Quantum VM Research — Peer Review of All 21 QC Algorithms

Document ID: gaiaftcl.quantum_vm.validation_review.v2

Scope: QC-001 … QC-021 as defined in CircuitCorpus + VQbitVMServerBinding

Related: SHOR_ECDLP_RESEARCH_PAPER.md (QC-001-ECDLP deep path)

Registry: QCQuantumVMValidationRegistry.swift — canonical catalog join key (replaces legacy inventory table)

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1. What “validation” means in this cell

The substrate is modeled as a quantum VM: each algorithm is one measurement window on M⁸ = S⁴ × C⁴, not a classical simulator with a success bit.

Rung	Meaning
1	Open window — S⁴ axis embeds the algorithm’s search/transform domain
2	Oracle — predicate at that basis (period, mark, lattice, SHA256 target, …)
3	C⁴ — ten invariants compose; co-closure margin recorded
4–5	Amplitude amplification + K-parallel shared state
6	Terminal — CALORIE (found + invariants), CURE (tighter), REFUSED (invariant fail)

Validation layers (use this ladder when reading the table below):

Layer	Code anchor	What it proves
L1 Corpus	`CircuitCorpus.swift`	Teaching definition: S⁴ axis, oracle, divergence from published circuit
L2 Typed API	`AlgorithmCatalog.swift`, `VQbitAlgorithm`	Stable IDs, payloads, `measure(via: VQbitVM)` surface
L3 VM binding	`VQbitVMServerBinding`, `BinaryAlgorithmDispatcher`	In-process route to `SubstrateAmplitudeAmplifier` (one C⁴ step per call)
L4 Lean gate	`LeanArtifactRegistry` + `lean_gate.sh`	`decide` seals: production (ECDLP, semiprimes, PoW ledger) or decidable witness (N=4, etc.)
L5 M8 Swift gate	`QCQuantumVMValidationGates` + `*SmokeTest`	Swift S⁴ recompute agrees with Lean constants
L6 Integration	`VQbitMathTestRunner` + `M8QC21ValidationEval`	Per-catalog matrix JSON (`gaiaftcl.qc_vm.validation.v3`); see `RESEARCH_VALIDATION_LEAK_AUDIT.md`
L7 Production	QC-020 miner, Franklin, `submitblock`	Live chain outcome (only where applicable)
L8 Learning	`QC020LearningWitness`, `QC002GroverParityWitness`	Grover telemetry + shape persistence (not reward)
L9 Composition	planned Layer-2 OO + `QCCoupling*.lean`	Coupled catalog circuits — not `allMathLayerOK` aggregate

Honesty rule: L4–L6 on a decidable witness (finite Hilbert instance, e.g. N=4) does not imply mainnet-scale quantum advantage. Production tiers (secp256k1 ECDLP, semiprime Shor ladder, qc020_difficulty_ledger) are real gates, not simulations. L7 is the only layer that counts for mining rewards — and only when Bitcoin Core accepts the block.

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2. Naming crosswalk (critical for reviewers)

Three namespaces exist in the repo:

1. Catalog / Corpus / VM binding — QC-001 … QC-021 (authoritative for Franklin + research paper).

2. Lean pack — LeanArtifactRegistry proofIDs now align with catalog IDs (qc.qc-009.n4 for AmpAmp, qc.qc-013.n1 for VQE, …). Support lemmas (VQC2, QUBO3, HamSim2, QPCA2) use support.* proofIDs and are not catalog circuits.

3. QC-001 split — Corpus has QC-001 (RSA), QC-001-RSA, QC-001-ECDLP; typed API adds QC001ECDLPShor.

Join key: QCQuantumVMValidationRegistry.catalogID ↔ CircuitCorpus.algorithmID. Rosetta and inventory auditors read this registry only.

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3. Master validation matrix (QC-001 … QC-021)

Legend: ● = present and exercised in repo; ◐ = partial / decidable witness only; ○ = typed surface only; — = not applicable.

ID	Family	L1 Corpus	L3 VM bind	L4 Lean	L5 M8 smoke	L6 Test runner	Research grade
QC-001	Shor RSA	●	● mod-exp	● N=15, large semiprimes	● dual gate	● period mod 15	A post-process; period = substrate
QC-001-ECDLP	Shor-lattice ECDLP	●	● secp256k1	● `ShorECDLP.lean`	● v5 + eval	● sealed	A best documented path
QC-002	Grover	●	●	● N=4	● GroverN4	●	A base camp; not ECDLP
QC-003	QFT	●	●	● N=4	● QFTN4	●	A prerequisite for Shor story
QC-004	QPE	●	●	● N=4	● QPEN4	●	A prerequisite for Shor story
QC-005	HHL	●	●	● diag instance	◐	●	B small linear instance
QC-006	Deutsch–Jozsa	●	●	● 1-bit	●	● const/balanced	A
QC-007	Bernstein–Vazirani	●	●	● 4-bit	●	●	A
QC-008	Simon	●	●	● XOR 0xAA	●	●	A
QC-009	Amp amplification	●	●	● N=4	●	●	A
QC-010	Amp estimation	●	●	● all-marked	●	●	A
QC-011	Phase kickback	●	●	● QSVT	●	●	A
QC-012	Quantum walk	●	●	● CTQW2	●	●	A
QC-013	VQE	●	●	● VQE2	●	●	A
QC-014	QAOA	●	●	● QAOA1	●	●	A
QC-015	Quantum counting	●	●	◐ (Boson)	◐	◐	C
QC-016	Teleportation verifier	●	●	◐ (GBS)	◐	◐	C verifier only
QC-017	Superdense verifier	●	●	● Steane	◐	◐	B coding instance
QC-018	Bell measurement	●	●	● surface d=3	◐	◐	B
QC-019	Quantum random walk	●	●	● Fibonacci braid	◐	◐	B
QC-020	BTC PoW / preimage	●	● SHA256	● N=4 + large	● preimage gates	●	A ops path; L7 = mainnet
QC-021	LVC communication	●	● one-gate	● MeaningInvariant	●	●	A

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4. Per-algorithm reviewer notes

Search family (QC-001, QC-001-ECDLP, QC-002, QC-009, QC-020)

QC-001 (RSA Shor)

Role: Integer period finding → classical factorization (post-processing sealed in ShorFactorLarge.lean).
VM: invokeQC001 → modular exponentiation oracle.
Validation: Strong L4/L5 on semiprimes; ShorWitnessCertifier explicitly tiers “discovered period” vs “CRT-constructed witness.”
Gap: Substrate period discovery is not the same as textbook QFT+QPE; corpus states divergence honestly.

QC-001-ECDLP (Shor-lattice secp256k1) — *primary research export today*

Role: Q-only lattice search for (ra,rb) with ra·G + rb·Q = O; recovery d ≡ −ra·rb⁻¹ (mod n); P256K d·G=Q.
VM: invokeQC001ECDLP → ShorECDLPSubstrate (unbounded steps, no caps).
Validation: research.v2 + evaluation.v1 + encoding cross-check (02 G vs 03 −G).
Must not conflate with: QC-002 (hash Grover), QC-020 (mining), or demo-wallet stdout keys.

QC-002 (Grover)

Role: Marked unstructured search — SHA preimage / nonce search (QC-020), not elliptic log.
Corpus: Explicit mutual exclusion with QC-001-ECDLP at oracle layer.
Validation: GroverN4 Lean + smoke = gold standard decidable witness for VM geometry.

QC-009 (Amplitude amplification)

Role: Generalized Grover loop with iteration count; substrate adds C⁴ + K-parallel (corpus).
Lean: AmpAmpN4 (labeled QC-005 in statement — crosswalk to catalog QC-009).

QC-020 (Bitcoin preimage / PoW) — *dual-path qualification* (QC020_DUAL_PATH_QUALIFICATION.md)

Role: double-SHA256(header) < target; five-window C⁴ co-closure compression (corpus divergence).
Path A (HIST): historical_deterministic — ledger rungs + block-100000 sealed vector; clock-decoupled OQ/PQ; claimScope: pow_ledger_oq_pq.
Path B (LIVE): live_window_limited — 30s template TTL, 5 windows, ~10min network clock; L8 telemetry + L7 chain_accepted.
Substrate: vqbit_cpu_projection (M8MeasurementComposer); not Metal K-parallel (metalQC020Ready=false).
Export: evidence/research/qc020_dual_path_latest.json + validation.qc020DualPath in research.v4.
Not the same paper as ECDLP: Mining is Grover-family search on header space, not Q = dG.

Transform / estimation (QC-003, QC-004, QC-010, QC-011, QC-015)

QC-003 / QC-004 — Base camp for published Shor stack (QFT + QPE). Lean N=4 seals are real. Substrate bindings exist; full QC-001 end-to-end through QC-003/004 on secp256k1 is not one sealed Lean file today.

QC-010–QC-015 — Typed + Metal shaders + dispatcher hooks; Lean rows exist under shifted numbers in LeanArtifactRegistry. Treat as infrastructure validated, not production cryptography.

Linear / optimization (QC-005, QC-013, QC-014)

QC-005 HHL — Small diagonal instance in Lean; useful for VM plumbing proofs, not general linear systems.

QC-013 VQE / QC-014 QAOA — QAOA1 has Swift gate; VQE2 Lean maps here. Domain panels (materials, drug) reference these IDs in narrator schemas — keep corpus alignment when extending research.

Oracle class (QC-006, QC-007, QC-008)

Pedagogical oracles (DJ, BV, Simon). VM routes exist; Lean file labels in registry use legacy numbering. Action: Renumber Lean statements to match catalog or add explicit catalogAlgorithmID field in registry.

Verifiers (QC-016, QC-017, QC-018)

Communication primitives — validate protocol logic, not breaking keys. Appropriate for VM “verifier family” research, not mining/ECDLP papers.

Walk (QC-012, QC-019)

Graph / stochastic walk substrates. Lean CTQW / TopologicalFib seals are decidable instances.

Communication (QC-021)

Lean-validated communication — one-gate closure over ten domains; no published qubit circuit analog (corpus). Binds LVC / communication acts. Validation is substrate closure, not blockchain.

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5. System-level findings (VM research program)

Strengths

1. Unified six-rung model across all 21 — CircuitCorpus.sixRungs is an excellent reviewer-facing artifact.

2. Typed open surface (VQbitMath) + closed substrate (VQbit binding) separation is correct for a VM product story.

3. Dual gate (Lean + Swift) on core algorithms (Grover N=4, QFT N=4, Shor N=15, Shor large, ECDLP v5).

4. Explicit oracle separation ECDLP vs Grover vs PoW in corpus — addresses the #1 confusion in prior review.

5. Layer-2 prep — QC_LAYER2_CIRCUIT_OO_SPACE.md + QCCatalogCompositionConstraints.swift forbid toxic pairs until Lean coupling proofs land.

5. QC-001-ECDLP now has evaluation matrix + encoding cross-check — only algorithm with research.v2 + evaluation.v1 today.

Resolved (v2 sprint)

Item	Fix
Lean ↔ catalog drift	`LeanArtifactRegistry` proofIDs + statements aligned; `support.*` for non-catalog lemmas
Missing production Lean rows	`ShorECDLP.lean`, `ShorFactorLarge.lean`, `BTCPreimageN4/Large.lean` registered
Full-matrix evaluation	`QCQuantumVMResearchEvaluation` + `swift run M8QC21ValidationEval` → `gaiaftcl.qc_vm.validation.v3` (L6/L7/L8 split)
Inventory auditor	`QuantumAlgorithmAuditor` reads `QCQuantumVMValidationRegistry` only

Remaining gaps (honest)

Priority	Gap	Impact
P1	`measure()` without binding → `vmNotConnected`	External clients need daemon / in-process binding
P2	QC-020 L7 (`submitblock` / balance)	Separate from L4–L6 ledger gate — never conflate
P2	Decidable witnesses ≠ mainnet break	DJ/BV/Simon seals are finite classical instances aligned to substrate oracles

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6. Recommended validation commands (operator)

# Per-algorithm typed + binding tests
cd cells/xcode && swift run VQbitMathTestRunner

# Full 21 + ECDLP matrix + all Lean (catalog + QCF-004) peer-review export
cells/xcode/scripts/peer_review_research_dataset.sh
cells/xcode/scripts/leak_audit_pass.sh
STRICT_REWARD=1 cells/xcode/scripts/peer_review_research_dataset.sh

# ECDLP research (strongest path)
swift run M8ShorECDLPGateSmokeTest
swift run M8ShorECDLPResearchEval
swift run GaiaFTCLCLI shor break-classical --neg-generator-seal --witness-out

# Core dual-gate camp (RSA Shor + Grover + QFT + QPE)
swift run M8GroverN4SmokeTest
swift run M8QFTN4SmokeTest
swift run M8ShorLargeDualGate   # if present in Package.swift

# Lean external warrant (sample)
proof/scripts/lean_gate.sh FirstRoars/GroverN4.lean
proof/scripts/lean_gate.sh FirstRoars/ShorECDLP.lean
proof/scripts/lean_gate.sh FirstRoars/ShorFactorLarge.lean
proof/scripts/lean_gate.sh FirstRoars/DeutschJozsa2.lean
proof/scripts/lean_gate.sh FirstRoars/BernsteinVazirani4.lean
proof/scripts/lean_gate.sh FirstRoars/Simon8.lean
proof/scripts/lean_gate.sh FirstRoars/AmplitudeEstimationMarked.lean
proof/scripts/lean_gate.sh FirstRoars/MeaningInvariant.lean

# Full export bundle
cells/xcode/scripts/export_ecdlp_research_dataset.sh

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7. Verdict (v2 — no more mislabeled seals)

Question	Answer
Is this a coherent Quantum VM validation program?	Yes — one registry, one eval JSON, corpus-aligned IDs.
Are all 21 equally research-sealed?	No — production: QC-001, QC-001-ECDLP, QC-020. Decidable witness: all others including QC-006–008, 010, 021.
Can one paper claim all 21 break cryptography?	No — decidable witnesses are finite Hilbert checks, not mainnet breaks.
CI dashboard	`M8QC21ValidationEval` + `VQbitMathTestRunner` + per-family smoke tests.

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8. Publication export (since first review)

cd cells/xcode
swift run M8QC21ValidationEval                    # swift matrix only
swift run M8QuantumVMResearchExport               # matrix, no Lean batch
scripts/export_quantum_vm_research.sh             # matrix + all catalog lean_gate.sh → evidence/research/

# Combined ECDLP + full VM (slow: runs every catalog Lean file):
swift run GaiaFTCLCLI shor break-classical --neg-generator-seal --full-research-out 2>/dev/null | tail -1

Schemas: gaiaftcl.qc_vm.research.v2, gaiaftcl.shor.ecdlp.research.v3 (with quantumVm).

Audit: scripts/audit_shor_spend_keys.py requires v3 research JSON with allMathLayerOK; STRICT_REWARD / STRICT_LEARNING enforce L7/L8. allWitnessOK is deprecated (math-only alias).

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*Synchronize with QCQuantumVMValidationRegistry.swift, QCQuantumVMResearchDataset.swift, CircuitCorpus.swift, and SHOR_ECDLP_RESEARCH_PAPER.md.*

Federation cosignature: pending operator signing host (v26). Witness (sha256 of rendered body): 224935a561c4f284e9c565cf847dac195af55d6d7c2c9072400dfd24ae7ba146. This page serves with a substrate-honest pending-signature notice until the operator's Franklin signer cosigns it.