Horizon — Prospective Forecast Console

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ENGAGE HORIZON

Launch Horizon — Prospective Forecast Console

The City’s prospective invariant-event instrument. Governing question: What invariant is about to exist?

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City role

Horizon is the Prediction member of the eight-lab public Octet and the forecast stage of the executable conductor. The City intentionally preserves two different orders:

Interface/question cycle: SPECTRA → Fold → Murmuration → Mnemosyne → Density → Horizon → Wave → Identity → SPECTRA.
Executable dependency order: SPECTRA → Fold → Density → Murmuration → Horizon → Mnemosyne → Wave → Identity → SPECTRA_REVEAL → SCORE. Canonical contract: Octet Experiment Packet — Cross-Lab Transport and Verification Contract.

Station	Horizon role
🔬 SPECTRA	Locks the finite spectral kernel and admissible invariant sector.
🧬 Fold	Challenges the forecast under rigid motion and relabeling.
🐦 Murmuration	Supplies the time-dependent point-cloud / Vietoris–Rips trajectory and Betti state.
🌀 Density	Provides an incomplete-view reconstruction channel. Measurement only.
🧠 Mnemosyne	Commits forecast tuples cryptographically and preserves reveal / correction lineage.
🛰️ Horizon	Forecasts the next invariant event.
🌊 Wave	Evolves or perturbs the carrier only after the Horizon output is bound by Mnemosyne.
🪞 Identity	Evaluates persistence across the Wave transformation before independent reveal measurement and score.

Forecast grammar

From history frames $X_{t-1},X_t$, Horizon forms a local extrapolation and searches the predicted Rips trajectory for the first change in first homology:

$$ \widehat X(t+\tau)=X_t+\tau(X_t-X_{t-1}), $$

$$ \widehat\tau=\inf\{\tau>0:\beta_1(\mathcal R_\epsilon(\widehat X(t+\tau)))\neq\beta_1(\mathcal R_\epsilon(X_t))\}. $$

The sealed forecast packet is

$$ \mathcal F_t=(\widehat\tau,\widehat{\Delta\beta_1},\widehat{\mathrm{event}},\mathrm{SHA256}). $$

After reveal, Horizon scores timing, Betti transition, event sign, Fold invariance and retained failures.

Current executable run · seed 47 · frame 30

HORIZON · prospective forecast
seed=47  t=30  Ωc=0.376  dim H=125  E47=47
SPECTRA  ker K = E47  sectors J=2,5  ρ*=0.882353
Murmur   β0=2  β1=1  n1=106  n2=132
Forecast τ̂=1.976499  1→2  event=birth
Fold     pass=True  Δτ=1.110e-14  residual=0
Seal     a809ca325c29ae86c7e756a2006b60290a4b4e758c179ebed6e42ee5a1c96dfe
Reveal   τ_obs=2.000  |τ̂−τ|=0.024  β 1→2  sign_ok=True
Density  measurement only · gated mean=0.0398
boundary E2 synthetic · failures kept · no evidence-class upgrade

Canonical source SHA-256: 23949b4e376424324d0b018fb1d05b607f5caf8f33ac6a3a243cf0c01b49ae82

City role

Forecast grammar

Current executable run · seed 47 · frame 30

Source and evidence authority