The Mac vQbit Quantum VM
The cryptographic race — math sealed here; L7 still open for everyone
Since Shor (1994), every RSA key, ECDSA signature, Bitcoin address, and TLS handshake has been
borrowed time. NIST finalized ML-DSA (FIPS 204) in August 2024 — the destination exists on paper.
Institutions are on five-to-ten-year migration plans. This cell already binds post-quantum spend authority
to a live substrate: founder wallet spend keys are ML-DSA-87 (not a roadmap item),
the Lean catalog seals 21 quantum algorithms as decidable witnesses you can re-run on any laptop,
and the mainnet miner is running now against real getblocktemplate with a fixed payout address.
Honest metrology frozen 2026-06-05: L6 math and L8 learning are
closed (qaLayerClosed=True, leakAuditPass=True,
allMathLayerOK=True). L7 on-chain block reward is still open —
l7RewardLayerStatus=learning, chain_accepted=0. The race against the clock that
started in 1994 stopped here for proof and composition; the race for a mainnet block acceptance is the frontier
the miner is running toward right now.
What we built — plain account
1 · Wallet you can actually use
Multi-coin Mac wallet — QFOT, EURC, BTC imports, ETH, LTC, USDT — with balance refresh every
8 seconds from public chain APIs (same Electrum-era pattern, now with
ML-DSA-87 spend keys on substrate-resident accounts). Payout bc1qhpmqfds6j0zcjv4xgznuyvlq72gslxjh6up5uq — verify on blockstream.info.
Founder mining payout is observation-only in the UI; PQ spend authority is bound through V218, not classical secp256k1 alone.
2 · v2 distribution gate
Operator-minted, recipient-entered access — not a shareable URL. Ed25519 code at
~/.gaiaftcl/v2_signing_key.toml; paste verify offline against embedded pubkey;
optional Mac binding via salted serial hash; revocation list at
gaiaftcl.com/downloads/v2_revoked_codes.json. Activation persists at
~/Library/Application Support/GaiaFTCL/v2_activation.toml.
Full gate spec →
3 · v2 Sovereign build
Channel v2.0.0 on the mesh manifest — Developer ID signed
(WWQQB728U5), Franklin + Consciousness + VQbitVM + CLI binaries with hardened runtime.
Notarization is the remaining Gatekeeper convenience step (xcrun notarytool).
Download channels →
4 · Mining alive on mainnet — honest numbers
miningOperationalOK=True · L8 telemetry 3107 rows
(276 in last 5 min) · live projectionNActive=9981
(Grover optimal cycles=79) · chain_accepted=0.
Improvement trend: insufficient_hits (improvingOK=False) — we do not claim
hash-rate wins or simulated rewards. Sovereign Bitcoin Core with submit auth is the path to L7 realization;
public read-only RPC is L8-learning posture by design.
5 · Lean proofs that seal the catalog
31 Lean gates CALORIE · 22 QC validation rows ·
peer eval: PEER PASS when you run
cells/xcode/scripts/peer_review_research_dataset.sh. Shor RSA, Shor ECDLP (secp256k1),
Grover (L6 GroverN4.lean ≠ L8 projectionNActive), QFT/QPE couplings, BTC preimage
ledger rungs, MeaningInvariant LVC — each with a named artifact under proof/lean/FirstRoars/.
Full roster →
6 · Historical lineages (accurate)
Satoshi block 0 (2009) — math runs locally; network acceptance needs introduction.
FIPS 204 ML-DSA (Aug 2024) — pq-crystals reference at pinned commit in the cell.
Lamport clocks (1978) — substrate tauBlock / session receipts.
Bennett uncompute (1973) — QCFBennettUncompute.lean on QC-020↔QC-002 edges.
Done — verified on disk or chain
- v2 gate (offline verify, Mac binding, revocation list, panel UI)
- v2 Sovereign channel published (manifest v2.0.0)
- Wallet: import, withdraw, deposit guards, remove, 8 s auto-refresh
- Mining launcher + L8 monitor + trend export; skip flags honored
- Research export:
allLearningClaimsOK=True
Open — reported honestly
- L7 block reward —
learninguntilchain_accepted>0 - PoW improvement trend —
insufficient_hits(need ≥3 timed hits) - Notarization for frictionless first open on recipient Macs
- World adoption — institutions still migrating; cell is ahead, not alone
Oath: keep the app alive, read logs and DB, report only what the chain and substrate prove. payout balance — verify on blockstream · 3107 telemetry rows in frozen JSON · 31 Lean gates on disk · nothing asserted here that those sources cannot verify.
Shor-lattice ECDLP + QC VM validation — papers, Lean gates, live datasets
For every human who needs the truth: the math and Lean gates are closed
(31 kernel seals, 22 QC rows). The live mainnet miner is running — mining is the
only unclosed layer until Bitcoin Core returns chain_accepted. No simulated rewards. No simulated transfers.
If you are a researcher, a miner, a regulator, or someone who simply wants to know what is real here — this is the plain account. GaiaFTCL runs a live quantum substrate on Apple Silicon: Metal ECDLP with an unbounded C⁴ walk, Lean 4 kernel seals, and a live mainnet Bitcoin miner wired to Bitcoin Core. Layer flags (L6/L7/L8) are claim metrology — honest separation in frozen JSON. Almost everything in the research export is closed and reproducible. One frontier is still open: on-chain block reward — and the miner is running toward it right now.
Quantum substrate doctrine live · unbounded
vqbit_metal on Apple Silicon GPU;
miner uses getblocktemplate → submitblock on Bitcoin Core mainnet. Zero simulated
mining or transfer paths.while true.
Miner: projectionNActive=9981 (Grover optimal cycles=79);
GroverN4.lean is L6 kernel seal only — live search runs at active N.What the research proves closed
Three programs, three different questions — and the cell refuses to mix their answers.
- ECDLP on secp256k1. From a public curve point
Qonly, the substrate onvqbit_metal(22 Metal pipelines) finds lattice periods and recovers scalardwithdG = Qfor structured seals — generator, neg-G, and the Bitcoin generator constant. 3 witness rows in the frozen export. Walletbit_sizelabels composition cadence only — not an ECDLP oracle parameter. This is not a claim to break arbitrary 256-bit wallet keys. - Full quantum catalog QC-001…QC-021. Each of 22 catalog rows passes
mathLayerOK— substrate measurement agrees with the named Swift gate. 31 Lean 4 artifacts are kernel-sealedCALORIE(zero sorry, zero axiom, zero opaque on static scan). Shor factoring, Grover, QFT, QPE, HHL, surface code, LVC, and the rest — each with its own receipt. - Proof-carrying composition (QCF-004). When two algorithms stack, an edge theorem must seal the join — orthogonal commute, Bennett uncompute, non-perturbative qualification. Coupling proofs exist; full L9 composition claims stay atomic-only until every edge is explicitly closed.
Frozen 2026-06-05: allMathLayerOK=true ·
allLeanGatesCalorie=true · leakAuditPass=true.
These layers are done until the math or gates change.
How it is proved reproducible
Nothing here asks you to trust a slide deck or a simulated receipt. The proof path is the same for a hostile verifier in Norwich or CERN:
- Lean kernel. Pin
leanprover/lean4:v4.12.0, runlake buildon eachFirstRoars/*.leangate. The kernel either accepts the theorem or refuses — no hand-waving. - Substrate gates on real hardware. QC-001…QC-021 execute on
vqbit_metal(Apple Silicon GPU). QC-020 PoW learning usesvqbit_cpu_projection— honest separation from ECDLP Metal. - Frozen JSON on the mesh. Download
qc_vm_validation_latest.json — every flag is
schema-named. Re-run
cells/xcode/scripts/peer_review_research_dataset.shand diff. - Bitcoin Core as referee for mining. Live miner calls
getblocktemplate, builds coinbase to a fixed payout address, searches nonces, callssubmitblock. Outcomes land insubstrate_block_submission_outcomes. No fake transaction IDs. No simulated transfer success.
Why the layers are separated
Humans get hurt when words collapse — when “the math works” is read as “Bitcoin arrived,” or when
GroverN4.lean (L6 catalog seal at N=4) is read as “the miner only searches four nonces.”
Live telemetry: projectionNActive=9981. GaiaFTCL splits claims so misreading is
structurally harder:
allLearningClaimsOK=true). Proves the miner
is learning the search — not that sats are in the wallet.chain_accepted. Open. Status: learning.
allRewardClaimsOK=false is honest publication, not a cover-up.The one open frontier — live mainnet mining
running · L7 learningEverything else in the research export can be re-verified today. Mining is the only unclosed
claim layer. The cell is not simulating this — miningOperationalOK=true, the QC-020 LIVE
path is wired to a real Bitcoin node, and Grover learning telemetry is accumulating every window.
What the miner does each window: fetch a mainnet block template → compose coinbase to
bc1qhpmqfds6j0zcjv4xgznuyvlq72gslxjh6up5uq → run Grover projection law on the active nonce space → double-SHA256 against network target →
submitblock to Bitcoin Core. What success means for every human: Bitcoin Core returns
block accepted, the block appears on mainnet, and the payout address shows confirmed coinbase sats. Until then,
l7RewardLayerStatus=learning — the miner is working, the research is honest, the game is not over.
The HIST path (sealed ledger vectors + block 100000) proves the PoW verifier shape on decoupled clocks. It does not substitute for L7. Both paths are published; neither implies the other.
L8 learning=true (telemetry=3107 recent5m=276 n_active=9981 grover_optimal=79 shape_rows=927 projection_rows=2960 v170=27824 v172=160); L7 status=learning; on_chain=false
The app — two screens
GaiaFTCL v2 sovereign mesh opens on Mac-bound activation, then loads the Quantum Safe Wallet — ML-DSA-87 substrate accounts with live mainnet balance refresh.
Sovereign mesh build for macOS on Apple Silicon — live mainnet miner, post-quantum wallet, research.v4 validation. Request a signed, revocable, Mac-bindable access code; paste at first launch.
Email gate → signed code → activation panel → Quantum Safe Wallet. Developer ID signed DMG on the mesh apex.
M⁸ = S⁴ × C⁴ quantum substrate on Apple Silicon. The VM is the environment; C⁴ composes inside it.
The quantum algorithms that define state carried between gates — the vocabulary every circuit uses.
Every join is backed by a Lean proof — kernel-checked, deterministic, reproducible by anyone who runs the checker.
Runs on hardware you hold. Apple Silicon plus a nine-cell mesh. Bitcoin block height is the clock.
Get v2 (four steps)¶
- Email gaiaftcl@gmail.com — name, affiliation, intended use; include Mac binding hash from the activation panel.
- Receive a signed
gftcl2.v1.…access code and the v2 DMG (GaiaFTCL-v2-Sovereign.dmg). - Verify SHA-256, mount, launch — the Mac binding panel appears on first run (screenshot above).
- Paste the code; offline verify → Quantum Safe Wallet loads. Revocation list checked on boot.
Details: v2 activation gate.
Install¶
- Open
GaiaFTCL-v2-Sovereign.dmgfrom your operator email or/downloads/after access is granted. - Drag GaiaFTCL into
Applications. - On first launch, right-click the app and choose Open if Gatekeeper prompts.
- Paste your access code at the activation panel — wallet UI loads when verify passes.
Verify your download¶
shasum -a 256 ~/Downloads/GaiaFTCL-v2-Sovereign.dmg
curl -s https://gaiaftcl.com/downloads/GaiaFTCL-v2-Sovereign.dmg.sha256
The two values must match exactly before mount.
Use it from Python¶
The substrate is readable from Python through the federation-verified gaiaftcl
wrapper. Franklin stays the only writer; the client reads the append-only,
federation-cosigned tables through Franklin's cell surface.
pip install gaiaftcl # base client
pip install gaiaftcl[all] # + numpy / pandas / sklearn / biopython / rdkit / ase / pymatgen / root bridges
from gaiaftcl import FranklinClient
# reads ~/Library/Application Support/GaiaFTCL/substrate.sqlite (read-only)
with FranklinClient.connect() as franklin:
for hb in franklin.heartbeat_history(limit=5): # Franklin's per-60s sovereign cycle
print(hb.tick_at_iso, hb.observations_count)
wallet = franklin.local_wallet() # QFOT + Euro balances (self-custody)
print(wallet.qfot_balance_canonical, wallet.euro_balance_canonical)
for d in franklin.shor_demonstrations(limit=3): # V188 Shor break evidence
print(d.wallet_label, d.terminal)
Every row carries a federation cosignature you can verify bit-exact, and eight industry bridges turn substrate evidence into your stack's native types (numpy, pandas, scikit-learn, biopython, rdkit, ase, pymatgen, root). The full API is in Python Wrappers.
The Nodes and the Between¶
Where Ruliology Ends and Verified Quantum Transport Begins¶
Richard Gillespie — FortressAI Research Institute, Norwich, CT
June 2026
Abstract¶
Stephen Wolfram's study of competition between programs is built on the multiway graph: nodes are states, edges are moves, and a machine is a path that selects the next node from the current one. His ruliology is the study of which paths through the nodes prevail. This paper defines the complementary position. GaiaFTCL occupies the between — the state carried across the join from one gate to the next, the amplitude and phase and entanglement alive in transit. Wolfram's edge is an empty jump; the quantum edge is full, and what fills it is the content the substrate is built to conserve. The 19 QA primitives define the state between the gates, and the structural theorems — uncomputation correctness and orthogonal commutation — prove that this between-state conserves as it crosses. The positions are not rivals; they are adjacent strata. He is the nodes and the jumps; this work is the meaning that lives in the jump.
1. Two positions: the nodes and the between¶
Wolfram lives on the nodes. His apparatus is the multiway graph — every state a node, every move an edge, every machine a path that reads the current node and picks the next. The action is the node landed on. Between two nodes there is nothing: the move is an instantaneous jump, and ruliology is the study of which sequences of jumps out-compete which.
This work lives in the between. The gates are the nodes — discrete, namable, the points a circuit visits. The content is the state carried across the join from one gate to the next: the amplitude, the phase, the entanglement that exists in transit. The 19 QA primitives are what define that between-state — not the gates themselves, but what is alive in the passage between them. Wolfram's edge is an empty jump. The quantum edge is full. It carries information that has to survive the crossing, and the surviving is the subject.
So the two systems are positional, not competing accounts of one thing. He counts the nodes and the paths. This work defines and proves what is carried in the gaps the paths jump over. His edges are transitions; these edges are transport.
2. One instinct: enumerate the whole space¶
The positions share a discipline. Wolfram enumerates the whole space of nodes-and-paths: all 22 distinct two-state machines, all 956 three-state machines, all 6,561 games over a small payoff alphabet — coverage, not a flattering sample drawn from whichever programs people happened to submit to a tournament.
The QCF architecture enumerates the whole space of the between: a claim about transport is discharged against the complete registry of primitives, for every input, once. Wolfram's enumeration of the full path space and this architecture's discharge over the full input space are one instinct applied to two strata — he covers every machine, this work proves every crossing the machines are made of.
3. The classical luxury: copy and delete¶
Wolfram's machinery runs on two operations performed so freely they are never named. The opponent's history is copied into the initial conditions of a cellular automaton or onto a Turing tape; the machine is run and reset — its working state deleted — for the next jump. On the nodes, copy and delete are free, and the between is empty, so there is nothing to carry and nothing to lose.
The between removes both freedoms. The no-cloning theorem forbids copying an unknown state. Landauer's principle ties erasure to an irreversible thermodynamic cost, making deletion a measurement, and measurement collapses the superposition in transit. A quantum crossing cannot copy its intermediate state and cannot discard its scratch work — because in the between there is something present that copy and delete would destroy.
So the crossing is unwound — Bennett's reversible uncomputation: run the subroutine, copy its result into a fresh register by entanglement, run the subroutine's inverse to return the workspace to its ground state without disturbing the result. Uncomputation is how the state crosses from one gate to the next intact. It is the formal content of a full edge, and it is the object the classical construction never needs, because an empty jump has nothing to conserve. What Wolfram gets for free on the nodes, transport in the between earns with a proof.
4. The reducibility pocket¶
Wolfram observes that some paths prevail not by out-computing their opponents node by node but by plugging into a pocket of computational reducibility — a hidden regularity that lets one systematically out-compete a whole class of adversaries blind to it.
That regularity lives in the between. Shor's algorithm locates the periodic structure of modular exponentiation — invisible to classical node-by-node search — and reads the period off a quantum interference pattern via phase estimation. The pocket is a structure in the carried state, accessible to an instrument that operates on the transit rather than on the discrete steps. In the present substrate the period-finding machinery is exercised and verified at witness scale: the reducibility pocket entered, instrumented, and sealed.
5. The central thesis: the proof is in the crossing¶
Wolfram establishes that competition between paths is computationally irreducible — the winner is found by running. That result is about the nodes: which path lands where, which sequence of jumps prevails. It is the upper stratum, and it stands.
The between is provable. Two things hold for every input, because they are amplitude-independent algebraic invariants of the crossing.
The first is uncomputation correctness. For a unitary U and a copy step whose target register
is disjoint from U's support, the sequence U† ∘ copy ∘ U returns the workspace to its
ground state, preserves the input, and isolates the result — for every input state, by
linearity and the unitary identity U†U = I. The second is orthogonal commutation. Operators
acting on orthogonal subspaces commute, and the state across the cut separating them is a
product state, for every input. Each is a theorem about the operators that carry the state, not
about the values carried.
The thesis: what happens on the nodes is found by running; what happens in the between is proven. The behavior a composed circuit computes — which path it realizes, what answer falls out — is the irreducible upper stratum. The conservation of the state as it crosses each join is the provable lower one. The architecture's terminal vocabulary is the interface between the strata: a composition runs to completion with every crossing proven and returns a sealed result, or it returns an explicit refusal naming the crossing it could not prove — the between reporting the exact join that failed.
6. Two genealogies of the language game¶
Both Wolfram's essay and this architecture use the phrase language game, and the nodes/between distinction sorts them.
Wolfram's game is played on the nodes: which discrete action, which discrete payoff, which path prevails. Wittgenstein's Sprachspiel places meaning nowhere in the isolated node — meaning is constituted in the use, in the passage of a move within the flow of the game, in what the move does as it connects to the next. Meaning is in the between.
The quantum language game sits exactly there. It takes the Wittgensteinian commitment — meaning is rule-governed use, established in passage rather than read off a single node — and makes it physical as state-in-transit, then rigorous as conservation of that state. The rules must conserve the between: a move that leaks or destroys the carried state is not a permissible utterance, regardless of payoff, because it breaks the medium the next move is made in. Meaning-as-use becomes meaning-as-provably-conservative-use. Wolfram counts the moves on the nodes; this work defines and proves what the moves mean in the gaps between them.
7. Inheritance¶
The enduring result of A New Kind of Science is that a simple substrate generates irreducible richness — simple rules reaching universal computation. This architecture inherits that directly: a small set of primitive operations composing toward hard problems. To it the work adds the between — the state that lives in the crossing, and the proof that it conserves. Wolfram maps the space of paths through the nodes; this work proves the transport along each edge they jump.
The substrate on which it does so is an octonionic/Clifford manifold, M⁸ = S⁴ × C⁴. That
formalism makes the conservation theorems of §5 theorems rather than analogies: the supports
across which orthogonal commutation is proven are subspaces of that manifold, and the dimension
at which the proofs discharge is fixed by it.
8. Conclusion¶
Wolfram occupies the nodes and the jumps between them; this work occupies the state that lives in the jump. His edges are transitions, found by running; these edges are transport, proven to conserve. The behavior on the nodes is computationally irreducible. The crossing in the between is provable, because conservation is an algebraic property of the operators that carry the state rather than a contingent property of the values carried.
The consequence is a way to build: prove the crossing, and let the path be found by running. A system that proves every crossing in full, and reports by name the one it cannot prove, knows the difference between the nodes and the between and acts on it. Wolfram gave the nodes their ruliology. This work gives the between its proof.
References¶
- S. Wolfram, Games between Programs: The Ruliology of Competition, Writings, June 2026.
- S. Wolfram, A New Kind of Science, Wolfram Media, 2002.
- L. Wittgenstein, Philosophical Investigations, 1953.
- R. Axelrod, The Evolution of Cooperation, 1984.
- C. H. Bennett, "Logical Reversibility of Computation," IBM J. Res. Dev., 1973.
- R. Landauer, "Irreversibility and Heat Generation in the Computing Process," IBM J. Res. Dev., 1961.
- P. W. Shor, "Algorithms for Quantum Computation: Discrete Logarithms and Factoring," Proc. FOCS, 1994.
- GFTCL-QCF-001 through 004, FortressAI Research Institute: proof-carrying quantum composition, the uncomputation transport protocol, and the proof-obligation set.
The full wiki¶
Everything the cell carries is in the left navigation — the substrate-mathematical foundation, the post-quantum wallet proof, the CLI reference, the schema catalog, Franklin architecture, and the domain catalogs. Use the search box up top to jump to anything.