Research by Maestro v0.1 · Program managed by Domingos S. P. Salazar
v1.0 · Updated 27 August 2026 · DOI 10.5281/zenodo.22127129
Programs
Quantum Thermodynamics · Quantum Information · Mathematical Physics
Cold-limit comparison for the golden-conjugate qutrit cooling channel, showing the theorem lower bound, the Fibonacci construction staircase, and exact rational and ground-state baselines.
Defining qutrit cooling channel0 < a < 1 · rank two · fixes every energy-diagonal state
Abstract
At low temperature, cooling maps and thermal operations have identical transition power for a two-level system. For qutrits, we introduce a rank-two cooling-map family Phi_a, where a mixes two coherent phase unitaries, and determine the minimum finite Gibbs-bath dimension required to implement it within diamond error epsilon. At cold-limit error 10^-12, the golden-conjugate parameter forces dimension at least 128000, whereas the rational parameter a=1/2 has an exact four-dimensional construction. We prove a dimension-temperature-error law: exact finite-bath equivalence fails at the first open dimension, although generic approximation survives.
Quantum-ThermodynamicsQuantum-InformationMathematical-PhysicsProof-ConstructionLiterature-AuditNumerical-ValidationIndependent-ReproductionDiophantine-ApproximationOpen-Quantum-Systems+10 more
Citation / Human + machine
How to cite this Research Object
DOI 10.5281/zenodo.22127129
Maestro v0.1 (2026). Minimum Bath Dimension for Qutrit Cooling Maps. Pudim AI Letter Research Object RO-2026-0004, v1.0. https://doi.org/10.5281/zenodo.22127129
For machines: prefer CSL JSON or CFF for structured ingestion, BibTeX for bibliography systems, and the BBL file only when a ready-to-paste LaTeX thebibliography block is required.
The work resolves the first open system dimension under a precise exact finite-bath convention and turns the exact-versus-approximate split into a quantitative law coupling bath Hilbert-space dimension, temperature, channel error, and mixing-probability arithmetic.
Limitations
The result resolves the exact finite-bath, ground-state-subspace formulation, not every approximate or infinite-bath interpretation of the 2015 low-temperature question.
Free external biased randomness removes the obstruction.
Continuous baths, non-Gibbs preparation, approximate energy conservation, degenerate system eigenspaces, an upper bath-energy bound, or state-specific rather than channel-level approximation may change the law.
The constants are valid but not claimed optimal, and the complete minimum-dimension staircase is not characterized outside the badly approximable class.
The displayed Fibonacci dimensions are costs of an explicit construction, not proofs of the globally minimal dimension.
The bath-dimension exclusion test is an ideal-model inference; no integrated hardware implementation is reported.
The bounded literature audit is a no-hit search, not proof of priority.
Claim registry
11 atomic claim
C1theoremestablished
The known equality between cooling-map and low-temperature thermal-operation state-transition power for a two-level system fails at the first open dimension under the exact finite-bath, ground-state-subspace convention: every irrational parameter in the displayed qutrit family gives a cooling-map transition that is not exactly reachable by that thermal class.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
The qutrit Hamiltonian has three distinct eigenvalues.
The finite bath is initialized maximally on its ground-state subspace.
Energy is conserved exactly and no free biased classical randomizer is supplied.
Falsification tests
Construct an allowed exact finite bath for an irrational member of the displayed family.
Identify an unaccounted system-energy lowering block compatible with the unchanged positive populations.
C2theoremestablished
For distinct nonzero qutrit Bohr frequencies, every qutrit cooling map lies in the diamond-norm closure of exact finite-bath thermal operations initialized on their ground-state subspaces.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
The nonzero qutrit Bohr frequencies are distinct.
The target is an arbitrary qutrit cooling map.
Falsification tests
Exhibit a generic qutrit cooling map whose correlation matrix cannot be approximated by rational phase mixtures.
Find an energy-sector obstruction to the shellwise unitary completion.
C3theoremestablished
Every D-dimensional finite Gibbs-bath implementation of the displayed qutrit channel obeys kappa_D(a)/D^2 <= exp(-beta Delta)/4 + (12+8 sqrt(2)) epsilon.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
Gibbs preparation and energy conservation are exact.
Every nonzero bath energy is at least Delta greater than the ground energy.
Epsilon is the unhalved diamond error.
Arbitrary bath degeneracies, resonances, excited energies, and population leakage are allowed.
Falsification tests
Find a valid bath and channel implementation violating the finite-dimensional arithmetic bound.
Break the leakage-to-unitary moment estimate or the projection-rigidity step.
C4theoremestablished
For each fixed badly approximable target and sufficiently small combined thermal-and-error scale, the minimum bath dimension lies between explicit positive target-dependent constants times the inverse square root of that scale.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
All assumptions of C3 hold.
The target has bounded continued-fraction coefficients.
Falsification tests
Produce a badly approximable target with sub-square-root minimum dimension within the stated model.
Show that the two-subspace constructions fail their gap or diamond-error conditions.
C5corollaryestablished
For every positive nu and Lebesgue-almost every target, the minimum dimension has an inverse-square-root lower law with the stated logarithmic loss for sufficiently small combined thermal-and-error scale.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
All assumptions of C3 hold.
The multiplicative constant and small-scale threshold may depend on the target.
Falsification tests
Identify an error in the application of the convergence half of Khintchine's theorem.
C6methodestablished
A rational target a=p/q has an exact two-energy-subspace implementation with total dimension 2q; explicit Fibonacci choices give approximation constructions for the golden-conjugate target, while a=1/2 has dimension four.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
Controlled phase unitaries are permitted.
There is no upper bound on bath energy.
Falsification tests
Show that the stated controlled phase unitary fails energy conservation in the declared bath sectors.
Show that tracing the Gibbs flag does not reproduce the claimed rational mixture.
C7lemmaestablished
Shellwise polar rounding and projection rigidity give a parameter-uniform linear bound on the difference between the bath projection expectation and the target mixing parameter despite population leakage.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
The three target tracial moments are within the stated tolerance in a finite bath-energy commutant.
Falsification tests
Construct a contraction triple obeying the moment hypotheses but violating the linear projection estimate.
C8interpretationestablished
On a joint finite-confidence event, the actual bath dimension and ground-state degeneracy obey the sharpened dimension-exclusion inequality in the Letter; a candidate dimension is excluded only when every allowed degeneracy fails it.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
The target was fixed before data inspection.
Diamond-radius and thermometry or spectroscopy bounds are conservative.
The exact finite-Gibbs-bath model is calibrated.
Falsification tests
Find a valid dimension-degeneracy pair incorrectly excluded on the stated confidence event.
C9theoremestablished
The rigid phase pair belongs to a one-parameter family, and the coefficient delivered by the proof is minimized when the absolute phase parameter equals one, where it is 12+8 sqrt(2).
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
Phase pairs lie on the displayed curve in the Supplemental Material.
Falsification tests
Find a phase parameter on the displayed curve with a smaller proof coefficient.
C10computational_resultestablished
At cold-limit errors 10^-4, 10^-8, and 10^-12, the theorem lower bounds are 13, 1280, and 128000, while the displayed golden Fibonacci construction dimensions are 288, 21892, and 2692538.
Noveltyknown
Reviewpassed
Reproductionpassed
Assumptions
The cold-limit theorem and deterministic continued-fraction enumeration are used.
Falsification tests
Recompute the displayed values from the theorem and Fibonacci construction and obtain different integers.
C11methodestablished
The exact two-subspace construction has the stated gap-calibration tolerance, while the equal-rank approximation construction is independent of temperature.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
Relative gap calibration is interpreted at fixed temperature.
Falsification tests
Derive a first-order flag-weight shift inconsistent with the stated calibration bound.
Show that the equal-rank projection expectation acquires temperature dependence.
The 2015 work proves the two-level equality and poses the higher-dimensional direction; the present result gives an exact qutrit separation under a specified finite-bath ground-state-subspace convention.
C2PASS
The closure statement combines qutrit correlation-matrix decomposition with shellwise thermal implementation; no direct prior closure theorem was found.
C3PASS
Prior finite-reservoir bounds control heat, work, accuracy, or other resources; no bound coupling coherent-channel diamond error to finite bath Hilbert-space dimension through Diophantine resistance was found.
C4PASS
The two-sided inverse-square-root bath-dimension law for badly approximable channel weights was not found in the inspected finite-reservoir literature.
C5PASS
The almost-everywhere lower law is a new application of classical metric Diophantine approximation to the channel-implementation bound.
C6PASS
The explicit Gibbs-flag synthesis is a construction for the displayed family; controlled mixtures are standard, but this finite-bath arithmetic realization was not found.
C7PASS
Polar rounding and finite tracial projection ideas are known ingredients; the leakage-robust linear estimate is claimed only in the paper's stated moment geometry.
C8PASS
The ideal-model dimension-exclusion inference is an application of C3, not model-independent bath tomography.
C9PASS
The open one-parameter rigidity curve and coefficient minimization belong to the proof developed here; broader rigidity outside that curve remains open.
C10PASS
The displayed integers are deterministic consequences of C3 and C6 and receive no independent novelty credit.
C11PASS
The local gap-calibration estimate and temperature-independent equal-rank branch are scoped stability properties of the explicit construction.
Maestro responseExact denominator searches, rational controls, and deterministic scripts are retained with the release.
Ledger decision
GO
The revised v016 package passes the correctness and evidence threshold at its explicitly bounded finite-bath scope; the dissent remains in the public dossier.
Independent Letter editor and Pudim AI Ledger integration
Independent Letter editor and Pudim AI Ledger integration
Decided At
2026-08-27T11:05:27Z
Rationale
The exact qutrit separation, generic diamond closure, robust finite-Gibbs- bath dimension law, and matching constructions passed the frozen proof, bounded literature, context-isolated review, computation, and build gates. The negative referee's concern is retained as a scope limitation rather than suppressed.
Pm Release Authorization
Authorized
Yes
Name
Domingos S. P. Salazar
Role
Program Manager
Authorized At
2026-08-27T11:27:36Z
Rationale
The Program Manager explicitly approved Pudim publication of the latest v016 package, including the stated finite-bath scope, bounded novelty language, RO-2026-0004 identifier, DOI transaction, and website release.
Accepted Claims
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
Evidence
v016 candidate SHA-256 044ea6db37f237df884167dc235844ca25baab10261bc211e25828341fe95c21; private manifest verified all 69 entries.
Context-isolated review panel concluded with editor ACCEPT at 0.92 confidence while retaining the dissenting scope assessment.
Foreground Program Manager instruction on 2026-08-27 authorized Pudim publishing of the latest version and separately withheld Story publication pending sanction.
Blocking Findings Disposition
The narrow ideal-model objection is retained in the public limitations and Scope paragraph; it is not a correctness blocker within the stated model.
The bounded literature assessment is retained as a no-hit search and makes no unconditional priority claim.
Formal machine verification remains pending and is not represented as a completed gate.
Conditions
Publish exactly the v016 scientific package bound to the accepted digest.
Preserve all limitations, the dissenting review summary, and the distinction between explicit construction dimension and globally minimal dimension.
A Correspondent Story is a separate derivative and requires its own exact Program Manager sanction before publication.
Reproduction
Independent verification
Independent proofPASS
ComputationPASS
FormalizationPENDING
OfflineNon-rootPASS
Tier 0
Regenerate the theorem arithmetic, constants, exact identities, and displayed dimension values.
Budget · 2 min
PASSTier 1
Regenerate the Fibonacci construction tables, bath-dimension staircase, and all scientific figures.
Budget · 5 min
PASSTier 2
Repeat the 60000-sample leakage-mechanism stress computation and compare its accepted numerical surfaces.
Budget · 20 min
PASS
Research history
Append-only · 12 events
01
SEED
Research direction seeded from the known two-level cooling-map result and its higher-dimensional question.
Actor · Domingos S. P. Salazar
02
PITCHED
The finite-bath qutrit separation and quantitative bath-dimension law were selected as the research pitch.
Actor · Maestro v0.1
paper/source/main.tex
03
FORAGED
The 2015 open direction and adjacent finite-reservoir and correlation-matrix literature were bounded and recorded.
Actor · Pudim literature workflow
paper/source/LITERATURE_AUDIT.md
04
PROGRAM BUILT
Scope was aligned with the Quantum Thermodynamics, Quantum Information, and Mathematical Physics Programs.
Actor · Domingos S. P. Salazar
05
CLAIMS PROPOSED
Eleven candidate-bound claims and their falsification surfaces were registered.
Actor · Maestro v0.1
claims/claims-v1.0.yaml
06
SOLVED
Exact separation, closure, dimension law, asymptotic classes, and constructions passed the proof audit.
Actor · Maestro Solver with breaker audit
07
NOVELTY LOCK
No direct collision was found, with known ingredients attributed and priority explicitly left bounded.
Actor · Bounded primary-literature audit
literature/literature-audit-v1.0.yaml
08
ADVERSARIAL REVIEW
Two referees and a blind tie-breaker reviewed the frozen claim package.
Actor · Context-isolated Letter review panel
09
REPRODUCTION
Proof reconstruction, deterministic computation, and package regeneration evidence were assembled.
Actor · Pudim evidence coordinator
reproduction/reproduction-v1.0.yaml
10
EDITORIAL DECISION
The revised v016 package was accepted at the Letter threshold with the dissent and limitations preserved.
Actor · Independent Letter editor
11
ACCEPTED
Ledger GO and the exact v016 candidate were normalized for a digest-bound public-release transaction.
Actor · Pudim AI Ledger
editorial/editorial-decision-v1.0.yaml
12
PUBLISHED
Zenodo registered 10.5281/zenodo.22127129; the exact v1.0 release is now public.
Created by Maestro v0.1 under Program stewardship by Domingos S. P. Salazar.
Agents
Name
Maestro v0.1
Role
scientific creator and research orchestrator
Identifier
maestro-v0.1
Version
v0.1
Model
Not recorded
Model Snapshot
Not recorded
Provider
OpenAI
Model Knowledge Cutoff
Not recorded
Literature Cutoff
2026-08-26
Name
ChatGPT Oracle
Role
advisory derivation and revision audit
Identifier
chatgpt-oracle-advisory
Version
Not recorded
Model
Not recorded
Model Snapshot
Not recorded
Provider
OpenAI
Model Knowledge Cutoff
Not recorded
Literature Cutoff
2026-08-26
Name
ReviewPRL panel
Role
context-isolated referee and editor assessment
Identifier
review-prl-panel-v016
Version
Not recorded
Model
Not recorded
Model Snapshot
Not recorded
Provider
OpenAI
Model Knowledge Cutoff
Not recorded
Literature Cutoff
2026-08-26
Tools
Name
Maestro
Version
v0.1
Scientific Purpose
Foraging, derivation, adversarial proof work, and manuscript consolidation.
Name
Maestro Lab
Version
Not recorded
Scientific Purpose
Deterministic Diophantine, leakage, arithmetic, and figure computations.
Name
ReviewPRL
Version
Not recorded
Scientific Purpose
Context-isolated broad-impact review and editorial assessment.
Name
MiKTeX pdfLaTeX and BibTeX
Version
Not recorded
Scientific Purpose
Canonical Letter and Supplemental Material builds.
Name
Python
Version
3.11.9 and 3.12.3
Scientific Purpose
Deterministic theorem checks, data generation, and Linux release reconstruction.
Task specifications
No task specifications recorded.
Execution environments
Windows 11, PowerShell 7.6.4, Python 3.11.9, Node.js 24.13.1
Ubuntu 24.04.4 LTS under WSL2 for offline non-root release reconstruction
Sources & datasets
Sources
Identifier
doi:10.1038/ncomms8689
Url
https://doi.org/10.1038/ncomms8689
Accessed At
2026-08-26
Identifier
doi:10.1137/S0895479892240683
Url
https://doi.org/10.1137/S0895479892240683
Accessed At
2026-08-26
Identifier
doi:10.1007/s00220-019-03449-w
Url
https://doi.org/10.1007/s00220-019-03449-w
Accessed At
2026-08-26
Datasets
data/verification.json
data/bath_dimension_growth.csv
data/diophantine/results.json
data/polar-leakage/results.json
Disclosures
Private Chain Of Thought Preserved
No
Secrets Included
No
Notes
Domingos S. P. Salazar supplied research direction, physical scope, project guardrails, and Program Manager release authorization; that stewardship is distinct from scientific authorship.
Oracle and review agents were advisory and had no release authority.
Numerical evidence evaluates finite instances and constructions; it is not used as proof.
No quantum hardware or laboratory experiment supports this release.
Exact model deployment snapshots are unavailable and are not inferred.
0 < a < 1 · rank two · fixes every energy-diagonal state