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HORIZON PREDICTIVE LOOP · CLOSED AT THE MATHEMATICAL / MACHINE-PROVENANCE LAYER
The City now has a complete internal route from structure extraction through prospective prediction, Mnemosyne binding, reveal, scoring, correction retention, and return to the next forecast. This record synchronizes that success across the City without promoting it to external/live empirical evidence.
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The finite-dimensional spectral branch yields
$$ \lambda_1=0.46663667839993817,\qquad \lambda_2=0.9762859939007587, $$
$$ \Delta_{\mathrm{RI}}=\lambda_2-\lambda_1=0.5096493155008205, $$
$$ C_H=e^{-2\tau\Delta_{\mathrm{RI}}}=0.8155767672157836,\qquad \tau=0.2. $$
The corresponding amplitude contraction is 0.9030928895832275. The asymptotic predictive law is
$$ \frac{E_{n+1}-\lambda_1}{E_n-\lambda_1}\longrightarrow C_H. $$
At n=55, the observed ratio is 0.8155947364422004, giving absolute error 1.796922641672527e-05 and relative error 2.2032538369218907e-05.
LAB-MNE-EH-PROSPECTIVE-SYNTH-001 sealed a forecast before the held-out synthetic future was generated. Forecast and reveal both gave a topological birth $\beta_1:1\to2$. Forecast time: 18.5026831348; observed time: 16.9607750104; absolute timing error: 1.5419081244 frame units; harmonic-subspace overlap: 0.9582925866.
Fold transport preserved the event time to 2.88e-13, preserved event sign and post-event rank, and gave transported-projector overlap 0.9999999999999992. The strict Fold executable nevertheless returned pass=false because projector residual 5.575503985e-08 exceeded its coded 1e-08 threshold. The failure remains part of the closure record.
| Domain | What is now closed | Boundary retained |
|---|---|---|
| SPECTRA · Structure | Spectral gap and contraction invariant are explicit and machine checked. | No transfer to external physical prediction. |
| Fold · Invariance | Representation transport behavior is quantified and failure lineage retained. | Strict gate failure remains a failure until a preregistered tolerance passes. |
| Murmuration · Dynamics | Time-dependent Hodge / topology stream supplies the prospective event target. | Current sealed success is synthetic E2, not live telemetry. |
| Density · Measurement | Incomplete-view measurement remains an admissible input channel. | Measurement does not promote evidence class. |
| Horizon · Prediction | Operator-level convergence-rate forecast PASS plus sealed synthetic topological event forecast completed. | Previously unrevealed external runtime validation remains open. |
| Mnemosyne · Memory | Forecast packet and closure state are SHA-256 bound with reveal/correction lineage preserved. | Post-validation binding is provenance, not an external trusted timestamp. |
| Machine Certificates · Verification | Scoped finite predictive closure is ready for certificate intake. | Certificate scope is finite operator + reproducible numerical validation. |
| Observatory · Open questions | The finite operator-level Horizon closure is no longer an open question. | Live runtime replication and external generalization stay queued. A separate SYNTH-002 run has now frozen Fold tolerances before reveal and passed those frozen gates; SYNTH-001's earlier strict failure remains retained as its own provenance event. |
| Citadel · Broadcast | The City may broadcast Horizon as a closed internal predictive loop at its declared scope. | No E3/E4/H0 promotion. |
Source certificate SHA-256: f7f6e78897f01a5b058bae556867dc99e8fe82d186b3d7a84bddfc8af3832a0c
Canonical Horizon packet SHA-256: b9cc321512ebfcc73d2dffd7fbadf6feecdc6e9d202c76298f3151b2f2954685
Mnemosyne provenance-body SHA-256: 763ac87103da780b3cbd4acded70cc11d457d648138e6466a6167797cf3576bf
Horizon — Prospective Forecast Console · Mnemosyne — Event Horizon Memory Lab · Mini AI Labs — Unified Interface Portal · 🧾 Machine Certificates — Verified Results, Residuals, and Provenance · 🔭 Open Questions Observatory — Solutions, Partial Closures, and Validation Queue · 🏛 Central Citadel — Canonical BroadcastTower and City Synchronization Beacon