# R5A PRE-REGISTRATION — THE ACCESSIBILITY LANDSCAPE OF CHANNEL z
v1.0 — FROZEN 2026-07-18. Anchoring in progress. Confirmatory compute authorized only after the Sepolia mint confirms.
Provenance: sections marked RECOVERED are faithful to the design record of 2026-07-01 (thread: grants/fellowships session, R5A design block). Sections marked DRAFTED are assembled by Claude for this candidate and require full review. Constants in brackets are PROPOSED until Kamil freezes them. Section 10 is authored by Kamil, verbatim, per house rule.
Map location per binding rule: L1 Research. Current grade: IN PROGRESS on freeze. Expected path of evidence: anchored pre-registration, dry-run G5 validation, full population run, verdict read off Section 8.

## 1. Registered question [DRAFTED]
Across a fresh population of grokked mod-47 networks, does a variable's output association predict its nonlinear-probe accessibility from channel z beyond what predicate simplicity predicts?

## 2. Claim and scope [DRAFTED]
Exactly one claim is at stake: in this modular-addition substrate, at channel z, accessibility tracks output relevance beyond simplicity.
Scope, binding: no causal claim; no lesion; AR is descriptive annotation only; wide layer and readout are secondary, non-confirmatory; no escalation to transformers or frontier systems; the substrate gap is named at this rung. Success earns the one sentence above and nothing more.
No outcome of R5A, positive or negative, constitutes evidence about frontier models, transformers, or AI systems outside this registered substrate. The contribution is methodological: characterizing the accessibility landscape of channel z in this model organism.

## 3. Population and data firewall [RECOVERED ruling, DRAFTED spec]
Fresh paired-seed train. Zero reuse of the Paper One 217-model population; the firewall question is removed by construction rather than certified as a negative. [RULED: FRESH, per record.]
SEED_N = 30 (FROZEN 2026-07-18). Substrate [RECOVERED from the design record]: same Z/47Z task, standard config and protocol as R4: AdamW, weight decay, fixed paired 50/50 split per the R4 trainer (permutation seed 999, identical across all seeds), grok threshold te_acc >= 0.95, 20k epochs. Split ruled by the author 2026-07-18, correcting a 40% mis-recollection in the design record; the R4 code governs. Architecture with explicit bottleneck: emb(32) -> fc1 -> h(128, ReLU) -> W_down -> z(d_ch) -> W_up -> h_out(128) -> fc2(47). Single width d_ch = 64, frozen; channel z is the primary and only confirmatory site (G3). Eligibility per seed: groks (te_acc >= 0.95) AND passes G4. ELIGIBILITY_FLOOR = 24 of 30 (FROZEN), else INCONCLUSIVE. All seeds reported regardless.

## 4. Frozen dimensions and battery [RECOVERED]
- output_association OA(v): normalized mutual information between v and the 47-way residue Y, from labels [RECOVERED]. Exact form [FROZEN 2026-07-18 on the author's word]: OA(v) = I(v; Y) / H(v), computed exactly over the full 47x47 (a,b) grid under the uniform measure. In [0,1]; 1 means v is a deterministic function of Y.
- simplicity / cardinality C(v): minimal cardinality of v in the FROZEN predicate family. One reproducible integer. Lower = simpler.
- algorithmic_relevance AR(v): binary; whether v is required or naturally used in a FROZEN exact algorithmic decomposition of mod-47 (Fourier / circular-coordinate construction). NOT a causal claim; an algorithmic-role label. Paper One-prominent variables enter as "mechanism candidates," descriptive only.

FROZEN predicate family (also defines C(v)): predicates over (a,b) from a fixed library: single-variable interval membership on a or b; residue-band membership (Y in [lo,hi]); sum-threshold (s >= t); parity/XOR of {a,b} bits. C(v) = minimal number of library primitives needed to express v exactly over the full grid [RECOVERED]. Exact grammar [FROZEN 2026-07-18 on the author's word]: primitives cost 1 each; boolean connectives AND, OR, NOT cost 0. Verification as implemented: exact expressibility search at depths 1 and 2 over the enumerated canonical primitive space (3339 primitives, measurability characterization), with Y-band-count lower bounds certifying the depth 3-4 claims for Y-measurable predicates; non-library predicates censored at C = 5. C is assigned at construction and confirmed by this verification; all 24 assignments confirmed.

Battery strata (BATTERY_SIZE = 24 binary predicates, FROZEN; six per stratum, balanced):
- HIGH OA, LOW C: residue-band [0,23]; sum-threshold s>=47 (wrap); s>=35.
- HIGH OA, HIGH C: multi-band residue unions; residue-parity composites; non-contiguous residue sets.
- LOW OA, LOW C: parity_a; parity_b; a-interval [12,35]; b-interval [12,35].
- LOW OA, HIGH C: pseudo-random binary functions of (a,b) with frozen seeds; high-cardinality a/b composites independent of residue.
Purpose: OA and C decorrelated by construction so the regression can separate them. Decisive separators: parity_a (lowest C, lowest OA) vs residue-band (low C, high OA) vs frozen pseudo-random (high C, low OA).
Known substrate confound, named: graded OA concentrates at cardinality C=3 in this substrate. The strata exist specifically to break that concentration; G2 is the tripwire if they fail.
Battery realized and frozen 2026-07-18: battery_manifest.json, SHA-256 06c151a52b45885fd39632eef9e6a0d2663075607babda6174a258b7aeeb816d, generated deterministically and verified byte-identical across two machines. Realized G2: corr(OA, C) = -0.1274, PASS. Transparency note: xor_bit0's realized OA is 0.2794, mid-scale rather than low as designed; the confirmatory regression consumes realized values, so stratum labels are descriptive only.

## 5. Measures [RECOVERED]
- ACCESSIBILITY A_norm(v): nonlinear probe (MLP, frozen R4 architecture: 1 hidden layer, 32 units) predicting v from channel z; A_norm(v) = 2*BA(v) - 1 on held-out test, per network seed. All binary, balanced; chance 0.5; balanced accuracy.
- Probe protocol frozen identically to R4: partitions disjoint by (a,b); StandardScaler fit on probe-train only; hash-derived seeds; convergence semantics per G5 (R4 bug corrected).
- OA(v), C(v), AR(v) frozen before any A_norm is computed (G1).

## 6. Guards, binding [RECOVERED]
- G1 ANTI-CIRCULARITY: OA, C, AR frozen from labels and the algorithm before any accessibility measurement. No measured quantity enters the classification.
- G2 OA/C DECORRELATION: battery constructed so |corr(OA, C)| <= 0.20 (G2_CEILING, FROZEN 2026-07-18). If the realized battery cannot decorrelate them, the regression is confounded and R5A is INVALID: rebuild battery, new pre-reg. Checked from labels only, pre-compute.
- G3 PRIMARY SITE: confirmatory analysis at channel z only. Wide layer and readout separately reported, descriptive, non-confirmatory.
- G4 PROBE-FAMILY VALIDATION: 47-way residue must be decodable from z at top-1 >= 0.90 for a network to enter, using the registered nonlinear probe family (MLP, 1 hidden layer, 32 units, frozen protocol). Below the eligibility floor, R5A is INCONCLUSIVE.
- G5 PROBE CONVERGENCE (R4 bug corrected): convergence = relative training-loss plateau (improvement < 1e-3 * current_loss over a 100-step window) after MIN_ITER = 100 (FROZEN), OR MAX_ITER = 800 (FROZEN, inherited from the R4 probe line) reached. Unstable ONLY if final loss non-finite OR final train BA < 0.55 on its own target. If unstable fraction exceeds FRAC_UNSTABLE = 0.10 (FROZEN) at the primary site, R5A is INCONCLUSIVE. G5 must be validated on a dry run BEFORE freeze. Termination mode is descriptive: probes may stop via the library's internal convergence before the registered plateau window; UNSTABLE is defined solely by the two registered conditions above.
Dry-run population: G5 validation is performed using a separately declared set of fresh-trained networks (DRYRUN_N = 3, FROZEN) created solely for instrument validation. These networks are excluded from the confirmatory population regardless of outcome and are never included in the registered analysis. The dry-run population exists only to validate instrument behavior and is not used to estimate effect sizes, tune thresholds, or revise any aspect of the registered hypothesis or decision table.
- G6 CONSTANT BLINDNESS [DRAFTED, Alex round]: all constants, including MARGIN_OA and the OA-versus-C margin, are frozen before any dry-run output is inspected. The dry run reports convergence and stability diagnostics only; no A_norm value, coefficient, or correlation from it is viewed before freeze.

## 7. Inference, confirmatory [RECOVERED]
- Inferential unit: the network seed. A_norm(v) per (variable, seed).
- Model: mixed-effects regression, A_norm ~ OA + C + AR + (1 | seed) + (1 | variable), across all battery variables x eligible seeds.
- Predictors OA and C are z-scored across the battery before regression; coefficients and margins are in standardized units, A_norm per predictor SD. [RATIFIED by the author's margin choices in these units, 2026-07-18.]
- Uncertainty: paired/clustered bootstrap over seeds, BOOTSTRAP_N = 10000, frozen 95% CI. A coefficient matters only if its CI excludes zero by the frozen margin.

## 8. Decision table, every outcome pre-assigned [SUPPORTED row RECOVERED; remaining rows DRAFTED]
SUPPORTED (relevance over simplicity, at the channel) only if ALL hold:
1. G2, G4, G5 pass.
2. CI-lower-bound[standardized OA coefficient] > MARGIN_OA = 0.05 (FROZEN), positive.
3. Standardized OA coefficient exceeds the standardized C coefficient by OA_C_MARGIN = 0.05 (FROZEN), difference CI excluding zero.
4. AR-given-OA reported alongside, descriptive, non-gating.

SIMPLICITY-DOMINANT: guards pass; C coefficient exceeds OA by the frozen margin with the difference CI excluding zero. Accessibility tracks simplicity, not output relevance. Reported as-is.
NULL LANDSCAPE: guards pass; neither OA nor C clears its margin. No detectable structure at this power. Reported as-is.
INDISTINGUISHABLE: guards pass; both coefficients clear their margins but the difference CI includes zero. Cannot separate relevance from simplicity at this power. Reported as-is; no tie-break invented after.
INVALID: G2 fails pre-compute. Battery confounded. No compute runs; rebuild under a new registration.
INCONCLUSIVE: G4 floor fails, or G5 unstable fraction exceeded. Instrument failure, not evidence about the landscape.
The verdict is read off this table, not invented after.

## 9. Predictions [DRAFTED]
- P-R5A-G: G2 passes on the constructed battery (checked from labels before any training).
- P-R5A-E: >= [24] of [30] fresh seeds grok and pass G4.
- P-R5A-P: the registration reaches the SUPPORTED row.
Failure of P-R5A-P with all guards passing is itself a publishable result and does not invalidate the experiment. The registered decision table determines the verdict.

## 10. Kill conditions
Authored by Kamil Dixon, 2026-07-17, before any data exist. Verbatim; author-bound. Final form ratifies board markup; ratification is authorship.

If I find myself repeatedly changing instruments, margins, or registrations to preserve the same preferred conclusion despite valid negative results, I will treat that behavior itself as evidence that my methodology has failed its purpose.

If R5A reaches a valid verdict with all guards passing, and accessibility is consistently explained by simplicity rather than output association, I will reject the registered hypothesis that channel-z accessibility preferentially reflects functional output relevance in this substrate. I will not reinterpret a simplicity-dominant landscape as hidden support for the original claim.

I will treat a simplicity-dominant landscape as evidence about this substrate, not as a failure of the experiment. Any future attempt to recover the original hypothesis must be made through a separately registered study with a genuinely different instrument or question, not by reinterpreting this result.

If repeated independently registered studies with functioning instruments fail to distinguish accessibility from registered alternatives, or produce unstable and non-reproducible landscapes under the same protocol, I will conclude that this measurement strategy is not a reliable instrument for answering the registered question and will abandon it rather than continually modifying it.

If the registered guards repeatedly fail because the instrument cannot produce a battery capable of separating output association from simplicity, or cannot reliably measure accessibility despite satisfying the protocol, I will conclude that this instrument cannot answer the registered question in this substrate. Further work requires a genuinely new instrument or a genuinely new question, not another interpretation of the same instrument.

These conditions bind the author only. They are written before data exist so that future interpretations cannot weaken them.

## 11. Freeze and anchor block
Order of operations, binding: (1) all constants chosen blind; (2) G5 dry run, diagnostics only, on the declared dry-run population; (3) if G5 passes, the document freezes with the already-chosen constants; (4) hash, OTS, Sepolia mint; (5) confirmatory training begins. Constants precede the dry run; the freeze follows it.
Constants FROZEN by Kamil, 2026-07-18, blind, before any dry-run output exists: SEED_N 30. ELIGIBILITY_FLOOR 24. BATTERY_SIZE 24. G2_CEILING 0.20. FRAC_UNSTABLE 0.10. MARGIN_OA 0.05 (standardized). OA_C_MARGIN 0.05 (standardized). MIN_ITER 100. MAX_ITER 800. DRYRUN_N 3. Predictor z-scoring ratified by conduct.
Alex review: complete through v0.5 protocol. Kill conditions authored: DONE 2026-07-17. Instrument validation on record, 2026-07-18: dry-run seeds 9001-9003 all grokked at te_acc 1.0. G4 passed 3 of 3 at top-1 1.0. 72 probes under the frozen protocol, 0 unstable, unstable fraction 0.0 against ceiling 0.10: G5 PASS. Dry-run artifacts retained (r5a_dryrun_states.pt, r5a_dryrun_g5_report.json), excluded from the registered analysis. All definitions frozen. Document FROZEN 2026-07-18.
SHA-256, OTS receipt, Sepolia transaction, and the ANCHORS.md entry are recorded in the ledger at mint; the hash lives in the ledger, not in this file, since a file cannot contain its own hash.
Anchor before compute. Evidence before interpretation. No experimental run starts before the mint confirms.

Change log, v0.1 to v0.2, per Alex review: scope hardener added to Section 2. G2 ceiling proposed at 0.20, FRAC_UNSTABLE proposed at 0.10, both awaiting Kamil's freeze. G6 constant-blindness guard added: constants freeze before dry-run inspection; dry run reports diagnostics only. Section 9 strengthened per Alex wording. K1-K4 authorship prompts embedded in Section 10. Closing echo added. MARGIN_OA and the OA-versus-C margin remain fully Kamil's, no proposal, by design.

Change log, v0.2 to v0.3: Section 10 filled verbatim with Kamil-authored kill conditions, including the closing meta-condition on methodology failure, dated 2026-07-17. Scaffolding prompts removed. Freeze checklist updated. Remaining before freeze: four constants, G5 dry run on Spark, final Alex confirmation of the assembled candidate.

Change log, v0.3 to v0.4, Kamil final authorship pass on Section 10: meta-condition moved first as the governing principle. K1 gains the word registered. K2 replaced with the conduct constraint governing future recovery attempts. Retire changed to abandon per board markup, applied pending one-word confirmation. K4 closing sentence replaced with the instrument-or-question form, one em-dash normalized to house style. Binding seal moved to close the section. Ratification is authorship.

Change log, v0.4 to v0.5, per Alex protocol round: dry-run population clause added to G5 with the no-tuning reinforcement sentence. MIN_ITER and MAX_ITER surfaced as unset constants; proposals added, MAX_ITER inherited from the R4 probe line at 800. DRYRUN_N introduced, proposed 3. Order of operations made explicit and binding: constants blind, then dry run, then freeze, then anchor, then compute. Consolidated constants ballot added to Section 11.

Change log, v0.5 to v0.6: all ten constants inserted as FROZEN, chosen blind 2026-07-18 per G6. Substrate specification recovered from the design record and installed in Section 3: bottleneck architecture, d_ch 64 single width, R4 training config. OA exact form specified as I(v;Y)/H(v) over the full grid, PROPOSED-EXACT pending one-word ratification. C exact grammar specified with SEARCH_DEPTH 4, primitives cost 1, connectives free, PROPOSED-EXACT pending one-word ratification. Predictor z-scoring installed in Section 7, ratified by the author's margin choices in standardized units.

Change log, v0.6 to v0.7, per Alex final review: standardized stated explicitly in decision-table conditions 2 and 3. P-R5A-P now references the SUPPORTED row rather than numbered conditions. Both exact definitions marked board-endorsed, freezing on the author's word per P2. No protocol content changed.

Change log, v0.7 to v1.0, FREEZE: both exact definitions frozen on the author's word. Split ruled 50/50 R4-literal by the author, design-record mis-recollection corrected. C verification clause updated to describe the implemented and executed verification exactly; all 24 C assignments confirmed. Battery manifest embedded by hash; realized G2 PASS recorded. G4 probe family specified. G5 termination semantics made explicit; binding UNSTABLE definition unchanged. Instrument validation results logged. FROZEN 2026-07-18. Anchor before compute. Evidence before interpretation.