The Network
That Learns to Invent

MONTREAL.AI RESEARCH EDITION / 27 OCTOBER 2026
AGI ALPHA FLYWHEEL
THE NETWORK
THAT LEARNS
TO INVENT
Profitable Work, Experience-Trained Specialists
and Shared Alpha
Vincent Boucher
President of MONTREAL.AI
An executable scientific relay, with its economic limits intact.
A thermal-design job leaves behind a numerical component. Bounded practice changes its
stored representation. Fresh diffusion and inverse-design missions reveal what transfers, what
ordinary methods already supply, and whether any additional advantage pays for itself.
TRANSFORMATIONAL INTELLIGENCE ∞
LEARNING TO CHANGE THE GAME
FIND YOUR ALPHA. BUILD YOUR SUCCESSOR Ω.
Evidence scope: locally executed numerical learning and research lifecycle replay; simulated enterprise opera-
tions; no customer sales or live authenticated deployment.

AGI ALPHA FL YWHEEL THE NETWORK THA T LEARNS TO INVENT
Abstract
An engineering team needs a reusable temperature-response calculation; a second team needs
fresh diffusion responses; a third needs informative sensors for a finite inverse problem. We connect
these useful computational objectives through an inspectable numerical component, then test
whether its benefits survive ordinary technical alternatives and complete incremental costs. A
researcher-constructed learning system retains an orthonormal basis from twelve founder solves
and enriches it through thirty-two residual-directed Gym actions. Four candidates are preserved,
one version is frozen, and unseen cases compare the original component, its developed successor
and competent numerical baselines. Fresh confirmation comprises 128 paired in-domain cases,
64 shifted cases and 32 inverse-design missions per composition arm. The resulting component
reduces mean raw relative field error 26.3-fold on the fresh transfer distribution; this is a measured
representation change, not autonomous algorithm invention. Exact correction, assessment, setup
and serving remain separately accounted for. All corrected forward methods satisfy the declared
numerical requirements. Distribution shift increases the learned solver’s correction cost, while the
sensor-design gain is also available to the equally funded competent generalist.
A matched, finite-cash enterprise experiment uses sourced service-rate anchors and explicit
assumptions about frontier execution, demand, quality and collections. The reference Beta-only
policy produces mean modeled operating profit of $191,886 over 104 weeks; no cash revenue was
earned by this study. Optional retention decisions reject the numerical candidates at the declared
service scale. The contribution is an executable separation of learning, useful transfer, composi-
tion and commercial value, including negative evidence and an existing production admission
boundary. It does not establish specialist superintelligence, graph superiority, profitable sharing or
self-acceleration.
The evidence in one sentence
Experience changed a reusable numerical representation and improved its fresh approximation;
complete-cost admission rejected the reference retention program. Complementary experimental
design helped, but did not establish a unique network advantage.
1 Begin with the useful work
The immediate work product is a small scientific-software package that computes and checks responses
of a heterogeneous diffusion model. Its founder mission represents a thermal-design service: provide
reproducible response fields and a numerical envelope over specified material and source variations. A
recipient then needs responses across a wider diffusion–reaction regime, and an experimental-design
mission needs sensor locations that identify unknown coefficients from noisy observations. The
deliverables are executable computations with finite, published acceptance rules. They are not verified
physical products, customer engagements or human-expert trials.
This choice makes learned capability tangible. A saved numerical matrix contains information extracted
from solved cases. Loading the matrix changes the recipient’s calculation, even though the recipient
never observes the original training solutions. A second procedure chooses informative sensor locations.
These objects can be independently hashed, transferred, executed, rejected and retired. Their practical
value is measurable without assigning an agent a specialist label.
The research question is whether such experience can produce an advantage beyond competent
ordinary tools, and whether that advantage justifies the additional resources required to develop and
share it. The commercial foundation remains a separate question: can expertly operated frontier AI
produce accepted digital outcomes at a cost below a price referenced to equivalent human services?
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A negative answer about this particular retention program does not refute profitable Beta delivery.
Conversely, attractive modeled delivery margins do not establish that learning, a graph or an agent
network adds value.
Three distinctions organize the paper. First, a technical result is not a customer outcome. The compu-
tation is executed; model-operated engineering and market transactions are simulated. Second, an
accuracy improvement is not automatically an improvement in accepted throughput: a competent
solver may already meet the requirement cheaply. Third, an accessible capability is not necessarily
a capability that every recipient independently possesses. Executable transfer, trained-component
transfer and specialist-service access preserve different things.
1.1 A focused portfolio with intact purposes
Offering Beneficiary and complete computa-
tional deliverable
Obstacle, acceptance and recurrence
Thermal response
engine
Engineering R&D team comparing
proposed material/source configura-
tions; runnable solver, fields, enve-
lope receipt and verification.
Heterogeneous coefficients and repeated
solves. Preserve the stated operator, bound-
ary and forcing. Repeat demand is related
design revisions, assumed commercially.
Diffusion re-
sponse service
Scientific-software team evaluating
a broader diffusion–reaction model;
fresh response fields and checks.
New coefficient/source ranges. Meet the
same final residual and field-error tolerances.
No right to discard hard cases or replace the
target model.
Inverse experi-
ment design
Experimental team selecting a finite
sensor plan; selected locations, obser-
vations, inferred coefficient pair and
uncertainty conditions.
Limited sensors, noise and non-identifiability.
Recover the correct member of a published
sixteen-element coefficient grid; retain failed
reconstructions.
Table 1: Research offering scopes. Human-team scope equivalence and recurring demand are assumptions. The
numerical artifacts and their stated finite tests are executed.
The work has a transformational aspect when it changes the representation or the experiment: reuse a
low-dimensional response space instead of repeatedly starting from an uninformative state, or choose
a measurement that resolves uncertainty instead of collecting more uninformative data. These are
established scientific methods. The novelty claimed here is their joined, reproducible learning–transfer–
composition experiment and its accounting, not the invention of reduced-basis methods or optimal
design.
The finite discretization is deliberately reproducible on an ordinary CPU. It is much smaller than
many industrial simulations. A positive result cannot be extrapolated to industrial geometry, physical
fidelity or expert service quality without another evaluation. This limitation makes the empirical claim
narrower; it does not turn the result into an assumed financial uplift.
2 The actual system and its boundaries
The implementation baseline is the repository commit 80b345828f34fd8a6e592977dd17ef37141305f4 .
Coordination was refreshed through issue #4850, including general-execution owner #4960 at
2163c2e12c1a7385241aca9bf813815b40c6e82c and the active specialist-network lane. This research is
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additive under studies/agi-alpha-invention-network-v1/ . It does not replace a registry, executor,
publisher or existing study.
The protected production capsule on the frozen main branch supports a bounded public-source-
selection scope. A generic diffusion component cannot truthfully be inserted into that scope. Its
production admission therefore remains NOT QUALIFIED. The general-execution draft is evidence of
ongoing engineering, not evidence that arbitrary specialist capsules, model accounts or authenticated
peer trials are already qualified.
For the research replay, eleven unchanged files from the existingbeyond-beta-network-v1 lifecycle at
commit 2727262caa52766a78916f2ed81f5afaf668edce are reused with recorded Git-blob and SHA-
256 identities. The actual native Journal, TrustRegistry and CostLedger are imported from the frozen
main implementation. The research adapter distinguishes simulated mission authority from execution,
retains rights and version bindings, and keeps real research costs unknown where no invoice or
metering record exists. Signing a fixture does not authenticate an ENS owner on mainnet.
The supplied Transformational Intelligence, Validated Skills Graph, Proof Loops, Gym and Successor
Ω materials establish the intended progression: useful work, retained evidence, bounded development
and fresh outcome checks. Their architectural proposals are not counted as executed performance.
The source audit records the reviewed originals, exact identities and applicable interfaces. A valid
provenance chain establishes which object was used; it does not establish that the object is useful.
2.1 Why earlier negative retention results matter
Earlier research editions provide distinct counterexamples. The Profitable Work First study reported
attractive conditional Beta economics in its reference world while retaining no optional capability in
its primary campaigns. A separately frozen diagnostic improved one network policy slightly but still
underperformed Beta after complete cost. Other editions recorded assets that were reused without
repaying their own incremental costs. The audit preserves their source links and distinguishes reported
results from new replications.
Those failures suggest three bottlenecks: screening can cost money without creating an admissible
asset; expected reuse can be too small or mismatched to the admission belief; and a capability can
improve a task without saving enough of the enterprise’s scarce resource. The present experiment
does not repair those findings by assigning guaranteed gains or lowering costs until a win appears.
It constructs a real changed artifact, compares against a strong technical baseline, and asks which
bottleneck remains.
3 The inspectable relay
3.1 Agent A: the founder mission
The founder solves twelve thermal cases. Each case specifies diffusion coefficients, a localized hetero-
geneous component, a reaction term and a spatial source. The complete response fields are retained as
an orthonormal basis using two-pass orthogonal enrichment. The initial artifact, v1, contains twelve
basis vectors. The modeled founder offering includes a reusable numerical engine, so its solves, checks
and basis construction are allocated to A once. The executed founder receipt independently checks
the twelve fields and their envelope; it is not customer acceptance of the retained basis. Additional
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A / USEFUL WORK
12 thermal solves
Rank-12 checkpoint
BOUNDED GYM
32 enrich actions
Four candidates
B / FRESH TRANSFER
64 new response cases
Frozen v1 vs v2
C / COMPOSITION
32 inverse missions
Equal tools + budgets
Artifact identity  •  fresh outcomes  •  failed candidates  •  A / B / C costs
EXECUTED
Numerical learning +
existing research lifecycle
NOT QUALIFIED AS LIVE OPERATION
Scientific production capsule / ENS / sales
Competent ordinary solvers and experimental design remain available to every comparator.
Figure 1: The executed relay and its authority boundary. Founder computations create v1; bounded experience
updates a numerical basis to v2; protected fresh work evaluates transfer and composition. Local research artifact
use is separate from production capsule admission, which remains unsupported for this scientific scope.
packaging and subsequent lifecycle costs remain separate. No customer paid for the research proxy.
“Agent A” names a scripted research role. The surrounding algorithm, task generators and acceptance
rules were constructed by the AI-assisted research team. No frontier model independently invented
the basis algorithm during a purchased customer job. Nevertheless, the basis entries are determined by
executed solutions, rather than written as a desired performance score. This is identifiable numerical
learning.
3.2 Gym: change a representation through bounded experience
The Gym exposes observations, allowed actions, transitions, budgets and termination. Its state includes
the current basis, available training cases and remaining enrichment actions. An observation evaluates
residuals for a declared pool of seventy-two practice cases. An action selects an available practice
case, solves it, orthogonalizes the new field and records the resulting artifact. The controller selects
the largest residual, subject to a cap of thirty-two enrichment actions. A case cannot be selected after
removal; an exhausted budget terminates the campaign.
Four candidate checkpoints at ranks 20, 28, 36 and 44 are assessed on development cases. The frozen
selection rule prioritizes final accepted count, raw accepted count, then mean raw field error, with rank
as a tie-breaker. It therefore selects for numerical fidelity, not secretly for final enterprise profit. All
candidates, observations, assessment work and the original development attempt remain available.
The initial six-sensor inverse task reached a development ceiling; a two-sensor, higher-noise challenge
was specified before confirmation, with the original control retained.
The update changes a stored numerical representation. It does not modify proprietary model weights,
learn a general skill-selection policy or demonstrate that an agent learned how to learn. Sensor selection
is an executable procedure applied to current mission fields. Keeping these mechanisms separate
prevents a larger basis, a higher practice score or more inference from being mislabeled as a general
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intelligence improvement.
3.3 Agent B: use the component on unfamiliar work
Fresh diffusion–reaction cases broaden coefficient and source ranges. The recipient loads the exact
frozen artifact and computes a reduced initial solution. A residual-corrected solver then returns a
response meeting the same final acceptance criteria as the ordinary methods. The raw approximation is
also evaluated separately. Thus the experiment can detect learning even when a correction step makes
the final outputs equally accurate.
The transfer domain shares a discretization and operator family with the founder but changes the
parameter distribution and job context. It is a meaningful related-domain test, not evidence of
unrestricted transfer across physics or software ecosystems. The artifact requires compatible grid
indexing, operator parts, units and numerical libraries. Out-of-distribution cases deliberately increase
anisotropy, local contrast and source concentration; their failures and overhead remain in the results.
3.4 Agent C: compose numerical and experimental expertise
The composition mission evaluates sixteen possible coefficient pairs. A sensor-design procedure derives
low-dimensional response features and greedily selects locations using an information-gain criterion.
No hidden true coefficient is available to the design procedure. Observations are generated from a
held-out true grid member plus the declared noise; reconstruction minimizes the finite observation
mismatch.
The comparison includes the numerical component alone with fixed sensors, the design procedure
alone with the ordinary forward solver, and their combination. The primary competent generalist
receives the same design method and ordinary tools. Fixed sensors are an ablation, not the generalist
ceiling. Every arm receives the same candidate grid, sensor count and noise realization. Measured
forward, design and reconstruction costs are attributed to each arm even when measurement reuse
avoids physically rerunning identical code in the experiment. Unmetered research orchestration and
authoring remain unknown; additional enterprise coordination costs are modeled explicitly.
This design can reveal complementarity without assuming a network advantage. If informative sensors
improve reconstruction but the competent generalist can use the same procedure at equal resources,
the result supports experimental design and does not establish retained Alpha.
4 Numerical method, acceptance and protection
4.1 The discrete system and the learned object
For parameter vector θ, the finite-difference model is
A(θ)u = b, A(θ) = kx Ax + ky Ay + cA c + ρAr, (1)
on a square with homogeneous Dirichlet boundary conditions. The grid has44 × 44 = 1, 936 unknowns.
Positive diffusion coefficients, a nonnegative local contrast and a nonnegative reaction coefficient make
the operator symmetric positive definite. The public generators define the exact distributions. They are
assumptions about a computational workload, not empirical industrial demand.
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For an orthonormal basis V, the reduced approximation is
bu = V

VT A(θ)V

−1
VTb. (2)
The projected affine operators are built explicitly. The stored basis preserves learned numerical
information; a prose explanation of the method would not reproduce its entries. The construction
is a greedy reduced-basis method, not a claim that an arbitrary neural checkpoint has been trained.
Established reduced-basis and POD work supplies the methodological context; the sensor procedure
uses an SVD of current response fields.[1–4]
4.2 Acceptance includes an independent numerical check
Ordinary baselines include sparse LU, incomplete-LU-preconditioned GMRES and a separable spectral
preconditioner with conjugate gradients. Incomplete LU is used with GMRES, not assumed to be
an SPD preconditioner for CG. The primary ordinary solver is selected on development runtime
and frozen. Valid factorization reuse is allowed whenever matrices repeat. An explicitly declared
improved-generalist numerical policy tests a stronger ordinary choice on the shifted regime; this is not
a newly measured API-model release.[5, 6]
Final residuals are recomputed by a flux stencil separate from the sparse assembly. A direct solve
supplies a research reference for field-error assessment. The final tolerances are relative residual
2 × 10−8 and relative field error 2 × 10−6. Raw-surrogate tolerances are separately declared and are
not substituted for the final requirement.
There is also a computable discrete error bound. Let r = b − Abu and let α be a valid lower bound
on λmin(A). Positive semidefiniteness of the local-contrast part permits a lower bound from the two
directional Laplacians and the minimum reaction term. Then
∥u −bu∥2 ≤ ∥r∥2
α =: E, ∥u −bu∥2
∥u∥2
≤ E
∥bu∥2 − E when ∥bu∥2 > E. (3)
The second relation follows from the reverse triangle inequality. Without a valid stability bound a
small residual alone is not a general field-error guarantee. Neither this bound nor the direct reference
measures discretization error, real material properties or physical model mismatch.[7]
4.3 Protection and uncertainty
Training, development and fresh confirmation use distinct case seeds. Candidate bytes and source
identities are frozen before root-supplied confirmation seeds are evaluated. No post-confirmation
candidate tuning is admitted into the primary comparison. The shared research team and public
generators do not constitute an external, adversarial evaluation service; the protection is procedural
and source-auditable. Public release intentionally makes the cases reproducible after the experiment.
Paired cases receive identical equations, reference answers and mission noise. Numerical methods run
with one BLAS thread, warmups and rotating execution order. Wall-clock differences at millisecond
scale remain vulnerable to host noise; per-case rows and paired uncertainty are reported alongside
iteration counts and error. Timing savings are not generalized to another machine by a clock-rate
multiplier.
The reported 95% timing intervals are percentile intervals from 5,000 bootstrap resamples of paired
cases (seed 81221) within one local run. They do not measure reproducibility across machines or
independent sessions, and resampling does not remove host drift shared by several case pairs.
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20 30 40
Basis rank after enrichment
10−1
Selected practice residual
Experience signal
20 30 40
Candidate rank
10−3
6 × 10−4
2 × 10−3
3 × 10−3
4 × 10−3
Mean raw relative error
Development selection
Thermal Transfer Shift
10−4
10−3
10−2
10−1
Mean raw relative error
Protected fresh work
Paid-work v1
Gym v2
Figure 2: Numerical development and fresh performance. Candidate development results are retained; fresh
v1/v2 comparisons use frozen artifacts. Practice residuals and fresh field errors answer different questions and
are not plotted as a single interchangeable score.
Confirmation estimates finite-distribution performance, not the probability that the assumed workload
resembles a real customer portfolio. Repeating seeds reduces Monte Carlo uncertainty conditional
on the generator. It cannot remove uncertainty about the generator, the scope of a human service or
market demand.
5 What changed, what transferred, and what did not
The frozen Gym candidate has rank 44, compared with rank 12 for v1. On the 64 fresh transfer cases,
mean raw relative field error falls from 0.02869 to 0.00109, a 26.3-fold reduction. However, neither raw
component meets the separately declared raw acceptance rule on any of those 64 cases. The corrected
methods all pass. Accuracy learning is therefore established within this workload; a standalone
approximation meeting the recipient’s requirement is not. On the 64 fresh thermal cases, v2 passes the
raw rule on 9 cases.
The meaningful learned change is the basis itself. It supplies a better initial representation of previously
unseen response fields. This does not imply a proportional reduction in completed-job cost. The
recipient’s competent baseline can solve the original finite system, and the corrected learned method
still pays for projection, a linear solve, residual checks and any remaining iterations.
Method Cases Accepted Time (ms) Iterations Raw error
Sparse LU 64 64 4.075 0.00 –
ILU-GMRES 64 64 16.357 42.20 –
Expert baseline 64 64 2.106 15.08 –
Improved ordinary 64 64 2.037 15.08 –
Paid-work v1 64 64 2.121 13.95 0.02869
Gym v2 64 64 1.981 12.19 0.00109
Table 2: Fresh numerical confirmation. Runtime includes assembly, per-case setup, solve and verification.
One-time artifact construction and independent assessment are reported separately. A learned checkpoint’s raw
error is distinct from its corrected accepted output.
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0 5 10 15
Mean verified forward execution (ms)
Sparse LU
ILU-GMRES
Expert baseline
Improved ordinary
Paid-work v1
Gym v2
4.08
16.36
2.11
2.04
2.12
1.98
Fresh recipient mission
0 2 4 6 8 10
Mean verified forward execution (ms)
Sparse LU
ILU-GMRES
Expert baseline
Improved ordinary
Paid-work v1
Gym v2
4.31
9.17
6.31
4.51
6.69
6.70
Deliberate distribution shift
Figure 3: Paired transfer and distribution shift. Ordinary numerical baselines remain available to recipients. A
lower raw error can coexist with no runtime gain, and distribution shift can impose negative transfer. All failed
cases remain in the denominator.
On fresh transfer, the observed mean saving of v2 against the frozen ordinary baseline is 0.125 ms per
solve (paired bootstrap 95% interval 0.052 to 0.199 ms). Against the improved ordinary implementation
it is 0.056 ms (interval -0.007 to 0.125 ms). The improved policy uses the same numerical algorithm in-
domain, so this difference also exposes local timing noise. On shifted cases, v2 takes 6.702 ms, compared
with 6.306 ms for spectral-PCG and 4.508 ms for the improved ordinary router. No shifted raw learned
output passes the raw acceptance rule. The negative transfer remains part of the conclusion.
5.1 Composition and the equally funded generalist
2 sensors, 5% noise 6 sensors, 1.8% noise
Method Correct/total Time (ms) Correct/total Time (ms)
Fixed sensors 7/16 43.13 16/16 38.91
Solver only 7/16 38.04 16/16 38.14
Competent generalist 10/16 44.15 16/16 40.16
v1 + design 10/16 40.56 16/16 42.40
v2 + design 10/16 39.00 16/16 39.39
Table 3: Inverse-design composition, with identical candidates, observations and sensor budgets. The competent
generalist includes the design procedure. Fixed-sensor arms are ablations. Success concerns the finite numerical
identification task only.
With two sensors and 5% peak-field noise, fixed sensors recover 7/16 coefficient pairs. Both the
competent generalist and the v2 combination recover 10/16. With six sensors and 1.8% noise, every
arm recovers 16/16. The observations support the value of selecting informative measurements in
the harder finite task, but the composition does not improve identification over the equally resourced
generalist. The sixteen-case challenge is too small to support a broad reliability claim. Combination
runtime is reported without converting it into an assumed price or scientific discovery.
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0 4 8 12 16
Correct finite identifications (out of 16)
Fixed sensors
Solver only
Competent generalist
v1 + design
v2 + design
7/16 43.1 ms
7/16 38.0 ms
10/16 44.1 ms
10/16 40.6 ms
10/16 39.0 ms
2 sensors / 5% noise
0 4 8 12 16
Correct finite identifications (out of 16)
Fixed sensors
Solver only
Competent generalist
v1 + design
v2 + design
16/16 38.9 ms
16/16 38.1 ms
16/16 40.2 ms
16/16 42.4 ms
16/16 39.4 ms
6 sensors / 1.8% noise
Figure 4: Component ablations and composition. Accuracy is measured on protected inverse cases and shown
with measured task execution cost. Any gain shared by the equally funded generalist is ordinary available
capability, not exclusive network Alpha.
5.2 The productive frontier at fixed resources
Define the finite empirical productive set at budget B and required acceptance q as
F (B, q) = {j : Pr(accepted outcome for j) ≥ q, E[Cj] ≤ B}. (4)
The operational definition must fix the beneficiary, original requirements, workload distribution and
accounting boundary. A faster approximation that abandons accuracy does not enlarge this set. A
composition expands the frontier only if it crosses a required reliability or cost boundary that the
equally resourced generalist cannot already cross.
The descriptive time-frontier curves show local differences in verified execution latency. They do not
show a new reliable offering beyond the competent generalist: all corrected forward methods meet the
numerical requirement, and the composition ties generalist identification. No prospectively specified
service-level deadline was crossed uniquely by the learned network. The enterprise model therefore
assigns no automatic new-product revenue or quality premium to these objects.
6 From numerical value to enterprise value
6.1 Frontier intelligence is Beta, with verified public specifications
The reference commercial workflow assumes competent use of frontier reasoning, coding, tools,
validation and correction. It does not model a one-shot no-tool prompt as the ceiling. Public API
documentation checked on 27 October 2026 lists gpt-6-astra , gpt-6.1-sol and gpt-6.1-terra . Their
Standard short-context input/output tariffs are respectively $10/$50, $2/$10 and $1/$5 per million
tokens. The published roles can be replaced by better verified successors; the model names are not
restrictions on future design.[8–10]
The source register records context/output limits, documented reasoning efforts, tool support and
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1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Forward time allowance (ms)
0.0
0.2
0.4
0.6
0.8
1.0Fraction of all cases accepted in time
Fresh transfer / 64 cases
Expert baseline
Improved ordinary
Paid-work v1
Gym v2
30 40 50 60 70
Mission time allowance (ms)
0.0
0.2
0.4
0.6
0.8
1.0Fraction of all cases accepted in time
Two-sensor challenge / 16 cases
Fixed sensors
Competent generalist
v2 + design
Figure 5: The observed finite resource frontier. The curves count accepted outcomes within a solver/mission
time allowance. They do not value a proposed venture, establish physical validation or assume additional
demand. The strongest ordinary comparator is included.
advertised rate tiers. Those specifications establish neither account entitlement nor available quota. No
API call or account-funded experiment was executed. ChatGPT Pro is not an API model or evidence of
API access.[11] All dollar-valued model consumption is an explicit token-budget assumption using
the sourced tariffs. Fine-tuning is not assumed; the portable trained object in this experiment is a
numerical component.
6.2 The human-service reference and the pricing decision
SDSU lists an external scientific-computing service rate of $80/hour; Vanderbilt research software
engineering starts at $84/hour; UTEP lists an external analyst rate of $190.31/hour for services
including study design. These are service-rate anchors, not quotes for our artifacts.[12–14]
The central scope estimate uses 72, 96 and 120 hours at $84/hour for the three offerings: $6,048,
$8,064 and $10,080. The effort includes formulation, implementation, independent numerical checks,
correction, documentation and delivery. Every effort estimate remains an assumption; rates for more
complex specialist work can differ. Demand and price acceptance are modeled separately.
A frozen finite grid compares price fractions 0.30, 0.45, 0.60, 0.75, 0.90 and 1.05 of the human-service
reference. Development simulations select 75% under the declared reference belief. This is a conditional
grid optimum for the stated objective, not a global optimum or an observed willingness to pay. The
same selected prices apply across matched policies. The comparison therefore does not give shared
specialists easier customers or a hidden price increase.
6.3 Disjoint costs and cash
The model distinguishes three expense categories:
A: delivery. Frontier use, tools, computation, acceptance, corrections, base delivery overhead and the
common startup capacity needed to supply the outcomes. Learning required to finish the paid job
belongs here once.
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Input Declared reference assumption
Seed / common startup $20,000; 96 engineering hours at $84, totaling $8,064
Base resources / overhead 40 agent-hours per week; $100 per week
Model-use bundles (thermal / transfer / in-
verse)
$66 / $96 / $138; itemized assumed token counts at
sourced tariffs
Integration / acceptance bundles $38/$22; $54/$32; $68/$48, respectively
Estimated human participation per attempt Operator 0.25 / 0.40 / 0.50 hours; reviewer 0.25 /
0.35 / 0.50 hours, included in those bundles
Optional retention / sharing / Gym $192 assessment and packaging; $42 sharing; $168
Gym development, plus recorded numerical work
Second specialist, if elected Additional $192 assessment/packaging and sepa-
rate serving cost
Screen / maintenance / invocation $2.40; $1/week; $0.002 per specialist invocation
Collections and reserves Assumed 3% + $0.30 fee; four-week warranty expo-
sure; eight-week base operating reserve
Table 4: Commercial assumptions that materially determine profit. These are neither observed invoices nor a
requirement that every automated service use human review. Human participation is an explicit conservative
service-design choice in this edition; sensitivities do not establish the real need or sufficiency of that choice.
B: additional retention. Candidate screening, extra assessment (including every rejected rank), pack-
aging, admission, sharing, serving and upkeep that are not already in A.
C: optional development. Additional Gym experience and discretionary development beyond the
paid deliverable. Candidate assessment belongs to B; extra Gym enrichment belongs to C. Capacity
expansion is separately identified.
Research labor and subscription/model use during this authoring session were not fully metered.
Actual complete research cost is therefore unknown, not zero. Commercial scenario costs are projected
operational expenses. They must not be described as invoices paid in this study.
For a simulated enterprise, cash obeys
Kt = K0 + collectionst − refundst −At − Bt − Ct. (5)
Cash-based operating surplus excludes seed capital. Outstanding obligations, receivables, operating
reserves and available funds are separately reported. Failed delivery, corrections, late collection, default
and refunds are retained. Capacity exclusions represent displaced work; they are not also charged as
fictional cash expenditures. There is no token issuance, staking yield or proposed venture valuation in
operating revenue.
The model’s nano-dollar accounting preserves numerical computation and small serving costs instead
of rounding them out of existence. Native CostLedger replay checks a complete selected synthetic
history and, separately, preserves unknown actual-research costs. The full ensemble is reconciled by
the study’s transaction audit; it is not misrepresented as thousands of native production deployments.
7 Matched enterprise experiments
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7.1 Five choices, equal starting conditions
The policies are: competent generalists without retention; private retention; private retention with
optional Gym; selective sharing; and sharing with optional Gym and composition. They begin with the
same seed, opportunity streams, quality shocks, price menu and resource limits. Candidate admission
uses development evidence and declared demand beliefs. The policy cannot inspect future demand,
future true quality or its exact date of obsolescence.
No policy is forced to buy training or retain an asset. The primary screen first asks whether even
free elimination of all numerical computation could repay minimum retention cost; if that optimistic
bound fails, the controller declines without consulting an unpurchased Gym result. When forecast
incremental value is negative, declining is the correct policy outcome. Composition uses an equally
funded generalist with ordinary access to the experimental-design procedure. Because no graph-
specific advantage is claimed, an ordinary library with the same authorized bytes and permissions is
an equality control, not a deliberately impoverished search baseline.
The horizon is 104 operating weeks plus collection runoff. Three primary environments vary oppor-
tunity arrival, trust, willingness to pay, quality, model cost, default and successor timing. A stronger
frontier scenario changes base execution cost and quality for every policy, while an independent
numerical comparison tests a stronger ordinary solver. The former is simulated; the latter is executed.
The assumptions and all sampled histories are included.
First, resources remain fixed. A separate high-demand experiment allows expansion only after available
earned funds exceed the capital and reserve conditions and forecast capacity value exceeds expansion
cost. Extra output from purchased capacity is labeled expansion. It is not counted as evidence that
retained intelligence compounded.
7.2 Results and uncertainty
Beta-only result Adverse Reference Favorable
Collections (USD) 9,934 228,078 759,583
Refunds (USD) 469 3,175 6,282
Complete costs (USD) 19,639 33,016 62,595
Operating profit (USD) -10,174 191,886 690,706
Useful outcomes 1.86 40.42 132.52
Cost/useful outcome (USD) 10,530 817 472
Closing cash (USD) 9,826 211,886 710,706
Outstanding obligations (USD) 0 0 0
Uncollected receivables (USD) 0 0 0
Reserved cash (USD) 800 800 800
Available cash (USD) 9,026 211,086 709,906
Available earned funds (USD) 327 191,086 689,906
Table 5: Conditional enterprise results, mean over 200 matched worlds per primary environment. All monetary
results are simulated USD; the study earned no customer revenue. Closing balances follow the collection-runoff
period. Available cash includes remaining seed funds; available earned funds excludes seed capital and is
floored at zero separately in each world. Percentile variation describes the chosen model, not uncertainty about
its real-world validity.
Mean Beta-only modeled profit is $-10,174, $191,886 and $690,706 across the adverse, reference and
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adverse reference favorable
0
100
200
300
400
500
600
700Mean modeled operating profit ($000)
$-10.2k
$191.9k
$690.7k
Commercial foundation / 104 weeks
−4 −3 −2 −1 0
Mean incremental profit vs matched Beta (USD)
Private
Private + Gym
Shared
Shared + Gym
 $-2.40
 $-2.40
 $-2.40
 $-2.40
Optional retention / reference
Figure 6: Commercial foundation and incremental retention. Beta profit is conditional on the declared market
and delivery assumptions. Incremental Alpha is assessed against matched Beta after all additional costs. A
profitable reference enterprise is compatible with rejecting optional retention.
favorable environments. The reference enterprise supplies 40.42 useful outcomes on average at a
pooled complete cost of $817 each. Its false-pass share among accepted outcomes is 1.52%, which
remains a modeled quality risk. The shared/Gym policy’s paired mean increment is $-2.40. No primary
policy retains or trains a capability after its optional economic assessment. Differences from Beta arise
from screening, rather than from claimed profitable peer reuse.
The compulsory-retention diagnostic is deliberately separate from the selectable main policies. It asks
what happens when the numerical artifact is retained despite its economic assessment. It includes
extra assessment, packaging, serving, maintenance and any elected development. It cannot be used to
infer the outcome of a rational policy that would decline the purchase.
In the forced-retention diagnostic, the shared/Gym/composition policy changes mean profit by $-
641.71 relative to its matched Beta. The diagnostic does not rescue the optional program. Additional
conditions stress congestion, correlated errors, late collections, low value, absent demand and rapid
baseline improvement. The separate surplus-financed expansion condition changes purchased capacity;
its output is reported separately and is not attributed to learned intelligence. In the congestion and
surplus-expansion diagnostics, the optional policies show about USD61.18 mean advantage (Monte
Carlo standard error USD111.01), despite zero retention, training or technical use. The small screening
expense changes later cash-admission and order-mix outcomes; it does not debit a training or screening
time budget and is not Alpha.
The resulting dollar levels are not forecasts. Unmeasured quality, customer trust and service equiva-
lence dominate uncertainty. A simulation can identify consequences of those assumptions and expose
accounting errors; it cannot validate the assumptions by generating more seeds.
8 The admission boundary is an economic inequality
Let ∆t be the validated time saving per eligible use against the competent recipient; pc the applicable
compute price per second; f additional serving cost; N eligible uses before retirement; and F all
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101 103 105 107 109
Eligible fresh uses before obsolescence
101
103
105
107
109
Required compute valuation ($/hour)
Retain only when extra value repays extra cost
Zero incremental serving fee
$0.002 per invocation
$3.52/hour institutional equipment proxy
Figure 7: When retention could repay its additional cost. This algebraic boundary uses measured timing at the
tested scale and explicit cost assumptions. Regions requiring a different compute valuation or workload are
sensitivity scenarios, not demonstrated industrial speedups.
additional assessment, retention, failed-candidate and Gym costs. With maintenance M,
∆V = N

pc∆t − f


− F − M. (6)
This is a restricted decision model: it values measured runtime only. There is no assigned quality
premium, avoided human project or extra demand merely because an artifact exists. If reliable new
quality were measured, its customer value would require a separately supported term.
Two necessary conditions follow. First, ifpc∆t ≤ f , more reuse cannot repay a positive fixed investment.
Second, if the per-use margin is positive, then N > (F + M)/(pc∆t − f ) is required. A large number
of agents does not change either condition. It helps only insofar as it creates eligible, authorized and
valuable uses after coordination, maintenance and congestion.
At the declared $3.52/hour equipment proxy, the observed transfer time saving is worth approximately
$0.000000122 per solve. An assumed $0.002 invocation cost already exceeds that gross benefit, before
extra assessment or training. Even with zero serving fee and no maintenance, repaying $402 of
assessment, packaging, sharing and additional Gym development would require approximately 3.28
billion eligible uses at the same measured saving. With the invocation fee, the compute valuation
would first need to exceed about $57,512/hour before any positive fixed-cost repayment is possible.
These are algebraic thresholds, not claims that the measured solver advantage survives at a different
scale or price.
The $402 illustration is a lower bound: $168 assessment, $24 packaging, $42 sharing and $168 Gym
development. It excludes screening, initialization, numerical assessment, maintenance, serving and the
optional second specialist’s additional $192 assessment and packaging. The enterprise histories include
these additional costs when applicable; the illustration is not the full cost of the composite program.
This boundary explains why improving a component can be scientifically worthwhile while admitting
it commercially is premature. It also gives a practical next experiment: identify a workload whose
bottleneck the learned object actually removes, with enough related demand to repay measurement and
upkeep. Increasing a supposed asset value, erasing rejected searches or moving original development
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cost into someone else’s ledger would not answer that question.
9 Three transfer forms and their consequences
Form What this edition transfers or exer-
cises
What the evidence does not establish
Executable skill Reduced solver, residual check and
sensor-design procedure; repro-
ducible local code.
Novel algorithm discovery, portable exe-
cution in every environment or superior
graph routing.
Trained component Exact numerical basis bytes, ver-
sions, dependencies and hashes; lo-
cal loading changes the response
approximation.
Neural fine-tuning, proprietary weights,
general intelligence or compatibility out-
side the declared discretization.
Specialist service Existing research authority/rights
and serving-cost interfaces exer-
cised with synthetic actors; posi-
tive transport control and revoca-
tion.
Provisioned protected endpoint, live
ENS authentication, actual external in-
vocation or possession of the specialist
by every caller.
Table 6: Availability, possession and performance are separate claims.
The empirical numerical candidates are evaluated with observed numerical resource costs and explicitly
estimated additional B/C scopes. Actual complete research expense remains unknown. If that assay
rejects admission, the study preserves the rejection. A separately labeled positive conformance fixture
tests byte-preserving transport and revocation with declared synthetic economics. Its recipient executes
the first saved transfer case again using the retrieved bytes. This is a later replay, not another fresh
trial. Fresh confirmation had used the frozen local artifact directly. The control is not evidence that
the empirical candidate earned its way into production or delivered fresh authenticated work after
admission.
The source-pinned lifecycle tracks rights, prerequisites, version, baseline, evidence expiry and protected
evaluation material. Eligible capabilities can be made visible to every authorized fixture member;
private rights restrict them to the owner. Revocation and baseline changes invalidate use under the
expected rules. The production boundary remains in force. Existing Jobs validators and settlement are
neither modified nor emulated as actual on-chain acceptance.
10 Interpretation: what has been established
Experience-based learning is a productive research direction. Silver and Sutton’s essay and Ineffable
Intelligence’s stated mission motivate investigating agents that learn through environmental interaction.
They do not imply affiliation, equivalent methods or reproduced outcomes here.[15, 16] FunSearch and
AlphaEvolve offer precedents for evaluator-guided executable improvement; their accomplishments
do not transfer to a new system by analogy.[17, 18]
This study’s strongest result is methodological and experimental: the learned object, fresh work,
ordinary alternative, transfer mechanism and economic boundary can all be inspected together. It
rejects the tempting inference that every improvement is automatically an asset. It also preserves the
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Claim level Finding and limit
Profitable Beta delivery Positive in some declared enterprise worlds, negative in adverse
conditions; entirely simulated commercial evidence.
Technical learning Executed change to a numerical representation, with fresh error
comparison and retained training history.
Useful peer transfer Exact component used on related fresh numerical work; local
research roles, without live network admission.
Positive retention or Gym net value Evaluated against complete additional costs; not established at
the reference service scale.
Positive network-sharing value Not established by transport conformance or accessibility.
Expanding productive advantage No claim of sustained expansion beyond the equally resourced
competent generalist.
Specialist ASI An ambition; no human-expert comparison or general superior-
ity established.
Table 7: The claim ladder prevents one successful step from standing in for the whole mechanism.
positive commercial hypothesis that expertly operated frontier models may supply useful services
profitably without such assets.
10.1 Limits that determine the next study
The workload is synthetic, low-dimensional in its parameters and restricted to a fixed grid and affine
operator family. It lacks human trials, customer purchases, physical validation and measured frontier
agent performance. The confirmation is protected procedurally within one AI-assisted research session,
rather than administered by an independent laboratory. Timing is local. The enterprise assumes task
quality and customer demand. The generic scientific component is outside the frozen production
capsule scope.
These limits identify concrete next tests. The first is a customer-relevant scientific-software task with a
costly repeated computational bottleneck and independently specified acceptance. The second is a
competent frontier generalist that may discover or construct the same ordinary method, with all model
and tool costs recorded. The third is an actual authorized service or component transfer with versioned
operating permissions and a fresh recipient. Only then should an expanding network be credited with
earned economic advantage.
11 Reproduction, authorship and publication
The companion contains the complete code, original and final development records, frozen candidates,
case manifests, confirmation outputs, all enterprise histories, source registers, native-interface identities,
tests, figures and an offline English/French demonstration. The README provides exact commands.
Frozen measurement outputs are not overwritten by a reproduction; new results receive a new directory.
Timings may differ, while numerical identities and tolerances are directly checkable.
The paper is attributed as requested to Vincent Boucher, President of MONTREAL.AI. AI assistance
was used extensively for research, implementation, literature retrieval, simulation, analysis, figures
and drafting. The numerical algorithms and environments were researcher constructed; the executed
training updates the numerical basis. No customer endorsement, independent institutional validation,
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proprietary model training or autonomous invention is represented as having occurred.
This edition follows the existing repository review and publication path. The current release lease,
protected checks and prior editions are preserved. A review artifact or source link is not a deployed
service. The companion records the final publication state and verified links without treating an
unmerged draft as a qualified live release.
Research decision. Preserve profitable useful delivery as the commercial foundation. Preserve
the learned numerical component as evidence. Admit additional capability only when fresh
useful performance and complete incremental value justify it. At the tested scale, a better
representation is real; a profitable shared specialist network remains unestablished.
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