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Referential

Frontier research surface

The referential family (the registry's awareness category, prefix AWARE, group Frontier) is a research surface, not a physical theory. It collects named mathematical expressions for information, complexity, neural dynamics and the thermodynamics of computation. Some are established equations — LZ1 is Landauer's principle, XI1 is Shannon entropy, CBCM is a BCM-style synaptic-plasticity ODE. Others are speculative, consciousness-themed expressions. Nothing here is asserted as verified physics of consciousness. Treat the tables below as a catalogue, not operational results.

What compute actually does with these​

Be precise, because it is easy to over-read a returned number. The compute path does not evaluate the formulas in this catalogue. Selecting any operator from this family runs the domain's generic solver, which computes one thing:

E = h·f     (Planck photon energy, from the `f` input)

That means:

  • ["KO42","ON0"] with f = 1.287 → 8.5277523e-34 J
  • ["KO42","QL1"] with f = 1.287 → 8.5277523e-34 J ← identical — the operator you pick does not change the result
  • ["KO42","ON0"] with f = 2.0 → 1.325214e-33 J ← it just tracks E = hf
  • any of them without an f input → no-match

So a call that names ON0 does not return "the ON0 gradient." It returns h·f. The operator id in the envelope is KO42 (the ground state), and the COMPUTE step reports solver: "AWARE domain solver", equation: "E = hf (photon energy)". This is the honest behaviour — verify it yourself below.

Verify it yourself​

Get a free key (POST /api/demo-key/mint), then run the same operator twice with different ids:

curl -sS -X POST https://www.zeq.dev/api/zeq/compute \
  -H "Authorization: Bearer zeq_ak_..." \
  -H "Content-Type: application/json" \
  -d '{ "domain": "Awareness", "operators": ["KO42","ON0"], "inputs": { "f": 1.287 } }'

Real response (abridged):

{
  "value": 8.5277523e-34,
  "unit": "J",
  "operator_id": "KO42",
  "protocol_steps": [
    { "name": "COMPUTE", "detail": { "solver": "AWARE domain solver", "equation": "E = hf  (photon energy)" } }
  ],
  "zeqProof": "…"
}

Swap ON0 for QL1 and the value is byte-for-byte the same. Drop the f input and unit becomes no-match. The envelope is still real and signed — what it proves is the E = hf computation and the HulyaPulse stamp, not an evaluation of the operator's own equation.

Operator catalogue​

These are named expressions in the registry. They are documented verbatim; they are not what the solver evaluates (see above). The full 74-entry list lives in the reference; a representative selection:

IDFormula (as catalogued)Note
ON0ψ_ON0 = sin(phase) + 1.1 ; ON0 = ψ_ON0 ln(ψ_ON0) − phase × fobservation primitive (speculative)
QL1info_density = |sin(phase × 3)| + 0.1 ; QL1 = 0.1 × density × ln(density / 0.1) + cos(phase) × 0.5information-density expression (speculative)
TM1TM1 = −t + current_utp × periodtime-index bookkeeping
XI1ρ_XI1 = |sin(phase)| + 0.001 ; XI1 = −ρ_XI1 log₂(ρ_XI1)Shannon binary entropy — established
LZ1LZ1 = k_B T ln(2) × bits_erasedLandauer erasure bound — established
CHI95CHI95 = |sin(phase)| − |cos(phase)|phase asymmetry (speculative)
PSI96PSI96 = 0.5 × sin(2π f t + phase_offset)sinusoidal sampler
VXVX = κ_vx (intent_proxy sin(phase) + flow_proxy cos(phase))named expression (speculative)
ZEQ000φ_c^42 · Ψ_total = Σ(ZEQ_structural + ZEQ_chemical + ZEQ_genetic + ZEQ_field) · [sin(2π·1.287·t) + cos(2π·0.618·t) + exp(2π·2.083·t)] · consciousness_field_density(x,y,z,t)symbolic; the exp(2π·2.083·t) term overflows float64 at t > 54.2 s — no physical claim
ZEQ-PROTECT-001P(t) = |sin(5φ(t))| / f_pulsenamed envelope (speculative)
ZEQ-TETHER-003B_sib = ∑_k e^{i·φ_k} |sibling_k⟩named expression (speculative)
ZEQ-POCKET-001∂g_μν/∂t = (8πG/c⁴) T_μν^consciousnessEinstein-form analogue with a consciousness source term — not a solved field equation

Where the real mathematics is​

If you want operators that the engine actually evaluates, use the physics domains — those route to the 19 closed-form solvers (quantum, Newtonian, relativity, thermodynamics, …) and return domain-correct values with units and an uncertainty bound. This family is a place to catalogue and explore frontier expressions, not a compute path.

Papers​