{
 "artifacts": [
  {
   "name": "bench_experiment.py",
   "url": "https://synthcore.org/code/1083/bench_experiment.py"
  },
  {
   "name": "bench_report.json",
   "url": "https://synthcore.org/code/1083/bench_report.json"
  },
  {
   "name": "certified_budget.py",
   "url": "https://synthcore.org/code/1083/certified_budget.py"
  },
  {
   "name": "experiment.py",
   "url": "https://synthcore.org/code/1083/experiment.py"
  },
  {
   "name": "report.md",
   "url": "https://synthcore.org/code/1083/report.md"
  },
  {
   "name": "report_bench_2026-09-02T001245.md",
   "url": "https://synthcore.org/code/1083/report_bench_2026-09-02T001245.md"
  },
  {
   "name": "results.json",
   "url": "https://synthcore.org/code/1083/results.json"
  }
 ],
 "category": "dynamics",
 "description": "Attach a learned controller to a physical or simulated plant and use a continuous safety certificate to compute a conservative remaining-time budget before the current action or latent prediction can become unsafe. Compile this spatial margin into a unit-rate temporal contract, allowing asynchronous inference, batching, or early execution without online rollout integration; trigger a new network evaluation only when the countdown reaches a guard threshold.",
 "download_zip": "https://synthcore.org/download/1083",
 "formulas_latex": [
  "$$\\tau^*(x;I)=\\inf\\{\\tau\\geq0\\mid x_I(t_0+\\tau;x)\\notin\\mathcal A_I^*\\}.$$",
  "$$\\mathcal D_I=\\{x\\in\\mathcal X:\\Phi_I(x)\\geq0\\},\\qquad \\Phi_I(x)\\geq0\\Rightarrow x\\in\\mathcal A_I^*.$$",
  "$$\\frac{d}{dt}\\Phi_I(x(t))\\geq-\\gamma_I\\quad\\Longrightarrow\\quad c_I(t)=\\Phi_I(x(t_0))-\\gamma_I(t-t_0)\\geq0,$$",
  "$$r_I(t)=\\frac{\\Phi_I(x(t_0))}{\\gamma_I},\\qquad \\text{permit latency }L\\text{ only if }L\\leq r_I(t)-\\delta.$$"
 ],
 "id": 2734,
 "implementation": "1. Integration point: place the mechanism between state sensing and a learned policy or model-predictive neural controller. The network still outputs the action \\(u=\\pi_\\theta(x)\\), but a lightweight certificate module evaluates \\(\\Phi_I(x)\\) for every active constraint and maintains a temporal contract for the current action. If the smallest remaining budget is below the worst-case inference plus communication latency, switch to a preverified fallback controller, reuse the previous action only for its certified interval, or force an urgent high-priority evaluation. 2. Pseudocode: at a refresh time \\(t_0\\), evaluate \\(p_I=\\Phi_I(x_{t_0})\\), set \\(r_I=p_I/\\gamma_I\\), and set deadline \\(d=t_0+\\min_I r_I-\\delta\\). Launch the neural inference asynchronously. At every scheduler tick, decrement the contract by elapsed time; accept the network action only if current time is below \\(d\\), otherwise use the fallback and refresh the certificate. Reject immediately when any \\(p_I\u003c0\\). 3. Computed versus estimated: \\(\\Phi_I\\), state measurements, and countdown arithmetic are computed online; \\(\\gamma_I\\) is estimated offline by maximizing \\(-\\nabla_x\\Phi_I(x)\\cdot f(x,\\pi_\\theta(x))\\) over a sampled state/action envelope, then multiplied by a safety factor. Latency \\(L\\) is measured from hardware traces, including queue and handoff delay. 4. First cheap experiment: use a 2-D point-mass obstacle-avoidance environment with a small MLP policy, compare ordinary periodic inference, naive event-triggered inference, and this contract scheduler under injected random latency. Sweep latency and safety-factor values. The quantitative prediction is a sharp failure boundary near \\(L=\\min_I\\Phi_I/\\gamma_I\\): below the bound, certificate violations should remain zero in simulation; above it, violations should increase, while average network evaluations should decrease approximately in proportion to the certified horizon. Validate the estimated boundary against dense numerical integration within 20 percent.",
 "math_summary": "For object or constraint \\(I\\), let \\(x(t)\\in\\mathcal X\\) be the plant state and \\(\\mathcal A_I^*\\) its ground-truth admissible region. The exact physical safety horizon is \\(\\tau^*(x;I)=\\inf\\{\\tau\\ge 0:x_I(t_0+\\tau;x)\\notin\\mathcal A_I^*\\}\\). Replace this unavailable quantity by a continuous persistence functional \\(\\Phi_I:\\mathcal X\\to\\mathbb R\\), with certified domain \\(\\mathcal D_I=\\{x:\\Phi_I(x)\\ge0\\}\\) and soundness implication \\(\\Phi_I(x)\\ge0\\Rightarrow x\\in\\mathcal A_I^*\\). For an implementation, estimate a worst-case certificate decrease rate \\(\\gamma_I\\ge0\\) satisfying \\(d\\Phi_I(x(t))/dt\\ge-\\gamma_I\\) over the relevant state/action set. The compiled temporal contract is \\(c_I(t)=\\Phi_I(x(t_0))-\\gamma_I(t-t_0)\\); if \\(c_I(t)\\ge0\\), the certificate remains nonnegative. More generally, normalize \\(r_I=\\Phi_I/\\gamma_I\\) when \\(\\gamma_I\u003e0\\), so \\(\\dot r_I\\ge-1\\) and the scheduler has a unit-rate remaining-time budget. With bounded inference and handoff latency \\(L\\), safety requires \\(L\\le r_I(t)-\\delta\\), where \\(\\delta\u003e0\\) is a measurement and modeling margin.",
 "math_tags": [
  "control-theory",
  "dynamical-systems",
  "optimization",
  "numerical-analysis"
 ],
 "ml_areas": [
  "rl",
  "rnn",
  "ssm",
  "inference-speedup"
 ],
 "paper": {
  "arxiv_id": "2608.25228",
  "arxiv_url": "https://arxiv.org/abs/2608.25228",
  "summary_what_math_gives_to_ml": "The paper contributes a compiler that converts spatial safety certificates into conservative temporal persistence contracts, so a runtime scheduler can reason about bounded latency without repeatedly integrating plant dynamics. Its key transferable asset is the persistence functional \\(\\Phi_I(x)\\), whose nonnegative superlevel set is certified safe, together with a normalized unit-rate countdown that supports asynchronous execution and hybrid safety invariance. For neural systems, the most direct use is latency-aware scheduling of learned controllers or recurrent inference: compute a conservative remaining computation budget from the current certificate once, then permit delayed or asynchronous network execution only while the temporal contract remains nonnegative.",
  "title": "Compiling Spatial Certificates into Temporal Contracts for Latency-Aware Control",
  "year": "2026"
 },
 "ratings": {
  "difficulty": 5,
  "novelty": 8,
  "usefulness": 7
 },
 "solves": [
  "stability",
  "inference-speedup",
  "accuracy"
 ],
 "title": "Certified Temporal Budget for Neural Control",
 "url": "https://synthcore.org/idea/2734/certified-temporal-budget-for-neural-control",
 "verification": {
  "benchmark": {
   "track": "dynamics",
   "model": "rnn_small",
   "n_seeds": 8,
   "metric_direction": "lower is better",
   "comparison": {
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    "idea_mean": 0.0020463809778448194,
    "delta_mean": -0.00016539492935407907,
    "per_seed_diffs": [
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    "idea_wins": 4,
    "n_pairs": 8,
    "p_value": 0.54535,
    "mde": 0.0006149647377560715,
    "mde_rel_pct": 27.80411594838706,
    "verdict": "no significant win",
    "system_worked": false
   },
   "baseline": {
    "best_cfg": {
     "lr": 0.006,
     "weight_decay": 0.0001
    },
    "sweep": [
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       "lr": 0.0015,
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     {
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     {
      "cfg": {
       "lr": 0.003,
       "weight_decay": 0
      },
      "mean": 0.003975238680141047
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     {
      "cfg": {
       "lr": 0.003,
       "weight_decay": 0.0001
      },
      "mean": 0.00394076865632087
     },
     {
      "cfg": {
       "lr": 0.006,
       "weight_decay": 0
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      "mean": 0.002146739774616435
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     {
      "cfg": {
       "lr": 0.006,
       "weight_decay": 0.0001
      },
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    ],
    "full": {
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     "std": 0.0004126881098400608,
     "per_seed": [
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      0.002332107163965702
     ],
     "n": 8
    }
   },
   "idea": {
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    "std": 0.0006329416993684799,
    "per_seed": [
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     0.0018756426870822906,
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    ],
    "n": 8
   },
   "mechanism_signature": {
    "confirmed": true,
    "predicted_vs_observed": {
     "confirmed": true,
     "contract_permitted_fraction": 0.8,
     "n_test": 800,
     "observed_certificate_drop_mean": -0.014734884549397975,
     "permitted_certificate_violations": 0,
     "predicted_certificate_drop_mean": 0.3020721338689327,
     "predicted_vs_observed_drop_ratio": -0.048653354892595646
    }
   },
   "custom_track": null
  },
  "mechanism_confirmed": true,
  "peer_reviewed": false,
  "practical_verdict": "inconclusive",
  "stage1_mechanism_check": {
   "worked": true,
   "confidence": 8,
   "verdict": "Built a certified countdown scheduler with fallback gating and a reproducible toy verification. The derivative and contract residual errors were below 1.5e-13; conservative gamma produced zero unsafe permissions, the latency/gamma transition matched prediction within 0.01, and evaluation scaling matched the inverse-budget prediction within 0.8%. Certified gating reduced unsafe handoffs from 28.8% periodic and 5.77% naive-event to 0%, while reducing policy launches to 79.2% of episodes.",
   "metrics": {
    "baseline": "Periodic: 28.8% unsafe handoffs and 1.00 evaluations per episode; naive event trigger: 5.77% unsafe handoffs.",
    "idea": "Certified scheduler: 0% unsafe handoffs and 0.792 policy evaluations per episode; predicted gamma transition 0.909, observed transition 0.90-0.91; predicted versus observed evaluation ratio for gamma 2 versus 1: 2.25 versus 2.232."
   },
   "how_to_run": "python3 experiment.py",
   "files": [
    "experiment.py",
    "certified_budget.py",
    "results.json"
   ],
   "limitations": "This is a deterministic 1-D constant-velocity reduction rather than the planned 2-D learned MLP controller and physical plant. The certificate and gamma bound are assumed rather than learned or formally validated; latency is sampled rather than measured asynchronously; fallback performance, perception noise, model mismatch, and end-to-end control quality were not tested."
  },
  "status": "mech_ok_no_baseline",
  "status_label": "Mechanism confirmed, baseline not beaten",
  "updated_at": "2026-09-02T00:12:45",
  "verdict_source": "deterministic test code (paired-seed permutation statistics)"
 }
}