RED PRE-REGISTRATION — H-CYCLE-01

Inter-layer update schedule as a cycle ratio (the operator's golden-ratio hypothesis)

• Status: FROZEN. Committed before any instrumentation code exists and before any arm is run.
• Prospectivity: decided by the commit graph (D9). This record must be a proven strict ancestor of the commit introducing any result. A result whose prediction record is not an ancestor is retrospective, permanently.
• Operator co-sign obtained (2026-08-19): (1) the reading of "must not impact the bound on surprisal" adopted in §4; (2) lifting the standing design fence on @l2_period (docs/specs/generative_model_depth.md:111, docs/specs/rung1_graded_viability.md:58, docs/RESUME_RUNG1.md:77).
• Verdict vocabulary: PASS / PARTIAL / FALSIFIES / NOT_ESTABLISHED / WITHHELD. Never percent-scored. Never "equivalent". Never "no difference". Underpowered is not equivalence.

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0. The hypothesis under test (the operator's, decomposed — not the agent's claim)

H1 — CYCLE-RATIO MECHANISM. There exists an inter-layer update schedule, defined purely as counts of cycles, such that the ratio of update rates between adjacent nested layers is the golden ratio, realised as the Fibonacci sequence: an outer layer runs r cycles before it moves the layer below, cascading down.

• H1a — SPECIFICITY. The ratio is φ ≈ 1.618 specifically, not merely "some ratio > 1". An effect that is flat in r around φ FALSIFIES H1a even if the Fibonacci arm beats the flat control.
• H1b — PURITY / TIMING ONLY. The schedule alters only when a layer updates. It must not adjust the decision rule and must not impact the bound on surprisal.
• H1c — NO CLOCK. The schedule is indexed by integer cycle counts; no wall-clock quantity enters it. (Already true of the incumbent: mc.ex:337 gates on rem(tick, @l2_period), tick a pure counter initialised mc.ex:104, incremented mc.ex:180.)

H2 — DIRECTION (the operator's registered prediction). Update rate increases monotonically with layer height: lower/bodily layers run at the LOWEST frequency; the OUTERMOST layer runs at the HIGHEST frequency.

ADVERSE, RECORDED FIRST: H2 is the exact inverse of what is built. mc.ex:32/:337 runs the outer L2 once per 12 inner L1 ticks; strategist.ex:2-4 states "the SAME discrete engine instanced a level up, running slower"; and test/sp/brain/strategist_test.exs:51-66 asserts L1-fast / L2-slow and currently PASSES. This is good for the programme — H2 is a risky contradiction of the incumbent, not a restatement of it. That test will NOT be edited to accommodate any result. The incumbent is kept alive as scored arm A7.

H1b is currently VIOLATED by the shipped code (recorded now, before measuring): when mc.ex:337 fires, modulate/4 (mc.ex:359-367) runs Strategist.apply_context (absolute C overrides, strategist.ex:96 → efe.ex:99/plan.ex:155) and Hormones.modulate (policy precision γ × (1 + 1.5·stress), plasticity lr × (1 − 0.6·stress), hormones.ex:20-23,29-35). Changing the period therefore changes the decision and the learning rate. Cadence and gain are the same lever today. Neutralising this is a pre-condition of the test, not an optimisation.

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1. Substrate and depth

Colony only (UNI.Minecraft). The flagellum side has no update loop for a schedule to act on (static hierarchical density, latent integrated out, 2 free parameters, deterministic quadrature).

Depth N = 3, using three structures that already exist and are already wired: L1 Factors (mc.ex:136), the SlowContext/Hierarchy2 scene parent (mc.ex:98,134,140; built and injected, merely OFF by default at genome.ex:198, coupling δ = 0.0 at genome.ex:202), and L2 Strategist (mc.ex:337).

N = 3 is the minimum at which φ is measurable at all: N = 2 yields ONE ratio, and one number cannot exhibit a sequence. Any N = 2 sweep is a pilot for the confound, never a test of H1a.

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2. The schedule (frozen generator)

Layers indexed n = 1 (innermost/bodily) … N (outermost). One BASE CYCLE = one observation delivered to the agent. Schedule = adjacent ratio vector r = (r_1 … r_{N-1}) plus an orientation flag O ∈ {OUTER_FAST, OUTER_SLOW} naming which end is pinned to the base cycle.

Cascaded Beatty gate (one rule covering integer, irrational and unit ratios identically). With k the 1-based firing count of the layer nearer the driver, the farther layer fires iff

floor(k / r) > floor((k - 1) / r)

and always fires at k = 1 (registered phase convention: every layer fires once at cycle 0, so all arms begin from an identically initialised state and differ only in schedule thereafter).

Properties (why this generator):

• r = 1 everywhere reproduces the FLAT engine exactly — the identity control.
• r = 12 reproduces the incumbent gate, so the shipped system is an arm, not an unmodelled baseline.
• r = φ is admissible directly; the realised firing pattern is the Fibonacci/Zeckendorf word, and integer truncation gives exactly the Fibonacci periods (1, 2, 3, 5, 8, 13, 21, 34). "Golden ratio as cycle ratio" and "Fibonacci sequence of periods" are therefore the SAME arm.
• Reversing O permutes which layer gets which rate but leaves the MULTISET of per-layer rates unchanged, so A1 and A2 are compute-matched: identical total layer-updates per episode. The direction test is a controlled contrast, not a budget comparison.

Action emission is NOT gated — the agent emits an action every base cycle, holding its last committed action where no layer refreshed (the semantics already used at mc.ex:340-342). Otherwise arms would differ in rate of acting, which is not timing of inference.

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3. Arms — the ONLY thing that differs is r and O

Same genome, seeds, world, spawn, initial model bytes, base-cycle count, δ, precision rule, RNG stream.

arm	r	O	role
A0	(1, 1)	—	FLAT CONTROL; doubles as the identity arm
A1	(φ, φ)	OUTER_FAST	the operator's prediction (H1+H2)
A2	(φ, φ)	OUTER_SLOW	standard deep-temporal convention; compute-matched to A1
A3	(1.571, 1.571)	OUTER_FAST	NEAR-DECOY π/2 — the numerology killer
A4	(1.45, 1.45)	OUTER_FAST	far-decoy low
A5	(1.80, 1.80)	OUTER_FAST	far-decoy high
A6	(r̂, r̂)	OUTER_FAST	FITTED-FREE; r̂ by grid search [1.0, 3.0] step 0.05 on TRAINING seeds only
A7	(1, 12)	OUTER_SLOW	INCUMBENT as a scored arm

DECOY DISCIPLINE: 1, 2, 3/2, 5/3, 8/5, 13/8, 21/13 are Fibonacci convergents and are DISQUALIFIED as decoys. (1.5 looks like an obvious decoy and is actually 3/2, a convergent.) A3/A4/A5 bracket φ from both sides so a MONOTONE-in-r effect is distinguishable from a PEAK-AT-φ.

CROSSED FACTOR (not an arm; every arm run at both): down_payload ∈ {:full, :neutral}. :neutral makes Strategist.apply_context a no-op and Hormones.of_context constant, so the only thing the schedule changes is when each layer's posterior is refreshed. :full (default) is byte-identical to today.

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4. The interpretive reading of H1b — OPERATOR CO-SIGNED

"Must not impact the bound on surprisal" is ambiguous between (i) the bound's form is untouched and the inequality always holds, and (ii) the bound's value is unchanged. Reading (ii) makes the hypothesis unfalsifiable — a schedule with no measurable consequence cannot be tested, and if it had no consequence there would be nothing for φ to be the ratio of.

This programme adopts reading (i), proved by P1–P3 below. Operator co-signed 2026-08-19.

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5. Mechanical proofs — all green BEFORE any arm is scored

• P1 — STATIC FENCE. AST/compile-time test: SP.Brain.Schedule exports only boolean-returning predicates, and Infer, Efe, Plan, Precision, Learn reference neither tick, counts nor Schedule. Falsifier: any reference. This is the "it is a timer, not a gain" proof in code.
• P2 — IDENTITY AT r = 1. The scheduled engine must be BYTE-IDENTICAL to the flat engine: same emitted action sequence AND same sha256 of :erlang.term_to_binary(brain.model) over K = 500 cycles × M = 20 seeds. Falsifier: any byte differs. IF P2 FAILS THE PROGRAMME IS VOID — the instrument would be measuring an accidental side effect (most likely differential RNG consumption; the gates must not draw from brain.rng).
• P3 — BOUND HOLDS POINTWISE. At every cycle of every arm, for every factor, F ≥ −ln p(o). The schedule may change the value of F — it must, or it does nothing — but never the inequality. Falsifier: one violation anywhere.
• P4 — CONTENT-vs-TIMING ABLATION. The :full/:neutral crossing above.

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6. Scoring rule

Primary metric — one-step-ahead PREDICTIVE log score (strictly proper), formed from the FORWARD PRIOR, not the posterior:

p̂(o_m) = ( A^m · softmax(forward_prior(m)) )[o_m]
arm score = mean over cycles of  −Σ_m ln p̂(o_m)      [nats per cycle, lower better]

LOAD-BEARING CORRECTION: neither existing quantity is usable. Infer.vfe/2 (infer.ex:55-62) and Precision.surprise/3 (precision.ex:56-59) are both computed against the POSTERIOR m.qs — post-hoc fit, not prediction. A schedule that updates a layer more often would look better on them for a reason that is not predictive skill. Requires one new pure read-only function Infer.predictive_surprise/2, built from the existing private forward_prior/1 and obs_log/2; it touches no state and enters no decision.

• AGGREGATION UNIT = THE AGENT, never the cycle (frames/time points are not independent replicates). N = 40 agents per arm, paired by seed across arms.
• SPLIT: seeds partitioned once, frozen here. Training seeds are used ONLY to pick r̂ in A6; held-out seeds are never touched by any tuning in any arm.
• UNCERTAINTY: paired agent-cluster bootstrap, 2000 replicates, house RNG seed 20260717, 95% percentile interval on the paired difference. Decision threshold 0.0.
• MATERIALITY FLOOR δ_mat — NOT imposed by hand. Computed BEFORE unblinding any treatment arm as the half-width of the NULL contrast: the flat arm A0 split into two random halves of seeds and scored against itself. That is this assay's own resolution floor. Any effect smaller than δ_mat is NOT_ESTABLISHED regardless of its CI.
• SECONDARY (reported, never primary, confounded): survival cycles, harvest, action entropy, distinct-cell visitation, Dirichlet mass growth per layer.

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7. Gates

VOID — if P2 fails, or P3 fails anywhere, the run is VOID and nothing is reported as a result.

• G1 PASS (H1+H2 supported): A1 beats A0 and A1 beats A2, both paired CIs excluding 0 and both |effects| > δ_mat, in BOTH down_payload settings.
• G2 FALSIFIES H2 (the DIRECTION TEST): A2 beats A1, CI excluding 0, |effect| > δ_mat. The standard convention wins and the operator's registered direction is falsified. Because A1 and A2 are compute-matched, no "the fast arm just got more updates" rebuttal is available to either side.
• G3 FALSIFIES H1a (SPECIFICITY / numerology): A1 and A3 (π/2) indistinguishable — CI contains 0 AND width < δ_mat — while both beat A0. Verdict: the effect is "slowing the inner layers helps", NOT "the golden ratio". This must be reported as the headline of the receipt, not as a caveat, and the words "golden ratio" may not appear in any positive claim thereafter.
• G4 SUPPORTS H1a: A1 beats A3, A4 and A5, all CIs excluding 0 and all |effects| > δ_mat, AND A6's r̂ CI contains φ and excludes 1.0. This is the only route to a φ claim. Anything weaker is G3.
• G5 FALSIFIES H1b (timing-only): the schedule effect is present at :full and absent at :neutral, interaction CI excluding 0. The effect was carried by the DOWN message's content (C, γ, lr) rather than by timing. Given how mc.ex:359-367 is wired this is the most likely single outcome, and it is pre-registered as such so it cannot be reframed after the fact.
• G6 NOT_ESTABLISHED: any primary CI contains 0, or |effect| < δ_mat.

MULTIPLICITY: the PRIMARY contrast is A1 vs A0 at down_payload = :neutral. All others are SECONDARY; the family (8 arms × 2 payload settings) is stated here. G2, G3 and G5 are named secondary contrasts with pre-declared directions and retain falsifying force; unnamed post-hoc contrasts do not.

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8. Pilot (explicitly NOT a test of φ)

Before the N = 3 ladder, an N = 2 pilot sweeps the period over {1, 2, 3, 5, 8, 12, 13, 21} crossed with down_payload ∈ {:full, :neutral}. One ratio is not a sequence; this is not evidence for or against H1a and will not be reported as such. It answers exactly one question: is cadence separable from content in this codebase at all?

Pre-registered prediction: at :full the curve is NOT flat (the held option rewrites C, γ, lr). At :neutral it should be much flatter. If flat at :neutral and non-flat at :full, the shipped cadence is a gain lever wearing a timer's coat, H1b is measurably violated by the estate's only cycle ratio, and the neutral-DOWN arm is thereby earned as a pre-condition of every later arm.

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9. Tests expected to move — and why that is not permission to edit them

gen2_hierarchy_test.exs:49,63-64,72 assert outcomes after 15 and 3 ticks and depend on period-12 arithmetic; they will change under any non-incumbent arm. PREDICTED FROM TICK ARITHMETIC, NOT MEASURED. They are pinned to the INCUMBENT arm A7 and must pass there; under other arms a difference is data, not breakage. strategist_test.exs:51-66 (L1-fast/L2-slow) is likewise pinned to A7 and will not be edited.

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10. Superseded

A prior test applied φ to the sensory precision gain gamma_m and returned INCONCLUSIVE-leaning-against (optimum ≈ 1.80; φ tied with a planted decoy). That test is about a different object — a gain term, not an update schedule — and is hereby SUPERSEDED. It is not evidence for or against H1/H1a/H2 and must not be cited as such in any receipt for this programme.

11. Provenance of introduced constants

8 (layer count) and φ = 1.618… are class-3 introduced design thresholds: DESIGN_ONLY, evidential for nothing. The operator states plainly that 8 is the working number to test, not a derived one. Note the trap: the 8 appearing in flagellum evidence is stator occupancy N ∈ {1..8}, a STATE count, not a layer count; conflating them would be the category error the truth contract exists to catch.

12. Claim ceiling

Nothing in this programme licenses a claim about the flagellum (no update loop), about any human outcome (L0..L12 is DESIGN-ONLY/NOT-SCORED/NOT-CLAIMED; emotions in this engine are labels on posteriors, not states), about biological active-inference identity (G10/X12 NOT_ESTABLISHED, discriminating interventions: 0), or about parity (X16 FAIL; P4 the first unsatisfied rung; P4/P5/P7 irreducibly external). The strongest allowable sentence concerns a simulated agent in a Minecraft-like world, and no more.

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13. CORRECTION — H-CYCLE-01 IS WITHDRAWN (appended 2026-08-19, same day, before any arm was run)

This programme was REJECTED by lab-team review before a single line of instrumentation was written and before any result existed. Nothing above this line has been edited; it is preserved verbatim as the refuted design. Merged verdict: REJECT (math-breaker REJECT short-circuits the protocol). No Schedule module, no gate change, no down_payload, no predictive_surprise was built; the working tree was verified clean.

Four defects, each independently reproduced.

D-1 — P3, this record's own VOID condition, was ALREADY FALSE in shipped code. Closed form: after Infer.infer_states sets qs to the exact softmax minimiser, F = −ln Σ_s p⁻(s) · Π_m A^m[o_m|s]^(γ_m). The tempered likelihood A^γ is never renormalised, so γ parameterises no probability model, ∂F/∂γ > 0 everywhere, and F → 0 as γ → 0: the engine's objective pays maximally for blindness. The bound holds with equality at γ = 1 and fails for every γ < 1.

γ_m	F	−ln p(o)	P3
2.0	0.891598	0.693147	holds
1.0	0.693147	0.693147	equality
0.5	0.458145	0.693147	violated
0.1	0.114375	0.693147	violated 6.06×
0.01	0.011979	0.693147	violated 58×

(A = [[0.9,0.1],[0.1,0.9]], d = [0.5,0.5], o = 0.) Measured on the live default agent (5 seeds × 200 cycles × 12 factors, comparator using the engine's own softmax(ln B·s) forward prior): min γ_m 0.635, 7261 / 12000 = 60.5% of factor-cycles violate P3, worst shortfall 0.765 nats. Precision.update_sensory drives γ_m toward 2.0/(s+1.0), so γ_m < 1 whenever a channel's surprise exceeds 1 nat — routine. The VOID condition is violated in the majority of factor-cycles, in shipped code, with no schedule anywhere near it. Note also that precision_test.exs's test named "the upper-bound property holds" only asserts F falls under perception; it never compares F to −ln p(o). The estate has never tested this property.

D-2 — the L1 gate in §2 is a content change dressed as timing. Factors.infer_states itself calls Precision.update_sensory (factors.ex:89), so the single proposed gate would gate perception

• Dirichlet learn + grow + sensory precision in one act, while commit_action (mc.ex:153 → factors.ex:111-121) bumps the habit prior pe/e outside any gate, every base cycle, and nothing decays pe. An arm at ratio r buys ~1/r of the model-evidence mass against habit accruing at rate 1. P1 (a static fence over five callee modules) cannot see it, because the asymmetry lives in mc.ex.

D-3 — the depth-3 ladder does not exist. w is written in exactly one place (Hierarchy2.new/3, hierarchy2.ex:39); no update path exists anywhere. MC.build_slow_context (mc.ex:460-473) hands it uniform columns, so child_priors = W·q(scene) is uniform for every q(scene) — the DOWN message is literally invariant to the parent's belief, hence invariant to how often the parent refreshes. r_2 produces exactly zero variation, by construction. Worse: the one non-trivial thing a δ>0 coupling does (infer.ex:36) is vscale(forward_prior, 1-δ) — it tempers the forward prior, i.e. a gain carrying no scene information. The middle layer's only live effect is the thing H1b forbids. Real depth is 2, and by §1's own sentence one ratio cannot exhibit a sequence, so H1a was untestable as designed.

D-4 — §2's generator cannot reproduce the incumbent, and §2 says it can. Literal §2 (floor(k/r) > floor((k-1)/r), always fire at k=1) at r=12 fires at [0, 11, 23, 35, 47]; the incumbent rem(tick,12)==0 fires at [0, 12, 24, 36]. The rate matches, the phase does not, and no value of r fixes it — the required Beatty index {1,13,25,…} is not {ceil(r·j)} for any r. Structural, not tuning. Consequence: arm A7 was not the incumbent, and the claim in §2 that "r = 12 reproduces the incumbent gate" is FALSE as written. (floor → ceil reproduces [0,12,24,36] exactly, makes the k=1 clause redundant, and still leaves r=1 as the identity control — but that is an amendment to a frozen record and is the operator's to co-sign, not an agent's to apply.)

Feasibility, recorded for any successor design. Default genome (plan_depth: 5, plan_beam: 3, 12 factors, nu: 10) costs 207.4 ms/step; at plan_depth: 1, 1.0 ms/step. P2 alone (K=500 × M=20) is ~35 min per arm at default depth; the §8 pilot is ~9.2 hours at default depth versus ~5 min at depth 1. "The default genome" and the sample sizes in §6 are not simultaneously affordable — any successor must state which decider depth it scores.

Preserved and reusable (scratchpad, pre-change/pristine tree): a deterministic capture harness and four P2 reference captures at depths 1 and 5. They already establish that flat ≠ incumbent under that harness at both depths, i.e. a P2 comparison would have had the resolution to detect a schedule change rather than passing vacuously. Step-0 baseline on the pristine tree: 4 doctests, 1049 tests, 2 failures (4 excluded) — the two expected control-plane ledger-tally tests, by name.

STATUS: WITHDRAWN. No successor may be pre-registered until D-1 is repaired, because every arm of every schedule test inherits an objective whose gradient points at blindness. The indicated repair is to normalise the tempered column, p_γ(o|s) = A[o|s]^γ / Σ_o' A[o'|s]^γ, giving F → ln(n_o) as γ→0 and finite F as γ→∞ — a bounded interior optimum, which converts precision from a clamped heuristic into a derivable quantity. That is an FE-touching engine repair and is principal-gated.

This correction is appended, never substituted. The refuted design above is the evidence that the gate worked.