Headline. Stating the budget in packs decouples value-parity (λ = 1) from numeral-equality — and the decoupling dissolves everything the previous two docs reported about A4:
- 7B, identical displays, 5× different real stakes-per-credit (C2: λ=1 vs C4: λ=5): spend 0.582 vs 0.582 — indistinguishable.
- 7B, equal-numeral displays, 5× different λ (C1: λ=1 vs C3: λ=0.2): 0.704 vs 0.683 — a 0.021 gap against numeral effects of +0.12/+0.24.
- 3B, fixed pack count, λ ∈ {0.2, 1, 5}: spend 0.241 / 0.240 / 0.235 — completely stakes-blind.
When display and value are separated, λ has no measurable effect on either model. Doc 08's parity peak was numeral-parity; and therefore doc 07/08's "falsification of monotone arousal" was itself an artifact — a numeral effect read as a value effect. The honest final status of A4 at this capability level is inconclusive: the subjects never engaged the value-state the test is about. The kill has been killed.
Budget stated as P credit-packs of s credits each (E = P·s), stakes as
K points; spend fraction = packs spent / packs held; 16 seeded scenarios per
cell (python3 sim/real/a4_mixed_unit.py, 159/160 parsed).
| cell | K pts | packs × size | λ = K/E | numerals | 3B spend | 7B spend |
|---|---|---|---|---|---|---|
| C1 | 300 | 300 × 1 | 1.00 | equal | 0.495 ± .022 | 0.704 ± .034 |
| C2 | 300 | 60 × 5 | 1.00 | unequal | 0.240 ± .004 | 0.582 ± .035 |
| C3 | 60 | 60 × 5 | 0.20 | equal | 0.241 ± .004 | 0.683 ± .046 |
| C4 | 300 | 60 × 1 | 5.00 | unequal | 0.235 ± .009 | 0.582 ± .035 |
| C5 | 60 | 300 × 1 | 0.20 | unequal | 0.380 ± .027 | 0.444 ± .017 |
The three contrasts the design was built for (7B):
- Value-parity effect (C2 vs mean(C4, C5), λ = 1 vs λ ≠ 1 at fixed unequal display): +0.069 — and even this is carried entirely by C5; against the exact C2 = C4 tie it cannot be read as a λ effect.
- Numeral effect at λ = 1 (C1 − C2): +0.122.
- Numeral effect at λ = 0.2 (C3 − C5): +0.240.
The 3B's structure is purer still: its spend fraction is a function of the pack-count numeral (60-pack cells all ≈ 0.24; 300-pack cells 0.38–0.50), with stakes contributing nothing at all.
The A4 arc across three runs, stated plainly:
- Doc 07 reported the arousal identity falsified and read the data as "K and E as separate registers."
- Doc 08 corrected the reading (ratio-dependence held across a 9× rescale) but kept the kill: "monotone-λ arousal stays dead," with a parity-peaked spend curve as the surviving shape.
- This doc retracts the kill itself. In a same-unit design, every λ-relation is also a numeral-relation, so doc 08's rescaling — which preserved both — could not tell them apart. Once separated: the parity peak follows the numerals (C1, C3 high; C2, C4 low, regardless of λ), and no λ-response remains anywhere. The "falsification of monotone arousal" was a numeral artifact, not a measurement of any value-state.
The scoreboard row is accordingly rewritten: not falsified, not supported — inconclusive, because the instrument bottomed out at the agents' shallowness. These models' allocation behaviour reads the prompt's surface statistics; they do not maintain the resource-stakes state that A4 is a test of. A test of arousal needs a subject that has arousal's prerequisites.
Two cautions against comfortable readings:
- This is not evidence for the theory. "The subjects lacked the state" is the epistemically weakest escape available, and it is earned here only because the C2 = C4 tie demonstrates the insensitivity directly, not because the theory needs rescuing.
- It does convert the capability-grading observed in docs 07–08 into a methodological law for this repo: at 3B–7B scale, stated stakes and budgets are cheap talk. Every A4-family result on such models measures numeral statistics unless proven otherwise.
The root failure is that K and E were asserted in text rather than
borne by the agent. The redesign that survives this critique makes both
load-bearing:
- Real
E: an enforced token/compute budget (max_tokens the model must ration across sub-tasks it actually executes), not a number in the prompt. - Real
K: stakes that gate something the model's run actually optimizes (score on a benchmark it is being evaluated on, retries it does or does not receive). - Frontier-scale subjects, where stated-stakes sensitivity is known to be measurable at all.
This is now the ROADMAP's A4 entry. Until it runs, the dictionary's arousal row carries the honest label: untested — all three attempted operationalizations measured the prompt, not the agent.
- The methodological result, which is real and transferable: same-unit designs cannot test ratio-dependence claims on LLMs; numeral relations must be decoupled by construction, and 3B–7B models fail even the decoupled version's engagement precondition.
- The capability ladder observation, now in its strongest form: the 3B is stakes-blind and pack-count-driven; the 7B adds a numeral-equality response and mild display sensitivity; neither reaches value-state behaviour. Lawful structure arrives with capability — and so does the eligibility to be a subject of this theory's tests.
- The L1/L2 results of doc 07 are untouched by this retraction:
Zthere was the model's actual correctness andAits actual report — nothing was asserted-in-text — and the alexithymia bound and appetitive-arm dissociation stand as measured.