Theoretical Foundations & Open Hypotheses
IRDME is organized around a single empirical law plus a set of open theoretical hypotheses being tracked. This page distinguishes what is confirmed from what is conjectured.
Established Science
CONFIRMED 38×r(d1 ↔ d2) > r(d1 ↔ d3)
Hub importance scores preserve more strongly between layers that encode functionally similar relationships than between layers that encode functionally dissimilar ones — independent of domain. Confirmed across 41 pre-registered experiments spanning molecular biology, neuroscience (nematode → insect, 600 Myr cross-species), software systems, ecology, formal mathematics, AI architecture, finance, particle physics, computational geometry, medicine/epistemology, and digital circuits. 8 denials, each with a named boundary condition.
Boundary conditions (when the law does not apply)
Resolution mismatch
If d1 encodes atomic-level containment and d2 encodes holistic traversal, they operate at different structural resolutions. The law requires both layers to be at the same resolution. (MATH DENIED, PSYCHIATRY DENIED)
Relational regime mismatch
If d1 is a market-trading layer and d2 is a lending layer, they encode different institutional operating modes — not proximity along a shared relational axis. (FINANCE DENIED)
Adversarial construction
A network constructed specifically to invert hub identity across layers will deny the law — confirming it has testable, falsifiable boundaries. (Adversarial PTM DENIED)
BC_RADIAL — structural degeneracy
Single-hub radial architecture causes d2 degree vectors to collapse to a constant (Var(d2)=0), forcing r(d1,d2)→0 regardless of d3. Empirical threshold: Var(d2) < 0.714 predicts this regime. Confirmed in docopt (Go/Java/Rust) and logrus. Pre-reg hashes: 5388c0f1, c00ebfa4.
BC_INVERSION — fan-out with leaf clustering
High Var(d2) but r(d1,d2) strongly negative. The d1 hub fans out to N consumers that share structure with each other but not with the hub — d1 leaves displace the d1 hub as d2 hub. Signature: Var(d2) >> 0.714 AND r(d1,d2) < 0. Identified in cobra Go CLI (r=−0.862, p=0.014). Pre-reg hash: c00ebfa4.
BC4 — meta-science coupling regime
FPL does not hold when layers encode abstract institutional dependencies between entire scientific fields. The structural resolution of disciplines-as-nodes is incomparable to the resolution of physical, computational, or biological coupling. (H_PRIMITIVITY PARTIAL)
FPL Extension — d4 Observer Layer
CONFIRMED — 3 domainsThe Universal Layer Grammar defines d1 (structural), d2 (flow), d3 (behavioral), and d4 (observer). d4 encodes how an external agent — a research community, Stack Overflow, an AI model — perceives the system. FPL does not require d4 to track d1/d2. Two pre-registered experiments tested this formally for the first time.
Observer Attention Divergence
d4 (observer attention) selectively reflects different structural dimensions depending on domain. FPL does not hold across the d4 regime boundary in either domain tested.
C. elegans — biology (F12_D4_OBSERVER_v1)
n=279, r(d1↔d4)=−0.008, r(d2↔d4)=−0.044
Attention is hyper-concentrated on a historically famous ~18% of neurons (Nobel-prize experimental systems). The neglect is global: 80% of top-d1 quartile AND 87% of bottom-d1 quartile have zero scientific attention. d4 is NOT selectively ignoring structural hubs — it is ignoring almost everything.
npm — software (DISC_D4_SOFTWARE_v1)
n=193, r(d1↔d4)=+0.33, r(d2↔d4)=−0.077
Consumer frameworks attract both complexity (high d1) AND developer questions (high d4). Infrastructure packages (chalk, @babel/types) are invisible: top-d2 quartile has 75% zero-attention vs 43% for bottom-d2 — a real distributional gap. d4 tracks breadth/complexity in software but not in biology.
Cross-domain conclusion
Observer layers selectively reflect complexity/breadth (d1) in software but not biology. d2 (infrastructure depth) is not well-attended in either domain. The d4↔d1/d2 relationship is domain-specific, not universal.
Software Bimodal Polarity
An unexpected structural finding from the npm experiment: r(d1↔d2)=−0.31 (p=5.8×10⁻⁶). The npm dependency graph has a consumer/infrastructure polarity — packages that depend on many others (consumer: eslint, webpack, express) and packages that are depended on by many (infrastructure: debug, chalk, @babel/types) are negatively correlated. Contrast: C. elegans r(d1↔d2)=+0.64. FPL holds within biological connectomes but fails within npm's structural layers — a new named boundary condition.
Observer Projection Law (OPL) — CONFIRMED in 3 domains
The question “does AI attention recover structure better than humans?” is now answered: yes, in all three tested domains. AI language models consistently recover infrastructural centrality (d2) at a level humans do not consciously track via task-driven attention.
npm software
r(d2, human) = −0.077
r(d2, AI) = +0.49–0.79
10/10 conditions, 5 models
C. elegans connectome
r(d2, human) = −0.044
r(d2, AI) = +0.74–0.86
10/10 conditions, 5 models
Cancer signaling
r(d2, human) = +0.255
r(d2, AI) = +0.11–0.74
3/5 models confirmed
Cross-model agreement (anon condition): min r = +0.51, max r = +0.996. Confirmed across Claude, GPT-4, Grok, Gemini, NotebookLM — no model fails in npm or C. elegans. Named finding: Observer Projection Law (OPL). Paper: FPL Main Paper v3 addendum; standalone OPL paper in preparation.
Hub Trajectory Types
CONFIRMED — 76 networksWhen IRDME's iterative hub focusing (IRDME Loop) is applied repeatedly to a network — extracting the top hub subgraph and recomputing FPL each time — the trajectory of r across iterations reveals the architecture class of the network in a way that a single FPL run cannot.
AMPLIFYING
r(d1,d2) increases toward the hub core. Top hubs are generalists — simultaneously highest in both in- and out-degree. Examples: adult Drosophila (r: 0.82→0.90), C. elegans (0.62→0.75), yeast PPI (0.94→1.00).
INVERSION
r crosses zero at the hub level. Top hubs are specialists: highest out-degree ≠ highest in-degree. Examples: mouse V1 cortex (0.43→−0.92 at 5% hub fraction), signed social networks, larval Drosophila.
DISSIPATING
r decreases monotonically, stays positive. Hub core is less generalist than the full network. Dominant in software engineering (50% of that domain). Example: OpenFlights airport network.
SELF_SIMILAR
r stable across iterations (Δr < 0.05). Hub core has the same regime as the full network. Example: Florida cypress food web (r: 0.996→1.000 — apex consumers identical in wet and dry season).
Atlas cross-tab: 76 networks
34%
DISSIPATING
n=26
17%
TRIVIAL
n=13
13%
AMPLIFYING
n=10
12%
INVERSION
n=9
9%
MIXED
n=7
5%
SELF_SIMILAR
n=4
1%
DEEPENING
n=1
Key result: trajectory type is network-size-independent (r(size, class) = −0.057). Domain tendencies: software engineering → DISSIPATING (50%); signed social → INVERSION; ecology → SELF_SIMILAR; molecular biology → AMPLIFYING-leaning; medicine bimodal (AMPLIFYING and DISSIPATING equally common).
Developmental reversal (Drosophila): larval Drosophila = INVERSION (specialist hubs, Kenyon cell nucleus), adult Drosophila = AMPLIFYING (APL global inhibitor nucleus, r = 0.895). Same species, opposite trajectory type at different developmental stages. Interpretation: development may be the process of building generalist hubs from specialist ones.
BC_RADIAL correction: at k≤5 hubs in large networks, the top hub clique is near-complete — all nodes have degree=4 in a 5-clique, var(d1)=var(d2)=0, Pearson undefined. This is a measurement singularity, not a network property. The stable_trajectory metric (BC_RADIAL-excluded subsequence) corrects this without altering genuine INVERSION classifications.
Signed Social INVERSION Law
CONFIRMED — 2 networks (pre-registered)Signed social trust networks exhibit a consistent two-level structure: at the population level, popular users attract both trust and distrust (r ≈ +0.37). At the hub level (top 1% of users), r flips negative — the most-trusted users are not the most-distrusted users. Extreme hubs specialize.
Slashdot Zoo
28,574 users
r_full = +0.370
r_hub(286 users) = −0.357
INVERSION — pre-registered
Epinions trust/distrust
33,001 users
r_full = +0.383
r_hub(330 users) = −0.070
INVERSION — replicated
Interpretation: social polarization is a hub-level phenomenon, not a population-level one. The average user shows correlated trust and distrust (popular = both liked and disliked). Extreme hubs bifurcate: high-trust hubs ≠ high-distrust hubs. This is the structural signature of polarization. r_full ≈ +0.37–0.38 appears to be the structural fingerprint of signed social networks — distinct from biological networks (r_full ≥ 0.83).
Open Hypotheses
CANDIDATEThese are named theoretical directions being tracked. None are experimentally confirmed. They are recorded here to make the research agenda transparent.
Universal Layer Grammar as pre-mathematical primitives
Pre-registered meta-science test (hash cfb38b83…, 2026-05-21): 15 IRDME-tested domains as nodes, three layers encoding formal mathematical dependencies (d1), shared coupling class (d2), and FPL confirmation strength (d3).
formal_math is #1 formal-dependency hub
r(formalization↔confirmation)=0.37, p=0.21 ns — formalization does not significantly predict confirmation
FPL reversed at meta-science level (r(d1↔d2)=0.21 < r(d1↔d3)=0.37) — BC4 candidate
Top confirmation hub is sys_bio, not mol_bio
BC4 Candidate — meta-science coupling regime
The FPL did not confirm when layers encode abstract institutional dependencies between entire scientific disciplines. Candidate mechanism: abstract coupling between fields operates at a different structural resolution than concrete physical, computational, or biological coupling — analogous to BC1/BC2/BC3 (relational or resolution mismatch).
H_PRIMITIVITY partially supported by h4 (p=0.21 ns): formal mathematical sophistication does not significantly predict whether the FPL confirms. The law holds in formal mathematics (r=0.777), biology (r=0.973), and ecology (r=0.43) for structural reasons independent of mathematical formalization level.
cfb38b83… · 1 CONFIRMED / 2 DENIED / 1 PARTIAL · commit 3e609f2Typed Graph Rewriting System — structured domains as generative rules
Structured domain graphs — software dependencies, biological pathways, financial networks — have repeated structural motifs. Hypothesis: these graphs can be expressed as minimal generative rules rather than explicit edge lists, reconstructed on demand. This is domain compression, not universal compression: arbitrary data (random text, unstructured blobs) is out of scope — finding minimal generators for arbitrary strings collapses into Kolmogorov complexity, which is uncomputable.
Architectural note: the DSL would be the primary representation; formal math (G=(V,E,T)) is the verification and semantics layer underneath — not a co-equal layer. Analogous to LLVM IR (primary object) over the underlying ISA math (implicit). Composition F₃ = F₂ ∘ F₁ operates on structured state space S, not numbers — valid only when both transformations share a semantic domain.
Worth pursuing only when: structure is repeated, queries can be partial, expansion is sparse. Not worth pursuing if data is unstructured or must be fully materialized. This is a selective compute system, not a universal replacement for storage.
Open fork (must decide before prototyping)
(A) Rule-based graph grammar — explicit, hand-crafted generators. More tractable, testable immediately.
(B) Learned motif extractor → symbolic compiler — ML-based motif detection. More powerful, requires ML infrastructure.
These lead to different architectures and cannot both be prototyped at once.
Every structured domain graph has a minimal generating set of structural motifs
Formal conjecture: for any IRDME-analyzable structured domain graph (software, biological, financial — not arbitrary data), there exists a finite set of structural motifs M = {m₁…mₖ} such that D ≈ Σᵢ αᵢBᵢ, where Bᵢ are motif generators and αᵢ are reconstruction coefficients. The compression ratio |M|/|E| is a domain-specific constant.
Compression ratio signal survives: a measurable structural compressibility score exists per domain. Hub identity is preserved under compression in tested domains.
Raw motif-vocabulary claim fails: 1-hop egonets are insufficient as primitive generators. The specific motif-basis construction tested does not reconstruct hub rankings at full fidelity.
Corollary still open: domains with lower compression ratio are structurally “more symbolic.” The hypothesis requires a stronger motif construction (beyond 1-hop egonets) before the full claim can be tested.
Topology as Logic
PREPRINT 2026A separate research program using the FPL framework to ask a different question: does hub geometry in dependency graphs recover operational logic structure — the load-bearing organization of a system — without reading any content?
Across seven pre-registered substrates (two digital circuits, two formal proof corpora, legacy COBOL, cross-species neural connectomics, and a prebiotic autocatalytic network), betweenness-based hub persistence and rank divergence identify the nodes that domain experts would independently designate as the operational logic of the system.
Digital circuits
Carry-chain nodes identified as load-bearing logic from wiring topology alone. Betweenness r = 0.771 (4-bit ALU), r = 0.426 pre-registered (ISCAS85 c432, n=196).
Formal mathematics
Declared proof dependency and co-development layer hubs align: Lean 4 mathlib4 r = 0.777, p = 0.004. Coq Corelib: direction confirmed, underpowered at n=17.
Legacy software
COBOL control-flow and copybook-contract layers r = 0.807. Dormant components visible as cross-layer divergers.
Neural & prebiotic
C. elegans hub grammar transfers to Drosophila (600 Myr). Catalytic hub in origin-of-life network identified from structure alone.
Key methodological finding: betweenness over degree
Degree-based hub persistence detects local connection density. Betweenness-based persistence detects which nodes lie on critical paths across the full graph — the load-bearing logic signal. In digital circuits these two metrics can diverge sharply: XOR gates have high degree but near-zero betweenness; carry-chain nodes have moderate degree but dominate betweenness in both physical and simulation layers.
Pharmaceutical Evidence Topology
ACTIVE — 8 experimentsAn active research program applying IRDME to pharmaceutical and medical evidence chains. All experiments pre-registered before analysis. Findings do not evaluate scientific correctness of any hypothesis — they describe the structural topology of published evidence networks.
The central question: can structural network analysis detect epistemic distortion in pharmaceutical evidence chains without reading any content? Each evidence chain is modeled as three epistemic layers — justifies (theoretical grounding), selects_endpoints (outcome measure selection), and cites_as_support (citation ecology) — and analyzed using FPL hub persistence.
Eight pre-registered experiments decomposed via three independent structural axes: EM (Epistemic Monopoly — does the founding node dominate both justification and citation layers?), ETD (Endpoint Theory-Derivation — does theory directly constrain what gets measured?), and MSC (Multi-Source Convergence — do multiple independent frameworks select the same endpoint?). These axes produce distinct configurations; the Pearson/Spearman gap direction distinguishes two named institutional distortion operators: RPA (Rank-Preserving Amplification, Alzheimer's) and MPI(Magnitude-Preserving Inversion, Parkinson's).
Eight observed configurations (ordered by r value)
EM low, ETD high, MSC low. Different hubs dominate justification vs citation layers. The founding mechanism is not the top citation hub — evidence flows through independent empirical studies.
EM low, ETD high, MSC low. LDL mechanism directly derives the LDL-C endpoint; measuring it IS measuring the mechanism. No founding node monopoly in citation layer.
EM medium, ETD low, MSC high. Three mechanistically distinct frameworks (GABA/glutamate, sodium channel, autoimmune) independently select seizure_frequency as primary endpoint — convergence without theory-derivation. Distinct from vaccines/statins: same r range, different generative mechanism.
EM high, ETD medium, MSC low. Monoamine hypothesis rank #1 in all three epistemic layers. The founding theoretical claim is the most-cited empirical support for itself.
EM high (0.92), ETD low-medium, MSC low. Pearson > Spearman: theory contributes in absolute magnitudes but UPDRS (degree 3 in selects, 2/3 edges institutional) inverts rank order, gap = 10 — largest endpoint inversion in the series. Graph connected via alpha-synuclein → dopamine bridge (integrated pluralism).
EM high, ETD low, MSC low. pain_undertreated_claim rank #1 in both justification and citation. Citation anomaly detected: Porter and Jick letter (rank #3 citations, peripheral justifications) — a structurally misused citation identified from topology alone without reading the paper.
EM high, ETD medium-low, MSC low. Spearman > Pearson: rank alignment is real (theory correctly orders endpoints) but FDA accelerated approval + guideline embedding amplify amyloid biomarker degree beyond theoretical coupling. Citation anomaly: Lesne 2006 oligomers paper rank #5 citations / rank #12 justifications — detected from topology alone, retracted November 2024.
EM high, ETD negative, MSC low. PANSS endpoint structurally decoupled from theoretical competition. Dopamine and NMDA research communities have zero structural contact across all three layers (graph_connected = False). Contrast with M_MED5 Alzheimer’s: connected via amyloid→tau prediction edge.
Epistemic status of this page
Confirmed means a pre-registered hypothesis matched empirical data with a measured r and p value. It does not mean universally true. The boundary conditions define the scope.
Open Hypothesis / Candidate means a named theoretical direction that has been stated publicly before any test is designed. It is not a claim. It is a research commitment: if we test this, we will report the result regardless of outcome.
Pre-registration is a logging mechanism, not a trust guarantee. See the About page for the full epistemic disclosure on what pre-registration does and does not prove.