The ordinary picture

The familiar bottom-up picture says that reality is built from the smallest independent things:

particles → atoms → molecules → stars, bodies and observers

AC–WFP asks whether this may be correct as an effective description while being reversed at the deepest level:

a globally constrained Whole Ω
→ stable local restrictions and modes
→ particle-like sectors, fields and geometry
→ the familiar physical world

This does not say that electrons, atoms or tables are unreal. It asks whether they are ultimate bricks, or whether they are more like persistent patterns supported by a deeper whole.

A simple analogy

A whirlpool is real: it has a location, lifetime, shape and causal effects. But it is not a separate substance added to water. It is a stable pattern made possible by the organization of the larger flow.

The whole-first hypothesis asks whether a physical “part” could be similar:

A particle or local subsystem may be a stable, reconstructible and predictive mode of a deeper global relational structure, rather than an independently existing primitive from which the Whole is assembled.

The analogy is only an intuition. The scientific work begins when “stable pattern” is replaced by measurable requirements.

What the Python arena actually does

The arena does not simulate the birth of our universe and does not test consciousness directly. It tests a smaller prerequisite:

1. generate finite relational worlds with hidden organization;
2. give proposal mechanisms only the allowed training view;
3. ask them to discover candidate effective parts without seeing held-out or sealed information;
4. test whether those candidates predict unseen data and independently reconstruct disjoint information;
5. charge the full cost of the model, search, codebook and machinery;
6. test the same mechanisms on matched null worlds designed to look tempting without containing valid closure;
7. repeat the scoring under two codebooks and require audit, signature, replay and reference-evaluator agreement.

A positive result would mean only that a specific observational closure mechanism candidate survived this finite test. It would not yet derive particles, spacetime, quantum theory, gravity, consciousness or AC.

The one-sentence project summary

We are turning the philosophical idea “parts may be expressions of a Whole” into a programme that can fail: a candidate part must earn prediction, recovery, stability, representation robustness and null specificity under blind, cost-complete testing.

D6.1 Current live status: the repaired multiday run is healthy and near the end of PROPOSE

The latest safe RICH3 snapshot records the active multiday profile at 19 July 2026, approximately 11:22 CEST:

The inventory and safe row scan agree on 12,484 candidates and 12,484 receipts. The live-progress JSON was read one write earlier and showed 12,483 / 12,483 while already counting 12,484 completed heartbeats. That one-file difference is a normal concurrent-snapshot race, not evidence of lost persistence.

All 23 arms were at either 542 or 543 completed tasks out of 576. Every recorded task remained on attempt 1, and the extract reported zero unreadable heartbeats. The run therefore shows no arm starvation, retry storm, deadlock or recurrence of the earlier false pool timeout.

The scientific boundary is unchanged: the evaluator has not opened, no held-out result exists, and proposal-stage aggregates cannot be treated as wins.

completed proposal heartbeats
= candidate files
= candidate receipts
= 3,970

D6.2 What has already completed in the current-generation ladder

The 19 July extract contains finalized, replayed evidence for:

smoke
instrument_smoke
mini
standard
adversarial_nulls
deep
daily

The active multiday run is still in proposal generation and therefore is not yet a scientific result. weekly has not started; the canonical launcher begins it only after multiday finalization and strict replay pass.

D6.3 The most interesting completed result: a narrow MPRC2 signal in deep

The deep profile contains 336 independent systems, 7,728 signed proposals and 15,456 evaluation rows. Its most relevant arm-level results are:

This comparison suggests a specific development hypothesis:

The temporal component of MPRC2_FULL may not increase raw sensitivity, but may improve specificity by rejecting structures that look part-like without persisting as the same organization through time.

That is compatible with the whole-first idea that an effective part is not merely a cluster visible in one frame. A real part-like sector should retain predictive and reconstructive identity through change.

This remains a post-hoc development interpretation, not a confirmed mechanism.

D6.4 One codebook-stable observational certificate candidate

One MPRC2_FULL candidate in deep passed the observational certificate under both codebooks:

Across all 336 MPRC2_FULL system pairs, the two codebooks were strongly aligned:

predictive-delta Pearson correlation: 0.9982
recovery-delta Pearson correlation:   0.9995
predictive sign agreement:            98.21%
recovery sign agreement:             100.00%
certificate-pass discordances:         0

This makes a pure codebook artifact less likely for the observed candidate. It does not make the candidate a physical discovery.

D6.5 Why the result is still weak

The signal is rare and does not yet replicate cleanly across profiles:

standard: MPRC2_FULL 0 wins / 0 null wins
deep:     MPRC2_FULL 3 wins / 0 null wins
daily:    MPRC2_FULL 1 win  / 1 null win

The development-only secondary max-statistic permutation p-value is 1.0 for MPRC2_FULL and the other arms. The intervention axis is explicitly RESERVED_UNEARNED. No candidate is promotion-eligible.

The honest statement is therefore:

MPRC2_FULL has a small, scale-dependent and codebook-stable development hint in deep, with better null specificity than its non-temporal ablation; it does not yet have robust cross-profile replication or confirmatory statistical support.

D6.6 Useful negative evidence

The negative results matter because they show that the instrument is not designed to praise every preferred concept.

• The current LEC variants produced no system-level wins in deep or daily. Energy-based language remains a proposal lens, not a physical energy claim.
• The current MSR2 finite proxy and its NO_D, NO_FLOW, NO_RECOVERY, D_SHUFFLE and RHO_SHUFFLE ablations produced no wins. They do not justify modular-time or spectral-geometry interpretation.
• SINGLETON won often but also won on many null systems. This demonstrates that a highly local, particle-like decomposition can be a useful effective code without being a specific indicator of fundamental particle ontology.
• ENVELOPE_MPRC_SYNERGY did not show specific arm-level success in deep.

Under Rank-Don’t-Eliminate, these mechanisms remain archived for new representations, scales and intervention tests, but they are not currently load-bearing.

D6.7 What this means for the Whole → parts idea

The latest evidence modestly strengthens one limited bridge:

global relational process
→ discoverable stable effective restrictions

It does not yet establish the much longer physical chain:

Ω
→ quantum structure
→ spacetime and causal geometry
→ fields and particle sectors
→ Standard Model and gravity

The best current interpretation is:

1. whole-first effective parts are operationally definable rather than merely metaphorical;
2. simple local decompositions can work while remaining nonspecific, so effective usefulness does not prove ontological primacy;
3. persistence through time may be part of what distinguishes a genuine effective sector from a static pattern;
4. the current evidence is still synthetic, observational and development-only;
5. AC remains an exact interpretive twin at AC0 and adds no earned equation or prediction.

D6.8 What would count as a meaningful next advance

The active multiday run should complete proposal generation, open the sealed evaluator in the correct audit order, finish all 26,496 evaluations, finalize, close the audit chain and pass strict replay. The canonical launcher should then repeat the process for weekly.

The key scientific question is whether larger-scale held-out evidence preserves the same pattern:

MPRC2_FULL gains on structured systems
+
low matched-null leakage
+
codebook stability
+
separate predictive and disjoint-recovery advantages
+
cross-profile replication

If that survives, the next campaign should freeze a fresh preregistered split, preserve one source identity across its ladder, and add a genuinely intervention/autonomy axis. If it does not survive, the right response is a sharper collision design—not a larger brute-force run chosen merely to rescue the preferred hypothesis.

D6.9 Current verdict

Whole → effective parts:     alive; increasingly testable
Whole → physical particles:  open; not yet derived
Whole-first physics:         formal seed / development programme
Current multiday state:      healthy PROPOSE at 94.2331%
Held-out multiday evidence:  not yet available
AC interpretation:           AC0; scientifically unearned
Arena 0A:                    closed

The correct tone is positive but exact. The programme has progressed from a philosophical reversal to a working instrument that can produce clean negative results, detect false local shortcuts, preserve rare candidates, enforce blind evaluation and expose its own engineering failures. That is meaningful progress. The next potential gain is no longer “another interesting idea”; it is a larger-scale held-out test of a frozen mechanism.

D6.10 What we are building and what success could mean

We are not trying to prove AC by attaching a grand interpretation to one attractive equation. We are building a research laboratory for a smaller and sharper question:

When does a stable local part deserve to be treated as real relative organization inside a larger Whole, rather than as a convenient but misleading compression shortcut?

The arena has already established several durable methodological lessons:

• compression by itself is not closure;
• a temporal break is not automatically a part;
• low-rank, spectral and latent organization can imitate deeper structure;
• prediction and genuinely disjoint recovery must be earned separately;
• a preferred mechanism must be capable of losing against matched nulls and strong baselines.

The strongest current working shape is still provisional:

global organizational or accounting envelope
+
local predictive–reconstructive operation that persists through change
=
possible effective-part signature

A realistic success ladder is:

1. Reliable effective-part detector. A reproducible method that finds stable predictive/reconstructible restrictions on fresh systems and rejects matched nulls after full costs.
2. Theory of relative autonomy. The same criterion survives interventions, scale changes, representation changes, causal-state tests, local-to-global gluing and redundant recovery.
3. Physical bridge. A compact whole-first mechanism begins to recover causal order, locality, geometry-like structure or stable field/particle-like modes without inserting the answer.
4. Independent prediction. The programme fixes a nontrivial quantitative consequence in advance, distinguishes it from serious rival programmes and survives independent replication.

Even Level 1 would be useful beyond foundational physics—in complex systems, causal emergence, automated scientific discovery, AI representation learning, biology and network science. Level 2 would amount to a general theory of when parts become relatively autonomous. Level 3 would make AC-WFP a serious candidate programme in foundational physics. Level 4 would be the decisive scientific breakthrough.

The maximum credible Ω-neutral horizon is a new whole-first foundational programme that derives part-like structure and at least one protected prediction. The maximum AC-specific horizon is harder: AC must alter an equation, admissible structure or probability relative to the neutral Ω twin, and that difference must survive independent experiment. A neutral success does not silently become AC evidence.

We do not yet have a new physical theory. We do have an original hypothesis, an increasingly rigorous self-falsifying instrument and a concrete sequence of tests that could—if the evidence continues to cooperate—grow into one.

D5.1 Why this update changes the document

V4-DRAFT.4 recorded an A3 partial live snapshot. V4-DRAFT.5 replaces that partial snapshot with the completed A3 evidence capsule.

The status boundary is unchanged:

A3 completed operationally;
A3 did not confirm AC-WFP;
A3 did not open Arena 0A;
A3 did not promote any physics claim;
A3 produced better A4 hypotheses.

The correct reading remains:

progress is allowed before confirmation;
promotion is not.

D5.2 Plain-language interpretation

The project is trying to make the Whole-first idea testable. Instead of assuming that local parts are primitive, the arena asks whether stable effective parts can be discovered as predictive and reconstructible restrictions of a larger relational process.

The completed A3 result is useful because it learned to say “no” more precisely. It distinguishes several false friends:

big compression gain
≠ closure mechanism

time segmentation
≠ effective part

latent proposal
≠ discovery

low-rank/spectral regularity
≠ whole-first evidence by itself

The strongest current content-level hint is not raw MPRC2. It is the combination of a global accounting envelope and a local non-temporal structural operation:

global low-rank or spectral/accounting structure
+
local non-temporal MPRC2 move/overlap operation
=
A4-worthy effective-part candidate signature

This is still a post-hoc development clue. It becomes evidence only if frozen in advance and tested on a fresh A4 split.

D5.3 Mechanism summary under both-codebook gain

The table counts systems where the mechanism gains against the best trivial control in both codebooks. Positive systems are structured systems; null systems are matched adversarial systems. The precision column is descriptive development telemetry, not a promotion criterion.

D5.4 MPRC2 operation diagnostics: the main A3 lesson

Raw MPRC2 mixes several behaviours. A3’s main improvement is to split MPRC2 by operation type.

This is the most important A3 scientific-method result:

A candidate effective part should not be accepted merely because the time series can be segmented. It must survive operation diagnostics that separate non-temporal structural changes from change-point compression.

D5.5 Official frozen certificate rows from A3

A3 tested A2-derived frozen post-hoc certificate hypotheses as development hypotheses. None reached scientific promotion. The best official row was useful but failed the null ceiling.

A3 therefore correctly refuses promotion:

scientific_promotion_allowed = false
arena_0a_unlocked = false
fresh_final_v4_preregistration_required = true

D5.6 New A3-discovered post-hoc clues for A4

The following are not scientific results. They are A3-discovered development clues that should be given to MAL and then either frozen for A4 or demoted.

The strongest A4 design question is whether LOW_RANK accounting or SPECTRAL accounting gives the better non-temporal closure certificate under a fresh split.

D5.7 LEC status after completed A3

LEC failed specificity:

LEC specificity gate: FAIL
positive-specific wins: 20 / 768
null-specific wins:     89 / 384
null specificity rate:  0.2318
ceiling:                0.05

Interpretation:

• LEC_PROPOSAL_ONLY should remain a proposal lane, not a judge.
• LEC_NO_HIDDEN being cleaner than several hidden-energy variants weakens the current hidden-energy story.
• Future LEC must beat LEC_NO_HIDDEN, LEC_RANDOM_ENERGY, LEC_SHUFFLED_TIME and LEC_SHUFFLED_RELATIONS before it earns any mechanism status.
• This is a demotion, not deletion: RDE keeps LEC in the archive for redesign.

D5.8 MSR2 status after completed A3

MSR2 remains theoretically important but implementation-weak:

Interpretation:

• D and flow appear behaviourally relevant because shuffles/ablations change results.
• rho and recovery are still too close to the full arm.
• MSR2 must be redesigned before it can carry any Ω-MSP claim in the finite arena.
• RDE keeps MSR2 alive as a redesign lane rather than deleting it.

D5.9 Temporal-order sensor failure

A3 passed 30 / 31 implementation gates. The failed gate is important:

06_TEMPORAL_ORDER_SENSOR: FAIL
time_reversal_delta = 0 bits

This does not invalidate A3 as a development run, because A3 explicitly remains NOT_ELIGIBLE. But it must be fixed or explained before A4. Since the whole purpose is to avoid confusing temporal compression with effective parts, A4 must include a stronger temporal-order sensor and an explicit time-reversal/null diagnostic.

D5.10 Rank-Don’t-Eliminate upgrade

A3 demotes several mechanisms, but demotion must not become permanent deletion. The next arena should implement:

rank_dont_eliminate_archive.jsonl

Each candidate should be stored with:

• mechanism name and version;
• representation and scale;
• codebook context;
• public family tags;
• positive coverage and null leakage;
• reason codes;
• demotion reason;
• resurrection eligibility;
• next-lens triggers.

A new lens, representation, codebook, intervention family, causal-state sidecar, sheaf sidecar, QEC recovery sidecar, or multiscale sidecar should automatically trigger a resurrection sweep over demoted candidates.

D5.11 A4 / MAL handoff

The next honest move is not Arena 0A. The next honest move is a MAL-assisted A4 design council.

MAL should not be asked:

Is AC-WFP true?

MAL should be asked:

Given final A3, what is the smallest strict A4 confirmation design
that freezes candidate rules in advance, improves temporal controls,
keeps AC0, prevents low-rank/spectral/latent self-deception,
and implements Rank-Don’t-Eliminate?

Recommended A4 candidate set for the MAL council:

PRIMARY:
LOW_RANK + MPRC2_NON_TEMPORAL_OP

SECONDARY:
LOW_RANK + MPRC2_MOVE_OVERLAP

EXPLORATORY CHALLENGERS:
SPECTRAL_CLUSTERING + MPRC2_NON_TEMPORAL_OP
SPECTRAL_CLUSTERING + MPRC2_MOVE_OVERLAP

LOW-RECALL CLEAN CHECKS:
LOW_RANK + MPRC2_MOVE_ONLY
LOW_RANK + MPRC2_OVERLAP_ONLY

NEGATIVE / ADVERSARIAL CONTROLS:
MPRC2_CHANGEPOINT_ONLY
LOW_RANK + MPRC2_CHANGEPOINT_ONLY
CHANGE_POINT
DYNAMIC_SBM
HMM_LATENT_REGIME
spectral_without_recovery nulls
low_rank_without_parts nulls

D5.12 Current content-level conclusion

The completed A3 run is the best AC-WFP arena result so far, but for the right reason: it did not promote a theory. It sharpened the instrument.

The updated content verdict is:

A3 completed cleanly as an engineering/development run.
A3 remains DEVELOPMENT_ONLY and NOT_CONFIRMATION.
A3 shows raw MPRC2 is contaminated.
A3 shows change-point-only wins are a temporal trap.
A3 shows non-temporal MPRC2 operations are the best current closure-like signal.
A3 shows LOW_RANK and SPECTRAL accounting are not optional controls.
A3 demotes LEC and MSR2 to redesign lanes.
A3 produces A4-worthy hypotheses, not evidence.

W1 — compatible local facts admit a Whole

Every jointly admissible family of perspective-indexed local facts belongs to at least one compatibility class.

W2 — whole-first purification

Every mixed local state has a pure completion, essentially unique up to reversible transformations on the complement, under the assumptions of the reconstruction theorem used.

W3 — no privileged classical distinction

Pure alternatives of the same operational type are reversibly connected unless an independently stated conserved structure distinguishes them.

W4 — causal composition

Present outcome probabilities cannot depend on later freely chosen operations.

W5 — local distinguishability or an explicit replacement

Global relational states must be operationally reconstructible from an adequate family of local tests, or the theory must state precisely why a weaker composition rule is used.

Known operational reconstructions show that quantum theory can follow from suitable informational principles, with purification playing a central role [1,2]. AC–WFP has not yet derived the complete axiom package from one smaller Whole-first postulate.

Stage-I status: a disciplined reconstruction programme, not a completed derivation of QM.

9.1 Candidate object

For a finite relational history

\[ X=(A_t)_{t=0}^{T-1}, \]

a candidate closure is

\[ C=(M,z,r,H). \]

• M={M^(0),…,M^(R−1)} is a finite list of binary node-to-part covers. Covers may overlap, but every node must be covered.
• z=(z_0,…,z_{T−1}) selects which cover is active at each time. Static candidates use one cover and z_t=0.
• r is a declared train-fitted recovery/reconstruction map.
• H is an optional hierarchy of coarser effective parts. It is serialized and charged even when empty.

The canonicalizer removes duplicate covers, remaps regime labels deterministically, removes empty parts, canonicalizes part-column order and rejects uncovered nodes. Candidate identity is the SHA3-256 hash of the canonical serialized object.

9.2 Blind temporal split

The mechanism receives only the visible finite relational system and the declared training times. It may use internal train/validation splits within training history, but it cannot inspect held-out score times, generator identity, target cover, target regimes, effect target or oracle score.

A mechanism returns one serialized candidate and a complete proposal trace. The held-out scorer fits no new proposal parameters. A recovery map is estimated from the permitted fit history and evaluated on later held-out time.

9.3 Temporal predictive code

For every unordered node pair (i,j) at time t, the context contains:

• the candidate regime z_t;
• the canonical part signatures of i and j under M^(z_t);
• whether the pair shares one or more parts;
• the previous relational symbol A_(t−1,ij), or BOS at the beginning.

A frozen Dirichlet-multinomial prequential code supplies

\[ L_{\rm temporal}(X_{\rm score}\mid X_{\rm fit},C). \]

Because the code is sequential, reversing time can change the score. Because category priors are symmetric, a global permutation of relation labels must leave the total score invariant when the candidate is transported consistently.

9.4 Reconstruction code

The fit history determines a context-indexed modal recovery map. On score time, the arena records whether each recovered symbol is correct and integrates the resulting error sequence under the frozen codebook. For alphabets larger than two, wrong-symbol identity carries an additional declared cost.

This produces

\[ L_{\rm reconstruction}(X_{\rm score}\mid X_{\rm fit},C,r). \]

Prediction and reconstruction are both required because a model may predict aggregate statistics without supporting a reusable local recovery map, or reconstruct isolated observations without learning temporal law.

9.5 Complete objective

The decisive sensor is

\[ L_{\rm total}(C;X) = L_{\rm structure}(C) +L_{\rm temporal} +L_{\rm reconstruction} +L_{\rm intervention} +L_{\rm machinery}. \]

In Arena 0X-H, L_intervention=0 and is marked reserved. It cannot be silently interpreted as an intervention result.

The best trivial/random or strong classical baseline is the comparison point. The planted oracle is evaluator-only and appears after every proposer has committed its candidate. Oracle underperformance is retained as an objective-domain warning rather than hidden.

9.6 Canonical machinery ledger

The primary ledger contains explicit non-negative fields:

common_kernel
mechanism_dsl
recognition_model
generative_model
energy_grammar
latent_state
negative_generator
training_schedule
sampler
temperature_precision
search_grammar
candidate_structure
recovery_map
calibration
compute
memory
synthetic_replay
D_debt
rho_debt
channel_debt
prediction_residual
reconstruction_residual
exceptions

Python source-file compression is retained only as a secondary audit if desired. The primary scientific code length is a canonical mechanism language and serialization, so comments and formatting cannot decide a scientific winner.

9.7 Three independent checks

1. The production scorer writes the decisive ledger.
2. A separately implemented reference scorer must reproduce total bits and candidate hash.
3. An audit scorer independently reconstructs additive totals and the reconstruction residual.

The reference and audit modules may not import the production coding or mechanism modules they check.

10.1 MPRC2 — richer predictive–reconstructive search

MPRC2 begins from degree, spectral, random and—where finite size permits—exhaustive partitions. Its grammar includes:

node move
split
merge
overlap add
overlap remove
part birth/death through split/merge
local repair
change-point regime split
multistart selection

Every proposal is independently scored on an internal training split. Proposal count, scorer evaluations, compute and memory are recorded. The final candidate is chosen by deterministic (train total bits, candidate hash) order.

MPRC2 earns credit only if at least two distinct move classes are exercised in known-answer or smoke systems, the proposal budget is obeyed, repeated runs are deterministic and held-out gains survive strong baselines.

10.2 MSR2 — operational modular–spectral recovery

MSR2 constructs an intrinsic weighted relational operator from training history, derives a normalized Laplacian-like D, a state weight ρ, a flow scale s and a channel mixture/noise parameter η. These quantities must change the similarity matrix from which candidate covers are recovered.

Required controls include:

D_shuffle
rho_shuffle
random_D
no_D
no_flow

The selected D, ρ, s, η and numerical precision are serialized or charged. A run that logs these symbols without changing a proposal fails the mechanism-causality gate. Finite matrix experiments are described as finite spectral analogues; they do not demonstrate nontrivial outer modular time.

10.3 LEC — proposal-only Latent Energy Closure

LEC separates:

• a recognition path that maps visible training history to candidate latent organization;
• a generative compatibility model that assigns energy to (X_train,C);
• an independent MDL judge.

The first safe energy is small and log-linear:

\[ E_\theta(X_{\rm train},C) = \theta^\top f(X_{\rm train},C), \]

with features such as within/cross separation, compactness, temporal persistence, overlap burden and regime count. The candidate distribution is only a proposal device,

\[ q_\theta(C\mid X_{\rm train}) \propto \exp[-E_\theta(X_{\rm train},C)]. \]

For small domains, the finite normalizer is computed exactly. For larger domains, any approximate sampler or contrastive method must first be calibrated against exact cases and is charged in sampler, negative_generator, training_schedule and precision fields.

The operational firewall is:

energy ranks a bounded pool
→ top-K candidates are exposed
→ independent train MDL selects one
→ independent held-out production/reference/audit scorers judge it

Top-K search advantage is not free: pool size, top-K, energy grammar, parameter precision and evaluations are charged.

Mandatory LEC arms are:

LEC_PROPOSAL_ONLY
LEC_NO_HIDDEN
LEC_RANDOM_ENERGY
LEC_SHUFFLED_TIME
LEC_SHUFFLED_RELATIONS

A latent-state claim is not earned unless the full LEC arm beats LEC_NO_HIDDEN; a meaningful energy claim is not earned if random energy or shuffled controls reproduce the gain.

10.4 Why the challengers are not merged

A blended mechanism could hide which assumption carries the result. MPRC2 tests a generic closure grammar. MSR2 tests a typed spectral/state/flow route. LEC tests learned latent compatibility. They share the external scorer and budgets but not proposal logic. A later hybrid requires separate factorial ablations and a fresh contract.

10.5 Strong classical baselines

The minimum nontrivial implemented A2 baseline set is:

SPECTRAL_CLUSTERING
DYNAMIC_SBM
HMM_LATENT_REGIME
CHANGE_POINT
LOW_RANK
PREDICTIVE_STATE_HEURISTIC

The current code’s legacy report label PREDICTIVE_STATE refers to the final heuristic arm above. It does not implement epsilon-machine or causal-state reconstruction. A challenger that beats only random cover has not earned novelty.

The next isolated predictive-equivalence challenger is:

CAUSAL_STATE_MACRO

It is specified in this paper but is not claimed as implemented in Arena v0.2.0a2.

10.6 Trivial and evaluator-only controls

WHOLE
SINGLETON
RANDOM_COVER
SEALED_ORACLE_EVALUATOR_ONLY

Random cover receives the matched proposal budget. The sealed oracle never proposes, tunes thresholds or influences stopping. It reports whether the frozen objective can reward the planted target at all.

10.7 CAUSAL_STATE_MACRO — true predictive-equivalence challenger

Let two visible histories h and h' be equivalent when they induce the same conditional future law within a frozen finite-sample tolerance:

\[ h\sim_\epsilon h' \quad\Longleftrightarrow\quad D\!\left[P(X_{t:}\mid h),P(X_{t:}\mid h')\right]\le\epsilon. \]

CAUSAL_STATE_MACRO must infer the equivalence classes from training history only, serialize the state map and transition law, and pay for:

• history depth and feature grammar;
• distribution estimator and smoothing;
• equivalence tolerance or clustering code;
• number of causal states;
• transition/emission parameters;
• search and calibration;
• held-out predictive residuals.

Known-answer tests must include processes with analytically known predictive states, processes where a simpler Markov order is sufficient, and nulls where finite-sample clustering invents spurious states. This challenger is valuable precisely because it reaches prediction and minimal state from a formalism independent of MPRC2, MSR2 and LEC [38].

11.1 Predictive causal states are not causal emergence

Two uses of “causal” must remain separate:

causal state
= equivalence class of histories with the same predictive future law

causal emergence
= intervention-level causal informativeness of a declared macrodescription

A causal-state model may be strongly predictive without establishing intervention-level macro causation. Causal emergence requires a frozen intervention set, macro map, causal channel, estimator and model-cost ledger. The later evaluator records

\[ \Delta_{\rm CE} = EI_{\rm macro}-EI_{\rm micro} -L_{\rm coarse\ grain} -L_{\rm intervention\ model}, \]

but does not replace held-out MDL and cannot be computed from observational compression alone [41].

11.2 Sheaf compatibility as the G certificate

For a cover of local contexts U, define local sections F_U, restriction maps \rho_{UV} on overlaps and a gluing obstruction:

\[ \mathfrak S_\Omega = \left(\{F_U\},\{\rho_{UV}\},\mathcal O_{\rm glue}\right). \]

The sidecar must distinguish:

• exact global sections;
• pairwise-compatible but globally obstructed cases;
• multiple inequivalent global completions;
• noisy cases with a minimum repair cost;
• presentation-equivalent cases under node, relation and local-basis changes.

SHEAF_COMPATIBILITY_EVALUATOR is initially an evaluator, not a proposer. It cannot be promoted until finite KATs have exact answers. This formalizes Ω_compat without treating category/sheaf vocabulary as evidence by itself [43].

11.3 QEC-style recovery as the Q certificate

A recovery ladder separates a real reconstructible restriction from a fragile single copy:

1. identifiable restriction;
2. persistence under the declared dynamics;
3. explicit train-fitted recovery map;
4. recovery after bounded erasure/noise;
5. redundant recovery from more than one authorized region where predicted;
6. covariance across equivalent presentations;
7. graceful degradation rather than an unreported cliff.

Development families should include:

QEC_RECONSTRUCTIBLE_PART
FRAGILE_SINGLE_COPY_CONTROL
REDUNDANT_BUT_NONLOCAL_CONTROL
RANDOM_LINEAR_CODE_CONTROL

These are controlled mathematical analogues, not evidence that our universe is a holographic code [7,42].

11.4 Predictive rate-distortion and multiscale persistence as the S certificate

A scale ladder should expose the trade-off

\[ L_{\rm macro} \quad\leftrightarrow\quad D_{\rm future}, \]

where D_future is a frozen future-prediction distortion. The proposed PREDICTIVE_RATE_DISTORTION_LADDER asks whether related macroparts recur across neighbouring compression levels and whether repeated

micro model → parts → effective model → parts

approaches a stable orbit or fixed point. The required outputs are the rate-distortion frontier, candidate transport across scales, basin size, hysteresis, perturbation recovery and full hierarchy cost [39,40,44].

This is a later sidecar. A flat-cover A2 win does not silently earn multiscale physicality.

Capacity

For a suitable weakly gravitating bounded system,

\[ I_{\max} \lesssim \frac{2\pi EL}{\hbar c_*\ln2}. \]

Distinguishable-change rate

\[ \dot N_\perp \le \frac{2(E-E_0)}{\pi\hbar}. \]

Irreversible erasure cost

\[ E_{\rm erase} \ge k_BT\ln2\,\Delta I. \]

These formulas answer different questions [15–17]. A common calibration is promoted only if one non-arbitrary definition of region, energy above ground, causal extent and cone works across held-out systems.

The deeper WFP lesson is:

Energy alone is not information. Physical information is energy-enabled structured distinguishability within a causal and relational boundary.

Branch M1 — unitary relative records

global quantum evolution
→ system–apparatus–memory entanglement
→ decoherence and stable relative records
→ internal access by a self-maintaining centre

Schematically,

\[ \sum_k c_k|s_k\rangle \longrightarrow \sum_k c_k |s_k\rangle|m_k\rangle|r_k\rangle|\chi_k\rangle. \]

AC is not allowed to choose k or alter Born weights by assertion.

Branch M2 — Penrose-style objective reduction

A gravity-related instability may produce genuine reduction, heuristically [10,11]

\[ \tau_{\rm OR}\sim\frac{\hbar}{E_G}. \]

This branch must define EG, regularization, stochastic dynamics, conservation and experimental consequences. If spacetime is emergent, it must also explain what defines EG before a classical metric exists.

Branch M3 — agnostic operational measurement

Predict stable records and observed statistics without committing to collapse or no-collapse ontology.

These branches must remain separate. No-collapse, objective reduction, twistor theory, CCC, microtubule biology and consciousness are not one package.

Local expression

\[ \boxed{ RC_i:=\mathcal R_i(AC) } \]

or heuristically

\[ RC_i=AC\cdot R_i, \]

where Ri denotes the local relation/resonance, embodiment and access structure.

Global reconstruction

\[ \boxed{ AC \simeq \operatorname{Glue}_{R} \bigl(\{RC_i\}\bigr), } \]

which is the disciplined meaning of AC = RC × R: the Whole is not a sum of isolated minds, but the globally compatible actuality reconstructed through their relations and all other admissible restrictions.

Neither equation is currently a laboratory law.

H₀ — no specific closure mechanism

Any apparent gain is reproduced by a strong classical model, random proposal search, representation leakage, objective alignment with one generator family or uncharged machinery.

H₁ᴹᴾᴿᶜ²

MPRC2’s richer closure grammar yields held-out temporal compression and reconstruction beyond matched classical and random controls, with stable transported candidates.

H₁ᴹˢᴿ²

Operational spectral/state/flow proposals yield a specific advantage that disappears under D, ρ, flow or channel ablations and survives full spectral debt.

H₁ᴸᴱᶜ

Proposal-only LEC finds useful latent organization beyond classical baselines; the advantage requires reachable latent candidates, meaningful energy features and hidden regimes rather than random energy, time shuffling or relation shuffling.

H₁ᶜˢ — predictive-equivalence sidecar

A true causal-state reconstruction yields a smaller held-out predictive representation than PREDICTIVE_STATE_HEURISTIC, HMM and matched Markov-order controls after state-inference cost.

H₁ᴳ / H₁Q / H₁I / H₁S — certificate sidecars

Sheaf gluing, redundant recovery, intervention efficacy and multiscale persistence each supply information not reducible to the core MDL score. These hypotheses are isolated, KAT-first and not active endpoints in Arena v0.2.0a2.

28.1 Positive development laws

1. block_static
2. markov_parts
3. change_point_parts
4. dynamic_membership
5. overlapping_hypergraph
6. causal_history
7. parity_xor
8. program_generated
9. spectral_aligned
10. spectral_anti_aligned
11. nonlocal_delayed

28.2 Adversarial null laws

1. clusterable_nonpredictive
2. global_latent_confounder
3. low_rank_without_parts
4. time_compressible_without_closure
5. spectral_without_recovery
6. local_prediction_without_reconstruction

These nulls prevent the arena from equating clustering, temporal predictability, low rank, spectral structure or local Markov persistence with effective closure.

28.3 Effect calibration

For selected development systems, the generator searches a frozen noise ladder and records the realized oracle-versus-control margin. Approximate targets are diagnostics, not guaranteed properties. A target that fails to clear the objective is retained in the objective-miss ledger.

Final confirmation must withhold entire laws or law constructors, not merely new seeds from familiar code paths.

29.1 Implemented Arena v0.2.0a2 core

MPRC2
MSR2
LEC_PROPOSAL_ONLY
LEC_NO_HIDDEN
LEC_RANDOM_ENERGY
LEC_SHUFFLED_TIME
LEC_SHUFFLED_RELATIONS
SPECTRAL_CLUSTERING
DYNAMIC_SBM
HMM_LATENT_REGIME
CHANGE_POINT
LOW_RANK
PREDICTIVE_STATE_HEURISTIC     # legacy runtime label: PREDICTIVE_STATE
WHOLE
SINGLETON
RANDOM_COVER
SEALED_ORACLE_EVALUATOR_ONLY

All non-oracle arms see the same visible data and declared training times. The oracle is evaluated only after proposals are committed.

29.2 Specified KAT-first sidecars — not implemented in A2

CAUSAL_STATE_MACRO
SHEAF_COMPATIBILITY_EVALUATOR
QEC_RECONSTRUCTIBLE_PART
CAUSAL_EMERGENCE_EVALUATOR
PREDICTIVE_RATE_DISTORTION_LADDER

A sidecar must first demonstrate exact known-answer behaviour, independent cost accounting and no leakage. It cannot join a final winner rule merely because it produces an interesting retrospective diagnostic.

29.3 Development-only diversity archive

A Quality-Diversity archive may retain high-quality candidates across descriptors such as part count, overlap, regime count, hierarchy depth, recovery redundancy, causal-state complexity, gluing obstruction and multiscale persistence. It is an anti-collapse search memory. Archive occupancy or novelty is never a scientific endpoint and all selected candidates still pay the complete search ledger.

36.0 Implemented A2 core

acwfp_arena/
  data/
    generators.py
    isomorphisms.py
    taint.py
  coding/
    production_ledger.py
  mechanisms/
    base.py
    mprc.py
    msr.py
    lec.py
    baselines.py
    controls.py
  reference/
    reference_scorer.py
  audit/
    audit_scorer.py
    import_firewall.py
  qualification/
    evaluation.py
    qualification.py
    kats.py
  operations/
    atomic persistence, resume, telemetry, timeout/requeue
  runners/
    master.py
    live_extract.py
    replay.py
    run0a.py

36.0.1 Specified next sidecar modules

acwfp_arena/
  sidecars/
    causal_states.py
    sheaf_compatibility.py
    qec_recovery.py
    causal_emergence.py
    predictive_rate_distortion.py
    quality_diversity_archive.py
  certification/
    effective_part_certificate.py

These paths describe the next isolated build target; they are not asserted to exist in v0.2.0a2.

36.1 Operational requirements

• true CPU processes through ProcessPoolExecutor with spawn;
• worker count from CLI or batch argument;
• one-line compact CMD status with elapsed time, ETA, rate, workers, active tasks, saved tasks and errors;
• atomic per-task data and receipt before progress advances;
• exact config/source identity on resume;
• quarantine and recomputation of corrupted tasks;
• retry-and-snapshot fallback for transient Windows file locks;
• active PID/task/arm/codebook/heartbeat visibility;
• per-arm and per-codebook timing separated from scientific score;
• optional timeout and whole-pool recycle with persistent recovery history;
• master ladders from selftest through smoke, mini, standard, evening, overnight, deep and multiday;
• leakage-safe live ZIP extraction during a running or interrupted experiment.

36.2 Required evidence bundle

qualification_report.json
outcome.json
all_ledgers.jsonl
production_scores.jsonl
reference_scores.jsonl
audit_scores.jsonl
all_candidates.jsonl
generator_diversity_report.json
naturality_report.json
promotion_readiness_report.json
effective_part_certificates.jsonl
budget_report.json
arm_timing.jsonl
worker_telemetry.jsonl
leakage_report.json
run_state.json
checkpoint.json
repair_ledger.json
manifest.json
file_manifest.json
SHA3SUMS.txt
SHA256SUMS.txt
report.md
report.html

Sidecar-specific files are required only when their endpoint is activated, and their absence must be recorded as UNEARNED, not interpreted as zero effect.

Phase V4-0 — instrument repair

Engineering status: completed in A2 reduced validation. The temporal candidate object, independent scorer, latent LEC path, generator laws, machinery ledger, production/reference/audit parity, telemetry, resume and fail-closed boundary are implemented. This is not a scientific pass.

Phase V4-1 — repaired A2 challenger tournament

Run MPRC2, MSR2, proposal-only LEC, LEC ablations and strong classical baselines on fresh A2 development outputs. Mine objective misses, false positives and disagreement cases rather than repeating easy seeds.

Phase V4-1S — KAT-first certificate sidecars

In separate outputs, build CAUSAL_STATE_MACRO, SHEAF_COMPATIBILITY_EVALUATOR, QEC recovery controls, causal-emergence evaluator and predictive-rate-distortion ladder. Each must pass exact finite KATs before touching a final endpoint.

Phase V4-2 — unseen-law transfer

Freeze complete generator laws as development holdouts. A mechanism that succeeds only on aligned latent-Markov, low-rank or code-like families is not promoted.

Phase V4-3 — final contract selection

Retain only mechanisms, certificate axes and controls that pass kill-tests. Freeze exact thresholds, codebooks, budget matching, approximation tolerances, statistics, multiplicity policy and complete failure rules.

Phase V4-4 — fresh confirmation

Generate a new sealed split after the final contract hash is fixed. Only a compatible signed pass from the final qualification instrument may open Arena 0A.

Phase V4-5 — evidence-driven paper freeze

Final V4 records what survived. Failed mechanisms are demoted explicitly; they are not preserved by changing interpretation after the data.

40.1 CAUSAL_STATE_MACRO

Test predictive-equivalence states against the heuristic predictive-state baseline, HMM and matched Markov-order controls.

40.2 SHEAF_COMPATIBILITY_EVALUATOR

Test exact gluing, obstruction, ambiguity and minimum repair under local-to-global consistency.

40.3 QEC/redundant-recovery control family

Test multiple authorized reconstructions, erasure/noise curves and graceful degradation without importing holographic ontology.

40.4 Arena 0X-I — causal emergence under interventions

Introduce bounded internal perturbations and require a candidate to predict what changes, what remains invariant and whether the effective boundary recovers. A pass can support INTERVENTION_ROBUST_CLOSURE, not spacetime.

40.5 Predictive rate-distortion and multiscale fixed-point closure

Test whether candidate organization persists across a compression/prediction frontier and repeated effective-model construction.

40.6 Quality-Diversity archive and Disagreement Forge

Preserve diverse high-quality candidate families and search domains where MPRC2, MSR2, LEC, causal-state and classical baselines disagree while exact evaluation remains possible. Archive and Forge outputs are curriculum/debugging evidence, never confirmation evidence [46].

40.7 Physics gates

Only after a robust closure mechanism and the certificate axes required by the next claim are earned should the programme activate finite causal-cone, dimension-attractor, geometry–matter, measurement and embodied-RC arenas.