The ULR Empirical Programme — From Observation to M1–M8

The question posed by the empirical programme#

The observation of latent alignment and the need for a distinct ULR object are different claims. The empirical programme was designed to close the following chain:

1. The first six empirical atoms#

These six rows are not six discoveries of ULR objects. They are active claims recording phenomena and artefact boundaries.

2. Quantities confirmed by the zero-assumption reopening#

The reopening audit did not simply reuse earlier headlines. It separated sources, nulls, and model families again.

Earlier numbers lacking sufficient provenance—including ≥17, shared/private 52%, 48% after principal-component removal, and an exact formation onset—carry no ontological weight in the current canon.

3. How gauge-typed replication changed the conclusion#

A raw representational metric can change under a function-preserving coordinate transformation. The T1–T3 replications compared raw-coordinate measurements with their quotient-normalised, gauge-typed counterparts.

• In T1, raw effective dimension changed from 20 to 16, while the typed value remained bit-identical.
• In T2, the raw modality-specific score fell from 0.251 to 0.119, while the typed score remained 0.237.
• T3 initially failed to replicate. After the discrepancy was traced to the extraction protocol, the original trend was recovered under the last-token, final-layer, fixed-prompt condition, with CKA correlation 0.997 and retrieval Pearson correlation 0.986.

The conclusion was frozen in one sentence:

The phenomenon was not a gauge artefact, but the raw measurement was exposed to gauge artefacts.

This does not mean that the entire full-model gauge orbit was tested. The result is limited to the specified permutation and positive-diagonal typing.

4. B0–B4 and combined B*#

The value of a new quantity $Q$ is not tested against one weak baseline, but against the strongest available explanation under the same information and port contract.

To open M8, $Q$ had to add incremental value for held-out behaviour or transfer after B*.

5. U0-v1 — Moving the exact toy into a small neural system#

This experiment connected the same trained core to two different persistence mechanisms.

• A: preserve the write activation in recurrent hidden state.
• B: preserve it in a one-item attention cache and reconstruct the activation at query time.
• 32 seeds, with 24 for meta-training and 8 for meta-testing.
• Pairwise-exact activations and probabilities during passive write, tick, and read operations.
• Hidden/cache reset, clone, and overwrite operations act on the actual state container.

The maximum difference in passive probabilities and activations was 0, and CKA was 1. In 32/32 seeds, the recurrent-hidden-minus-attention-cache response contrast was negative under reset and positive under clone. Under signed-permutation co-transformation, passive output and physical response were also preserved to numerical precision.

Held-out prediction#

$Q$ substantially outperformed B2, but its advantage over B3 and B4 fell below the preregistered 0.01 nonabsorption threshold. The operational bridge is therefore positive, while the ontology verdict is Z1_WEAKENED.

6. M1 — An emergent version of the Z1 physical response#

Because U0-v1 used engineered routing, M1 tested whether stable response classes would emerge naturally from seed-only training of a homogeneous tanh RNN.

• All 64 seeds passed passive eligibility.
• Stable classes failed to form: the majority-to-outlier cluster counts were 47:1 for meta-train and 16:0 for meta-test.
• The raw response also failed to improve on an ordinary-dynamics baseline.
• Local verdict: COLLAPSED@tanh-delay-v2.

This result does not refute every physical-response hypothesis. It closes the current implementation of emergent v2 while leaving Z1 as a weakened application programme.

7. M2 — Z5 external-relation cross-fit#

M2 fixed an external semantic relation and tested whether a relation law fitted on one dataset transported to another dataset and model family.

• The fixed WordNet 3.1 relation predicted held-out Caltech and CIFAR relations.
• The result held across architecture and objective holdouts.
• The geometry-relation gate was positive.
• The retrieval-behaviour bridge deteriorated and was negative.

Z5 is therefore a weakened external baseline. The finding that an external taxonomy predicts some representational geometry survives, but it is not promoted to an internal carrier or behavioural mechanism.

8. M3 — A uniform reduction audit of seven carriers#

The final count is 0/7. This verdict closes the current registry; it does not prohibit every possible future carrier candidate.

9. M4 — A conditional definition of formation#

Formation was defined not as the onset of a metric curve, but as an event in which the structural type of an object or family changes under identity and transport.

The required elements are:

1. object identity before and after formation;
2. cross-time transport;
3. a distinction between motion within a quotient and change of structural stratum;
4. a separate behavioural bridge, not built into the definition;
5. a distinction between deformation and boundary crossing.

Because M3 has zero survivors, the current target across neural models is NO_ADMISSIBLE_TARGET. The definition is complete, but no universal instance has been established.

10. M5 — Retraction of the UAR composite#

M5 re-examined the earlier impression that UAR-I had been completed. It found that injectivity of the full-channel incidence map and unramifiedness of the joint assembly map $a_{\mathrm{asm}}\colon \Theta^{\mathrm{adm}}/G_\Sigma\to\mathcal J$ are propositions about different sources and maps.

Accordingly, ULR-ASSEMBLY-UAR-MONO was downgraded to RETRACTED-MALFORMED-COMPOSITE. Two subordinate results were preserved:

• ULR-UAR-CH-TYPED-EXCLUSION;
• ULR-UAR-ASM-UNRAMIFIED.

The localisation identity and CERT-B/C were moved to an optional strengthening layer that does not block M8.

11. M6 — Closing the baseline contract#

M6 fixed B0–B4 and B* so that every subsequent candidate would be judged by the same standard. Candidate and baseline must share the same split, information access, intervention vocabulary, precision, and resource ledger. If a baseline can execute the candidate wrapper, excluding that execution requires a separate provenance-blind doctrine.

12. M7 — Closing the hypotheses and governance#

A contract was completed that preregisters the following for each of Z0–Z7:

• object and identity;
• strongest rival;
• rival-specific falsifier;
• independent prediction;
• data, split, hash, and amendment rule;
• finite termination;
• raw receipt and validator;
• separation of author closure from independent audit.

The 14-field schemas of all eight hypotheses passed format validation. Passing a format check does not establish truth or novelty.

13. M8 — The final ontology verdict#

M8 did not take a simple vote over the preceding results. It asked whether any residual remains after every typed baseline.

Therefore,

was adopted. This NO is a conclusion within the finite registry and the declared baseline scope.

14. Canon 24's post-verdict theorem#

Even after M8, the observer-relative role problem could still be characterised exactly. For role-conditioned transcript laws $P_L,P_I$, the equal-prior Bayes risk is

Adaptive distinguishability is the supremum of total variation over admissible policies. Separately, data processing contracts total variation when an internal transcript is a garbling of an external transcript. Under a fixed infinite policy, finite-prefix error tends to zero if and only if the full path laws are mutually singular. These distinct results did not reopen M8: they establish limited-observer identifiability boundaries, not a new ontology.

15. Lessons from reproduction and audit#

• Saved-output computations matched 13/13 stdout hashes in the current environment.
• The U0-v1 validator passed 12/12 checks covering preregistration, raw shape, split, gate, verdict, and deterministic replay.
• The finite verifier for the observer theorem passed 8/8 checks, including distribution pairs, garbling, and adaptive policies.
• Code reproduction does not replace the full input-provenance and external-access contract.
• Independent audit overturned an author-side self-audit finding of “not a result defect” and identified a conclusion-level defect.

The current empirical discipline therefore treats author-side closure, independent audit, and LEDGER promotion as distinct stages.

Final empirical conclusion#

Strong alignment phenomena and exact boundary theorems exist. Yet on the current data, the measured $Q$ gain over B3/B4 was nonzero but below the preregistered nonabsorption threshold; no neural-specific ULR candidate therefore retained preregistered meaningful incremental value beyond B*. The empirical programme did not fail: its present achievement is that it maintained null tests demanding enough to overturn its preferred ontology and reach a NO verdict.