamming sliding-window scan (arm + reverse-complement, per-arm per-kb gate; 4/4 self-check) over a reference pool = 6-mRNA toy + (CUG)ₙ low-complexity decoy + GENCODE v47 pc-transcript subset n=200 (ribozyme/spec/human_transcript_pool_snapshot.json, --refresh-gencode rebuilds, --full-pool runs vs all 206); + a FULL GENCODE v47 pc-transcriptome screen EXECUTED via RIsearch2 v2.1 (-s 6 -e -22 -z t04; per-query summary vendored ribozyme/spec/gencode_v47_offtarget_risearch2_summary.json, --full-screen-results; designed 14-nt arms → PASS, GC-rich / (CUG)ₙ arms → flood 24.8k–1.37M off-targets → FAIL; the RIsearch2 binary + the 48 MB FASTA aren't vendored — --gencode-pipeline-doc reproduces).
• _python_bridge/module/ribozyme_reaction_coordinate_quotient.py — ribozyme G26-RB-2 branch-lock: J₂ = |S₄| = 4! = 24, S₄ ≅ O (octahedral), regular action on the 24 catalytic-ladder orderings (14/14 deductive checks PASS).
• _python_bridge/module/ribozyme_kinetics_simulation.py — ribozyme G26-RB-1′ sim re-run: stdlib re-implementation of the R5-sunset hammerhead 12-nt 4-state kinetics simulator (Eyring TST → k_cat≈0.6/min, K_M≈0.12 µM, Eigen-Hammes margin 4.08 orders; 4-state RK4/Euler/analytic ODE; F-RB-4 6/6 PASS).
• tests/mpro_pocket_vqe_v7.py — quantum F-Q-6 / L3 Mpro [Cys145 thiolate + His41 imidazolium + nirmatrelvir nitrile] pocket-cluster VQE (2e/2o → 2 qubit → sub-µHa 0.0001 µHa vs CASCI(2,2)) — needs the ~/.hexabio_venv qiskit/pyscf stack.
• tests/mpro_warhead_library_vqe_v7.py — quantum F-Q-6-F (Phase D) 5-warhead covalent-Mpro-inhibitor library ranking: gas-phase model ΔE_rxn per warhead (nitrile/aldehyde/α-ketoamide/Michael/CF3-ketone), each fragment at sto-3g / 2e-2o → 2 qubit → VQE vs CASCI(2,2) — all 11 fragments VQE=CASCI sub-µHa; ranking α-ketoamide < CF3-ketone < aldehyde < Michael < nitrile (qualitative reactivity ordering — not a ΔG/affinity claim).
• _python_bridge/module/lean4_proof_witness_emit.py + weave/spec/canon_lean4_state_ref.json — GATE-26-2 consumer witness-emit: absorbs the dancinlab/canon@mk1 lean4 state (the formal/lean4/ 4-axis STUB LANDED [4-sorry, cycle-30+] + the lean4-n6/N6/ Theorem B σ·φ=n·τ⟺n=6 essentially fully proven [~4473 ln, ~2 sorry, ~99.99%]) and emits the 4 raw_77_lean4_proof_witness_v0 rows. Hexa-bio holds no .lean files by design — only the scaffold spec + the witness emitter + the state ref.
• nanobot/spec/canon_l7_acceptance_handoff_ref.json + nanobot/spec/handoff_l6_emission_v0.schema.json (lock_metadata) + nanobot/spec/proposed_l7_l9_witness_schemas/ (3 schemas + README) + _python_bridge/module/nanobot_l6_l7_contract_test.py — N-R2 hexa-bio-side lock + the L7-L9 acceptance schemas DRAFTED (consumer-proposed; canon adopts): a READ-ONLY ref copy of canon@mk1's raw_77_therapeutic_nanobot_l7_acceptance_v1 (DECLARED v1.0.0-stub) + the L6 emission schema locked v1.0.0 (emission unblocked, consumed_by_l7_l9 mapping) + 3 consumer-proposed L7-L9 per-layer witness schemas (raw_77_therapeutic_nanobot_l7_drug_load_v1/_l8_immune_evasion_v1/_l9_biodistribution_v1, derived from the canon@mk1 handoff JSON's per-layer primitives) + a consumer-driven contract test (8/8 PASS — the L6 emitter provides every field each L7-L9 schema consumes, declarations == canon handoff's consumes_from_l6, F-NB-1-c ratio 0.0).
• _python_bridge/module/virocapsid_pdb_corpus.py — virocapsid C3a + C3b (GATE-26-V-1b): re-implementation of the R5-sunset icosahedral-capsid corpus + Bayes σ(6)=12-vs-uniform{5..50} audit; the corpus is now sourced from VIPERdb v3.0's JSON web service -> vendored snapshot virocapsid/spec/viperdb_corpus_snapshot.json (n=527 / 87 families / 15 distinct T-strata; log10_BF 876.27, posterior 1.0 -> 7/7 C3a + 3/3 C3b PASS, --refresh-viperdb rebuilds) — i.e. C3b is closed in-repo, not the cycle-28+ stretch any more. Note: the three R5-sunset bio-axis simulators (ribozyme_kinetics_simulation.py, nanobot_actuation_simulation.py, virocapsid_pdb_corpus.py) are now all re-implemented in-repo from their documented MVP behaviour — reproducing the headline numbers; stochastic counts and the original 4th-digit values aren't byte-reproduced (the originals are gone), which the docstrings state honestly.
• virocapsid/spec/cage_output_v1.schema.json lock_metadata + 4 conformance fixtures + selftest/virocapsid_c5_conformance.py — closes the in-repo part of virocapsid GATE-26-V-R1 (C5).
• _python_bridge/module/nanobot_actuator_v2_reference_emit.py — raw_77_nanobot_actuation_v2 reference emitter (closes the in-repo part of nanobot N-R1).
• _python_bridge/module/nanobot_actuation_simulation.py — nanobot C0d dual-skeleton re-run: stdlib re-implementation of the R5-sunset 4-state 12-vertex DNA-origami actuation simulator; runs both truncated_icosahedron & cuboctahedron skeletons, each F-NB-4 6/6 PASS (work 50 kT, J₂=24 pose-canon speedup 24×, no Brownian collapse).

All of the above are wired into selftest/run_all.sh as gate steps.

Full v1.x axis-closure is not yet 100% — the remaining work is out-of-repo by construction (R5 sunset relocated the heavy simulators to ~/core/nexus/sim_bridge/, and quantum's pocket-VQE is a separate compute job): quantum F-Q-6 (SARS-CoV-2 Mpro / nirmatrelvir pocket VQE — target confirmed, ladder execution in a dedicated loop), virocapsid C3b (n≥100 RCSB PDB corpus + Bayesian re-audit ≥ 0.95), nanobot C0d (cuboctahedron dual-skeleton sim re-run) + N-R2 (canon-side L6 acceptance lock), ribozyme G26-RB-1′ (rubric sim re-run — values already in the MVP), and GATE-26-2 (all-axis lean4 cert → v2.0.0 — see docs/closure_100_research_2026_05_12.md §C: the appropriate target is a decide/RCA₀-level Lean certificate, not Π¹₁-CA₀). Per-axis grades, gates, deadlines and owners: AXIS_CLOSURE_PLAN.md.

For the full roadmap, see .roadmap.hexa_bio (repo-overall: lattice / gates / cycle history / deadlines) and the 5 per-axis sister files: .roadmap.quantum · .roadmap.weave · .roadmap.virocapsid · .roadmap.nanobot · .roadmap.ribozyme. The integrated platform manifest (5 axes + 5 cross-cutting platform layers + disease-orthogonal entries) is .roadmap.platform_index.

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16-cell C2 matrix (cycle 25, 2026-05-06)

Cycle 25 closed the C2 traversal of the 4 bio axis × 4 disease-class scaffold at IN-SILICO grade (the QUANTUM compute axis is tracked separately via the F-Q-* ladder). Each cell ships a wrapper script in _python_bridge/module/*_candidate.py that records candidate-spec metadata annotated against publicly catalogued disease-class markers and verifies via the corresponding C0b simulator. Each cell emits one raw_77_c2_<verb>_<class>_v1 witness row to state/discovery_absorption/registry.jsonl.

Axis \ Class	α (AML)	β (SCD)	γ (pan-cov)	δ (senolytic)
W (weave)	PASS	PASS	PASS	PASS
N (nanobot)	PASS	PASS	PASS	PASS
R (ribozyme)	PASS	PASS	PASS	PASS
V (virocapsid)	PASS	PASS	PASS	PASS

Aggregate: 16/16 PASS (in-silico verification of simulator+metadata internal consistency only).

Honest caveat (raw#91 C3 discipline): a C2 cell PASS confirms only that (a) the C0b simulator runs deterministically, (b) the candidate-spec metadata schema validates, and (c) the verifier's internal consistency check holds. It does NOT imply any therapeutic, clinical, regulatory, immunogenic, pharmacokinetic, or efficacy property. The disease-class markers are publicly catalogued reference annotations — not medical claims. C3+ (wet-lab → in-vitro → in-vivo → IND → phase I) is explicitly out-of-repo per cross-cutting Require (R6).

Per-row witnesses are archived under design/kick/ (2026-05-06_hexa-{weave,nanobot,ribozyme,virocapsid}-c2-row-cycle25_omega_cycle.json) plus the aggregate 2026-05-06_hexa-bio-cycle25-c2-matrix-closure_omega_cycle.json.

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n=6 invariant lattice

The lattice anchors the toolkit to a single algebraic identity:

σ(6) = 12        STRUCTURAL-EXACT for T=1 cage (vertex count, posterior 0.97)
τ(6) = 4         4 bio axes / 4-state ladder (free / pentamer / hexamer / cage)
φ(6) = 2         binary dichotomy (free vs assembled)
J₂   = 24        octahedral O ⊂ icosahedral I subgroup

master identity:   σ · φ = n · τ = 12 · 2 = 6 · 4 = 24

τ(6)=4 is the quartet of bio axes (weave / nanobot / ribozyme / virocapsid) — the tetrahedron. quantum is the fifth axis (compute substrate spanning all four); its n=6 binding is verified on the H₂ 6-Pauli expansion (σ(6)=12 = 6 Pauli terms × 2 qubits) and the d=1 hardware-efficient ansatz (τ(6)=4 = 4 parametric rotations).

Per-axis interpretation (where empirically grounded vs hypothesized — see Caveats §3):

Symbol	weave (verified)	virocapsid (T=1 exact)	nanobot (candidate)	ribozyme (candidate)	quantum (H₂/LiH verified)
σ(6)=12	cage vertex count	T=1 cage (verified via weave)	12-vertex polyhedron	12-nt catalytic core	6 Pauli × 2 qubits = 12 ops
τ(6)=4	4 ladder states	4 assembly stages	4 mechanical regimes	4 reaction states	4 ansatz rotations (Ry·Ry·CX·Ry·Ry)
φ(6)=2	free vs assembled	assembled vs disassembled	bound vs unbound	bound vs free	best_idx 0 vs other (symmetry break)
J₂=24	I ⊃ O subgroup (geometric)	I ⊃ O (T=1 exact; T>1 conjecture)	power-stroke trajectory	reaction-coordinate grp	σ·τ = 6 × 4 = 24 (eval surface)

---

Architecture

~/.hexa-bio/                          (or set HEXA_BIO_ROOT)
├── cli/
│   └── hexa-bio.hexa           # 5-axis router + status + selftest
├── weave/module/weave.hexa              # WIRED — Caspar-Klug + Zlotnick (cage 60)
├── nanobot/module/nanobot.hexa          # C0b skeleton — DNA-origami actuation
├── ribozyme/module/ribozyme.hexa        # C0b skeleton — hammerhead RNA kinetics
├── virocapsid/module/virocapsid.hexa    # C0b skeleton — viral capsid assembly + PDB corpus
├── quantum/module/                       # QUANTUM axis — qpu_bridge VQE / ML pilots
│   ├── quantum.hexa                      #   axis dispatcher (status / falsifiers / n6 / pilot-runner)
│   ├── external_pilot_runner.hexa        #   ProteinMPNN / Boltz-2 / RhoFold+ pilot smokes
│   ├── n6_lattice_check.hexa             #   n=6 binding self-check
│   └── …                                 #   (closure_summary, registry_witness_emitter, …)
├── selftest/module/selftest.hexa        # 5-axis sentinel sweep + 16-cell C2 sweep
├── _python_bridge/module/
│   ├── cage_assembly_simulation.py        # weave ODE (numpy/scipy opt-in)
│   ├── polyhedral_cage_bayesian_audit.py  # weave Bayesian audit
│   ├── virocapsid_pdb_corpus.py           # virocapsid RCSB PDB corpus fetch (stdlib)
│   └── …                                  # (nanobot/ribozyme C0b sims, quantum_*.py adapters)
├── _absorption_bridge/                    # cycle-30++++++++ backport from hexa-matter Phase G —
│   ├── README.md                          # 9 protein-structure ML + sequence adapters
│   ├── pyproject.toml                     # optional deps (requests/biopython/mdanalysis/torch)
│   ├── alphafold3/  af3_smoke.py          # DeepMind AF3 (NON-COMMERCIAL RESEARCH ONLY)
│   ├── rosettafold/ rosettafold_smoke.py  # Baker Lab RoseTTAFold + RFAA (BSD/Apache)
│   ├── esmfold/     esmfold_smoke.py      # Meta ESMFold (MIT, single-sequence)
│   ├── openfold/    openfold_smoke.py     # OpenFold (Apache-2.0, trainable AF2 reimpl)
│   ├── colabfold/   colabfold_smoke.py    # ColabFold (MIT, AF2+MMseqs2)
│   ├── foldseek/    foldseek_smoke.py     # Foldseek structural search (GPLv3)
│   ├── mmseqs/      mmseqs_smoke.py       # MMseqs2 sequence search (GPLv3)
│   ├── uniprot/     uniprot_api_smoke.py  # UniProt REST (CC-BY 4.0)
│   ├── pdb/         pdb_api_smoke.py      # RCSB PDB REST (CC0)
│   └── selftest/    run_all.sh            # aggregator → __HEXA_BIO_ABSORPTION_BRIDGE__ PASS
├── tests/
│   ├── test_weave.hexa
│   ├── test_nanobot.hexa
│   ├── test_ribozyme.hexa
│   ├── test_virocapsid.hexa
│   ├── test_quantum.hexa
│   ├── test_quantum_pilot_runner.hexa
│   └── test_selftest.hexa
├── examples/
│   ├── 01_quick_weave.hexa
│   ├── 02_quick_nanobot.hexa
│   ├── 03_quick_ribozyme.hexa
│   └── 04_quick_virocapsid.hexa
├── design/kick/                # omega-cycle witness archive (cycle 24/25 closures,
│                               # schema `omega_cycle.witness_v1`)
├── install.hexa                # hx hook (pre/post)
├── hexa.toml                   # package manifest
├── LICENSE                     # Apache-2.0
├── CHANGELOG.md
└── README.md                   # (this file)

---

Provenance

• WEAVE module imported from nexus/sim_bridge/weave/ (cycle 24 canonical, 2026-04-29). Original concept: canon/domains/ biology/hexa-weave/hexa-weave.md empirical companion.
• NANOBOT / RIBOZYME / VIROCAPSID modules created fresh during this extraction (2026-05-04) — no prior nexus implementation existed beyond .roadmap / atlas.append marker entries (e.g. nexus/n6/atlas.append.hexa-nanobot-domain-registration.n6). Their C0b skeleton simulators landed in cycle 24–26.
• QUANTUM axis (quantum/module/) created fresh in the hexa-bio session (per user directive 2026-05-07) as the qpu_bridge dispatcher; the Python VQE adapters (_python_bridge/module/quantum_*.py) bridge the qmirror CLI (ANU QRNG + Aer state-vector simulator). See .roadmap.quantum.
• Sister extractions:
  • qmirror v2.0.0 (registry L22, GitHub dancinlab/qmirror)
  • sim-universe v1.0.0 (registry L23, GitHub dancinlab/sim-universe)
  • hexa-bio v1.0.0 (registry L24) ← this repo

---

Caveats (raw#10 honest C3)

1. weave is the only fully-wired axis at v1.0.0. nanobot, ribozyme, and virocapsid run a C0b skeleton simulator + print falsifier preregister tables; quantum is at Phase 1+ (H₂/LiH VQE + ML pilots, F-Q-6 pocket VQE open). The __HEXA_BIO_*__ PASS sentinels confirm only that the module loaded and dispatched cleanly; they do not validate any empirical claim.
2. Falsifier deadlines for the non-weave axes are working dates. Concrete experimental refutation criteria are tracked per-axis in the .roadmap.* sister files; revisions land per cycle as the empirical sandboxes mature.
3. n=6 invariant lattice claim is empirically grounded only in parts. weave's σ(6)=12 (T=1 cage vertex count, posterior 0.97) and quantum's σ(6)=12 (H₂ 6-Pauli × 2-qubit) are the empirically / structurally grounded bindings. nanobot's 12-vertex polyhedron, ribozyme's 12-nt core, and T>1 virocapsid carry the lattice claim as STRUCTURAL-EXACT-CANDIDATE pending independent verification.
4. 5-axis count is locked (.roadmap.axis_expansion_decision_2026_05_08). Four 6th/7th-axis candidates (BIO-EVOLUTION, QUANTUM-BIOLOGY, PLANETARY-HEALTH, CONSCIOUSNESS) were reject/defer. Salvageable content lives in cross-cutting platform layers + disease-orthogonal entries (see .roadmap.platform_index). Annual axis-expansion review only.
5. Migration of nexus/sim_bridge/weave/ may break edge-case consumers. Cross-link consumers (canon papers, nexus/state/audit/cage_assembly_events.jsonl readers) reference the old path; the path-migration shim is left to the nexus consumer refactor cycle. The runs/ ledger (~10MB jsonl) is not vendored into this standalone repo by default.
6. GitHub-only distribution (HF Hub mirror retired 2026-05-04). HF Hub is designed for ML model weights / datasets, not CLI tooling. Maintenance burden (recurring token rotation failures) outweighed value. GitHub remains canonical at https://github.com/dancinlab/hexa-bio; HF Hub stays canonical for model weights / datasets in the wider stack.

---

License

Apache-2.0. See LICENSE.

Optional Python aux deps (numpy, scipy, qiskit-aer) ship under their own BSD-3 / Apache-2.0 licenses; in-process safe (no copyleft). hexa-bio core stays Apache-2.0 under FSF MereAggregation.

---

Sister repositories (live dependencies — CLI-direct, NO wrappers)

hexa-bio depends on multiple HEXA-family sister repos via CLI / file-system reads, not via Python wrappers or shadow-copied code. Each is a separate canonical SSOT that updates on its own cadence; hexa-bio picks up updates automatically through CLI invocations. The full operating rules are in AGENTS.md "Sister repositories — live dependencies". The compute substrate × workload × readiness × fallback matrix (and the universal fallback principle: every substrate is optional; absence → SKIP, never FAIL) is in COMPUTE_PORTFOLIO.md.

Live software dependencies:

• dancinlab/qmirror — ⚡ quantum-computer substitute (IBM Cloud / IonQ / Quantinuum cloud-API replacement). NOT a QRNG-only bridge: it's a full pure-hexa quantum computation substrate combining:

  • ≤30-qubit Aer-compatible state-vector kernel (replaces qiskit-aer Python dependency; native hexa-lang implementation)
  • ANU QRNG real quantum entropy (free public API, 4-tier fallback)
  • chemistry / molecular VQE pipeline (cond.14: H₂ STO-3G/0.74Å sub-µHa via UCCSD + active-space CASCI; closure PASS)
  • v2.1.0 = 14/14 closure conditions PASS (8 v1.0 + 5 v2.0 + 1 v2.1)

  The quantum axis's upstream — replaces the IBM Cloud / IonQ / Quantinuum cloud APIs for any workload ≤30 qubits. No vendor cloud account / API key / budget needed. Future >30-qubit fault-tolerant workloads (10-yr horizon) would need a separate vendor partnership; current hexa-bio Mpro pocket / 5-warhead library / 11-drug pocket VQE workloads all fit in ≤30 qubits and run on qmirror end-to-end.

  Hexa-bio integration: selftest/qmirror_chemistry_vqe_gate.sh invokes hexa run ~/core/qmirror/chemistry_vqe/module/chemistry_vqe.hexa --selftest directly (no Python wrapper); SKIP/PASS/FAIL semantics; wired into selftest/run_all.sh. qmirror updates pick up automatically via the CLI-direct call.

• dancinlab/hexa-meta — formal-axis Lean4 layer (formal/lean4/, active after canon RETIRED 2026-05-11). ✅ ALL 4 axes at v4 maximum semantics (cycle-30++++++, commit 7c0ec92; lake build N6 → 900/900 jobs PASS). hexa-bio reads via _python_bridge/module/lean4_proof_witness_emit.py --refresh from hexa-meta main; emits raw_77_lean4_proof_witness_v0 rows. NO .lean files in hexa-bio by design.

• dancinlab/xeno 🛸 — exotic compute substrate orchestrator (Tier C: neuromorphic + organoid + quantum-gate + random). Parallel to qmirror's quantum-computer- substitute role. Single canonical doc: XENO.md. Gate: selftest/xeno_substrate_gate.sh (wired in selftest/run_all.sh).

Family-related repos (no runtime dependency; cross-link only):

• dancinlab/florea 🌸 — cosmetic/ aesthetic substrate (7-verb library: cosmetic-surgery, hair-regeneration, perfumery, tattoo-removal, mens/womens-intimate-cleanser, skincare). Standalone HEXA-family brand (no hexa- prefix, Lumière style). Spawned 2026-05-12 cycle-30++++++ via hexa-medic decomposition. hexa-bio relationship: none operational; the skincare verb absorbed the ex-hexa-skin/ content that previously squatted in hexa-bio.
• dancinlab/hexa-brain 🧠 — neural substrate / cognitive architecture. Imported reference/dolphin*.md from hexa-bio 2026-05-12 (cetacean intelligence / bioacoustics; no longer in hexa-bio).
• dancinlab/hexa-bot 🤖 — robot substrate. Imported reference/hexa-limb.md from hexa-bio 2026-05-12 (AI prosthetic limb; medical-device adjacent).
• dancinlab/hexa-matter ⚛️ — materials substrate. Imported microplastics/ verb from hexa-medic 2026-05-12.
• dancinlab/hexa-medic — DELETED 2026-05-12 cycle-30++++++ (remote + local both removed). All 24 verbs decomposed: 8 migrated (Floréa + hexa-matter + hexa-bio medical-device) + 16 deleted (6 ambiguous + 10 therapy). See DECOMPOSITION_PLAN.md.

Frozen legacy:

• ~/core/nexus/canon-infra/legacy-canon/ — frozen canon@mk1 retirement snapshot 2026-05-11. Theorem B (σ·φ=n·τ⟺n=6) FULLY PROVEN (0 actual sorry, per cycle-30++++++ audit) + MechVerif legacy (0 actual sorry; 1 intentional Robin axiom). Read-only.

Cross-links

• Sister standalone: sim-universe v1.0.0 (simulation substrate)
• Sister standalone: honesty-monitor v1.0.0 (AI honesty-bit falsifier)
• Upstream concept SSOT: ~/core/nexus/canon-infra/legacy-canon/domains/biology/hexa-weave/hexa-weave.md (declarative; FROZEN at canon retirement 2026-05-11)
• Upstream formal SSOT (active): ~/core/hexa-meta/formal/lean4/ — see .roadmap.lean4_formal §1 status
• Upstream formal SSOT (frozen): ~/core/nexus/canon-infra/legacy-canon/lean4-n6/N6/MechVerif/
• Upstream paper SSOT: ~/core/nexus/canon-infra/legacy-canon/papers/hexa-weave-formal-mechanical-w2-2026-04-28.md (FROZEN)
• 5-axis lock record: .roadmap.axis_expansion_decision_2026_05_08
• 5-axis 100% closure plan (gates / deadlines / owners): AXIS_CLOSURE_PLAN.md
• 5-axis 100% closure — deep web + arXiv research (how to close the residual out-of-repo gaps): docs/closure_100_research_2026_05_12.md
• Integrated platform manifest: .roadmap.platform_index
• HEXA package registry: hexa-lang/tool/pkg/registry.tsv L24