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A robot replanning through a world whose costs drift faces a question classical planners never answer: how good is my current route, given that most of the map is stale? CERT-FLOW answers it every round, with a proof: a high-probability certificate LB ≤ OPT ≤ UB on the optimal route cost, built from age-weighted non-exchangeable conformal prediction over drift-adjusted observation residuals, and it spends paid sensing exactly where the certificate says the gap shrinks fastest.

Why it's different

property	classical replanning (D* Lite, AD*)	exchangeable conformal (CIA)	🏆 CERT-FLOW (wins)
stale map	silently trusts it	coverage collapses (0.95 → 0.20 measured)	prices it: width grows with age, claim degrades visibly
validity under drift	0.02–0.59 measured	gap-dependent	0.95–1.00, every condition ever run
sensing	none / heuristic	none	certificate-directed (oracle-level regret)
static regime	fast	tight	proof-gated preprocessing: ns–µs queries that self-expire

Results at a glance — CERT-FLOW wins every metric

metric	better is	CERT-FLOW	best alternative	winner
certificate coverage	higher ↑	1.000 (every condition)	AD* 0.02–0.59 · CIA → 0.20	🏆 CERT
travel-regret, unknown terrain	lower ↓	−0.12 (≈ clairvoyant oracle)	VOI 0.47 · freshness/blind 4–7	🏆 CERT
fully-certified round @ 60×60	lower ↓	3.7 ms p50 / 12 ms p95	— no certified planner reports one	🏆 CERT
road cost-change absorption	lower ↓	0.015–0.34 ms	CRP ≈ 1 s	🏆 CERT

“better is” shows the metric direction (↑ higher / ↓ lower); bold = best value; 🏆 = winner. Every per-condition table in docs/ is likewise marked and ranked best→worst.

Headline results (all reproducible below)

• Coverage ≥ claimed confidence on every condition ever run: 17 synthetic regimes, off-model worlds, and two real cities (METR-LA, PEMS-BAY) at up to 49% drift-model violation rates.
• Route quality: exactly optimal on known maps (≡ Dijkstra, plus the certificate); travel-regret −0.12 ≈ a clairvoyant oracle in unknown drifting terrain; 2–3× lower regret than freshness/uncertainty/random sensing at equal budget.
• Speed: 3.7 ms p50 / 12 ms p95 per fully-certified round at 60×60 (one CPU core). Certificate-gated preprocessing answers static queries in 269–394 ns (cost) / 8.7 µs (path), at or below published static-SOTA, and at road scale absorbs cost changes in 0.015–0.34 ms vs ~1 s for CRP-style recustomization, exact under ±20% perturbation.
• Theory T1–T7: coverage (observable + latent), a certifiability threshold (gap ε is sustainable iff sensing rate beats drift, both directions), a √L sum-aware upper certificate with a measured selection-bias hazard and its gate, an impossibility theorem (no uniform lower bound can beat Bonferroni by more than log factors, so the certificate's asymmetry is optimal), decision-uniform validity, and a churn-measured floor.
• Honest negatives, kept: the corridor-memory speed hypothesis failed (documented), a predictor's regime claim was downgraded after its test, and the maze negative-control shows exactly where route-critical sensing cannot help. Every known limitation and its disposition: docs/results/limitations.md.

Quickstart

pip install "certflow[fast]"   # "fast" = numba (needed to reproduce the speed numbers)
python - <<'PY'
from certflow import CertPlanner, PlannerConfig
from certflow.drift import grid_world

world = grid_world(6, 6, seed=0, kind="bounded", rho=0.02, noise_scale=0.05)
planner = CertPlanner(world, (0, 0), (5, 5),
                      PlannerConfig(epsilon=5.0, alpha_prime=0.2))
for _ in range(150):
    cert, sensed = planner.round()
print(f"[{cert.lb:.2f}, {cert.ub:.2f}] @ confidence {cert.confidence:.2f}, "
      f"gap {cert.gap:.2f}")
PY

To develop or reproduce the paper numbers, work from a clone:

git clone https://github.com/Archerkattri/CERT-FLOW && cd CERT-FLOW
python -m venv cert_env && source cert_env/bin/activate
pip install -e ".[dev,fast,realworld]" h5py
pytest   # full suite: 227 with datasets; data-dependent tests skip cleanly without data/

Reproducing every number

Every quantitative claim traces to a script; the core sweep runs in ~100 s on a multicore machine (CERTFLOW_WORKERS=N parallelizes seeds bit-identically).

Result	Script	Documented in
Tier-0 coverage (17 conditions, provable + strict modes)	scripts/run_tier0.py	docs/results/tier0-coverage.md
CERT vs Gaussian (path level)	scripts/run_tier0_baselines.py	docs/results/tier0-coverage.md
Edge-level audit (Gaussian break)	scripts/run_gaussian_break.py	docs/results/gaussian-break.md
Incremental repair latency (T3)	scripts/run_tier1_latency.py	docs/results/tier1-latency.md
Ablations (κ churn, pre-widening)	scripts/run_ablations.py	docs/results/ablations.md
Travel regret, unknown terrain	scripts/run_tier2.py	docs/results/tier2-regret.md
Real traffic (METR-LA / PEMS-BAY)	scripts/run_metr_la.py [--pems-bay]	docs/results/metr-la.md
MovingAI maps + maze negative control	scripts/run_movingai.py	docs/results/movingai.md
External algorithms (AD*, VOI, TASP-degenerate)	scripts/run_extern_baselines.py	docs/results/extern-baselines.md
CIA exchangeability collapse	scripts/run_cia_comparison.py	docs/results/cia-comparison.md
E-Graphs + networkx anchors	scripts/run_repeated_queries.py	docs/results/extern-baselines.md
Lifelong missions (memory vs memoryless)	scripts/run_lifelong.py	docs/results/lifelong.md
Feature regimes (predictor, decision-uniform)	scripts/run_feature_regimes.py	docs/results/feature-regimes.md
Scale + engine benchmarks	scripts/run_scale.py	docs/results/scale.md
Road networks (DIMACS NY/FLA, ALT)	scripts/run_roadnet.py	docs/results/published-speed-comparison.md
Certified Contraction Hierarchies	scripts/run_ch.py	docs/results/published-speed-comparison.md
Extended validation (baselines, stress, scaling)	scripts/extval/*.py	docs/results/extended-validation.md
FoMo off-road seasonal drift	scripts/extval/fomo_validation.py	docs/results/extended-validation.md (§6)
Comparison videos	scripts/viz_compare.py, scripts/viz_gen/*.py	site/ (project page)

All scripts accept --quick. Real-data runs need data/ (sources and loaders in data/README.md; ~230 MB + optional FoMo cost-signal ~150 MB, links inside).

Videos

Honest side-by-side comparisons — every clip replays a real run and the coverage/regret numbers shown are measured, not staged (warm-up rounds are drawn as "no claim", never counted as misses). Generators: scripts/viz_compare.py + scripts/viz_gen/; MP4 + supplementary reel in assets/videos/.

The certificate that holds vs. the one that breaks — CERT's band contains the true optimum every round it claims; AD*'s w-suboptimality band, trusting stale point estimates, drifts out of date.

Synthetic drifting grid — CERT coverage 100% vs AD* 43% (60 rounds).

Real MovingAI map (DAO arena) — CERT 100% vs AD* 42%.

Sensing that pays — gap-directed sensing converges near a clairvoyant oracle; random / max-age / drive-blind wander at equal budget.

Unknown drifting terrain — CERT travel-regret 1.96 vs random 7.84 / max-age 4.89 / blind 5.43 (15 seeds).

Real arena map — CERT 1.71, lowest of all policies.

Exchangeability collapse under staleness — exchangeable conformal (CIA, its own construction) covers on the static slice it assumes, then collapses; CERT widens to hold coverage.

METR-LA — CIA coverage 0.88 → 0.25 → 0.38 (width frozen) vs CERT ~1.0 (width grows).

How it works

1. Score every paid observation with a drift-adjusted residual; weight by age (data-independent geometric weights; exchangeability is not assumed).
2. Price each edge as ĉ ± (λq + ρ·age): the conformal quantile pays for noise, the drift term pays for staleness.
3. Bound the optimum from both sides with two incremental searches (optimistic ℓ, conservative u) over a flat-array engine (numba kernels).
4. Claim LB ≤ OPT ≤ UB at an honestly-annealed confidence: weak claims during warm-up instead of silence; the claim visibly decays as the map ages.
5. Sense the edge that shrinks the certified gap fastest (route-critical, churn-aware); certification is a rate, not a state (T2′).
6. When the certificate proves the map tight, that proof licenses preprocessing: an all-pairs oracle or certified Contraction Hierarchy answering in ns–µs, revoked the instant drift exceeds tolerance.

Layout

src/certflow/
  types.py      contracts (World, EdgeBelief, Certificate)
  conformal.py  weighted non-exchangeable quantiles, Δ_stale, ACI, blocks
  cert.py       the planner: certify → sense → repair loop, gates, annealing
  sensing.py    gap-shrink selection + baseline policies
  fastgraph.py  flat-array CSR engine (numba D* Lite, Dijkstra kernels)
  snapshot.py   certificate-gated all-pairs oracle (ns queries)
  ch.py         certified Contraction Hierarchies (231 µs on 264k-node NY)
  roadnet.py    DIMACS road graphs + exact ALT on landmark lower-bounds
  drift.py / realworld.py / movingai.py   synthetic, traffic-replay, game maps
scripts/extval/   extended validation (baselines, stress, scaling, FoMo)
scripts/viz_gen/  comparison-video generators; site/ = project page
  episodes.py / harness.py / baselines.py runners, seeds, parametric strawman
docs/results/   one markdown per experiment: numbers, anomalies, verdicts
docs/specs/     design spec; docs/theory/ working notes

Citation

Paper (engrXiv preprint): CERT: Certified Route Planning under Drifting Costs, doi:10.31224/7306.

@software{attri2026certflow,
  author = {Attri, Krishi},
  title  = {{CERT-FLOW}: Certified Route Planning under Drifting Costs},
  year   = {2026},
  doi    = {10.5281/zenodo.20631475},
  url    = {https://github.com/Archerkattri/CERT-FLOW}
}

The DOI above is the concept DOI (always resolves to the latest archived version); CITATION.cff carries the same metadata in machine-readable form.

Paper preprint (extended version): engrXiv, doi:10.31224/7306.

Author: Krishi Attri (ORCID · Google Scholar)

License

MIT, see LICENSE.