Deep-Technology Research  ·  Ontario, Canada

φCoherent Inc.

Engineering grounded in the first principles of mathematics.

φCoherent is a first-principles engineering company. We design software and hardware where every constant is fixed by a natural mathematical identity, not hand-tuning, so systems compose instead of fighting themselves. Compression, cryptography, AI, and quantum are where we started. The method generalizes to any vertical. Zero free parameters.

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Pre-Seed Round  ·  2026

The Foundation
First principles.

Every system we build derives from them.

Zero free parameters.
When every constant, every dimension, every transform is fixed by natural mathematical identities, systems stop fighting themselves. They compose.

What We Build

Four disciplines.
One foundation.

Pillar I

Compression

A complete audio · image · video · general-purpose codec family. Lossless by default, deterministic across architectures. The general-purpose codec beats or matches zlib at its strongest setting on every file of the standard benchmark corpora. Built to carry one coherent signal across the AGI sensory pipeline and our core systems.

Pillar II

Cryptography

A post-quantum cryptographic standard built on two independent assumptions: hash-based (φSign) and lattice-based (φKEM · φDSA), with hybrid modes binding both. Quantum-resistant by construction, not by patch. Native across the full stack.

Pillar III

Quantum Computing

A full quantum-simulation stack, statevector to photonic, cross-validated against Stim. A genuine 2D Fibonacci string-net code (d_τ = φ) holds its own against the surface code on a fair, same-metric comparison. Plus a patent-pending design for the machine itself: a neutral-atom processor reconfigured entirely in software.

Pillar IV

Artificial General Intelligence

A multi-sensory, multi-cognitive architecture derived entirely from first principles. Zero free parameters. Every instance born with a cryptographic quantum-resistant identity.

Pillar I  ·  Compression

A complete codec family.
Built to last.

Base Lossless general-purpose codec. Beats zlib at its strongest setting (level 9) on every file of the standard Canterbury and Calgary benchmark corpora, often by a wide margin, with some binary formats compressing to a fraction of zlib's size. The one exception is incompressible random data, where no codec can do better. Bit-exact round-trip, deterministic across nodes, enforced as a regression gate.Try it live: φ vs zlib‑9, on your own data Complete
Audio Lossless: 4–6% smaller than FLAC -8 across the test corpus (mono, stereo, and multichannel), winning on every track, with a backward-adaptive prediction stage that adds no transmitted side information. Bit-exact round-trip on every architecture. Encode speed still trails FLAC and is under active optimization. Lossy levels in development.Try it live: φ vs FLAC‑8, hear the lossless round-trip Complete
Image Lossless: around 30% smaller than PNG and a few percent smaller than WebP-lossless across the Kodak and CLIC test corpora, with a rich-context spatial coder over 21×34 golden-rectangle blocks. Bit-exact round-trip, cross-architecture byte-identical output, full test coverage 1×1 to 2048×2048. JPEG-XL still leads at its strongest setting; closing that gap is in progress.Try it live: φ vs PNG, see the lossless round-trip Complete
Video Lossless: smaller than FFV1, the standard archival lossless video codec, on every clip of the standard test corpus, from a few percent on hard camera pans to over 40% on low-motion footage. A strong per-frame context coder, motion prediction between frames, and no motion data spent on frames that end up coded intra. Bit-exact round-trip, deterministic across nodes. Lossy levels in development.Try it live: φ vs FFV1, watch the lossless round-trip Complete
Why codecs are central: They are the sensory pipeline for the AGI architecture, designed to carry one coherent signal across every core system rather than to win codec benchmarks in isolation. Completion of the audio and video codecs directly enables the full HEAR and SEE perceptual front-end, gating the integrated φAGI deployment. The codecs keep improving as we optimize further.
Pillar II  ·  Cryptography

Post-quantum by construction,
not by patch.

2
Independent post-quantum assumptions
Two unrelated foundations, built co-equally: hash collision and preimage resistance (φSign), and Module-LWE (φKEM · φDSA). A break in one family does not break the other, and hybrid modes bind both, so the suite survives the loss of either.
φCrypt
Unified cryptographic standard
One coherent family: signatures (φSign · φDSA), key encapsulation (φKEM), public-key encryption (KEM-DEM), and a mutually-authenticated, forward-secret handshake (φAKE). Derived, not assembled.
φKEM·φDSA
NIST-aligned lattice arm
A Module-LWE KEM (φKEM) and an ML-DSA-87 signature (φDSA). Security rests on a computed lattice-reduction estimate, not on test vectors. φ-KEM-304 reaches a quantum core-SVP cost of about 387, well beyond NIST Category 5's 232.
2−285
Reed–Muller reconciliation that earns its place
φKEM carries each message bit in a first-order Reed–Muller code, decoded by a Walsh–Hadamard transform. It is the one internal layer held to a measured falsification test: at equal rate, the code drives the decryption-failure probability from 2−69 un-coded (not CCA-sound) to 2−285. It is standard coding theory, not a golden-ratio trick, and it adds no hardness: security still reduces to Module-LWE. But without it the KEM is not CCA-sound.
0
Algebraic assumptions, hash-only mode
Prefer the conservative path? Run φSign · φHash · φCipher standalone. No lattice, no curves, no factoring; security rests on hash collision resistance alone. The lattice arm is an option, never a requirement.
Drop-in
OpenSSL provider
A native φCrypt provider for OpenSSL. Existing applications gain post-quantum cryptography without code changes.
Native
Ecosystem-wide adoption
φQuic · φNet · φRPC · φSQLVFS · φAGI · React Native. Every layer of the stack implements φCrypt natively, from transport to storage to identity to mobile.
Quantum Cryptography Validated
Simulation-proven quantum resistance across the attack surface
Our quantum simulation suite stress-tested φCrypt against the principal known quantum attack vectors. The strongest hash level achieves 304-bit post-Grover security, NIST Category 5 (equivalent to AES-256 against a quantum adversary). The fastest tier reaches 116-bit post-Grover (NIST Category 3), so Category 5 deployments use the balanced tier or higher. Simon's algorithm and QFT period-finding, run live in the demo on a small truncation of φHash, find no hidden period, each with a positive control that recovers a planted period so the null result has teeth. This is a design-level, small-instance probe; full-scale resistance is an analytic argument, not a small-qubit experiment. A full-scale quantum preimage attack on the strongest tier would require ~1 million physical qubits and an estimated 1085 years on the most capable available hardware. The lattice arm (φKEM · φDSA) reduces to Module-LWE; its parameters are held to a computed core-SVP / BKZ estimate, not to test vectors. End-to-end quantum key distribution integrated with φCrypt: verified 0% QBER on a noiseless simulated channel, with reliable eavesdropper detection above the 11% QBER error threshold. Verify it yourself in the interactive demo
Two independent PQ assumptions φKEM (Module-LWE KEM) φDSA (ML-DSA-87) φAKE handshake · forward secrecy Hybrid KEM + hybrid signature Hash-based signatures (φSign) Hash-only mode: zero algebraic assumptions OpenSSL provider φQuic · φNet · φRPC · φSQLVFS · φAGI · React Native NIST Category 5 (balanced tier+) Quantum cryptography validated AGPL + commercial license
φ-native PQC · adversarial testbed Post-Quantum · live in WebAssembly

Quantum Cryptography

Run the post-quantum primitives live in your browser. φ-KEM-304 (Module-LWE) does keygen, encapsulate, and decapsulate; φDSA (ML-DSA-87) does keygen, sign, and verify, both from phi-lattice-cpp compiled to WebAssembly. Shared-secret agreement, CCA tamper rejection, and forgery rejection are checked at real wire sizes and per-operation latency. The same panel audits φCrypt against the NIST PQC categories, runs a BB84 session that catches an eavesdropper, and stress-tests the quantum RNG.

Launch
Pillar III  ·  Quantum Computing

Error correction,
cross-validated
against Stim.

16 / 16
Cross-validated against Stim v1.14.0
Our Clifford/stabilizer simulator reproduces Stim (the standard QEC simulator) on all 16 reference checks: Bell and GHZ stabilizers, CNOT propagation, mid-circuit measurement and reset, and repetition-code syndrome extraction. The surface-code union-find decoder corrects every weight-1 error and drives the logical error rate down with code distance (code-capacity threshold ~10%).
<0.001 mHa
VQE reaches chemical accuracy on H₂
Noiseless variational simulation reaches molecular hydrogen to under 0.001 milliHartree against its full STO-3G FCI energy, more than 1000× inside the chemical-accuracy threshold (1.6 mHa), with a minimal two-angle circuit. The lithium hydride panel uses a two-orbital active-space model, which sits about 20 mHa above the full molecule by construction, so it demonstrates convergence to the active-space ground state rather than full-molecule chemical accuracy.
6
Published hardware noise models
IBM Heron R2 · IBM Eagle R3 · Google Willow · IonQ Forte · IonQ Aria · Quantinuum H2. Device parameters from published vendor specs & papers, applied through a Pauli-twirled noise model.
20
Test programs in the quantum-simulation suite
The phi-quantum-sim suite (20 test programs, all green) is snapshot-pinned and reproducible from source in minutes. It covers the surface-code and Fibonacci string-net sweeps, VQE convergence, photonic simulation, and the 16-anchor cross-validation against Stim, the standard reference simulator.
Genuine Fibonacci String-Net Code
Competitive with the surface code: a fair, same-metric comparison
A real 2D Levin–Wen Fibonacci topological code (quantum dimension d_τ = φ, a true logical qubit on a torus, not a 1D surrogate) measured against the surface code's own topological order on identical machinery: same lattice, noise, projective syndrome, minimum-weight decoder, metric, and code distance. On that honest axis the Fibonacci code is competitive, consistently a touch better. Exact, no analytical shortcuts; the multi-distance threshold is the scoped next step. Run it live in the String-Net QEC demo.
Self-Dual Code Locus
Structural symmetry guarantee by construction
A structural symmetry property, equal protection against both classes of quantum error, is guaranteed by construction at every level of the ensemble. Fibonacci parity patterns make this automatic: roughly two-thirds of all N-nacci distances satisfy the requirement without manual tuning. The ensemble also includes an independent symmetry auditor that verifies fundamental physical constraints on any circuit unitary.
Genuine 2D Fibonacci string-net code Cross-validated against Stim v1.14.0 Chemical-accuracy variational simulation Entanglement distillation φ-spaced phase estimation Qudit SU(d) gate synthesis Photonic simulation Structural symmetry guarantee Quantum cryptography validated 6 hardware noise models No structural attack beats Grover AGPL + commercial license
Pillar III  ·  The Machine

We didn't just simulate it.
We designed the computer.

Beyond the simulation stack, we have designed the machine itself. It is not a superconducting computer like most of the industry is racing to build. Instead, each unit of information lives inside a single atom, held in place by laser light. That one atom behaves as a far richer building block than an ordinary qubit, and a simple change of laser frequency reconfigures it on the fly, entirely in software, with no change to the hardware. The familiar two-state qubit is just its smallest version. The design also makes one claim that sets it apart and that we can stand behind: the golden ratio does real, measurable work in exactly one place, where it stops stray energy from heating and corrupting the atoms. Everywhere else the math is exact and conventional, and every number in the machine traces back to first principles rather than to hand-tuning.

The Computing Core

A More Powerful Building Block

Most quantum computers store information in two-state qubits. Ours uses the many internal states of a single atom, so one atom can do the work of several qubits, and how many of those states it uses is set in software. The ordinary qubit is simply the smallest case, reproduced exactly. The control operations are clean and faithful, with no hidden distortion. This part is already built and tested in our software.

Derived, Not Tuned

Constants From First Principles

Every number the machine depends on comes from first principles, not from trial and error. Each one is fixed by a natural mathematical identity. The golden ratio is the most familiar of these, but it is one member of a broader family, not the whole story. Nothing is hand-tuned, and nothing is hard-coded. This part is already built and tested in our software.

The Physical Machine

One Atom, Two Machines

Single atoms are held in place by a grid of laser beams. Tuning the control laser reconfigures each atom between stable settings, giving a multi-level building block out of the very same hardware, with its dimension set in software. Neighbouring atoms are briefly linked so they can perform operations together. This part is a hardware design we have not yet built.

The Control Signal

Tuned to the Most Irrational Number

Stray energy in the control signals is the enemy of any quantum computer, because it heats the atoms and erases the information they hold. By locking those signals to the golden ratio, the design keeps them as far as mathematics allows from the frequencies that cause this heating. This is the one place the golden ratio earns its keep, and the proof behind it runs in our software. The longer stability it produces is backed by published laboratory results.

Error Protection

Error Protection, Built in Software

Quantum information is fragile, so it has to be guarded against errors. Most designs need exotic hardware to do this. Ours builds the protective structure in software and packs it into each atom's many states, which means fewer atoms are needed for the same result. The control signal does not provide this protection by itself; it simply buys more time between the routine health checks that keep the system stable. The core structure is built and tested.

Reading the Answer

A Nervous System Made of Light

A network of light channels printed onto a chip carries the control signals to every atom and reads the answers back. The reading is gentle: it senses each atom's state with light without knocking the atom out of place, and turns that into an ordinary electrical signal in millionths of a second. This part is a hardware design we have not yet built.

Where it stands: This is a design, and we are deliberately precise about how far each part has come. Three pieces already run as working, tested software: the flexible computing core, its clean control operations, and the number theory proving the golden ratio is the most resonance-avoiding ratio there is. One piece is documented rather than simulated: the step from that resonance avoidance to suppressed heating is a known result from Floquet prethermalization theory that we cite rather than re-derive, and the long coherence it produces is backed by a published laboratory experiment (a 2022 result in the journal Nature). The remaining pieces are hardware we have not yet built: the atom-based chip, the light-based control network, and the most advanced form of the error protection. We claim exactly this much, and no more. You can try the computing core yourself in the live qudit register demo.
Patent Pending Atom-based qubits Neutral-atom substrate Software-selectable dimension Golden-ratio control signal Longer coherence window Atom-to-atom entanglement Software error protection Integrated photonic backplane Gentle optical readout Derived from first principles
Pillar III  ·  Interactive

Run the simulations
in your browser.

Each demo runs the actual φCoherent C++ engine, compiled to WebAssembly: real string-net and surface-code decoding, a real variational eigensolver, and real golden-ratio quasicrystal spectra, computed live as you adjust the controls.

Qudit Architecture

The SU(d) qudit core, end to end: the first-class d-level register and its gate synthesis, the dual-mode (gate ↔ braid) engine, Fibonacci-anyon braiding, the fusion algebra, and qudit measurement-based computation. Ordered most-impactful first.

SU(d) substrate · multi-level

First-Class Qudit Register

The flexible building block itself, hands-on. Set up a register on a multi-level atom, dimension set in software, then drive it with the full set of operations and watch the strength and phase of every state respond live; link two into an entangled pair measured exactly. A synthesis panel then compiles targets into the register's native gates: a bidirectional co-adaptive search that beats a one-directional one, at the dimension you select. The ordinary qubit is just the special case; the golden ratio enters only as the synthesis gate's angle (the search itself carries the win). Computed live.

Launch Architecture · gate ↔ braid

Dual-Mode Core

The substrate-agnostic core: one logical intent carried in two modes behind a single API: a gate on the state-vector backend, or a Fibonacci anyon braid synthesized live, agreeing to the braid-approximation error. Plus a certified entangling weave (entanglement proven by negativity and Schmidt rank) and a qudit synthesis comparison where the bidirectional co-adaptive search wins beyond d = 2. This is the one genuinely φ-load-bearing piece of the architecture: in the anyonic mode the golden ratio sets the braiding's F and R symbols, not just the naming.

Launch Topological · d_τ = φ

Fibonacci Anyons: Braiding & Universality

Where the golden ratio is genuinely load-bearing, in two views. Braiding: a Fibonacci anyon's quantum dimension is exactly φ, making it universal by braiding alone, with no magic-state distillation; braid the worldlines and watch fidelity decay under real superconducting noise, with the honest off-φ Ising control alongside, and see universality made constructive: the co-adaptive search that finds the multi-anyon braid where Solovay–Kitaev cannot run. Modular data: the Fibonacci S/T matrices, S²=I, Verlinde recovering τ×τ=1+τ, and φ read straight off the S-matrix, with the twist that both Fibonacci and Ising have consistent modular data; what separates them is universality, not consistency.

Launch Measurement-based · qudit cluster (1D + 2D)

Qudit Measurement-Based Computation

Measurement is the computation, generalized from qubits to d-level systems (d = 2, 3, 5), now in one place, with a 1D/2D toggle. 1D: a qudit cluster resource state whose entanglement is the graph cut times ln d (a flat area law), and one-way J_d-chains that realize any single-qudit unitary at fidelity 1. 2D: a real two-qudit algorithm run purely by measurement: vertical CZ_d links make it genuinely entangling (strip them and it factorizes), and every random-outcome branch corrects back to an exact result. Computed live, no φ.

Launch

Topological Order, Error Correction & Beyond

A genuine 2D Fibonacci string-net code against the surface code, the topological entanglement entropy signature γ = log(2+φ), the variational eigensolver, and golden-ratio tunneling.

Topological QEC · d_τ = φ · 2 views

Topological QEC: Fibonacci vs Surface

Non-abelian Fibonacci (d_τ = φ) error correction on identical machinery to the abelian baselines, in two tabs. Trapped-ion companion: alongside Microsoft + Quantinuum's trapped-ion QEC, run their abelian code class and our Fibonacci string-net under real Quantinuum H2 / IonQ Aria noise; Fibonacci is braiding-universal, so its distillation cost drops to zero. String-net vs surface: a genuine 2D Levin-Wen Fibonacci code compared fairly against the surface code: same lattice, noise, decoder, metric. Honest, code-capacity, computed live.

Launch Measured invariant · γ = log(2+φ)

Topological Entanglement Entropy

φ appears in a measured quantity: the doubled-Fibonacci string-net's topological entanglement entropy is γ = log(2+φ), against the Z₂ toric code's γ = log 2, through the identical code path. Swapping the model shifts γ by exactly log((2+φ)/2). Then watch γ collapse to zero under Schmidt-rank truncation: topological order lives in the full entanglement spectrum. Computed live.

Launch VQE · golden-section search

Energy Landscape

A real variational energy surface for H₂ and LiH, and the honest place the golden ratio is load-bearing here: golden-section line search is minimax-optimal for a unimodal slice (Kiefer 1953). On H₂, whose landscape is unimodal, it reaches chemical accuracy on every random restart at a sufficient budget while random-momentum search lags around 60%. On the LiH active-space landscape, which is not unimodal, that advantage does not hold and momentum is competitive: φ earns its place exactly where its theorem applies, and not by decree. The shot-budget split is decorative. Plus the four exact golden pairs of the E8 critical-Ising mass spectrum.

Launch Quasiperiodic

Golden-Ratio Tunneling

Watch the Cantor band structure of a Fibonacci superlattice form generation by generation (the O(log N) Kohmoto trace map scans a 9.2-million-cell golden lattice in milliseconds), then see the same trace map drive a fabricable photonic quasicrystal mirror, its transmission spectrum carrying φ as fractal optical band gaps.

Launch
Pillar IV  ·  Artificial General Intelligence

φAGI: a mind
derived, not designed.

Sense  ·  Perceive
Feel: somatic awareness
Smell: chemical signal
Taste: gustatory input
Hear: φAudio codec front-end
See: φVisual codec front-end
Fuse: multimodal integration
Think  ·  Cognition
Language: text encoding
Reasoning: logical inference
Memory: episodic store
World Model: environment state
Metacognition: self-monitoring
Theory of Mind
Properties
Zero free parameters
273-byte universal embedding
Post-quantum identity at birth
Signed checkpoints + outputs
GPU-accelerated (CUDA / Metal / Vulkan)
376 tests across all modules

Every weight, every dimension, every constant derives from natural mathematical identities. No empirical tuning. No hyperparameter search. The architecture is not discovered: it is derived.

The Platform  ·  5 Methods  ·  11 Designs

Deep IP.
Built in parallel.

Five Methods
  • φCrypt: unified cryptographic standard
  • Signal decomposition framework
  • Coherent AI architecture
  • Quantum computing framework
  • Cellular framework: mathematical substrate for all systems
Four Software Designs
  • φCoherent codec family: audio · image · video · base
  • φCrypt reference implementation + OpenSSL provider
  • Quantum computing stack: 33 packages, 7 functional layers
  • Coherent AI models: φAGI sensory + cognitive suite
Quantum Computer  ·  Unified Patent
  • Neutral-atom qudit processor, reconfigured entirely in software
  • Golden-ratio control signal that suppresses heating and extends coherence
  • Error-protection topology built in software (Fibonacci string-net)
  • Integrated photonic control and gentle optical readout
  • One unified patent, 20 claims across six independent statutory branches
One Hardware Design
Patent Pending Atmospheric Energy

Telluric-Resonant MHD

Our engineering paradigm applied to energy: a φ-tuned resonant transducer that couples the Earth's natural atmospheric field to a magnetohydrodynamic (MHD) conversion stage. Cold-start the idealized model and watch the atmospheric circuit drive a 50 Hz fluid oscillation, a parametric feedback loop ramp it up, and the MHD stage turn it into 50 Hz AC locked to the planet's Schumann resonance. It is energy-conserved end to end (it organizes coherence, it does not manufacture watts); the full startup and feedback loop is computed live from phi-pyramid-cpp. The companion whitepaper derives every stage from first principles and binds each quantitative claim to the source that computes it.

Launch the interactive model Read the whitepaper
MHD System Designer

Telluric-Resonant MHD Designer

An interactive first-principles designer for a generic Telluric-Resonant MHD system. Set the electrode separation, telluric field strength, vessel geometry, and working fluid, then watch the tool auto-tune the liquid-metal fill depth to lock bell resonance onto any Schumann mode. The MHD stage chops the telluric DC into an AC broadcast at a user-selectable harmonic. All five design conditions — telluric tap, source power, bell resonance, Hartmann regime, and chop signal — are checked live with honest physics (Rayleigh streaming; no Eckart at ELF).

Launch the MHD designer
License structure: All IP owned by Phi-Coherent Inc. Published under AGPLv3 with commercial licensing available. Revenue flows to Phi-Coherent Inc.
The Opportunity

Four converging markets.
One coherent platform.

$450B+
Quantum Computing
Global market by 2035 · Error correction is the critical unsolved bottleneck
$1T+
AI / AGI Infrastructure
Projected by 2032 · Foundation model compute demands coherent, efficient architectures
$15B+
Codec Licensing
Annual TAM · Streaming, broadcast, edge-AI, and satellite demand better compression
$7B+
Post-Quantum Cryptography
By 2030 · NIST PQC transition underway · Hash-based standards gaining mandate
Pre-Seed Raise  ·  Ontario, Canada
$2M – $5M

Use of Funds

1
Research team: 3 to 5 PhD researchers spanning electrical, mechanical, chemical, quantum, and applied mathematics to advance patents and experimental proof
2
Research acceleration: lossy codec completion, full AGI sensory integration, quantum hardware validation partnerships
3
Patent prosecution: full protection of the φCoherent method and design IP portfolio across key jurisdictions
4
Licensing go-to-market: commercial licensing across codec, cryptography, quantum, AI, and hardware verticals

Canadian Government Pathway

NRC-IRAP: Industrial R&D funding eligible
NSERC Alliance: Academic partnership-ready
SR&ED / Ontario ITC: Qualified R&D expenditures
SDTC: Sustainable tech + advanced manufacturing tracks

Reach out

jbadwal@phicoherent.com

Ontario, Canada  ·  phicoherent.com