# Second Close: The Economics of Unfinished Work

**RECORDS-FRAMEWORK-002 · internal research draft · 2026-09-23**

An enterprise can finish producing before it finishes bearing the consequences of
production. An account is useful when it preserves the distinctions needed to choose
what happens next. That usefulness is conditional: more records can be costly,
resolution can destroy value, and a conventional dossier can be fully sufficient.

This paper supplies a finite decision model, exact worked counterexamples and an
empirical discrimination plan. It does **not** establish a new general economic law,
a universal institutional floor, a financing advantage, or demand for Bulla.
The contribution is an explicit connection between surviving effects, information,
authority and a specified allocation decision, made inspectable in executable cases.

## 1. Question and reporting boundary

The enterprise persists; an executor may disappear. A **first close** reports accepted
work and the position at a cutoff while keeping unfinished effects visible. A
**Second Close** revisits those effects after evidence, settlement or permission has
changed and records the resulting decision. It is a repeated operating assessment,
not a claim that every consequence has finally ended. Neither close is a financial
recognition rule. Recorded assertions and modeled exposures are not adjudicated debts.

The historical Tablework 0.1.8 / revision 45 account remains unchanged in the parent
package. It cannot calibrate this model's money, probabilities, review capacity or
benefits: its billing and human effort are incomplete, its pending request survives,
and its six synthetic jobs do not establish market demand. Every number below is a
constructed assumption in SC/1, denominated in modeled USD where monetary.

The three distinct functions remain research, evidence preparation, and possible
future use by a capital provider. No new organization, financial product, public API
or protocol release follows from these demonstrations.

## 2. Finite model

Let x be economic position: output count, a remaining optional tranche, and an
identity-indexed set of unresolved effects. Each effect carries an assumed residual
loss and, separately, a number of reserved review slots. Let a be current declared
authority. A hidden state s=(x,a) also carries executor labels for invariance tests.
Let b be the operator's probability distribution over s given the transferred record
and subsequent observations. The model and prior are known; the realized hidden
state is not. Miscalibrated or adversarially supplied models are outside SC/1.

At h integer periods remaining the operator selects produce, investigate, reconcile,
defer or decline. There can be two resolution technologies of the same action kind.
Every action has strictly positive duration d, declared monetary inflow and outflow,
a transition distribution and an observation. It is feasible only when its permission
and capacity requirements hold throughout the positive-probability support of b.
This conservative feasibility rule excludes gambling on hidden permission; it is a
modeling choice, not a theorem about legally appropriate conduct.

Capacity K is measured in review slots. An action's slot demand plus other outstanding
reservations must fit K. Resolution may use the reserved slots of explicitly named
effects it addresses. The operator performs one action at a time: this is a finite
admission and scheduling model, not a calibrated queue with simultaneous arrivals.
Each action's slot constraint applies for its declared duration.

Investigation changes available information at a cost and consumes time. It does not
silently settle an effect or create permission. Reconciliation changes actual effects
and may supply evidence. An external settlement may occur before a reliable receipt.
Monetary outcomes do not automatically become observations: a case must declare them
as observations if the operator sees them. Authority changes require a separately
identified act by the case's authorized principal. This records an authorization
assumption; it is not cryptographic or legal authentication of that act.

All modeled costs are incremental flows, including any declared review or preparation
expense. Historical sunk work is excluded from the objective, not assigned zero cost.
No cash-solvency constraint or capital-market discount rate is inferred. With discount
factor one, delay matters through time lost, deadlines and explicit external events.

Every state has a terminal continuation H(s): minus its remaining distinct exposures
plus a separately declared adjustment. The adjustment is visible and challengeable.
SC/1 does not estimate it from a completed-output count. Actions too long to finish
inside h are unavailable; their outstanding consequences remain in H. If there is no
feasible action before the horizon, the implementation rejects the case rather than
silently declaring discharge. The examples retain a feasible wait or decline.

Writing r for inflow minus outflow, p(o|b,u) for observation probability and b' for the
updated belief, the standard finite-horizon recursion is

    V(0,b) = E_b[H(s)]
    Q(h,b,u) = E_b[r(s,u,s')] + Σ_o p(o|b,u) V(h-d(u), b')
    V(h,b) = max_{u feasible} Q(h,b,u).

This is established belief-state dynamic programming, not a new Bellman principle;
see [Smallwood and Sondik (1973)](https://pubsonline.informs.org/doi/10.1287/opre.21.5.1071).
The solver uses exact fractions. An independently implemented checker enumerates
whole observation-contingent policy trees and evaluates paths forward, without using
the solver's recursion or belief-update code. Agreement establishes the checked
finite results, not the truth of their premises or a universal economic theorem.

## 3. T1: a production summary can lose a decision

Consider two histories with ten accepted outputs, one remaining tranche, one unresolved
legacy effect, the same permission and review capacity, and one period remaining.
Reliable evidence in G establishes zero terminal loss; in B it establishes a loss of
20 if left unresolved. Production produces modeled inflow 6 at cost 2, net 4.
Reconciliation costs 8 and removes the effect. Both actions take one period.

In G the unique best action is produce, value 4. In B it is reconcile, value -8;
producing instead yields 4-20=-16. The completed-work summaries are identical but the
maximizing action sets are disjoint (`known-good`, `known-bad`). Therefore no decision
rule based solely on that summary can be optimal in both histories.

For an equal prior over the two histories, a free reliable signal before the last
choice yields (4-8)/2=-2. Without that signal, the best constant action is produce,
value 4-10=-6; always resolving yields -8. A randomized mixture cannot exceed the best
constant action under linear expectation. The minimum expected regret from suppressing
this distinction is therefore 4. Spending a whole last period to investigate is a
different intervention and cannot obtain this free-signal value.

**Disposition:** existential insufficiency proved under these explicit assumptions;
its decision-theoretic content reduces to information/state sufficiency. No minimal
universal account schema is established. Whether a specific real production dashboard
already includes the relevant exposure is an empirical question.

## 4. T2: resolving can beat producing, but need not

With one period, known unresolved loss L, production margin g and resolution cost c,
suppose production leaves L outstanding, resolution removes it, and the alternatives
have equal feasibility and duration. Then

    Q(produce)=g-L; Q(reconcile)=-c.
    Reconcile beats produce exactly when L-c > g.

For L=20, c=8 and g=4, resolution beats new production by 8. This is an avoided-loss
comparison, not new value creation from writing a receipt. If resolution costs 50,
this reasoning reverses. With multiple periods, use Q: the simple threshold is no
longer sufficient because delay, subsequent choices, observations and capacity matter.
Subtracting a separate opportunity-cost charge on top of the optimized continuation
would double count the forgone alternative already represented in V.

The two-period QAO case offers one optional tranche and uncertainty between G and B.
An investigation costs 1 and takes one period. Fast resolution costs 8, takes one
period and requires three review slots. Slow resolution costs 8, takes two periods
and requires two slots. With K=3, investigation followed by production in G or
resolution in B has value -1+(4-8)/2=-3. Producing first and then resolving regardless
of state has value -4. Investigation is uniquely optimal. With investigation expense
10 it is inferior; the optimal root choices are production or resolution, both -4.

Free optional information cannot reduce ex-ante attainable value: retain the old
policy and ignore the signal. This familiar dominance argument does not guarantee a
return on paid collection, a delayed investigation, or records that change permissions
or impose disclosure costs. Realized bad news can appropriately reduce subsequent
funding even when the signal has positive ex-ante value.

**Disposition:** the threshold and examples are proved for their stated settings;
general information value and waiting-option logic reduce to established results.
See [Blackwell (1951)](https://digicoll.lib.berkeley.edu/record/112749) and
[Pindyck (1991)](https://www.mit.edu/~rpindyck/Papers/IrreverUncertInvestmentJEL1991.pdf).
The optimal real-world spend on investigation remains unresolved.

## 5. T3: outstanding work can change admission

With one review slot, a one-slot production action is blocked by a surviving one-slot
reservation, even when the effect's known monetary exposure is zero. Removing that
reservation permits production with value 4. The two congestion cases isolate this
constraint. Conversely, increasing capacity from three to 99 in the QAO case changes
neither value nor the preferred action. Outstanding work is not sufficient to prove
an economically binding bottleneck.

Different dependencies also matter. Two distinct losses remain two losses even when
they share a cause. In `correlated-effects`, a common repair settles two effects for
6; in `independent-effects` separate repairs cost 12. Those cases change both dependence
and repair technology and cannot identify the effect of correlation alone. The
`joint-loss-*` pair supplies that control: the same contract loses 20 only when both
binary causes are adverse, with equal one-half marginal probabilities and repair cost
6. Perfect correlation makes expected loss 10 and favors repair; independence makes
it 5 and favors waiting. Joint economic terms make the difference; correlation of
additive losses alone would not change their expectation.

Cheap production does not by itself cause an optimal overload collapse. Holding
transitions, observations, authority, constraints, horizon and terminal values fixed,
reduce only nonnegative production costs. For every old feasible policy, its expected
payoff weakly rises. Taking the maximum over a set containing all old policies proves
that the new optimum cannot fall. `cheaper-production` increases the QAO optimum from
-3 to -2. A contrary overload claim needs another mechanism: mandatory admissions,
a changed arrival process, a constrained heuristic, mispriced consequences, or a
changed capacity/authority set. None follows merely from cheaper cognition.

**Disposition:** conditional finite admission effects proved; a universal congestion
law or cheap-production collapse under optional optimization is refuted. Known queueing
thresholds require their own assumptions; see
[Yom-Tov and Chan](https://business.columbia.edu/faculty/research/balancing-admission-control-speedup-and-waiting-service-systems).
This model does not estimate a stationary congestion coefficient or institutional beta.

## 6. T4: what replacement must preserve

Suppose a transferred representation preserves initial beliefs over decision-relevant
states, feasible actions including current authority, durations, monetary rewards,
joint transition and observation laws, effect identity, and terminal continuation.
A relabeling of executors under these conditions preserves attainable policies and V.

Proof: terminal expectations agree. Assuming continuation values agree for smaller
h, each corresponding action has the same expected reward and observation-weighted
continuation, hence the same Q. Feasible action sets agree, so their maxima and all
maximizing actions agree. Strictly positive durations complete induction. This also
constructs the corresponding contingent policy. Equal value at a single state alone
is not enough for such equivalence.

This is a specialization of policy-preserving state representation, with explicit
permission and observation requirements; compare
[Givan, Dean and Greig (2003)](https://cs.brown.edu/people/tdean/publications/archive/GivanetalAIJ-03.pdf).
The successor and repartitioned cases exercise executor-label invariance. The
conventional-equal-facts case preserves exactly the same decisions: it grants no
Bulla advantage. Actual unfamiliar-operator recovery cost and record completeness
are not tested by changing labels in a case file.

An account transfers information about authority; it does not grant the successor
permission. Removing production permission leaves legacy consequences intact.
`withdrawal-after-wait` encodes a principal's separate withdrawal, not an evidence
update masquerading as a physical or legal act. Additional access or custody costs
must be introduced before applying the invariance proposition to real replacement.

**Disposition:** conditional preservation proved and reduced to established policy
sufficiency. Universal preservation by the proposed record format, independent-reader
usefulness and measured Bulla preparation savings remain unresolved.

## 7. Bounded extension: investment in resolution capacity

Define ΔV=V(K+1,b)-V(K,b), holding other primitives fixed. This finite marginal value
is nonnegative when extra capacity only relaxes a constraint: every old policy remains
available. It can be zero. Net investment value is ΔV-F for upfront expense F, paid
once outside the operating value. This is a finite difference, not an assumed market
shadow price or a fee added to every mandate.

In QAO, K=2 permits slow resolution but not the fast technology. With two periods,
production, possibly deferred for one period, has value -6. At K=3 the optimal
investigate-then-act policy yields -3. The gross capacity value is 3. Upfront expenses
2, 3 and 4 therefore give net values +1, 0 and -1. At slack capacity the gross value
is zero; a positive investment expense is a loss. The improvement does not validate
these slot technologies or prices in an operating enterprise.

Separately reducing investigation expense from 1 to 0 raises the K=3 optimum to -2
without adding any review slots or permissions. That is an information-preparation
intervention, not capacity expansion. Actual permission changes remain a principal's
act. No favorable capacity result can be attributed to Bulla without measured evidence
that it caused the corresponding physical or informational improvement at full cost.

## 8. Continuation and the Second Close

Short horizons can favor different actions even when residual losses are retained:
QAO value is -6 at one period, -3 at two and -1 at three. More time permits sequences
that a shorter decision window excludes; these are different opportunities, not
accounting corrections. In `deferred-production-loss`, producing earns 4 now but
creates a surviving loss of 9, so declining or waiting is best. The deliberately
misspecified control inserts an unsupported +9 continuation adjustment and reports
production as best. Exact arithmetic accepts that assumption; scrutiny must reject
its economic basis. A reconciled model can still be wrong.

This motivates the [worked Second Close](WORKED-SECOND-CLOSE.md): the same ten-output
history is first carried as an uncertain effect, later narrowed by evidence, then
settled through a distinct act. The second close changes the warranted allocation
before the obligation disappears. State-time exposures should retain their own units:
USD-periods of a specified encumbrance or review-slot-periods, never a universal
capital-time index formed by adding unlike quantities. Their predictive usefulness
and measurement expense belong in the next operating study.

## 9. Contribution and commercial boundary

Existing decision theory supplies the optimization, information, waiting and state
representation results. Existing accounting supplies resources, events, agents and
policy concepts. Existing queueing work already retains unfinished work and studies
admission. The present addition is a contestable worked convention connecting these
to enterprise succession and the timing of later operating closes, with explicit
negative controls and a reproducible comparison of decisions.

Each proposed object must earn its measurement burden; see the empirical specification
and benefit ledger. A QAO report is worth buying only if it changes a consequential
decision enough to justify evidence collection, review, integration and maintenance.
Value to the enterprise is not provider revenue. The constructed capacity gain of 3
is neither an observed saving nor a fee the evidence producer can collect.

The next theory step is incentives and contractibility across independent parties.
The next empirical step is an unfamiliar operator conducting a real Second Close,
with equal-fact conventional controls and measured preparation burden. The larger
claims about organizational boundaries, capital formation and financing cost remain
conditional on evidence from those steps. Favorable ROI and novelty are not acceptance
criteria for this package.