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ERRAND: Budgeted Maintenance of Agent Memory

Beining Wu, Zihao Ding, Jun Huang

arXiv:2609.29545v1cs.AI

TL;DR

Handed-over knowledge can become stale as the world changes, while existing store governance treats validity as settled at admission. ERRAND prices rechecks against the task actions they displace and outperforms other non-oracle policies on the reported calibers.

  • Problem

    Handed-over knowledge can become stale as the world changes, while store-side governance treats validity as fixed at admission.

    Source: §1 · p. 2

  • Method

    ERRAND ranks rechecks by value per action, funds them only above a running wage, uses free en-route receipts, and repairs by versioning.

    Source: §1 · p. 2, §3.1 · p. 4, §3.2 · p. 5

  • Results

    ERRAND tops ITT in every setting and conditional caliber at binding budgets, leading eager revalidation by 10.0pp at the base cap.

    Source: §1 · pp. 2–3, §4.2 · p. 7

  • Takeaways & Limitations

    Maintenance outcomes depend on the prices assigned to rechecks before the budget size, with paid ordering mattering most where briefing coverage is thinnest.

    Source: §1 · p. 3, §5 · p. 10

    The setting covers handed-over briefing knowledge rather than knowledge earned through the agent’s own trajectories.

    Source: §3.1 · p. 4

Abstract

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Deployed agents run on handed-over knowledge: a frozen policy consults a briefing of consolidated items written before the stream begins. The world then moves while the store stands still: paths close, flags change, price bands move; every item was true at handover, and the failure is staleness, not ignorance. We introduce ERRAND, which treats revalidation as a priced errand: a recheck competes with the task it protects for the same scarce actions, funded only when the value per action of resolving a doubt clears a running wage. The errand index is single-peaked, vanishing at both ends of belief, so certainty in either direction costs nothing; free en-route receipts maintain on-path knowledge, and repair writes a version, never a deletion. Under equal action budgets in two drifting tool-use worlds, ERRAND clears every non-oracle policy on the preregistered calibers, primary in every setting and conditional at every binding budget, leading eager revalidation by 10.0pp at the base cap. Restraint wins: given no cap, ERRAND stops on its own, spending 11.0% of steps, while uncapped eager revalidation spends 70.7% and still finishes 4.5pp behind capped ERRAND. The margin sits where the briefing's coverage is thinnest, the shadow price of long-tail knowledge: a small budget, well priced, beats a bigger store that never rechecks.

1 Introduction

ERRAND treats revalidation as an action competing with task work, funding a check only when its value per action clears the budget wage. Its results challenge write-time-only maintenance: priced revalidation outperforms eager checks, while coverage gaps magnify the value of paid ordering.

1 Introduction

  • Store governance prices capacity and entry value, but typically fixes validity at write time; freshness checks, meanwhile, are unpriced or under-tested by benchmarks.The paper frames the gap as a missing budget line for upkeep as the world changes.Source: §1 · p. 2
  • ERRAND prices rechecks against the task steps they displace, funding them only when resolving a doubt per action clears the going wage.Certainty at either end needs no test: an item almost surely fresh needs no check, while one almost surely stale needs a takedown.Source: §1 · p. 2
  • The paper formulates budgeted memory maintenance, builds ERRAND, and maps where pricing matters, including drift and coverage-gap regimes.It reports that half-life priors collapse when real drift decouples from the calendar, while ERRAND holds flat; its premium rises as coverage thins.Source: §1 · p. 2
  • 10.0pp is ERRAND’s headline margin over eager revalidation at the base cap, the density-weighted average of a margin that grows where briefing coverage is thinnest.At equal budget, the margin rises from 2.3pp on fully covered steps to 12.9pp where coverage is thinnest.Source: §1 · pp. 2–3
  • With no cap, ERRAND stops on its own at 11.0% of steps, while uncapped eager revalidation spends 70.7%—6.4× more—and finishes 4.5pp behind the capped system.Source: §1 · p. 2

2 Related Work

Related work prices store capacity, value, and consistency, and separately studies freshness checks and freshness scheduling. ERRAND’s distinction is to price revalidation inside the agent’s task-action budget, where checks affect decisions and repairs preserve versions.

Governing a growing store

  • Store-governance methods price capacity, entry value, or consistency, but validity is generally fixed at writing or revised only when contradictory input arrives.GLOVE probes after detecting dissonance, but its probing is immediate, undifferentiated, and unbudgeted [Yin and Du, 2026].Source: §2 · p. 3

Free verdicts and where they fail

  • Self-audits can over-validate, confidence from historical success can inflate, and read-time filtering or detection scores may fail to improve behavior.The cited benchmark discussion says conversational suites rarely contain separating contradictions, while test-time continual-learning answer keys anchor to design-time state.Source: §2 · p. 3

Pricing freshness

  • Freshness scheduling often treats freshness as the objective and checks as dedicated probes; ERRAND instead makes checks compete with task actions and versions repairs for returning regimes.Its index is single-peaked, so certainty at either end spends nothing.Source: §2 · p. 3

3 Revalidation as a Priced Errand

ERRAND allocates scarce task actions to rechecks only when resolving doubt is worth its price, using drift-aware beliefs, free receipts, a value-per-action gate, and versioned repair. Its rules account for the path’s observations and the time an answer remains useful, while the running wage makes inaction an explicit decision.

3 Revalidation as a Priced Errand

  • ERRAND leaves the frozen policy and stored contents unchanged, governing only task actions diverted to recheck beliefs through a drift-aware index, wage gate, and versioned lifecycle.The budget buys trajectory changes, not attention.Source: §3 · pp. 3–4, Figure 2 · p. 4

3.1 Setting and Threat Model

  • Grounded atoms flip between recorded values under two-state drift, while off-path beliefs relax toward a prior; task traversals provide free receipts, but reaching a site is the scarce step.The model assumes declared independence for item-level beliefs, with most items single-atom and a correlated-flip suite deliberately stressing that declaration.Source: §3.1 · p. 4

3.2 The Errand Index and the Deadband Gate

  • Free en-route receipts update touched beliefs before pricing, while the single-peaked value of resolving depends on doubt, use, durability, and locality.Value vanishes for near-certain freshness or staleness, where a test is unnecessary; the live index orders off-path checks.Source: §3.2 · pp. 4–5
  • The gate funds the highest value-per-action candidate above the running wage; its deadband tolerates doubt, and it can choose an en-route wait, proxy, or direct retest.In the single-atom regime, costlier checks widen the deadband while more usage receipts narrow it.Source: §3.2 · p. 5

3.3 A Lifecycle That Closes Use, Never Eyes

  • Abeyance withholds retrieval but keeps comparisons active; a resolved flip supersedes the recorded value in place, preserving a version for possible regime return.This keeps redemption evidence available without deleting the item.Source: §3.3 · p. 5
  • A purchased answer’s durability horizon is the time until belief recrosses the disposition threshold; some answers never expire by drift alone.Because durability multiplies value, the scheduler favors questions whose answers stay decision-relevant longer.Source: §3.3 · p. 5

3.4 The Wage and the Meter

  • The wage rises while the budget cap binds and decays while slack, reaching an intrinsic floor that can stop spending before the cap does.Scheduling uses closed-form arithmetic over retrieved candidates and spends no model call; calibration of belief affects how much repair the same budget buys.Source: §3.4 · pp. 5–6
  • In the single-atom regime, the deadband width and durability horizon are exact; en-route comparison remains ungated, while suspension closes use and repair remains versioned.These rules let redemption and regime return rely on a traversal and a lookup.Source: §3.4 · p. 6

4 Experiments

The experiments test whether priced revalidation improves maintenance under action budgets across drifting tool-use settings. ERRAND beats non-oracle policies by directing checks toward doubts whose value justifies their cost, while free receipts and repair mechanisms support maintenance over time.

4.1 Setup

  • The setup hands over 26 items in scripted worlds with unannounced flips, varies coverage-gap regimes, and evaluates ITT as the primary metric alongside conditional success on knowledge-bearing steps.The experiments also use a second tool-API world for drift-rate sweeps; equal-budget comparisons match measured spend.Source: §4.1 · p. 6

4.2 Priced Revalidation Wins at Every Budget

  • At every measured spend, ERRAND exceeds eager revalidation by 4.5pp at the tightest cap and 10.0pp at the base cap; zero-spend policies remain at 51.1%.Without maintenance, knowledge-step success falls from 85.8% while items hold to 6.3% after flips, a 79.5pp collapse.Source: §4.2 · p. 6, Figure 3 · p. 6
  • Under equal action budgets, ERRAND clears every non-oracle policy on ITT in every setting and on the conditional caliber at every binding budget.At the base cap it scores 71.9% against eager revalidation’s 61.9%, and Table 1 reports a 7.1pp five-setting average margin.Source: Table 1 · p. 7, §4.2 · p. 7

4.3 The Scheduler’s Economics Are Real

  • At matched spend of 10.6% of steps, calibration adds 2.6pp over a blind-belief scheduler and pricing adds another 10.3pp.Measured gains exceed the closed-form forecasts across all twelve seed-level points; en-route receipts explain why the model undercounts recovered coverage.Source: §4.3 · p. 8

4.4 The Premium Is a Shadow Price

  • Across a tenfold range of flip intensity, ERRAND holds at 66.5–69.7% ITT, while a half-life policy drops from 68.3% to 46.7% when real drift diverges from its priors.Across coverage-gap bands, the conditional gap over eager revalidation widens from 2.3pp on fully covered steps to 12.9pp in the binding tail; the overall margin is the density-weighted average.Source: §4.4 · p. 8, Figure 5 · p. 8

4.5 Every Errand Pays Its Way

  • At the base cap, removing belief calibration costs 13.0pp ITT, compared with 3.5pp for the deadband gate; permanent flips cost 5.0pp and gating the comparator during abeyance costs 3.1pp.Scheduling uses closed-form arithmetic, averaging 1.10 model calls per step versus 1.40 for eager revalidation, while the scheduler itself makes none.Source: §4.5 · pp. 8–9, Table 2 · p. 9, Table 3 · p. 9
  • In a paired trajectory, eager revalidation spends budget broadly and serves a stale spec, while ERRAND receives the updated spec as a free co-located receipt and succeeds without spending the budget.The item flips at step 641; the failed task arrives at step 720, while ERRAND’s free receipt arrives at step 690 and its paired task succeeds at step 722.Source: §4.5 · p. 9, Figure 6 · p. 10

5 Conclusion

ERRAND funds a recheck only when resolving a doubt is worth more than the task action it displaces. The protocol implements this rule through free receipts, priced errands, and versioned repair.

5 Conclusion

  • ERRAND should recheck a belief only when resolving it is worth more than the task step displaced; upkeep of self-consolidated experience remains untested.The proposed next step is to price acquisition, consolidation, and maintenance together.Source: §5 · p. 10

A The ERRAND Protocol: Algorithms and Configuration

  • The scheduler leaves the frozen policy, retriever, and resting store unchanged, controlling only errand actions and the belief state.Its arithmetic operates over retrieved candidates in O(k) time per step and uses no model call for scheduling.Source: A The ERRAND Protocol: Algorithms and… · p. 17
  • Each deployment step harvests free traversal receipts, relaxes unobserved beliefs, then prices and gates candidate errands against the wage and cap.The protocol runs the task action and checks traversed atoms before its belief and pricing phases.Source: A The ERRAND Protocol: Algorithms and… · p. 17
  • Refutations supersede and version recorded values; abeyance withholds retrieval, while confirming free receipts or funded errands can restore an item.A recurring superseded value requires a version lookup rather than relearning.Source: A The ERRAND Protocol: Algorithms and… · p. 17
  • The comparator keeps checking traversed atoms in every lifecycle state, and each no-spend step logs the clause that blocked funding.The appendix identifies this as the contract that suspension closes use, never observation.Source: A The ERRAND Protocol: Algorithms and… · pp. 17–18

B Closed Forms and Formal Statements

The appendix derives closed-form belief and value rules under a two-state drift model, and states where the ordering premium applies. Its numerical and literature audits clarify the model’s evidence channels and flip-back scope.

B Closed Forms and Formal Statements

  • The analysis claims exactness only in the single-atom regime, and makes no theorem-level novelty claim for its scheduling mathematics.The paper places that mathematics in the restless-bandit lineage.Source: B Closed Forms and Formal Statements · p. 19

B.1 Preliminaries and Notation

  • Each atom flips between its recorded value and its negation with intensities λa and µa > 0, and beliefs change only on receipts.The two-state assumption declares atoms independent; receipts come from en-route observations or funded errands.Source: §B.1 · p. 19

B.2 Belief Relaxation

  • Between receipts, staleness belief relaxes exponentially toward q∞ = λa/κa at rate κa; with µa = 0, atoms are eventually presumed dead.The closed form follows from the two-state forward equation.Source: §B.2 · p. 19

B.3 The Single-Peaked Index and the Deadband Width

  • The resolving value is single-peaked and zero at both certainty endpoints; the deadband comprises those two ends, widening with check cost and narrowing with use.For a single atom, its unfunded-set width is exact when the peak clears the wage.Source: §B.3 · pp. 19–20

B.4 The Durability Horizon

  • After resolution, the durability horizon is the time until belief crosses the disposition threshold; items with stationary suspicion near that threshold can have τi → ∞.Their answers never expire by drift alone, so the index prioritizes them through the durability factor.Source: §B.4 · p. 20

B.5 The Value of the Free Channel, Numerically

  • The priced evidence-policy ladder is monotone at every (κ, c) cell, pooling to 0.060 < 0.175 < 0.236.The en-route increment is invariant to errand cost c, while the purchased channel scales with it.Source: §B.5 · p. 20

B.6 Zero Shadow Price Outside the Binding Regime

  • Ordering has a positive premium only when the budget binds and some priced doubt goes unfunded; outside that regime, the pooled premium is indistinguishable from zero at −0.01 pp.The appendix frames this as a scope condition for the relaxation, not a regret bound.Source: §B.6 · pp. 20–21

B.7 The Flip-Back Audit

  • The audited prior systems do not combine modeled regime return, versioned repair, and detection and redemption competing for one wage.The audit notes that some systems have revival edges, but without a trigger, price, or demonstration.Source: §B.7 · p. 21, Table B.3 · p. 22

C Preregistered Analysis Plan and Power

The appendix reports preregistered estimands, inference rules, outcomes, and power checks, with interpretation bands and fallbacks fixed before the full study runs.

C Preregistered Analysis Plan and Power

  • All headline estimands were frozen with interpretation bands and fallback readings before the first full-wave GPU hour.The appendix reports each band against its outcome and the design-stage power forecast against the realized study.Source: C Preregistered Analysis Plan and Power · p. 23

C.1 Estimands and Inference

  • Headline intervals use 95% paired t over seed-level means, while item-level matched pairs use seed-clustered inference with a bootstrap cross-check.Budget claims apply only to caps verified as binding by logged cap-hit events; slack-cap comparisons are descriptive.Source: §C.1 · p. 23

C.2 Bands and Outcomes

  • 1/3 strict dominance criteria resolve positively overall, so the preregistered fallback scopes the dominance claim to the base cap.At b=6 the spend leg fails by +0.03 pp of steps; at b=24 conditional caliber ties at -0.17 pp. The calibration ladder is +9.6 pp [+5.8, +13.4] for calibrated beliefs and +3.3 pp [-4.1, +10.8] for the lower segment, which is positive but unresolved at three paired seeds.Source: §C.2 · p. 23, Table C.1 · p. 24

C.3 Power, Forecast and Realized

  • 1016 matched pairs across eleven seeds yielded a seed-clustered half-width of 1.66 pp, beating the same-row forecast.The gate cohort reads +4.2 pp [+2.5, +6.0] and the extension +4.9 pp [+3.3, +6.6], with the same sign and overlapping intervals; caps 6 and 12 were predicted binding and 24 slack.Source: §C.3 · p. 23, Table C.2 · p. 24

D Environment, Instrumentation Principles, and Experimental Details

  • The configuration appendix records the errand world, briefing, instrumentation principles, evaluation safeguards, baselines, and adjudication stack as preregistered design constants.Calibration readings in Table D.2 are the stated exception; measured outcomes are reported in the main text and Appendix E.Source: D Environment, Instrumentation… · p. 25

D.1 The Errand World and the Task Stream

The study constructs a drifting tool-use world with handed-over knowledge and task-controlled coverage, then compares maintenance policies under matched budgets and evaluates their performance across caps and coverage tiers.

D.1 The Errand World and the Task Stream

  • The world runs 2,000-step go and fetch orders over 26 atoms in five groups, with four drift schedules and no signal announcing flips.The base tier has 82 orders and the high tier 110, with off-path groups doubled and on-path groups halved in the high tier; errand cost is c=d+1.Source: §D.1 · p. 25, §D.2 · p. 25, Table D.1 · p. 25

D.3 The Briefing and the Substrate Principle

  • Exogenous briefing seeding separates knowledge existence from task traffic, while dispatch and completion verbs make coverage and off-path uses controlled features of the instrument.With fetch orders off, off-path fetch-verb atoms record 0.00 uses per order; with them on, they reach 2.22.Source: §D.3 · p. 25, §D.4 · p. 26

D.6 Compared Baselines

  • The comparison spans zero-spend anchors, eager, cadence and random spenders, priced ceilings, known-rate and half-life references, plus component-removal arms.Truth comes from the harness event log, and each paired arm runs on the same machine for each seed and cap under matching run fingerprints.Source: §D.6 · p. 26, §D.7 · p. 27

D.5 Six Pitfalls of Evaluating Memory Maintenance

  • Calibration shows stale-item conditional success collapses by 79.5 pp against the fresh complement before maintenance mechanisms are evaluated.The evaluation also pins the judged domain before runs and clusters matched inference by seed to guard against denominator migration and pseudo-replication.Source: §D.5 · p. 26, §D.8 · p. 27

E.1 The Frontier at Every Cap

  • ERRAND clears eager revalidation on ITT at every cap and on conditional caliber at every binding cap; at b=24, eager runs exhaust the cap while ERRAND runs do not.At b≤12, both arms exhaust the cap in every run; the ledger shows the loose cap is unspent by ERRAND because its wage governs spending.Source: §E.1 · p. 28, Table E.1 · p. 28

E.2 The Inaction Ledger

  • At the loose cap, 81% of ERRAND’s unspent steps reflect active index or gate clauses, whereas 70% of eager revalidation’s tight-cap unspent steps reflect cap exhaustion.The ledger distinguishes wage-driven inaction from a policy that wants to spend but cannot.Source: §E.2 · p. 28, Table E.2 · p. 29

E.3 Baselines in Every Setting

  • Unpriced spenders do not close the gap in any setting, and the bigger store does not substitute for maintenance despite comparable spending at binding caps.The zero-spend anchors floor every column; eager revalidation alone spends the loose cap in full.Source: §E.3 · pp. 28–29, Table E.3 · p. 29

E.4 The Coverage-Gap Ladder

  • +4.9 pp [+3.3, +6.6] is the eleven-seed high-tier matched conditional gap; the ordering premium rises from +3.09 pp at base to +7.28 pp at high tier.The eight-seed cohort reads +4.2 pp [+2.5, +6.0], with the same sign and overlapping intervals; every item class is positive, from +8.4 pp on fast on-path items to +3.2 pp at the floor.Source: §E.4 · p. 29, Table E.4 · p. 29

E.5 Ablations, Per Arm

Component removals, allocator comparisons, and parameter sweeps test which parts of ERRAND matter and where priced ordering produces its gains.

E.5 Ablations, Per Arm

  • -13.0 pp is the cost of blinding belief; all seven component removals reduce success in their predicted direction.Belief blinding costs more than twice any single index term; four of seven effects resolve at 95% under three seeds.Source: §E.5 · p. 30, Table E.5 · p. 30

E.6 The Allocator Ladder

  • At the tight cap, Whittle gives up -2.2 pp and the myopic rule -4.8 pp against the numeric index; at the loose cap, the three run nearly parallel (-1.9 pp).The loose-cap result is the stated zero-shadow-price scope condition for ordering.Source: §E.6 · p. 30, Table E.6 · p. 30

E.7 The Coverage Grid and the Zero-Shadow-Price Layer

  • At binding open-channel budgets, ∆ord rises from +2.01 pp at full coverage to +11.0 pp [+10.4, +11.7] at zero coverage; the nonbinding premium pools to -0.01 pp.Across the coverage ladder, Spearman ρ = +1.00; gated-comparator columns run below their open-channel twins.Source: §E.7 · p. 30, Table E.7 · p. 31, Figure E.1 · p. 31

E.8 The Drift Envelope

  • ERRAND holds between 66.5 and 69.7% across a tenfold drift range, while the half-life-prior policy falls from 68.3% to 46.7%.At the fast-drift end, the half-life-prior policy crosses below eager revalidation; ERRAND tracks the known-rate reference without being given κ.Source: §E.8 · p. 31, Table E.8 · p. 31

E.9 Correlated Flips

  • Every correlated-flip group exceeds its forecast, pooling to an excess of 1.94±0.81 pp.The paper attributes the conservative forecast to co-located doubt being cheaper to resolve and en-route receipts repairing neighboring items.Source: §E.9 · p. 31

E.10 The Regime Axes: Capability and Closure

The results map ERRAND’s gains to agent capability, task-graph reach, time horizon, freshness, and operational overhead.

E.10 The Regime Axes: Capability and Closure

  • +10.0 pp [+8.6, +11.4] at 8B compresses to +2.1 pp [+1.5, +2.6] at 4B, while off-path fetch-verb uses are 0.00 per order without fetch orders and 2.22 with them.The smaller model retains a positive ordering gain; outside task-graph closure, usage is zero and the scheduler cannot matter.Source: §E.10 · pp. 31–32, Table E.10 · p. 32, Table E.11 · p. 32

E.11 Horizon

  • 6.2 pp is the gap at the 500-step prefix, compared with 10.0 pp on the five-seed full horizon.The paper reports that maintenance compounds as fresh items continue paying on later uses.Source: §E.11 · p. 32, Table E.12 · p. 33

E.12 Freshness Decouples from Performance

  • ERRAND wins ITT while stale-use share is 12.2±1.0%, versus 3.4±1.3% for the oracle filter and 21.9±1.0% for eager revalidation.The bigger unmaintained store has a 53.1±1.8% stale-use share; the paper distinguishes freshness from agent success.Source: §E.12 · p. 32, Table E.13 · p. 33, Table E.14 · p. 33

E.13 Overhead, Itemized

  • The scheduler costs milliseconds of arithmetic and makes no model call at any step.The spending baselines make more calls per step because unrepaired staleness converts into downstream retries.Source: §E.13 · p. 32, Table E.15 · p. 33

F Instrument Specifications

The appendix pins the instruments and run conditions, then traces paired cases where ERRAND succeeds through restraint and a free receipt while eager revalidation refreshes too early and fails.

F.1 The Briefing Item

  • Each briefing item stores one checkable atom with its handed-over value, belief, receipts, resolve-by date, and state; the live world may flip without notice.The example atom is required_fuse, initially recorded as short, with checking cost 3.Source: §F.1 · p. 34

F.2 The Work-Order Contract

  • Work orders specify only the task verb and target, with delivery fields for fetches; a whitelist blocks truth, freshness, belief, schedule, and maintenance hints.A truth-leak assertion runs at the start of every run.Source: §F.2 · p. 34

F.3 The Spend Ledger

  • The per-step ledger records errand costs, spend, wage, receipts, store size, and an explicit reason for each no-spend step.Reasons distinguish chosen restraint from budget exhaustion, no candidate, or an in-flight errand.Source: §F.3 · pp. 34–35

F.4 The Stratified Accounting Audit

  • The stratified audit checks billing, path passability, and encounter denominators separately because defects can concentrate in treated, off-path traffic.Companion ledgers track conditional estimates and per-edge flip interception.Source: §F.4 · p. 35

F.5 Baseline Instruments, Operationally

  • The baseline suite includes a zero-cost oracle filter, a true-drift-rate reference, cadence and equal-spend random checks, and mechanism and allocator variants.The allocator variants replace ERRAND's index with a Whittle rule or myopic value-rate ratio.Source: §F.5 · p. 35

F Instrument Specifications; F.6 Environment Card

  • Runs use a frozen Qwen3-8B agent in a 2,000-step drifting world; path locking can intercept nominal flips, so drift is accounted at its effective rate.Runs are compared only under matching instrument, dispatch, drift, and seed fingerprints; the case-study figure records a free receipt and the spend ledger.Source: F Instrument Specifications · p. 34, §F.6 · pp. 35–36, Figure G.1 · p. 37

G.1 Case 1: The Hold That Paid; G.2 Case 2: The Refresh That Didn’t

  • ERRAND holds until a neighboring errand supplies a free refresh before use; eager revalidation refreshes before the flip and serves a stale value that fails.The paired case was preregistered; ERRAND's receipt arrives at step 690 and its successful use at 722, while eager's refresh at 503 precedes the flip at 641 and its failed use at 720.Source: §G.1 · p. 37, G Case Studies · p. 37, §G.2 · p. 38

G.3 Case 3: The Inaction Ledger, Read Raw

The ledger separates spending, deliberate restraint, and forced inactivity, making ERRAND’s no-spend decisions auditable rather than opaque.

G.3 Case 3: The Inaction Ledger, Read Raw

  • In the 600–700 window, trailing spend ranged from 8 to 14 per hundred against a cap of 12, and every no-spend step carried a reason.The case reads a released ledger excerpt and attributes each unspent step.Source: §G.3 · p. 38
  • 9.5% of steps were spent over the full run against a 12% allowance, with fourteen free receipts; the wage, not the cap, set the pace.The wage remained between 0.026 and 0.047.Source: §G.3 · p. 38
  • Seven errands used one to two actions each, while 30 no-spend steps reflected priced restraint and eight reflected budget, candidate, or in-flight constraints.The 30 restraint steps comprised 17 index-at-or-below-zero decisions and 13 doubts priced below the wage; six steps hit the budget cap, one had no candidate, and one was in flight.Source: §G.3 · p. 38

H.2 Compute

The study reports its compute envelope and sampling design, including paired comparisons that control the world-side run conditions while acknowledging serving nondeterminism.

H.2 Compute

  • More than 260 instrumented GPU deployments ran for 2,000 steps each, with 1,700 scored, within roughly 900 GPU-hours across four waves.Coverage-grid simulations, value iteration, and power forecasting used CPU time; serving used frozen 8B and 4B models.Source: §H.2 · p. 40

H.3 Randomness and Seeds

  • Five seeds covered frontier main surfaces, while high-gap comparisons and simulation cells used larger preregistered cohorts; paired runs shared machine, seed, and cap.Paired contrasts use seed-level t intervals and seed-clustered bootstrap checks; fingerprints pin the world, but serving remains nondeterministic, so reruns reproduce cohort distributions rather than per-run numbers.Source: §H.3 · p. 40
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