Scientific use
A causal test bench for emergence
Deterministic twin runs can share their entire past and differ by one intervention. That makes formation, interaction, and failure accessible to controlled counterfactual tests.
A constructive research hypothesis
DOFT studies deterministic oscillator networks in which delay and memory make the present depend on the path taken to reach it. The aim is to understand how coherent structures form, acquire an internal history, interact, and fail.
Initial onions are drawn from a declared ensemble and evolved deterministically—not selected for matching a target number. Survivors are connected and become the next initial condition.
Wave 1 · onions → dynamical selection → waves 2–N · connected structures
Working theory, not established fundamental physics. The website distinguishes measurements, model-dependent interpretation, and open conjecture.
The proposition
The basic object is not an isolated particle analogue. It is a layered oscillator—informally, an onion—whose present dynamics retain information about prior phase relations and exchanges.
Supplies phase, frequency, and modes.
Makes interaction depend on a finite past.
Lets repeated relations alter future response.
A hypothesis to test, not an assumption.
Scientific use
Deterministic twin runs can share their entire past and differ by one intervention. That makes formation, interaction, and failure accessible to controlled counterfactual tests.
Practical use
The program develops observables for internal age, phase-sector organization, boundary drain, and precursors that appear before a coherent state is lost.
Long horizon
DOFT is compared with delayed resonators, synchronization, bright/dark modes, and dissipative symmetry breaking only when a measurable test can tell the descriptions apart.
Current evidence
Study 06 has moved the program from pattern finding toward event-resolved, paired causal experiments. These statements are intentionally narrower than the theory’s ambition.
In one configured failure mode, a fluctuation in edge-flow variability preceded 45 of 46 observed breakdowns. It is a promising precursor, not yet a universal failure law.
Fold-back and intervention tests found trajectories with comparable energy but very different growth rates. The relevant state is history-dependent: epoch, phase organization, and accumulated dissipation matter.
In the controlled S2 sector, the effective frequency follows ωeff = ω0√(1 + 0.1b), where b is accumulated model age. External readout tracks that age in near-homogeneous pairs and breaks when sustained age asymmetry becomes large.
Paired branches share a bit-identical trajectory until the connection is switched on. The same-sign differential clock splitting appears across four independent draws, while the controlled paired branches identify the link as its cause. Paired runs also expose an earlier death through boundary drain.
Paired counterfactuals
Lifetime of otherwise paired branches. In each pair, the connected branch fails first.
Study 07 · the delay-first campaign
Study 07 removes space as an input and keeps only delays. These are the campaign’s defensible statements—including the ones that had to be corrected. The search for composite structure (bound “things” made of things) is so far negative, and the notebook says so.
Every point in the explorer is an oscillator; every distance is a delay. The 3D scene is a projection (MDS over the delay matrix, with fidelity gauges on screen)—there is no space in the model, only timing. The physics does not depend on the picture: the headline correlation survives with the embedding removed, computed directly on the raw delay profiles. Seventeen experimental runs load live, including the complete species run.
The full population census (three batches) collapses to 84 unique genotypes. Each carries a bench card: its stability exponent (σmax, the real part of the dominant pole, cross-validated bit-exact against an independent derivation) and its resonant response. 57 are self-oscillators; 27 decay. The bench card is measured in isolation—in the soup, the deviation from the bench is the interaction.
Before running a species-only soup (one copy per genotype), we committed a prediction: constitutional instability drives outward drift. After an adversarial re-analysis the verdict is precise rather than simple. The signal is real but partitioned: it lives among the self-oscillators (ρ = +0.34, p = 0.009 at t = 60), survives removal of the visualization, but is concentrated in one batch and carries a wide confidence interval. An earlier claim that clone families “double” the correlation was a sample-size confound: with cohort size equalized, the correlations are statistically indistinguishable (p = 0.58). What the cohort does change is timing—it advances onset and ignition without changing slope, ceiling, destination, or correlation.
We kicked one oscillator and timed first arrivals at the other 149 (paired surgery: identical twin runs, kick minus control). Arrival order follows the delay map (ρ = 0.91, reproduced by an independent method)—but arrival times don’t wait for the direct link: the medium is a dense web where signals travel multi-hop, and what makes an arrival detectable is the rise of amplitude, not the delay of the edge. No arrival-speed number survived re-analysis, so none is quoted. Established so far for a single cone, from a single origin; multi-source tomography is the pre-registered next test.
Two frontier runs with different random seeds—and different lifespans—partition into exactly the same six blocks: identical sizes [68, 32, 30, 6, 6, 4] and identical membership, Jaccard 1.0 in all six. Earlier cross-seed comparisons scored 0.9–1.0; here the match is exact. The partition of this population is not a statistical tendency: membership is deterministic across the realizations tested.
Between two run lifespans the set of ignited units grows from 9 to 25—and the later set contains the earlier one. The wave advances mostly in constitutional order, with measurable exceptions in both directions: one unit ignites with a negative stability exponent (recruited by the network, not by its constitution), and the five most unstable genotypes never ignite in any run. An ordered process with exceptions we can point to—not a binary threshold.
Two realizations sharing a bit-identical present but different retained delay-line content evolve differently—and the difference is causal, measured, and replicated across seeds. Draining the present energy of the dominant subnetwork leaves the collective rate unchanged (0.994×); erasing that subnetwork's history—present verified intact—collapses it (0.171×), with recovery staggered link-by-link at times predicted blind, pre-registered, from each link's own measured delay (exact 6/6 order in the replication, p = 1/720). Patent pending.
A synthetic past that preserves the full cross-spectral matrix and variance of the original (phases randomized) accelerates the transient ×1.16–1.23—replicated on an independent second realization at matched magnitude. The information the system reads from its past is not contained in its spectral summary. Declared honestly: the surrogate also de-stationarizes the past; the operator family disclosed with the filing (band-selective, time-reversal, block-shuffle) is the tomography that separates those readings. Patent pending.
Reversing the retained past in time—power spectrum and autocorrelation preserved exactly—does not reproduce that acceleration: it suppresses the dynamics (0.52–0.56× in the mid window), and per-link growth tracks the epoch content re-read under the time mirror (6/6 links). Which epoch is read when carries causal effect beyond the spectral summary. Single-instance so far (n = 1 seed, declared). Patent pending.
A correction, on the record
We reported a run as dead at t = 63 and drew conclusions from that snapshot. The run was alive—a shell-scripting bug in a monitoring script had produced a false “terminated.” The run actually lived to t = 104.5, and its full life reversed one conclusion (three units ignite entirely alone, late: “ignition never happens alone” is retracted) and reinforced another (the inter-species blocks persist 44 more time units, with 92.8% pair agreement). Both the error and the reversal are sealed in the notebook.
Claim boundary
DOFT currently demonstrates nontrivial dynamics in a constructed deterministic system. It has not established a new particle ontology, reproduced the Standard Model, or received experimental confirmation in matter.
The near-term standard is therefore sharper and more useful: find causal invariants, map failure conditions, and test whether the same discriminants survive new seeds, topologies, and dynamical regimes.
The research program
Each study changed the question. The central repository keeps the useful findings, the invalidated claims, and the evidence needed to tell them apart.
A constrained prime-space grammar compressed selected superconducting and superfluid scale ratios. The patterns are descriptive; they do not establish a fundamental mechanism.
02A layered cluster pipeline turned fingerprint mismatch into structural noise. It remains useful as a model-building record, while its strongest physical interpretations stay unresolved.
These studies did not produce conclusions that survived review. Their role in the program is methodological: an explicit gap is more useful than inherited certainty.
The published aggregate remains reproducible, but coupling and metric defects invalidate its main physical interpretations. The failure directly shaped the controls now used in Study 06.
A deterministic laboratory for formation, aging, interaction, and failure. It contains the program’s strongest causal results so far—and its most disciplined record of retractions. Sealed 29 July 2026; Study 07 builds on it. Repository private since August 2026 (see access note).
The current laboratory removes space as an input: every distance is a delay, and geometry has to be earned by measurement. A population census, sealed out-of-sample predictions, and same-day public corrections. Repository private since August 2026 (see access note).
How claims are made
Studies 06–07 use a deliberately adversarial workflow: every campaign is pre-registered before it runs, verdict-bearing analyses are performed blind, and an adversarial critic reviews each design before data exists. A failed prediction, a broken instrument, and a surviving causal claim must all remain equally inspectable.
State the observable, gate, and possible verdicts.
Review for leakage, confounds, and circular tests.
Commit the driver before opening the result.
Change one cause and preserve shared history.
Recompute the claimed number from the artifact.
Retractions remain attached to the evidence trail.
A live correction record
“Same mathematical form” was withdrawn as “same law.” Instantaneous energy failed as a coordinate of instability. A proposed one-age rule broke under sustained asymmetry. Large within-run sigma counts were rejected as independent evidence. In Study 07, a “×2 cohort amplification” and “ignition never happens alone” were both retracted within a day—one by an adversarial re-analysis, one by a full-life census. Retractions keep the section numbers of the claims they replace.
North of the work
Study 07: a census-complete population with bench cards, sealed out-of-sample predictions, multi-source tomography of the delay geometry, and a composition law for an active, dispersive medium—with clone cohorts as timing controls.
Ask which precursors, clocks, and causal link signatures survive new draws, asymmetric pairs, larger networks, and alternate failure modes.
Compare against known delayed resonators and dissipative systems using discriminating experiments—before attaching fundamental interpretation.
Research record
The central index summarizes the program. Study repositories retain their code, data, logs, and exact historical context.
Access note — the Study 06 and Study 07 development repositories are private as of August 2026 while an intellectual-property review is completed. Every measured result summarized on this site remains public, the written summaries of both studies stay on this page, and the sealed records keep their integrity hashes. Reasonable access requests are considered by mail.