Sense, remember, act: what the engine keeps

1 · Three questions

Our first paper asked three questions of any system that learns: what does it keep, what does it want, and what does it put back into the world. This note answers the first for our own engine, in the order a question travels through it: what it senses, what it remembers, what it learns, and what it does with all three.

Everything here can be checked from outside the engine. How the engine does it is not described, and will not be.

What this note contributes, losses first, each with its basis and the sections that carry it:

1. Measured in the model, one run each. Five registered re-tests of this note's own sentences were falsified: wrong names on cues never stored, the ledger's sum, the chain against its keeper, the noise study's ratio and the second rule's collapse (sections 3, 4 and 8).
2. Measured in the model, one run. A fixed reading order is 10.9 % slower than a random one, so the registered test that they cost the same is falsified (section 8).
3. Prediction. Five predictions of the reading in section 7 are registered, not run, and one registered test is undecidable as registered (sections 6 to 8).
4. Measured, one run. Twenty planted fields read back exactly, recall measured against load in every cell of a table, and the cross weight learned from turns (sections 2 to 4).
5. Theorem in the model. One number per region gives both its pole and its entropy, and a settled answer carries no current (section 7).
6. Reading. Two textbook pictures, a pendulum and a magnet, offered as analogies and only analogies (section 6).

2 · What it senses

Your rules become the pulls between the parts. You hand the engine your problem as it already is: the choices, the rules and the preferences. Each rule becomes a pull between two parts of the problem or a lean on one of them, so two things that belong together pull toward each other and two that clash push apart. That is all it reads. There is no hidden prompt, and nothing is looked up anywhere else.

It reads a field of numbers the way a row of compass needles reads a magnet. To check the reading on its own, we laid twenty known patterns into a grid of numbers, strong in some regions and weak in others, and asked the engine which regions were strong. It read all twenty back exactly, with the grid cut into sixteen regions and again with sixty-four. Across our two runs a read took between 11 and 15 milliseconds with sixteen regions and between 160 and 190 with sixty-four, on the processor alone.

A question read against our own pages is quick. Over twenty set questions against these pages, half the reads finished within 26.7 milliseconds and 95 in 100 within 29.0, on a box with a graphics card. With the card switched off, the middle read took 704 milliseconds.

Every settled answer says how sure it is. It comes back with a margin, how far the winner sat ahead of the runner-up, and with one of three named certificates: exact, where every arrangement was scored; certified, where a computed bound says how far off it could be; or not measured, said plainly rather than filled in. Up to twenty moving parts it scores every arrangement, all 1,048,576 of them.

3 · What it remembers

The account is a hash-chained ledger, tamper-evident to everyone except its keeper. Every act is appended to the engine's account and none is edited. Each entry carries the fingerprint of the one before it (Haber and Stornetta 1991), so an entry changed in place breaks the chain at exactly the place it was changed. A registered re-test found the limit of that: a rewrite of an entry and of every fingerprint after it, done with the chain's own rule, read "chain intact" in 4 of 4 tries, so the test as registered is falsified, and an outside anchor is what the chain still needs.

Each settling step books one balanced entry, and the entries add up to the booked steps only. When the engine settles a problem step by step, each step that removes uncertainty is booked as one entry: what was taken from uncertainty and what was added to value, equal and opposite. Uncertainty and value here are the ledger's own bookkeeping quantities, not entropy and work in the physical sense. A registered re-test of the sentence that the entries match the run's own descent was falsified: on one of the two measures the booked entries hold between 0.5 and 35 % of a run's descent, because the top solve and the steps that lift a solution between scales book nothing, while on the other measure they match to within 2 × 10⁻¹⁶; no posting was positive, and every balance and chain flag read true. For the booked steps alone, the entries match to within 4.31 × 10⁻¹¹ on one measure and exactly on the other, with the books balanced and the chain intact, measured on 15 September 2026 and quoted as recorded.

What it stores is written the same way. We measured the engine's memory directly. It stores a pattern it has read by writing it into the pulls between its parts (Hebb 1949), and each store books one balanced entry. Five, ten and twenty stores booked five, ten and twenty entries, balanced, with the chain intact, and a memory reopened from the same account came back with the same pulls.

Its memory has a size, and we measured where it ends. We showed the engine each stored pattern again with some of its parts changed and asked which pattern it was.

The fewer patterns it holds for each region, the better it recalls them: five patterns in sixty-four regions came back almost every time, and twenty in sixteen never did.

Same observation, three vocabularies. Three fields (information theory, systems and graph theory) describe the same situation in different words, and an insight in one usually has a twin in the other two. This series names a twin only where its own model has the object, and says so where a twin is missing or runs the other way. Each twin is our reading, not an identity, unless a result the paper states makes the two one number. The memory's size is one such observation. In information theory it is a capacity: how many patterns the memory can hold and still return from a changed cue. Read as a graph, every pattern is written into the same pulls between the same regions, so each one added moves where the others come to rest. Read as a system, as patterns crowd the pulls, more cues settle where no stored pattern is, and the engine marks those recalls contested, though on cues it never stored it sometimes names a stored pattern instead, as the next paragraph says.

When it cannot tell, it usually says so, and on cues it never stored it sometimes does not. A registered re-test showed the engine cues drawn from patterns it never stored: 19 of 540 were named as a stored reading with a margin above the engine's own threshold, a wrong-name rate of 3.5 %, against the 1.3 % this note first gave for stored patterns; the test is falsified. Of the 540 recalls in our full table, 165 named the right pattern and 7 named a wrong one. Every other recall, 368 of them, came back marked contested: the engine settled on something that was none of its stored patterns and said so, rather than handing back the nearest one as if it had remembered it. On the same 540 cues, two readouts without a certificate were measured beside it on 30 September 2026, one run, quoted as recorded and not re-derived: the classical sign-update readout, run to a fixed point, named the right pattern 165 times, the certified settle's own count, and a dense readout that weighs every stored pattern by its overlap with the cue named it 491 times. Their wrong answers were not counted in that table.

4 · What it learns

The losses of this section come first: the noise study below was one draw, and a registered re-test with independent seeds falsified its linear ratio; and a registered re-test of the second rule found its collapse belongs to the engine's chosen score.

The cross weight, from what actually happened. When a decision is solved together with a continuous quantity it depends on, such as which stops a parcel drone serves and the wind it flies through, one number says how strongly each pulls on the other: the cross weight. The engine learns it from what a run actually cost, as a value fitted to observed costs (Boyd and Vandenberghe 2004). We planted a known value, 2.5, generated from it what twenty turns of the engine's own readings would have cost, started the engine at 0.5 and let it learn from those costs. It recovered the value exactly in one step. Told to take half a step each time, it closed exactly half of the remaining distance on every turn.

Where noise stops it, in one draw. We then added noise to what it observed. In one draw of the noise, the error grew in step with it: 0.005 at a noise of 0.5, 0.04 at 4 and 0.64 at 64. At 256, about sixteen times the signal it was learning from, the estimate ran to the edge of its allowed range and stayed there. With 20 independent seeds, a registered re-test found that linear ratio in 0 of the 20, so the sentence is falsified; the same-seed control reproduces the published number exactly. A second rule, which fits the model to its own internal score instead of to what was observed, cannot learn the value at all: it ran to zero. A registered re-test with a free-energy learner that keeps the observation's likelihood recovered the value to within 1.3 × 10⁻¹⁵, so the collapse belongs to the engine's chosen score and not to free-energy learning: the general reading is falsified, and the narrow one stands.

Solving the two together beat solving the decision alone on one example, and nothing certifies the joint best. On our parcel-drone example, one run, solving the stops and the wind together scored −5.89 against +4.05 for the stops chosen with the wind ignored, and three of the fourteen stops changed. The likely cause is the wind's pull on the stops, not isolated; how the gain changes with the wind's strength was not measured. The choice of stops is certified exact for the wind it was given. Nothing certifies the best answer for the stops, the wind and the cross weight taken together, and we do not claim it.

5 · What it does

It computes, and it shows its working. There is no language model in the answer path, a statement not yet audited: the engine computes an answer and returns it with its certificate, or it refuses.

Two models, one number between them. Two models owned by different parties can be settled together so that a single summary number crosses between them and neither can see the other's inner state. We checked that 62,000 times across 125 models composed at once, in one run of 15 September 2026, and it held all 62,000 times.

6 · Two pictures to hold it by

An analogy, and only an analogy. Two pictures from textbook physics are a useful way to picture what the engine does. We offer them as a way to hold the model in mind. They are not a mechanism, and we make no physical claim with them.

The magnetic pendulum. A weight on a string swings over three magnets and comes to rest over one of them. Where it ends up depends on where it started. Near the middle the answer is plain, and between the regions the boundary is folded so finely that a start close to it has to be measured very precisely to say which magnet wins, though a precise enough measurement does say (Motter and others 2013; Ott 2002). Read it as the engine: the three magnets are the choices, where the weight comes to rest is the answer it reads off, and the finely folded boundary is where it says contested and names a tie instead of an answer. A registered test of that boundary's uncertainty exponent ran to completion in one run and is undecidable as registered: no start changed magnet at the two finest scales, so the slope it registered does not exist, and a decidable run needs far more starts under a new registration; it is not run.

The field of a magnet. Around a bar magnet the field leaves one end, loops out through the space around it and comes back in at the other: a core, and lines that go out and return. Read it as the two levers of our first paper. The core is how settled a unit is, its coherence. The lines are its leverage: how far what it does reaches before it comes back.

7 · Where the two halves come from

Our engine keeps a driving half and a sensing half apart and joins them by one transformation. This section says where the two halves come from, and labels each step: what is derived, what is our reading, and what is not built yet.

One number per region gives both halves. Each region the engine reads settles to one number, m, between −1 and 1. Its sign and size are the region's pole: the answer it leans to, and how firmly. That is the sensing half. The same number fixes how undecided the region still is: its entropy, S = H₂((1 + m)/2), where H₂ is the entropy of a coin with that bias. The value a region settles to is the one that leaves a free energy, F = E − T·S, unchanged by any small move, where E is the cost of the arrangement, T is a temperature and S is the regions' entropies added up. The settle trades cost against certainty.

Read as a charge and a current. In textbook electromagnetism a field has two sources: a charge, which makes the part of the field that holds still, and a current, which makes the part that circles. We read the engine's two halves the same way. How decided a region is plays the charge: through S in F, it sets the steady pull of the driving half. The turning of a pair's phase, which our halo paper advances at the pair's energy gap, plays the current: it is what makes a halo circle. This is our reading, a matching of roles and only that. The engine holds no field of force, and the words name what each half does.

A settled answer carries no current. A settled answer, held still, is read from a model whose energy matrix has no positive entry off its diagonal; the textbook name for such a model is stoquastic. The lowest state of such a model can be written with real, non-negative weights, which is the Perron–Frobenius theorem, and an arrangement of fixed answers is real and non-negative too, so neither carries a phase. Real weights alone are enough to make the equatorial correlation that would carry a turning, T_xy, exactly 0. The lock, which says how well the halos ring in step, needs the weights non-negative as well: then every open halo points the same way and the lock is exactly 1, while a real model with a sign problem keeps T_xy at 0 and can lose the lock. A static charge makes no circling field, and a settled answer shows no turning halo. Only a reading taken on a clock, turning each pair at its own gap, can show a current.

In the textbook form of a state. Read onto the picture our halo paper uses, a choice is a quantum state ψ, and the two sources have textbook names. The charge is the probability density, ψ̄ψ: on a pair, the populations, the weight on each answer, which give m. The current is the probability current, Im(ψ̄∇ψ): on a pair, the coherences, which are the equatorial correlations of the halo paper's section 3. The two obey a continuity equation, so the density changes only where the current flows. A state whose amplitudes are real and non-negative has no current, which is the result above in these words, and a state turned by a clock is complex and carries one. The halo paper's third reading, the event that induced the pair, is in this form the larger whole the pair belongs to, and the pair is what remains when the rest of that whole is traced out. The fourteen coordinates our first paper gives each unit are features of the unit, not this space of states.

The state can be read back without settling again. A state the engine has met before need not be solved again to be read. Each state is reduced to a short address that nearby states share, and every step the engine takes warms a level kept at that address, so a warm address answers at once. Two things are not built: a public read that returns that level with a certificate of how far to trust it, and a refusal by name when an address is cold. Today a cold address is answered with a prior or a silent abstention, and the address keeps the size of a turn but not its direction, so a halo and its mirror image share one address.

Where the field comes from, in a reading the series records and has not tested. The series' reading adds one step above the pair. The body that induces a pair is itself a sphere, with its own pole, halo and clock, and the field the pair reads is what that body generates: its depth would set the steady pull, which a settle reads, and its turning would set the clock, which only a clocked reading sees. This is a reading, a model identification that no measurement has tested. The engine's version of that body today is a decided pole with no halo and no clock, and the wire from such a body into the field the engine reads does not exist. If the reading holds, three things will be seen once the wire is built. The regions a planted body switches on form one connected set around it, and the set grows with its depth. At one depth, a body with a wider halo leaves its pairs less decided. The quick read above agrees with a full settle within its stated tolerance, and refuses a cold address. Each of the three was written down before the run that will test it.

A region's entropy, in the three vocabularies of section 3. In information theory, a region whose entropy, the S of this section, is near its largest is an uncertain reading: its answer is close to a coin toss. Read as a system, it is the unsettled part. Read as a graph, it is a node whose own lean and the pulls of the regions it touches add up to little beside the temperature T, since the value it settles to answers all of them; so how unsettled a region stays is set in part by its neighbours.

8 · What we measured, and what we did not

Every figure below was measured on our own box with the processor alone, one run each, on the day this note is dated, unless its row says otherwise; the registered re-tests ran on 7 October 2026. Worst first: the falsified re-tests, then the losses of the first run.

What we did not measure: this memory on anyone's data but our own; the same table on a graphics card, which is still to be read; and anything at all about a physical field. The two checks section 7's reading predicts are registered, not run, on the engine's own records: that each region's entropy, computed on its own, equals the coin entropy of its pole, and that a decision forming moves the lock of its halo with the sign the model fixes. Simulations of these checks on our own fixtures, with the continuity check that holds section 7's textbook form to the engine's arithmetic and the field a quick read would add to a settle, test the arithmetic and not nature. Their results are kept in their own record and are not rows of this table. What held on its own re-test: the textbook capacity law, its knee at 0.175 patterns per region at 1,024 regions, inside the registered band; and the read time's growth, an exponent of 1.72, over two sizes only.

9 · How this was made: the method and the chain of records

Day ran the memory's recall measurements and drew both figures from the records they left. Claude (Anthropic), the consultant named in the byline, mapped each part of that concept onto what the engine already had, built the two pieces that were missing, the memory's store and recall and the learning of the cross weight from turns, and measured them, including the rows in section 8 where they lose.

The question was set on 30 September 2026 as a written brief: describe what the engine senses, keeps and learns, measure each, and describe no method. The chain of records, in order:

• the first run's tables of reading, memory and learning, measured on 30 September 2026 and written into the notes, where they are quoted as recorded and not re-derived;
• the predictions of section 7's reading, each frozen in a registration committed alone before any data, and not yet run;
• the re-tests of this note's own sentences, frozen in a registry committed alone at 65ff0d0b1 before their runs on 7 October 2026, with their verdicts;
• the tests that hold this page equal to its source and its numbers to their records, and this page, generated from its source.

10 · Limits, and what this note does not say

The open limits come first, each with what would close it.

• The chain is tamper-evident to everyone except its keeper (section 3). It would close with an outside anchor for the chain, re-tested with the same rewrites.
• The noise study is one draw (section 4). It would close with the study re-run over independent seeds and reported as a spread with its n.
• The margin is not calibrated against correctness: a margin above the threshold named a wrong pattern on cues never stored (section 3). It would close with the margin scored against right and wrong recalls on held-out cues.
• A dense readout without a certificate recalls far more of the same cues than the certified settle does. It would close with a certified dense readout, or the certificate's cost stated beside the dense readout's recall on the same cues.
• The hybrid's gain depends on the wind's strength, and its cause was not isolated (section 4). It would close with the gain measured across wind strengths, with a weaker-wind null beside it.
• The crossing number carries no stated precision. It would close with a stated precision, checked at two step sizes.
• The statement that no language model is used has not been audited (section 5). It would close with an audit of every model the recall path loads, recorded.
• The memory figures are for our fixture on our box, with the processor alone; the figures on a graphics card are still to be read. They would close with the same fixtures read on a graphics card and on a second machine, with the load recorded.
• The loop this note describes is closed in design and open at three wires. Nothing in the engine yet writes a belief back from what was observed; the phase clock is the model's own and has not been read on a running record; nothing yet chooses the next reading by what it is expected to teach. Each closes with its named writer, clock or chooser built and measured on the same fixtures.
• The wire from a generating body into the field the engine reads, section 7's last step, does not exist. It would close with the wire built and measured on planted bodies, with its predictions registered before the run.

The standing statements, which no measurement closes:

This is not a physics claim. The pendulum and the magnet are analogies for the reader: the engine contains no pendulum, no magnet and no physical field of force, and nothing here measures one. The engine's method is not described here and will not be. Every number is as of the date its source gives.

11 · Companion papers

Seven papers published beside this one take the same approach: each traces its figures to a recorded measurement and says what it did not measure.

• The Operational Unit: the model behind the engine, and how it was built.
• The periodic table as a ground-state ladder: each element read as the lowest-energy filling of its electrons, with every answer NIST lists checked against it.
• Closing the gaps: four sustainability problems an engine can schedule, and what it cannot do about them.
• The halo of a decision: a two-way choice, the partner it is tied to and the event that tied them, in textbook terms, with what an experiment could measure.
• The Earth as a two-state recorder: the Earth's dipole read as a two-way choice from public records, with a prediction written before the data, and the planet's clocks.
• HOPE: recall in a library of Hilbert spaces: recall as settling to the nearest stored state, in a library of small spaces kept one per model, with the measured answer that they do not make one large space.
• The unit of work: a receipt for one settled problem, booked on a hash-chained ledger, and what it is not, with the economy's measured losses first.

Acknowledgements

This paper reads no outside dataset. The published works it uses are in the references.

Replicate this paper, or tell us what is wrong

We invite replication and correction. The measured results come from records committed in our repository. The records are not yet published; until they are, write to us through the contact page, naming the paper and the number you want to rebuild or the error you found. We correct an error we can reproduce on the paper's web page, with its date.

The tests this paper registered before reading their data are frozen, each with the rule that would fail it, in docs/PAPERS_DUALFIELD_1_2026_10_04.md and docs/PAPER_EXPERIMENTS_REGISTRY_2026_10_07.md.

How to cite this paper

Please cite this paper as:

Agile Integrations LLC. 2026. "Sense, remember, act: what the engine keeps." Version 1, 30 September 2026. https://agileintegrations.net/blog/sense-remember-act.html

Citation file: CITATION.cff.

12 · References

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• Boyd, S. and Vandenberghe, L. 2004. Convex Optimization. Cambridge University Press. Fitting a value to observed costs. 10.1017/CBO9780511804441
• Bravyi, S., DiVincenzo, D. P., Oliveira, R. and Terhal, B. M. 2008. Quantum Information and Computation 8, 361–385. Models whose lowest state has real, non-negative weights, by the Perron–Frobenius theorem. 10.26421/QIC8.5-1
• Griffiths, D. J. and Schroeter, D. F. 2018. Introduction to Quantum Mechanics, third edition. Cambridge University Press. The probability current and its continuity equation.
• Haber, S. and Stornetta, W. S. 1991. "How to time-stamp a digital document." Journal of Cryptology 3, 99–111. A record in which each entry carries the fingerprint of the one before it. 10.1007/BF00196791
• Hebb, D. O. 1949. The Organization of Behavior. Wiley. Psychology Press reissue, 2005. Storing a pattern by strengthening the pull between parts that are active together. 10.4324/9781410612403
• Motter, A. E., Gruiz, M., Károlyi, G. and Tél, T. 2013. "Doubly Transient Chaos: Generic Form of Chaos in Autonomous Dissipative Systems." Physical Review Letters 111, 194101. The magnetic pendulum and its finely folded boundaries. 10.1103/PhysRevLett.111.194101
• Nielsen, M. A. and Chuang, I. L. 2010. Quantum Computation and Quantum Information, 10th anniversary edition. Cambridge University Press. Populations, coherences, the partial trace and the time evolution of a state. 10.1017/CBO9780511976667
• Ott, E. 2002. Chaos in Dynamical Systems, second edition. Cambridge University Press. For boundaries of this kind in general. 10.1017/CBO9780511803260
• Purcell, E. M. and Morin, D. J. 2013. Electricity and Magnetism, third edition. Cambridge University Press. For the field of a magnet, and for charge and current as the two sources of a field. 10.1017/CBO9781139012973