No. 03 · The observatory
The few results that touch real operations
Eight families sit near work companies already pay for. None of the eight changes what an operator should do this year.
- Status
- Open
- Families near real operations
- 8
- Algorithms a business could run
- 1, impractical as published
- Headline theorems checked in Lean
- 5 of 8
- Patents, standards or hardware changed
- None
Which results come close to real operations?
File most of these as confirmed, no action. Check the later chapters only if you sell or buy the named work.
Eight families sit near work that companies already pay for.
They touch exact statistical tests, cutting stock in paper and steel mills, and radar codes. Others touch medical imaging and computational chemistry. On a close reading, none changes what an operator should do this year.
- One real algorithm. Family 115 samples and counts tables with fixed totals. Its authors call the exponents "deliberately large".
- Two settled questions. No Barker radar code runs longer than 13 (179). No shortcut reaches exact molecular energies (275).
- Three imaging and chemistry theorems. Families 365, 372 and 278 assume measurements that no shipping device collects.
- Two worth a watch. Long low-interference codes exist (076). Packing guarantees hit a hard ceiling (118).
Information technology takes 17 of the 40 pathway results
One GICS sector per pathway result, so the bars sum to 40.
- Families
How to readEach bar counts results whose first buyer sits in that sector.
NoteEvery pathway is indirect or ten or more years out.
SourceOur labels, data/cards.json
The results come in three kinds. Counting and sampling asks how many tables fit given row and column totals. Limits prove that a better code, guarantee or calculation cannot exist. Inverse problems ask whether surface measurements fix only one interior.
Uniqueness differs from computing that interior stably from noisy, limited data. That second question decides whether a device works.
Does the one real algorithm speed up statistical work?
Nothing to ship. Cite family 115 only if you need a provable guarantee, and keep your current tools.
Family 115 is the only result here a business could, in principle, run.
It is the first such method with no limit on rows or margin sizes. Its authors call the exponents "deliberately large". They call the bound "a uniform complexity guarantee rather than a practical running-time estimate".
The common use already runs fast. Simulated p-values for exact tests rely on Patefield's 1981 algorithm. R's chisq.test, fisher.test and the ecology package vegan all call it.
Uniform sampling matters in narrower uses. One is estimating how many tables fit published totals, a disclosure question. Another is some species co-occurrence null models.
Those uses already run on sequential importance sampling and swap chains. The new result adds a guarantee, not a faster tool. Our deep read moved its time to market from 3-10 years to 10y+.
Do the packing and radar limits change what vendors can promise?
Packing vendors should drop any "within one bin" guarantee. Radar teams should treat 6.34 as a benchmark, not a ceiling.
Two results redraw what vendors may claim. Neither changes the tools.
Cutting-stock planners solve a configuration LP by column generation, then round to whole patterns. LINDO and GAMS ship this as stock examples. Folklore held the optimum never exceeds the rounded-up LP value plus one bin.
Family 118 shows the gap can grow to any size. It also proves that promising "optimum plus a constant" is NP-hard. Known real gaps stay tiny, with the worst at 1.0625 bins.
Planners see no change. Vendors should drop "within one bin of the bound" from sales material.
Radar and sonar pulse compression wants long +1/-1 codes with small echo sidelobes. Engineers score these codes by merit factor. The best known long-code families reach just over 6.34.
Family 076 shows codes exist with merit factors as large as you like. It gives no explicit code and no length threshold. Code-search teams get a target, not a code.
Barker codes of length 11 and 13 already serve pulse-compression radar. IEEE 802.11b uses the length-11 code at 1 and 2 Mbit/s. Computation had already excluded all but 4,489 lengths up to 4 x 10^30. So nobody was waiting for a longer code.
| Family | Mechanism before deep read | After |
|---|---|---|
| 118 Bin packing | Break | Proven limit |
| 179 Barker codes | Proven limit | Confirmation |
Should imaging and chemistry teams act on these theorems?
EIT, elastography and DFT users need no action. Quantum-chemistry buyers can use family 275 in diligence.
No. These theorems describe measurements that no shipping device collects.
Clinical EIT devices image lung ventilation with 16 or 32 electrodes. Dräger's PulmoVista 500 and Timpel's Enlight are two examples. The theorems assume a full, noise-free boundary map. Devices already rule out the counterexample's rough interiors through regularisation.
Shear-wave and MR elastography measure displacement inside tissue. Family 372 concerns static forces at the surface, a different problem. No product rests on it.
The Kohn-Sham counterexample in 278 places nuclei 2 x 10^200 / Z apart. It describes no real molecule. DFT codes use approximate functionals anyway.
Family 275 proves that exact molecular ground energy is QMA-hard. It confirms that exact worst-case energies stay out of reach, even for quantum computers. Any claim of general exact quantum speedups for molecules conflicts with this limit. A 2023 review by Lee and colleagues says such evidence "has yet to be found".
Who should act, and how far can we trust the results?
Act only if you sell packing guarantees, design codes or buy quantum-chemistry claims.
Only a few groups need to act on these eight.
- Waveform and code-design R&D: keep 6.34 as the practical benchmark. Watch for an explicit construction.
- Packing software vendors: remove "LP bound + 1" guarantees from documentation. The solvers stay the same.
- Statistical software teams: nothing to ship. Patefield and sequential importance sampling remain the tools.
- Quantum-chemistry buyers: use 275 to test any claim of general exact speedups.
- EIT, elastography and DFT users: no action.
Constant factors decide everything here. The one algorithm is explicitly impractical. The limits bind only on instances nobody meets.
These theorems sit near operations; the same AI search can work on operations directly. Scheduling, routing and forecasting heuristics with a simulator are the first targets. Vendor-reported gains run 5-30%, such as FM Logistic routing 10.4% better.