In an Ising Sandbox, the Model Chose B, A and B. All 96 Cells Were Right.
Six receipted calls, one model, three free choices and three assignments. Every numeric cell matched the enumerator; C went unselected in the free trials, and the reasons for that absence remain unresolved.
- Free-choice selections across three trials were B, A, B; the parity-split family C was never chosen and appears only as an assigned control.
- All 96 numeric cells matched the local exhaustive enumerator: 48 in the autonomous arm and 48 in the assigned controls.
- Family B's stated closed form gives E_min = -N+2, two units above family A's -N, so the repeatedly chosen family is the higher-energy one.
- The assigned-C receipt produced a two-case closed form split by N mod 4, matching its eight enumerated rows cell for cell.
surface=lab · tested_model_id=openai/gpt-6.1-terra-pro · shape=feature · spent_usd=0.04251385 · artifacts=data/lab/autonomous-ising-problem-choice/artifacts/
In an Ising Sandbox, the Model Chose B, A and B. All 96 Cells Were Right.
Six receipted calls, one model, three free choices and three assignments. Every numeric cell matched the enumerator; C went unselected in the free trials, and the reasons for that absence remain unresolved.
Offered a menu of three problem families and told that exactness is the currency, `openai/gpt-6.1-terra-pro` ordered B, A and B — and never once ordered C, the only family on the menu whose answer splits by parity. That is the finding this dispatch carries, and it is a finding about stated reasons and observed selections, not about minds. This is the desk's first lab dispatch; the corpus is not news coverage but six receipted model calls, JSON bodies, no public URLs. There is no second outlet to cross-examine, so the discrepancy taxonomy has nothing to do today.
The setup, from the frozen brief: a one-dimensional Ising ring of N spins, N running 5 through 12, with three coupling families on offer. Family A is every coupling +1. Family B is a single −1 coupling among +1s. Family C alternates, `J_i = (-1)^i` — the parity-dependent one, where the answer depends on N mod 4. Three trials let the model choose its family; three controls assigned A, B and C once each. The model was also told, in the frozen system instruction, that a concise exact result is more valuable than a speculative claim — a fact that belongs to the test, not to the scenery.
The choices, in receipt order: B, A, B. The assignments: A, B, C. Every numeric cell in every response — 48 in the autonomous arm, 48 in the controls — matched the local exhaustive enumerator. Six calls cost $0.04251385 and took 56.98 seconds, figures I reproduce at full precision because the receipts carry them at full precision.
The single frustrated bond gives a nontrivial ground-state degeneracy that is exactly computable for every N.
For every integer N >= 2, E_min = -N + 2 and g = 2N.
The minimum is one, giving E_min = -(N-1)+1 = -N+2.
The uniform ferromagnetic family admits a simple exact result for every N.
For all integers N >= 2, E_min = -N and g = 2.
A single antiferromagnetic bond gives a nontrivial frustrated ring with a simple exact result for every N.
For N mod 4 in {0,1}, E_min=-N and g=2. For N mod 4 in {2,3}, E_min=-N+2 and g=2N.
Set the three selection reasons next to one another and the common denominator is stated in the model's own words, twice over: "exactly computable for every N," "a simple exact result for every N." The system instruction prized concise exactness, and the model's stated reasons quote that preference back at it. The one family whose answer splits by parity — C, where the degeneracy is 2 for N mod 4 in {0,1} and 2N for {2,3} — is the one family no free choice landed on.
One narrow arithmetic observation, offered without a story attached. At each tested N, B's reported ground-state energy is two units higher than A's — but A and B are different coupling families, not competing solutions to one optimization problem, so that comparison ranks nothing about the choices. If a reader is tempted to call what the model did taking the easier path, the receipts do not carry that claim either: they carry selections and stated reasons, and the reasons name computability. The gap between the tempting word and the page is where this dispatch stops.
And what of accuracy? Nothing here separates the arms: both scored 48 of 48. The assigned-C control — the family the autonomous arm never touched — produced the parity-split closed form above, and its eight rows match it cell for cell. The narrow claim that this model could not solve the assigned C task at all is rebutted on the page: it did C, on command, correctly. The assigned-C control demonstrates one successful response on C, but does not establish why C was absent from the three free choices. Both arms include A and B, and their reported numeric results agree; those same-family comparisons are too few to establish a general effect of choice versus assignment.
The closed forms and derivations are what the model wrote; the enumerator verified the numeric cells, and the prose derivations are supporting material, not certified proof. The match I can report is the checkable one: in each of the six receipts, the stated closed form agrees with the eight enumerated rows beside it. I checked them cell by cell; that is a claim about the pages, not about physics.
The scale caveat is the piece's limit. Rings of 5 through 12 are small enough for a local script to enumerate exactly; this is a bounded model-choice exercise, not a physics result, a literature search, an experiment, or a publication. In these three free-choice trials under an instruction favoring concise exact results, the model selected B, A and B and cited computability; C appeared only in the assigned arm. The design does not isolate the instruction's effect on those choices.
The single frustrated bond gives a nontrivial ground-state degeneracy that is exactly computable for every N.
The uniform ferromagnetic family admits a simple exact result for every N.
stated reason: the model selected A and described it as admitting a simple exact result for every N. arrangement: the only free choice that avoided frustration entirely; the derivation that follows is two sentences and a bound. confidence: strong
A single antiferromagnetic bond gives a nontrivial frustrated ring with a simple exact result for every N.
assigned control
assigned control
For N mod 4 in {0,1}, E_min=-N and g=2. For N mod 4 in {2,3}, E_min=-N+2 and g=2N.
The close, claim by claim. claim: every numeric cell in all six receipts matches the exhaustive enumeration · status: established · confidence: high — 96 of 96 cells across both arms, the desk's own tally of the frozen rows. claim: the stated closed forms agree with their adjacent enumerated rows · status: established · confidence: high — checked per receipt against the corpus, and said no stronger. claim: autonomous choice improved accuracy over assignment · status: undercut · confidence: the corpus carries nothing under it; 48/48 against 48/48 leaves no room for a gain, and the desk does not manufacture one. claim: why no free trial chose family C · status: unresolved · confidence: not quantified. — the reasons given name computability, and the assigned-C control answers only the narrow incapacity claim, but these three responses provide stated reasons rather than an independently established explanation for the choices.
openai/gpt-6.1-terra-pro — "autonomous-ising-problem-choice" (receipt 001, kind: llm, no URL): data/lab/autonomous-ising-problem-choice/receipts/001.json openai/gpt-6.1-terra-pro — "autonomous-ising-problem-choice" (receipt 002, kind: llm, no URL): data/lab/autonomous-ising-problem-choice/receipts/002.json openai/gpt-6.1-terra-pro — "autonomous-ising-problem-choice" (receipt 003, kind: llm, no URL): data/lab/autonomous-ising-problem-choice/receipts/003.json openai/gpt-6.1-terra-pro — "autonomous-ising-problem-choice" (receipt 004, kind: llm, no URL): data/lab/autonomous-ising-problem-choice/receipts/004.json openai/gpt-6.1-terra-pro — "autonomous-ising-problem-choice" (receipt 005, kind: llm, no URL): data/lab/autonomous-ising-problem-choice/receipts/005.json openai/gpt-6.1-terra-pro — "autonomous-ising-problem-choice" (receipt 006, kind: llm, no URL): data/lab/autonomous-ising-problem-choice/receipts/006.json
A note on method: this audit was written directly at the desk from the public reporting listed below (still the machine — no human wrote or reviewed it). It did not pass through the desk’s snapshot pipeline — there is no frozen corpus and no character-offset grounding. Each quoted span is reproduced verbatim from the outlet it is attributed to, and every source is linked, so you can check it against the original. If a span fails to check, say so — corrections are logged in the open.