MIsCORE-RIUD: Paper III — Control-Native Evidence for Partially Shared Dynamics in Recurrent Gravitational-Wave Post-Model Paths

1. Introduction

Most gravitational-wave residual analyses are framed as goodness-of-fit or excess-power problems. Those tests are indispensable, but they do not exhaust the scientific role of post-model data. RIUD (Residual Is Undiscovered Data) treats the residual layer as unclassified rather than pre-classified: detector noise, waveform mismatch, conditioning effects, known but unmodeled physics, or a different physical origin remain competing explanations until structure has been defined and tested.

Paper I established a recurrent merger-local observational morphology and explicitly retained failed physical interpretations. Paper II raised the object from localized cells to connected multiscale paths and tested the frozen coordinates by fixed projection into H1/L1 raw strain. Paper III begins only after that path population is frozen. Its question is narrower and harder: do the observed paths exhibit recurring dynamics that remain unusual when null controls receive comparable freedom to construct paths of their own?

This distinction matters because a coordinate-only null can underestimate the search freedom of a path-based analysis. If the observed branch is allowed to discover a path but the null branch is evaluated only at the observed coordinates, the comparison no longer asks whether the dynamical organization itself is unusual. Paper III therefore uses a control-native design in which every control independently constructs its map, searches for a path, forms a trajectory, receives a frozen family classification, and only then contributes to the population statistic.

2. Methods

2.1. Scientific Question and Frozen Evidential Boundary

The confirmatory claim is restricted to family-level trajectory dynamics. Paper III does not re-estimate the Paper I morphology, does not reopen the Paper II path selector, does not use the Paper I A2 score as an analysis anchor, and does not combine Paper II and Paper III p-values.

Layer	Role in Paper III	Inferential status
Observed path assets	Frozen 13-event trajectories and family labels	Input object
Canonical R27	Primary H1/H2/H3 control-native population test	Confirmatory
Separate internal regeneration	New controls, new randomization namespace, new population draws	Computational replication; unpooled
Historical R27B auxiliary outputs	Off-source, injection, detector/waveform and permutation audits	Provenance only
Compact-law audit	Separate best-three-of-four governing-law question	Negative claim boundary
105-entry ledger	Engineering and provenance record	Not a scientific denominator

The frozen computational workflow recorded the label VALIDATED_PARTIALLY_SHARED_DYNAMICS. In this manuscript, that label is treated as provenance rather than as a substitute for the scientific claim. The scientific claim is limited to recurrent partially shared path dynamics under the specified control-native null.

2.2. Frozen Event Panel and Trajectory Assets

The confirmatory panel contains 13 gravitational-wave events with frozen event identities, path rows, family assignments, and event-relative trajectory coordinates. The observed source is R26C30R6_observed_path_nodes and the time column is tau_s. Path order is preserved. Interpolation, nearest-coordinate matching, tolerance snapping, score-only trajectory reconstruction, family relearning, renaming, and outcome-dependent event substitution are prohibited.

Event	Frozen family	Paper III role
GW150914_095045	quasi-stationary	H3
GW200129_065458	dip-rebound-rise	not primary
GW200224_222234	multistep	H1
GW230824_033047	oscillatory	H2
GW230831_015414	multistep	H1
GW230904_051013	oscillatory	H2
GW231206_233901	oscillatory	H2
GW231221_135041	quasi-stationary	H3
GW240629_145256	monotonic-rise	not primary
GW240919_061559	quasi-stationary	H3
GW240920_124024	multistep	H1
GW241006_015333	multistep	H1
GW241231_054133	rise-peak-fall	not primary

The panel therefore contains four multistep events, three oscillatory events, three quasi-stationary events, and three additional frozen families that remain in the panel but do not enlarge the confirmatory max-T family set. An initially contemplated H4 shared-cluster hypothesis was excluded before the final R27 confirmatory test.

2.3. Frozen Hypotheses and Dynamical Representations

H1 uses the multistep family under raw normalization and the M5 coupled frequency-width ordinary differential equation representation. H2 uses the oscillatory family under the same raw/M5 representation. H3 uses the quasi-stationary family under raw normalization and the M3 first-order power-law representation. Here raw is the frozen R27 trajectory-normalization label; it is not raw H1/L1 detector strain.

The baseline is M0. M3 is a first-order frequency power-basis model, and M5 uses coupled first-order frequency and width derivatives with the [1,f,w] basis. Exact fitted coefficients and row-level frozen exponents are not re-estimated in this manuscript.

Primary observed statistic: REL_IMPROVEMENT = (METRIC_M0 - METRIC_LOCKED) / |METRIC_M0|.

Hyp.	Family	Representation	Events	Relative improvement	Coeff. stability	Event influence
H1	multistep	raw/M5	4	0.295609	0.475133	400.229
H2	oscillatory	raw/M5	3	0.198292	0.372100	265.856
H3	quasi-stationary	raw/M3	3	0.338358	0.585786	147.533

Coefficient stability and event influence are descriptive frozen diagnostics. They are not p-values, are not independent effect-size claims, and do not determine confirmatory support.

2.4. Control-Native Population Null

Each of the 13 observed events contributes 1,000 controls. A control is not evaluated at the observed path. Instead, the control-native sequence is:

control input -> preprocessing / feature construction -> free path search -> trajectory -> frozen family classification -> hypothesis statistic

This is the central design feature of Paper III. It preserves the principal path-search freedom that could otherwise make an observed family appear artificially rare.

Figure 1. Control-native null architecture. Each null control constructs its own feature map and PATH before trajectory and family evaluation; the observed branch remains frozen.

Figure 1. Control-native null architecture. Each null control constructs its own feature map and PATH before trajectory and family evaluation; the observed branch remains frozen.

The null is unconditional. If a frozen family is absent from a population draw, its statistic is set to zero rather than discarded. If the family is present but the frozen leave-one-event-out requirement is insufficient, the statistic is also set to zero. Only genuine technical failures are invalid.

The canonical design contains 13,000 controls, 1,000 valid population draws, and 0 technical invalid draws. Empirical p-values use the plus-one rule p=(b+1)/(N+1), where b is the number of null draws at least as extreme as the observed statistic and N=1,000. Reported corrected values are the frozen selection-aware/max-T results over H1/H2/H3; they are not Bonferroni approximations.

2.5. Separately Regenerated Internal Computational Replication

A second full statistical run was generated under the same frozen scientific design but with a new randomization namespace, newly generated control-native controls and trajectories, new population draws, and an isolated output tree. It contains 13 event branches, 13,000 newly generated controls, 1,000 valid hypothesis draws, and 0 technical invalids.

The internal run does not import or pool the canonical null distribution, canonical p-values, or final verdict. It is evidentially separate from the canonical computation but is not an independent external-team replication.

2.6. Use of AI-Assisted Tools

Large language models were used for code assistance, literature navigation, terminology clarification, manuscript drafting support, and consistency checking. All research questions, methodological decisions, experiment selection, data interpretation, and final scientific claims were determined and approved by the author. The author reviewed the manuscript and takes responsibility for its contents.

3. Results

3.1. Canonical R27 Population Test

All three prelocked hypotheses pass the corrected alpha=0.05 threshold in the canonical analysis. H1 has raw p=0.003996 and corrected p=0.005994. H2 has raw and corrected p=0.002997. H3 has raw p=0.002997 and corrected p=0.026973.

The result is partially shared rather than universal. H1 and H2 are distinct morphology families but share the same raw/M5 dynamical representation. H3 is supported under a different raw/M3 representation.

3.2. Separate Internal Regeneration

The regenerated run preserves the overall family-level conclusion. H1 has raw p=0.006993 and corrected p=0.009990. H2 again has raw and corrected p=0.002997. H3 has raw p=0.009990 and corrected p=0.045954.

Hyp.	Canonical raw	Canonical corr.	Internal raw	Internal corr.	Internal exceedance	Interpretation
H1	0.003996	0.005994	0.006993	0.009990	9/1000 corrected	replicated; clear support
H2	0.002997	0.002997	0.002997	0.002997	2/1000 corrected	replicated; most stable
H3	0.002997	0.026973	0.009990	0.045954	45/1000 corrected	replicated; boundary-adjacent

H2 is the most stable family across the two unpooled runs. H1 remains clearly below threshold. H3 also passes the frozen threshold in both runs, but the internal corrected value is boundary-adjacent; it should not be presented as equally robust to H1 and H2. No combined p-value is computed.

4. Negative Compact-Law Audit

Family-level dynamical recurrence does not imply one compact governing law. The governing-law development corridor contained 58 candidate relations, reduced to 7 consensus candidates and then to one selected top candidate. The selected relation improved 3 of 4 discovery events and had term stability=1.0 before the required selection-aware null.

In the separately frozen best-three-of-four audit, the observed subset BCD selected A_MONOTONE_DEC_MASS_SCALED. The selection-aware control-native null produced 89 exceedances among 1,000 draws, giving p=0.089910. The corresponding fixed-law p-value was 0.677323. The locked verdict was BEST3OF4_PARTIAL_RELATION_NOT_SUPPORTED.

Claim boundary: recurrent family-level dynamics are supported; the tested compact universal trajectory law is not.

5. Discussion

The principal result is a change in scientific object. Paper I established a recurrent local morphology. Paper II established connected multiscale paths and fixed-coordinate support after a representation change. Paper III shows that the frozen paths are not merely a list of unrelated shapes: controls that receive their own path-search freedom seldom reproduce the same family-level dynamical improvements.

The evidence does not support the opposite extreme either. A single compact governing law does not survive its search-aware audit. The most defensible description is therefore a small set of recurrent dynamical regimes: H1 and H2 share one representation, while H3 supports a separate and weaker regime.

Several causal explanations remain possible, including waveform incompleteness, source-parameter mismatch, higher-mode or precession structure not absorbed by the selected description, detector or conditioning effects that survive the completed controls, or unmodeled source physics. Paper III does not assign probabilities among these explanations.

The negative compact-law result is scientifically useful rather than merely disappointing. It prevents the observed family-level recurrence from being rewritten as a universal physical equation. In other words, the paper establishes dynamical organization at an intermediate level: stronger than isolated event morphology, weaker than a universal governing law.

6. Limitations and Claim Boundary

Supported by Paper III	Not established by Paper III
Three prelocked family-level hypotheses pass selection-aware empirical nulls in canonical and separate internal runs.	Physical identity of the structures.
H1 and H2 share raw/M5; H3 supports raw/M3.	One universal dynamical or physical law.
Null controls construct their own maps, paths and trajectories.	Catalog-wide prevalence or blind prospective detection rate.
Separate internal regeneration reproduces the family-level conclusion with 0 technical invalid draws.	Independent external-team replication.
A selected compact law fails after search correction.	GR violation or Beyond-GR detection.

The frozen 13-event panel is not a random sample of the complete gravitational-wave catalog. The confirmatory family set is designed rather than exhaustive. No finite control bank spans every detector, calibration, waveform, conditioning, or astrophysical alternative. Paper III is not a raw-strain free-search discovery, and Paper II and Paper III p-values are not combined.

7. Conclusion

Across a frozen 13-event path panel, three prelocked morphology families show model improvements that are rare under controls allowed to construct their own maps, paths, and trajectories. The canonical analysis and a separately regenerated internal computational run both support multistep raw/M5, oscillatory raw/M5, and quasi-stationary raw/M3 dynamics at the frozen corrected threshold, with H3 explicitly weaker and boundary-adjacent in the regenerated run.

The supported scientific conclusion is recurrent partially shared path dynamics, not one universal law. The separate compact-law audit is negative after search correction. Paper III therefore occupies a specific position in the RIUD sequence: it raises a frozen path population into a recurrent dynamical object while preserving the boundary between empirical organization and physical law.