The physical structure of economics.

Accounts are entries on paper with an owner's name on them. For this picture only, let Alice's book record a claim of two loaves against Bob. Whether that entry is true is a separate question, taken up under different debts. Alice has two ready loaves; Bob has one.

If Alice splits her account into two accounts of one each, does a loaf appear? Does a person?

After the split, both entries belong to Alice and total two. Her goods, her obligations and her standing as a person are unchanged. An extra account supplies neither another loaf nor another person whose requirements must be met.

Go back to the start and take a different path. First Alice bakes, so the loaves that could be eaten rise from one to three. Then one of two things happens: Alice hands Bob a loaf, or Alice takes Bob's loaf without asking him.

Taking moves one ready loaf from Bob to Alice, just as Bob handing it to her would. Here Alice acts without Bob's authorization. The transfer is physically possible, but it fails the requirement that the holder authorize it.

Follow Bob's loaf through the two transfers.

On both tracks the bake leaves three loaves, and the next move only redistributes them. Under the gift, Alice ends with one and Bob with two. Under the taking, Alice ends with three and Bob with none, losing his only loaf without agreeing to it. The total is three either way, yet on the taking track Bob has less than he began with. Who gained, who lost and who agreed are separate facts.

Run the gift history a second time with one change at the very beginning. In the first history Alice offered the loaf as a gift. In the second she offered to deliver a loaf now in return for one loaf back later. Bob accepted in both. Every later movement of flour and bread is the same. The earlier offers and acceptances are different physical events, establishing different obligations. Suppose both people leave their books unchanged, recording zero throughout both histories.

At the end, what does Bob actually owe in each history?

Delivery makes one loaf owed under the second agreement. The shelves and the unchanged books cannot distinguish the two cases. Both parties can agree on a recorded number and both be mistaken. The accepted terms and the delivery establish the obligation. A description must retain those actual events; a mistaken entry does not change what happened or what remains due.

The complete gift history meets the example’s material constraints, authorization requirement and truthfulness requirement. Each move has its inputs, the holder authorizes each transfer, and both records of what is owed are truthful.

Alice can eat a loaf that she has undertaken to deliver. Eating it can destroy her remaining means of fulfilling that undertaking. Both the consumption and its effect on the obligation belong to the physical account. The moral law governs what that action does to her relation with Bob.

Now take a separate example. Alice has offered to deliver a loaf to Bob, Bob has accepted, and the loaf has not yet been handed over. Alice holds one ready loaf and nothing else that could serve: no second ready loaf, nothing in storage, and no flour or work to bake with. Bob has nothing. We will check one requirement only: keep a way to fulfill the accepted delivery. It is one requirement among others, and passing it does not settle every question about what Alice may do.

Alice eats the loaf. Can she still keep the promise?

Can Alice eat it? Yes. Does eating it preserve a way to deliver? No. Eating the only loaf fails this promise requirement.

If Alice also had a loaf in storage, eating this one would leave a way to deliver. She could retrieve the stored loaf and hand it to Bob.

An objective requirement holds whether or not anyone believes in it or feels bound by it. This example takes the duty to preserve a way to fulfill an accepted delivery as a premise whose full derivation belongs to the wider program. The calculation then asks whether a route to a delivered loaf remains: ready bread, stored bread, or enough flour and work to bake. Eating the last loaf closes every route; a spare in storage keeps one open. The arithmetic establishes whether the action meets that requirement; it does not derive the duty itself. The duty is owed to Bob.

Possibility also differs from control. A delivery can remain possible with Alice's cooperation without being something Bob can force her to do. Economics must describe the available means, the people controlling them and what each person can know. Those facts determine the actual moral situation to which the physical ethical laws apply.

A distinction belongs in the description when removing it changes the answer to a relevant test. Start each trial from the same kitchen situation. To count ready loaves, ask Alice to eat one after another. If she succeeds twice and the third attempt is refused, she started with two ready loaves. Start over and try retrieving instead: the number of successful retrievals counts her stored loaves. These trials ask different questions. A stored loaf cannot be eaten until it is retrieved. A description that kept only a single loaf count would treat two ready loaves and one ready plus one stored as the same kitchen. Yet the eating trial succeeds twice in the first and only once in the second.

Flour and work need a different test, because baking requires both. These tests may supply inputs from outside; the five kitchen moves do not create them. Start over, bring in enough work from outside, and count how many times Alice can bake before her flour runs out. Each bake uses one portion, so the count tells us how much flour she started with. To count her original work, start over and supply flour instead. Record everything brought in: the final stock must account for those supplies as well as what was there at the start. Without extra work, a kitchen holding only flour and an empty kitchen would both fail to bake. That test would miss the flour.

To test an agreement, continue it and see what becomes due. Start with the same shelves before delivery: Bob has accepted a gift in one case and one loaf now for one back later in the other. Let Alice deliver a loaf. Nothing becomes due under the gift; one loaf becomes due under the exchange. The move and final shelves match, but the answers differ. Other stages, such as an offer awaiting acceptance, require other continuations.

A book can be tested by asking how much must be added or subtracted to make its claim true. If one loaf is due, a record of zero needs one added; a record of two needs one subtracted. The corrections distinguish the records even when the shelves match. The same method that separates ready from stored loaves can therefore separate different records and obligations.

For the example's full set of tests, the smallest sufficient description keeps each person's remaining flour, available work, ready and stored loaves, together with the books and the stage of the agreement: whether an offer has been made, accepted or delivered, and the relevant terms or repayment due. For any two situations the example can reach, the answers agree exactly when this description agrees. The eaten loaves and spent work are useful for checking conservation, but these questions about what can happen next do not need their counts. A question about the past may need a longer record.

A more general test asks whether a description preserves the ways people can act together. It must retain every possible next step, and every step it reports must be possible from this actual situation, not merely from another situation with the same description. It must also retain who acts, what each person knows and requires, and whether an act meets those requirements. For guarantees, it must also keep who gets to choose each next action, which choices are allowed, and what counts as success. With those rules fixed, the paper proves that the description preserves whole finite sequences of acts and outcomes people can reach together. It also preserves what a person can guarantee within a specified number of moves using the information available to them.

That is why economics needs more than separate lists of what Alice and Bob could do. If one loaf is left and each person plans to eat it, those two plans cannot both succeed. A plan that depends on knowing whether to bake or retrieve a loaf may fail when that information is hidden. The description must keep those dependencies too.

Alice and Bob share one world and retain their own standing within it. Even if their stocks and balances happen to match, each remains a person whose loss or obligation must be considered. This description is compatible with a common underlying reality and distinct persons. Identifying its people with subjects who experience their lives is a further task; counting labels cannot establish that connection.

The two-kitchen example comes from Economics from Shared Reality and Distinct Persons (18 pages). Its conservation laws, account split, different histories and sufficient descriptions have checked mathematical proofs.

Making Provision Possible connects personal reserves, work, deadlines, accepted undertakings, information and control with continuing-supply conditions, retained response history and physical comparison accounting. Its care calculation separates burdens removed, capacity spent and each person’s ability to continue. The result follows from the example’s stated physical interpretation and response law; it does not establish a complete duty to provide care. Explore the worked calculations. Recovery after Interrupted Provision gives the carried-state recovery calculation and its service interpretation.

The program’s foundation is that moral relations have objective physical states and fixed laws. The proofs establish the stated consequences within the represented relations and processes. The delivery replay establishes feasibility under its supplied data and rules. Applying these results requires identifying actual people, needs, resources, authority and effects, then measuring the outcomes. The examples here do not report a human intervention.

The physical moral account explains why an economic account must retain physical relations, who acts, what happens and each subject’s ability to continue. The examples connect that foundation to production, agreements and assistance. A care example follows food through assisted intake and the recipient’s physical response. It shows why removing a burden, paying for the response and retaining the ability to continue are distinct facts.

Explore the worked calculations → Vary the response timing, energy budget and supply tanks. Each example states what the physical account establishes and what remains to be identified when applying it to people.

A need can exist before a promise. Maintenance continues while someone waits. A repair can benefit everyone and still require the worker’s own authorization and enough reserve to perform it. Scarcity leaves every affected person in the account.

The worked cases on physical need, agency and duty follow these distinctions through the actual models. They include a repair selected without a service promise and exact cases where the current decision rule has no eligible plan.

The cost engine keeps allocated charges, full incident changes and authored consent separate. Read the certificate schema, inspect a generated report and the conformance checks.

Assistance and agency

An assisted-care example follows a helper preparing food, storing it, moving it to a patient and assisting the patient to eat. The patient performs no work or scheduled action during the example. Both people remain in the account: their reserves, the patient's earlier permission and the helper's authorized work.

The calculation follows care through the next maintenance response. With the example’s baseline reserve, the helper finishes that response exhausted, even though both people’s represented burdens have been removed. One additional reserve unit leaves both with capacity to continue. Their internal responses remain distinct, and the recipient contributes no labor.

Under the stated technology and response law, care preserves both people’s capacity exactly when the helper has that additional reserve and intake is authorized. Deciding when care is required, permissible or unjustified also needs the moral assessment of the entire history, including withholding it.

A useful economic description must retain the physical differences that change what someone needs or what remains owed. The care model makes that requirement concrete.

Zero net flow can conceal a repair cost

In the care model, an internal bond returns to the same being. Its incoming and outgoing contributions cancel in the net-flow reading. Its recognition cost remains. Two states can therefore have the same zero net flow and different costs of repair.

Net flow here reads the directed bonds in the physical ledger. The example doubles the internal multiplier before each maintenance response. The charge is J(2m), the recognition cost of that doubled bond, in the model’s units. Net flow alone cannot recover it.

Recovery does not erase a missed requirement

A helper delivers food to a recipient with low capacity whose maintenance requirement has been accepted. Compare delivering it in the first step with waiting and delivering it in the second. Both schedules use the same food and work, pay the same repair costs and finish in exactly the same modeled state. Only the earlier delivery meets the recipient’s accepted requirement at both checkpoints.

The complete final modeled state is identical, including stocks, work and allocation. Each person also pays a total repair charge of ½ under either schedule. No test of the final state alone can distinguish which schedule met the requirement.

The research planner retains these checkpoints. When the decisive observation is missing, it reports the requirement as unverified. Its checks concern the modeled care history; it is not ready to direct care in practice.

One physical ledger preserves each person’s response

The two schedules involve a helper’s work and a recipient’s internal repair. Food is drawn from stock; work reduces the capacity available to the helper. The recipient uses provision to fund an internal response. The model carries both participants’ bonds and capacities together, while retaining the material account of stock and work.

1. 01Stock and work

   Account for the provision received and the work each person performs.

2. 02Exposure

   The example doubles each internal bond’s multiplier and adds net provision to capacity.

3. 03Repair

   Each owner repairs their bond when their capacity covers its recognition cost.

4. 04Carry forward

   Keep the resulting bond state and remaining capacity for the next interval.

Executing these repairs on the shared ledger gives exactly the same bond state and capacity as the economic calculation for every participant through any finite history of these operations. Each incurred repair charge is counted once. Repairing one owner’s internal bond leaves the other owners’ capacities unchanged at that repair step. The correspondence holds at every checkpoint, including the missed checkpoint in “wait, then deliver.”

The controller belongs in the physical account

The signal operation described above records part of a pulse and adjusts its phases to produce the care transformation. Those stages need something to carry their order. We construct a clock coupled to both signal paths: the main pulse and the emitted record. This concerns the physical signal operation; realizing a food delivery also requires its material and participant connections.

The clock has four distinct positions. The first carries the starting signal; two intermediate positions carry the recorded signal; the last carries the completed phase correction. One fixed Hamiltonian—the generator of the joint system’s motion—drives the operation. No outside switch changes its stages during this evolution.

1. StartPrepared clock and signal

   Both signal paths and the clock enter the account.

2. Transfer timeCare operation complete

   The final clock position carries the corrected signal and its emitted record.

3. Twice that timeStarting state returns

   The joint clock and signal return to their starting state. The corrected signal is not held at the output.

The constructed generator is nonnegative. Its expected energy stays constant throughout the trajectory, and an energy ceiling sets a minimum transfer time. This energy belongs to the controller calculation; it has not been identified with a person’s paid maintenance.

A separate Lean proof establishes the exact transfer and the later return for this construction. Making the result available permanently still needs a physical mechanism. Preparing and resetting the clock, realizing the joint coupling, and including the source’s free evolution remain further requirements. The construction establishes a timed autonomous operation; a complete care apparatus must meet those further requirements.

A shared cost can fall on people with different capacities to bear it. To see what a provision decision requires, consider two chemical systems supplied from separate tanks. Each needs two units over the next interval. A separate controller can transfer material and keep either supply running or interrupt it.

Keeping a system running preserves its reference condition. Interrupting its supply changes that condition. This example uses the recognition-cost law to measure departure from the reference and assigns each system’s burden to a separate affected party. It tests a requirement against increasing either burden. Applying that calculation to people requires identifying their actual maintained conditions and the moral relations involved.

With enough supply, the ethical requirement and the material balances jointly require a transfer while retaining enough at the source. Several quantities can satisfy both. When total supply is insufficient, an interruption remains materially possible and its burden remains real. None of these plans meets the requirement against increasing either burden. Deriving the governing rule for unavoidable loss from the physical moral foundation remains unfinished.

The two tanks above hold six units. Keeping both systems running for one interval needs four. Yet a slow delivery can leave the recipient without supply while material remains at the source.

There are four requirements: enough must remain at the source, enough must exist in total, delivery must start no later than the moment the recipient runs out, and the device must move enough before the interval ends. All four can be checked together.

In the late-delivery case, both final balances are nonnegative. The recipient nevertheless lacked half a unit before the delivery began. A record that shows only the ending balances loses that failure.

These schedules extend the chemical example above. A successful schedule preserves both systems’ reference conditions, so neither represented burden rises. Permission remains separate. This interactive example checks material and timing; it does not include the device’s energy use or establish human needs.

Enough material, too little energy

The note also models the pump’s energy use. Delivering one unit over half an interval uses twice the energy of spreading that delivery across the whole interval in its worked example. Enough stock and a fast enough device can still leave a plan impossible if its energy reserve is too small.

The planner checks available power and stored energy alongside the material requirements. It records who holds the energy reserve and requires permission for the complete powered action. What that person gives up, other claims on the reserve, and the apparatus’s effects still need to be included in the full ethical assessment. The pump example establishes a physical constraint; it is not a measured human application.

Can Alice help Ben without exhausting herself?

Alice has one meal to deliver. Two meal promises were accepted earlier, and one has already been fulfilled. She must check the old record to know which promise this delivery will fulfill. After delivery, she can repair an entrance they both use. Ben then decides whether to eat.

In this small model, each interval uses one unit of each person's reserve. Working costs Alice one more unit. Eating adds two units to Ben's reserve. Each person's reserve must stay above zero. These are stated example units, not measurements of a human body.

Inspection, delivery and repair are authorized. Repair is optional. The two plans below both check the history and credit the right promise.

Repair can benefit both people and still be unaffordable for the person doing it.

Recognition Economics starts from the physical moral structure described by Recognition Science. Each person has their own place in that structure. One person’s meal leaves another’s hunger unchanged; another person’s work and choice remain theirs.

Production, storage, transfer and use change this physical moral state: who acts, who bears a burden, what was authorized and what remains owed. An action can be materially possible and harmful. Its harm is one of its physical consequences under the moral law. An economic account must establish those consequences for every affected person.

A useful plan must answer three questions together:

1. Can it happen? Trace the material, work, time and access each action requires.
2. What happens to each person? Keep their capacity, permissions and outstanding obligations visible.
3. Can they continue? Check the path through time, including what each person can know and choose.

The applied paper joins these questions in one model. Each example identifies a part of the physical moral account and states what remains to be derived or measured. Those limits concern our account of the laws and their application; they do not make the laws a planner’s choice.

Asha has two raw ingredients. Ben prepares one; Asha combines it with the other to make two portions. Asha needs Ben’s work to obtain food. That dependence still leaves open what happens to Ben once the food exists.

Each person starts with five reserve units. Every step uses one, and doing the preparation or combination uses one more. After these three steps, each person has one unit left. The next interval uses that unit; each portion eaten restores four. Change the allocation below. The total stays at eight for these three choices.

Production, accepted terms and each person’s reserves describe different parts of one physical moral situation. Making the food changes what is available; taking it changes whose needs are met and which responsibilities are fulfilled. From this foundation, we must derive what people owe one another when the available resources cannot sustain everyone.

Alice shares two relations: one with Ben, one with Cai. Her action relieves Ben. What happens to Cai determines whether Alice has removed the burden or merely moved it.

This example uses the recognition-cost law for a strained relation. Each person carries the cost of the relations they share; changing one relation changes the burden at each end. The numbers are exact for this specified relation model. A human application must identify and measure the relations it represents.

The rule is the same in both comparisons: no affected person may carry an increased burden. A comparison limited to Alice and Ben would admit the move. Cai would still bear its cost.

The prototype identifies the people to check from the represented relations. If a supplied list leaves Cai out, it flags the missing person. Try removing Cai above: neither action can receive approval from an incomplete list.

That protection has been proved for the represented relations. It also requires a connection between the actor and the relations changed; entering a person's name as the actor does not establish that connection. A real application must still identify the people and effects its model describes.

A favorable comparison still needs an executable plan. It does not supply Alice's energy, permission or equipment. Energy expenditure and moral burden are distinct physical quantities. The account must retain both and establish how the particular action connects them.

Exact calculation and source · Complete comparison: source and checks

Start with one meal and two people who need it. Ben and Cai each need one meal to keep their reserve above zero through the next interval. Either can eat it; both cannot. Whichever person eats, the other person’s unmet need still matters.

An objective rule need not determine a unique recipient. If exchanging Ben and Cai changes no relevant fact, a rule that treats them equally cannot select a unique recipient from those facts alone. A prior undertaking, different physical need or different authority may change the answer. Their names do not.

The applied paper studies a public meal-delivery instance with 505 requests, 116 restaurants and 113 courier records. The instance was constructed from historical operations. Routes must meet food-readiness times, travel and service times, a modeled 90-minute delivery limit, and a rule requiring each assignment to finish within the courier's shift.

The additional service has a cost. Eleven existing deliveries become later, by 1 to 32 minutes. Five couriers do 130 more active minutes of work and 85 fewer minutes of waiting. Two finish later, within their shifts.

This repair uses the completed day's information. It demonstrates a feasible schedule, not an online dispatch advantage or an observed improvement in people's lives. The public records do not establish what those people actually agreed to. The paper tests obligations and permissions separately under stated example terms.

The framework makes that tradeoff visible: who gains, who carries extra work, and which permissions and promises the workable alternative depends on.

A living thing needs structure. If a comparison rewards the disappearance of that structure, it can mistake destruction for improvement. A measure of burden must preserve what makes continued life possible.

Consider two connected sites with positive numerical values. Hold the first at 4 and allow the second to change. Their combined structural cost is smallest when the second is 2. This is a minimum within the required boundary, not a demand that every value become 1.

The repair (4, 2) retains the boundary: structural cost 13/8 and relative burden 0. The uniform configuration (1, 1) breaks the boundary: structural cost 0 and relative burden 11/8.

The repair lowers the relative burden to zero while retaining positive structural cost. Making both sites 1 lowers structural cost to zero, but breaks the required boundary and raises the relative burden.

Keeping the reference state requires a continuing material flow.

Let material move through the two sites. Material passes reversibly between an inlet A, an interior X and an outlet held at 1. At A = 4 and X = 2, keeping both values unchanged requires a continuous supply into A and removal from the outlet. The burden relative to this state is zero, but the supply is positive.

Compare full, half and stopped supply. Each starts with eight units in a separate feed tank and the same material in the system. The outlet continues to be cleared in all three cases.

At k = 1 and time 1, full supply uses two feed units and keeps the burden at zero. Half supply uses one unit and leaves a burden of 0.0217. Stopping supply uses none and leaves 0.1069. All three conserve 15 units of material.

Full supply prevents deterioration while the state stays unchanged. Half supply reduces the deterioration, but does not prevent it. The amount supplied, the condition that remains and the difference the supply made are three separate facts.

Doubling the reaction speed doubles the supply needed to maintain exactly the same state. A snapshot of the state, even one with zero burden, cannot tell us how much provision it requires.

Stop the supply in the example above, let the system deteriorate, then turn it back on. The tank and both compartments begin the next interval with what is actually left. Nothing jumps back to its starting value.

With full maintenance supply restored, this model approaches its reference but never reaches it exactly in finite time. It can reach a specified tolerance in finite time. That tolerance must be part of the accepted service: a provider cannot quietly replace “keep this condition” with “come close enough later.”

Recovery can also be uneven. Just after supply resumes, the interior continues declining briefly, even while the combined physical deficit falls. A plan must account for the path through recovery as well as its destination.

Each installation draws from the real source stock. Two people may benefit from one maintained installation; two installations cannot each spend the same tank. A later repair or release can change what is possible or required next. It cannot erase an earlier missed interval.

A refrigerator contains many storage locations. If the average stays cool long enough but one location warms too soon, a promise covering everything inside can still fail.

In published NIST experiments, researchers added water bottles to two refrigerators and measured how long each monitored vial took to warm by 3°C after a power outage. The bottles act as thermal ballast: more water can slow warming, but it also takes up room.

Use those measurements to explore a shared allocation. Each recipient's goods have an assigned refrigerator and a requested storage window. The water must be divided before preparation. Choose an allocation and compare each window with the earliest crossing recorded in its experiment.

Try 3½ hours for each recipient. An 8% load in both units uses 69.6 L. Both averages exceed 3½ hours, but the earliest crossings are 3:02 and 2:48. Neither requested window is covered by those results. Within the tested loads up to 17%, no allocation fits both windows under an 80 L budget.

The unequal allocation above answers a different question: 2½ hours for the first recipient and 4 hours for the second. Giving both 8% misses the second window. Giving both 17% needs 147.9 L. Keeping the two requirements separate finds a choice that uses 111.9 L and covers both recorded windows.

A storage result also needs a history: who accepted which window, who has access, and what happened while the promise was in force. The accompanying calculation uses the existing service-history reader. It preserves an earlier failure even if the recipient releases the provider later.