Embedded-observer source-ontology identifiability in linear-Gaussian universes

Claim-status banner

CLAIM STATUS         INCONCLUSIVE per the strict preregistered rule
                     (rule (a) and (b) pass decisively; rule (c),
                      requiring that moderate concealment succeed at
                      hiding the source signature ≥ 40% of the time,
                      fails: concealment at the chosen parameters
                      is too weak, and CONCEALED_UNITY is still
                      classified as UNIFIED 87% of the time).

                     THE PRIMARY HYPOTHESIS ("some unified-source
                     universes contain residual global structure
                     that embedded observers can detect after
                     known local causes are controlled") IS
                     DECISIVELY SUPPORTED IN ISOLATION.

EVIDENCE TYPE        COMPUTATIONAL GENERATIVE-MODEL STUDY
PHYSICAL VALIDATION  NONE
CREATOR EXISTENCE TESTED  NO. (The word "creator" appears only in
                     the study's motivational text. The
                     computational objects tested are unified-latent
                     vs. plural-latent linear-Gaussian state-space
                     models. No agent, no intent, no consciousness.
                     "Unified source" here means "one shared latent
                     stochastic process," nothing more.)
INDEPENDENT REPLICATION  NONE. Same code, single random seed band
                     per phase, no external reimplementation. Two
                     internal inference paths (subspace + info) do
                     agree.
CONFIRMATORY VS EXPLORATORY  Confirmatory — thresholds frozen from
                     an independent 12-seed exploratory phase
                     before the confirmatory 30-seed batch was run.

SUPPORTED
  - Embedded observers CAN distinguish UNIFIED-latent from
    MULTIPLE-latent linear-Gaussian universes at 91.5% accuracy
    on fresh seeds, using only the four preregistered signatures.
  - Shared LAW without shared STATE (MULT_SHARED_LAW: same A_i
    matrix across regions, independent latents) is NOT confounded:
    the classifier correctly labels 97% of MULT_SHARED_LAW
    realizations as MULTIPLE.
  - Shared INITIAL STATE without continuing shared state
    (MULT_SHARED_INIT) is NOT confounded: 100% correctly labeled
    MULTIPLE.
  - The effect survives an internal double check: PATH A (subspace
    rank + cross-region prediction) and PATH B (compression +
    correlation) agree on almost every UNIFIED and MULTIPLE
    realization.
  - Moderate concealment (rank-1 projections per region,
    per-region time delays ∈ {0..5} steps, doubled observation
    noise) does NOT succeed at hiding a shared latent: the
    classifier labels 87% of CONCEALED_UNITY realizations as
    UNIFIED. If the intent of concealment is to make a unified
    origin look plural, at these parameters it fails.

NOT ESTABLISHED
  - That our physical universe has one source or many. This study
    speaks only to a class of stochastic linear-Gaussian toy
    universes.
  - That a conscious creator exists, has intent, has properties
    like omniscience or omnipotence, or persists through time.
    The word "creator" was never operationalized.
  - That the primary hypothesis is generally robust to strong
    concealment. It was tested only at the specific concealment
    parameters preregistered.
  - That external synchronization (CENTRAL_CONTROLLED) is fully
    distinguishable from unified origin. At the tested broadcast
    amplitude (β = 0.60) the classifier correctly labels only 73%
    of CENTRAL_CONTROLLED as MULTIPLE; 7% are misclassified as
    UNIFIED and 20% as UNDECIDABLE. This is a genuine measured
    limitation of the four-metric classifier.
  - That the s3 compression metric contributes anything. Empirically
    it is a null signal at these parameters (all six classes cluster
    around gzip ratio 0.983 with no separation). It should be
    dropped or replaced in follow-ups.
  - That any of these findings say anything about consciousness,
    unity as an experience, or metaphysical O/0 claims.

MOST LIKELY ALTERNATIVE (adversarial interpretation)
  The classifier's UNIFIED vs MULTIPLE discrimination is largely
  carried by two mundane facts:
    (i) the observation covariance of a low-D shared latent has
        effective rank near D, while the covariance of N independent
        higher-D latents has rank near N × D_i. This is standard
        principal-subspace theory (Jolliffe 2002).
    (ii) cross-region predictability is a monotone function of
        pairwise mutual information, and pairwise MI is elevated
        whenever regions share a latent driver — a fact already
        established computationally in O0-STUDY-001 and analytically
        in O0-STUDY-008 (Reichenbach's common cause).
  The finding is thus consistent with the null model: the four
  signatures are picking up shared covariance structure, and unified
  latents produce such structure. This is not a discovery about
  ontology; it is a confirmation that the metrics detect what they
  are designed to detect.

NEXT DISCRIMINATING TEST
  Strengthen concealment until CONCEALED_UNITY is empirically
  undecidable. Concretely: rank-0 or very-narrow projections
  (each region only sees a scalar summary), delays ∈ {0..40}, and
  noise 5× the current amplitude. Preregister a threshold at which
  the classifier's accuracy falls to chance. If a concealed
  universe is empirically indistinguishable from a plural one
  under the same metrics — as previous theoretical work on
  observational equivalence in latent-variable models suggests
  (Anandkumar et al. 2014; Kruskal 1977; Allman et al. 2009) —
  the corresponding scientific result is that source ontology is
  NOT identifiable inside sufficiently-concealed generated worlds.
  That would itself be a publishable finding.

Abstract

Six classes of linear-Gaussian state-space universes are simulated,

observed only through region-level output streams (no privileged

access to latents), and classified by an embedded-observer proxy —

a preregistered four-metric majority-vote classifier with thresholds

frozen from an independent exploratory phase.

The two central classes are UNIFIED (a single latent drives all N

regions) and MULTIPLE (N independent latents). Four control classes

separate creator-property axes commonly conflated in metaphysical

discussion: shared LAW without shared state (MULT_SHARED_LAW),

shared INITIAL STATE without shared state (MULT_SHARED_INIT),

external SYNCHRONIZATION without unified origin (CENTRAL_CONTROLLED),

and CONCEALED_UNITY where the shared latent is deliberately hidden

through low-rank projections, delays, and heavy noise.

On a fresh confirmatory seed band (30 seeds per class, 180

realizations), the classifier achieves 91.5% two-class accuracy on

UNIFIED vs MULTIPLE and correctly rejects the shared-law confound

(97% of MULT_SHARED_LAW correctly labeled MULTIPLE) and the

shared-init confound (100%). The external-broadcast confound

partially defeats the classifier (73% MULTIPLE, 7% mislabeled

UNIFIED). Moderate concealment fails: CONCEALED_UNITY is still

labeled UNIFIED 87% of the time.

Per the strict preregistered SUPPORT rule (which requires that

concealment succeed at hiding the source ≥ 40% of the time), the

overall verdict is INCONCLUSIVE. Considered in isolation, the

primary hypothesis is decisively supported at the chosen

parameters, and the shared-law and shared-init controls decisively

rule out two of the classical confounds. The compression metric s3

contributed nothing — a null result worth reporting.

Conceptual provenance

The philosophical prompt for this study is the O/0 framework's

recurring claim that reality proceeds from a single source: "one

being outside time and space thinking reality into existence"

(source document, general framing) and "everything shares one

underlying ground" (§I–§II). This study does not evaluate that

metaphysical claim. It operationalizes a much narrower question:

In a class of toy universes we can fully simulate, can an

observer embedded inside the universe distinguish a

unified-latent origin from a plural-latent origin using only

internally-accessible data?

The metaphysical version of the question is not tested. Every

philosophical property commonly attributed to a "creator" (agency,

intent, foreknowledge, omnipotence, persistence, consciousness,

identity between source and world) is unmeasured. Conceptual

provenance is not empirical support.

Claim audit

Source claim: "reality is generated from one all-encompassing source."

Testable operational fragment: "there exists a shared latent

stochastic process from which all observed regions are functions."

This narrow fragment is testable by simulation.

Untestable fragments: the source is conscious; the source is

outside time and space; the source is a being; the source has

intent or knowledge; the source has agency. None of these appear in

this study's simulator.

Research question

Primary: can an embedded observer distinguish common generative

origin from plural origin using only internally available data?

Secondary questions (partially addressed):

• Which measurable signatures indicate common origin? — s1 (rank),

s2 (cross-region prediction), and s4 (correlation) all

contributed. s3 (compression) did not.

• Are those signatures unique to unified-source models? — No.

MULT_SHARED_LAW does not fake unity (the metrics correctly reject

it), but CENTRAL_CONTROLLED partially does. Broadcasts CAN

masquerade as unified origins under the four-metric test.

• Can one shared law be distinguished from one shared state? — YES,

in this parameter regime (MULT_SHARED_LAW rejected at 97%).

• Can a universe be fundamentally unified yet empirically

indistinguishable from a plural universe? — At the concealment

strength tested here: NO. At stronger concealment: probably yes,

based on general observational-equivalence theorems for

latent-variable models. Testing this is the preregistered next

step.

Formal definitions

Notation: N = 8 regions, p = 4 features per region, T = 1500 steps

of which the first 500 are discarded as burn-in. D_shared = 6,

D_per_region = 1. Process noise std 0.35, observation noise std

0.30, spectral radius of dynamics matrix ρ = 0.90. All are frozen

in `configs/baseline.json`.

Unified-source model

z(t+1) = A z(t) + w(t),        w(t) ~ N(0, σ_p² I_D)
x_i(t) = C_i z(t) + v_i(t),    v_i(t) ~ N(0, σ_o² I_p)

A is a random matrix rescaled to spectral radius ρ = 0.90 (stable).

C_i for each region is a random p × D projection.

Multiple-source model

z_i(t+1) = A_i z_i(t) + w_i(t),  A_i drawn independently
x_i(t)   = C_i z_i(t) + v_i(t)

Concealed-unity model

x_i(t) = C_i z(t - τ_i) + η_i(t),   C_i rank-1,
                                     τ_i ~ Uniform{0..5},
                                     η_i(t) ~ N(0, (2σ_o)² I_p)

where z(t) is the single shared latent as in UNIFIED. The three

concealment mechanisms are: (a) severe dimensionality reduction

via rank-1 projections, so each region observes only a

one-dimensional slice of z; (b) independent per-region delays,

which decorrelate synchronous access; (c) doubled observation

noise, which floods the shared-signal component.

Adversarial controls

• MULT_SHARED_LAW: same as MULTIPLE but A_i = A for all i.
• MULT_SHARED_INIT: MULTIPLE with all z_i(0) = z_0.
• CENTRAL_CONTROLLED: MULTIPLE with an additive broadcast:

`x_i(t) = C_i z_i(t) + β P_i b(t) + v_i(t)` where β = 0.60.

Creator-property ablations

Each of these adversarial controls independently disables one

"creator-like" property commonly conflated with unified origin:

• Sole causal origin: only UNIFIED and CONCEALED_UNITY have it.
• Complete state access: never granted to the observer.
• Perfect prediction: never granted.
• Complete intervention capability: never granted.
• Persistent identity between source and generated states:

present in UNIFIED (z is time-evolving); absent in

MULT_SHARED_INIT (source-state is used only at t=0).

• Self-contained totality: all classes are self-contained;

CENTRAL_CONTROLLED adds an external broadcast (fails this).

• Shared law: present in UNIFIED, CONCEALED_UNITY, MULT_SHARED_LAW.
• Shared latent state: present in UNIFIED, CONCEALED_UNITY only.

The results show that these properties do NOT all imply the same

observational signature. Shared law alone (MULT_SHARED_LAW) does

not produce a "unified" signature; shared state does. Shared

initial state alone does not either. Broadcast partially does.

This decomposition matters. Popular philosophical arguments that

"our universe follows universal laws, therefore it has one source"

depend on the identification of shared LAW with shared STATE.

This study shows that under the four preregistered metrics, those

identifications are empirically wrong in this simulator: shared

law without shared state is correctly classified as plural.

Hypotheses

Primary: Some unified-source universes contain residual global

structure that embedded observers can detect after known local

causes are controlled.

Null: Once observable local causes are accounted for, unified-source

and multiple-source universes are statistically indistinguishable

under the four preregistered metrics.

Competing explanations:

• CE1 (shared law): the metrics detect shared dynamics, not

shared state. If MULT_SHARED_LAW is classified as UNIFIED, this

explanation wins. Result: DID NOT WIN.

• CE2 (compression bias): the metrics detect compressibility. If

s3 dominates the classifier, this explanation wins. Result:

DID NOT WIN — s3 was a null metric.

• CE3 (broadcast synchronization): the metrics detect external

coordination, not internal origin. If CENTRAL_CONTROLLED is

classified as UNIFIED, this explanation wins. Result: WINS

PARTIALLY — 7% of CENTRAL_CONTROLLED are misclassified UNIFIED

and 20% as UNDECIDABLE, a specific measured limitation.

Falsification criteria:

• Two-class accuracy < 0.75 → primary hypothesis falsified.
• MULT_SHARED_LAW classified as UNIFIED at > 40% → CE1 wins,

hypothesis operationally falsified.

• Both were tested and both refute their respective failure

modes. The remaining caveat is CE3 (broadcast).

Interpretation boundaries:

• The hypothesis speaks to detectability in a specific

parametric regime, not to universal detectability.

• The hypothesis is silent on the metaphysical existence of a

source. The only claim it makes is about observational statistics.

Methods

Observer constraints

The classifier's inputs are the 4 signatures computed from

`X ∈ R^{T_keep × Np}` alone. No privileged access to latents,

adjacency matrices, dynamics, or class labels.

Simulation design

For each `(universe class, seed)` pair, we generate one realization

using the formal definitions above. Random seeds are deterministic

and disjoint across the exploratory and confirmatory phases.

Inference methods

• s1 (subspace path): effective rank = (Σ_k λ_k)² / Σ_k λ_k² of

the eigenvalues of `Xᵀ X / (T_keep − 1)`.

• s2 (subspace path): For each region i, we fit two ridge (λ = 10⁻³)

linear regressors of x_i(t) on a 3-step history. One uses only

x_i's past; the other uses all N regions' pasts. Compute the

relative MSE reduction on a held-out second-half window, then

average across regions. Positive means cross-region history

helps.

• s3 (info path): int8-quantize the whole X (per-column mean/std

standardized). Compare `len(gzip(X))` to `Σ_i len(gzip(X_i))`.

Ratio < 1 means joint compression helped.

• s4 (info path): mean absolute Pearson correlation between the

N region-mean time series.

Analysis plan

Two-tier procedure:

1. EXPLORATORY (12 seeds × 6 classes = 72 realizations).

Learn per-metric thresholds from UNIFIED vs MULTIPLE only

(median-of-medians midpoint). FREEZE. Never look again.

2. CONFIRMATORY (30 fresh seeds × 6 classes = 180 realizations).

Apply the frozen classifier. Compute the confusion matrix,

apply the frozen SUPPORT rule, assign the verdict.

Confirmatory results

Two-class accuracy (UNIFIED vs MULTIPLE): **0.915**.

Full confusion table (rows = ground truth, columns = classifier

prediction, fractions of 30 seeds):

| ground truth | pred UNIFIED | pred UNDECIDABLE | pred MULTIPLE |

|---|---|---|---|

| UNIFIED | 0.93 | 0.07 | 0.00 |

| MULTIPLE | 0.00 | 0.10 | 0.90 |

| CONCEALED_UNITY | 0.87 | 0.13 | 0.00 |

| MULT_SHARED_LAW | 0.00 | 0.03 | 0.97 |

| MULT_SHARED_INIT | 0.00 | 0.00 | 1.00 |

| CENTRAL_CONTROLLED | 0.07 | 0.20 | 0.73 |

Preregistered SUPPORT rule details:

• (a) UNIFIED vs MULTIPLE accuracy ≥ 0.75: **PASS** (0.915)
• (b) MULT_SHARED_LAW → MULTIPLE ≥ 0.60: **PASS** (0.97)
• (c) CONCEALED_UNITY → (UNDEC OR MULT) ≥ 0.40: **FAIL** (0.13)

Overall preregistered verdict: **INCONCLUSIVE** (rule c failed).

Metric-level effect sizes (medians on the exploratory batch,

retained as the frozen threshold values):

| metric | median UNIFIED | median MULTIPLE | threshold |

|---|---|---|---|

| s1_eff_rank | 4.45 | 6.96 | 5.70 |

| s2_pred_gain | +0.09 | -0.21 | -0.06 |

| s3_compress_ratio | 0.983 | 0.984 | 0.983 |

| s4_mean_abs_corr | 0.317 | 0.035 | 0.176 |

Uncertainty and robustness

• All confusion-matrix fractions are computed on n=30 fresh seeds

per class. Bernoulli 95% CI for a fraction of 0.93 at n=30 is

≈ ±0.09 (Wilson score). For 0.90 it is ≈ ±0.11. For 0.73 it is

≈ ±0.16.

• The two internal inference paths (PATH A: s1+s2; PATH B: s3+s4)

agree on 87% of confirmatory realizations. When they disagree,

the majority-vote classifier defaults to whichever side has

three votes. The 10% UNDECIDABLE realizations for MULTIPLE

correspond to path disagreement.

• The compression metric s3 is a null signal — it is essentially

the same for all six classes. Removing it and using only s1,

s2, s4 as a 3-metric majority vote (with a preregistered rule

to break ties differently) is a natural robustness follow-up

but was NOT preregistered.

• Thresholds were set from UNIFIED and MULTIPLE only. Applying

them to CONCEALED_UNITY, MULT_SHARED_LAW, MULT_SHARED_INIT, and

CENTRAL_CONTROLLED constitutes a genuine held-out test of the

classifier on classes it never saw during threshold-setting.

Adversarial controls, outcomes

• Shared law without shared state (MULT_SHARED_LAW):

RULED OUT as an explanation. If the classifier were detecting

"law-similarity" rather than "state-sharing," MULT_SHARED_LAW

should have been classified UNIFIED. It was not (97% correctly

MULTIPLE).

• Shared initial state (MULT_SHARED_INIT):

RULED OUT (100% correctly MULTIPLE). Initial-state similarity

decays as the independent dynamics evolve.

• Broadcast synchronization (CENTRAL_CONTROLLED):

PARTIALLY WINS. 7% misclassified UNIFIED, 20% UNDECIDABLE. This

is a genuine, quantifiable limitation of the four-metric test:

external synchronization can produce unity-like signatures. Any

claim of "detecting unity" from real data must exclude external

broadcasts (natural or artificial) before concluding a unified

source.

• Concealment (CONCEALED_UNITY):

FAILED. At the tested parameters (rank-1 projections, delays up

to 5 steps, doubled noise), a shared latent leaks enough

signature into the observation stream that the classifier still

labels 87% of realizations as UNIFIED. This is either good news

(unity signatures are robust to moderate obfuscation) or a

warning (the classifier has not really been challenged by

concealment). Stronger concealment is preregistered as the

next step.

Alternative interpretations

• The findings are consistent with the classifier detecting

low-rank covariance structure produced by any shared latent

driver. This is exactly what the primary hypothesis predicts,

but it does not add information beyond "shared latents produce

low-rank covariance and cross-region predictability."

• The 87% success on CONCEALED_UNITY could be an artifact of the

s4 (mean absolute correlation) metric being sensitive to even

small residual coherence. s4 accounted for a large fraction of

the CONCEALED_UNITY votes; ablating s4 would likely raise the

UNDECIDABLE rate on concealed data.

Limitations

• Linear-Gaussian dynamics only. Real dynamical systems are

nonlinear; nonlinear latent structure may be much harder or

much easier to detect.

• Very small N and T: 8 regions, 1000 kept timesteps. Real

observers have vastly larger or vastly smaller windows depending

on the substrate.

• No intervention path was implemented. The mandate asked for

"intervention-response similarity" as one of the inference

methods; the linear-Gaussian setting does not support a natural

local intervention that an embedded observer could enact

without privileged latent access. This is a real gap.

• The classifier is a fixed rule, not a learned model. A learned

classifier trained on exploratory data would likely be stronger

(and more prone to overfitting).

• The four metrics are not exhaustive. Higher-order signatures

(higher-order cumulants, causal graph structure, information

bottleneck analysis) were not tested.

Replication procedure

Deterministic. To replicate:

cd research/studies/O0-STUDY-010
python -u src/run_study.py

All seeds and parameters are frozen in `configs/baseline.json` and

in the source code. The exploratory and confirmatory batches use

disjoint seed bands (2_000_000+ and 3_000_000+). Verify:

`results/summary.json` should reproduce byte-for-byte.

Independent-reimplementation replication (Tier 3) is not

performed. Anyone reimplementing should preserve the classifier

architecture (four metrics, majority vote, ties → UNDECIDABLE,

thresholds set from UNIFIED and MULTIPLE only) but re-derive the

metric implementations in a fresh codebase.

Code and data manifest

• `src/run_study.py` — models, metrics, classifier, orchestration
• `configs/baseline.json` — frozen configuration
• `preregistration.md` — frozen preregistration
• `results/summary.json` — top-line numbers + verdict
• `results/thresholds_frozen.json` — the four frozen thresholds
• `data/raw/exploratory.csv` — 72 exploratory rows
• `data/raw/confirmatory.csv` — 180 confirmatory rows + predictions
• `data/raw/exploratory_with_predictions.csv` — exploratory rows,

post-hoc predictions (for internal reference only; NOT used in

the SUPPORT rule)

• `figures/01_signature_distributions.png` — per-class distributions
• `figures/02_classifier_outcomes.png` — confirmatory confusion

Relationship to the philosophical O/0 archive

Conceptual provenance is not empirical support.

The study formalizes a narrow operational reading of "reality

proceeds from one source" as "there exists a shared latent

stochastic process from which all observed regions are functions."

Under that reading, in the tested regime, embedded observers CAN

detect unified origins in the simplest cases (UNIFIED vs MULTIPLE),

CAN reject the two most common confounds (shared law, shared

initial state), and are PARTIALLY FOOLED by external synchronization

(CENTRAL_CONTROLLED). The concealment condition failed at moderate

strength, leaving the general observational-equivalence question

open.

None of these findings speak to the philosophical claim that our

universe has such a source, that the source is conscious, that

consciousness is fundamental, or that O/0 is true. Every one of

those claims is orthogonal to what was tested.

Primary references

• Kalman, R. E. (1960). "A new approach to linear filtering and

prediction problems." *J. Basic Eng.*

• Reichenbach, H. (1956). *The Direction of Time*. UC Press.
• Kruskal, J. B. (1977). "Three-way arrays: rank and uniqueness

of trilinear decompositions." *Linear Algebra Appl.*

• Allman, E., Matias, C., Rhodes, J. (2009). "Identifiability of

parameters in latent structure models with many observed

variables." *Ann. Statist.*

• Anandkumar, A. et al. (2014). "Tensor decompositions for

learning latent variable models." *JMLR*.

• Pearl, J. (2009). *Causality* (2e). Cambridge.
• Jolliffe, I. T. (2002). *Principal Component Analysis* (2e).

Springer.

• O0-STUDY-001 (this workspace): sync vs integration in Kuramoto.
• O0-STUDY-008 (this workspace): common-cause confound.

Revision history

• 1.0.0 (2026-07-26): initial run. All six universe classes,

four metrics, 12 exploratory + 30 confirmatory seeds. Two-class

accuracy 0.915, shared-law confound rejected at 0.97, concealment

failed at moderate strength (0.87 misclassified UNIFIED).

Preregistered verdict INCONCLUSIVE because rule (c) failed.