# Convergence Catalogue: The Schema slug: oip-convergence-schema · https://miscsubjects.com/a/oip-convergence-schema · tags: philosophy, oip, convergence-catalogue, schema, systems-theory · updated 2026-07-17T02:36:09.561Z # The Schema 0. The Schema 0.1 Node Facets 0.2 Edge Types 0.3 Tier Definitions 0.4 Convergence Score Formula Convergence_Strength(Node) = Σ_i [claim_tier_weight(T_i) × domain_independence(D_i) × citation_depth(S_i)] Where: claim_tier_weight: T0=4, T1=3, T2=2, T3=1, T4=0.5, T5=0 domain_independence: 1.0 if domains derived pattern independently; 0.5 if partial borrowing; 0.2 if one imported from another citation_depth: 1.0 if named source + year + result; 0.5 if named source only; 0.1 if vague attribution A node is LOAD-BEARING if Convergence_Strength ≥ 6.0 and claim_tier ≤ T2. A node is CARRIED (visible, low-ranked) if claim_tier ≥ T3 or Convergence_Strength < 6.0. 0.5 The Axioms Referenced (A0–A12) --- ## Corpus map - Catalogue hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article) - Nodes: [C01](/a/oip-node-c01-gradient-dissipation-far-from-equilibrium-order) · [C02](/a/oip-node-c02-least-action-variational-principles) · [C03](/a/oip-node-c03-symmetry-conservation) · [C04](/a/oip-node-c04-symmetry-breaking-bifurcation) · [C05](/a/oip-node-c05-criticality-edge-of-chaos-power-laws) · [C06](/a/oip-node-c06-information-entropy-compression) · … (25 nodes) - Edge series: [Convergence 1](/a/oip-convergence-edge-1) · [Disconfirming 1](/a/oip-disconfirming-edge-1) --- # Convergence Encyclopedia: The Schema slug: convergence-encyclopedia-schema · https://miscsubjects.com/a/convergence-encyclopedia-schema · tags: OIP, convergence-encyclopedia, schema · updated 2026-07-17T02:35:59.753Z ## PART 0: THE SCHEMA ## 0.1 How to Read This Encyclopedia 0.1.1 The Facet System (9 Facets per Node) Every node in this encyclopedia carries nine facets. No node is complete until all nine are populated. The facets are: Facet Label Description F1 Tier T0–T5 assignment with justification F2 Sources Named source, year, venue — verifiable F3 Domains Fields where the pattern appears F4 Scale Spatial or temporal range of instantiation F5 Falsifier Observation or experiment that would invalidate the claim F6 Rival Strongest alternative explanation in its best form F7 Independence Independence assessment: HIGH / MODERATE / LOW, with flags for hidden common causes F8 Pattern type Mathematical / structural / energetic / biological / social / philosophical F9 Maps Adjacency: which atlas regions (A1–A12) this node belongs to 0.1.2 Tier Definitions (T0–T5) Tier Label Epistemic status Load-bearing? T0 Theorem / proof Mathematical truth; falsifier is “n/a (theorem)” Yes — logical necessity T1 Established Multiple independent sources; consensus in field; reproducible Yes — carries convergence load T2 Contested Active debate; some supporting evidence; critics published Yes — carries load with uncertainty flag T3 Interpretive Philosophical framing; not empirically decidable No — maps terrain, doesn’t bear structural load T4 Experiential Phenomenological report; first-person No T5 Metaphorical Poetic resonance; illustrative only No — zero load Rule: Only T0–T2 nodes bear structural load in the convergence claim. T3 nodes map boundary terrain. T4/T5 are admitted only as explicit markers of where the map ends. 0.1.3 Edge Types Convergence nodes connect via typed edges: Edge Meaning Example RECURS-WITH Mutual reinforcement; one pattern enables or appears within another C03 (symmetry) recurs-with C04 (symmetry-breaking) CONTRADICTS Tension; both cannot be fully true; the boundary between them is productive C06 (compressibility) contradicts C24 (fine-tuning) INSTANTIATES Specific case realizes general pattern C10 (fractals) instantiates C02 (variational) in specific geometric form IN-TENSION-WITH Unresolved opposition; both carry load but point in different directions C24 (fine-tuning) in-tension-with C06 (compressibility) Rule: Every edge must be typed. Untyped adjacency is not a claim. ## 0.2 The Sharpened Convergence Claim (Post-Audit) The signature is not the pattern. The signature is the compressibility of the convergence. v1 stated: “Unrelated systems keep rediscovering the same patterns.” This is true but weak — it invites the cheap objection that we are pattern-matching after the fact. The corrected claim is sharper: After every deflation — after removing coincidence, after removing shared mathematical ancestry, after removing observation bias, after removing definitional triviality — what survives is Wigner’s residue: so little math describes so much world. The convergence is not that patterns repeat. The convergence is that the same compressed description applies across scales and domains that share no causal history. This is the claim that must be defended. It is stronger than “patterns recur” and more falsifiable: if each domain requires its own incompressible mathematical apparatus, the convergence thesis fails. Wigner’s residue (named after Wigner 1960 “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”) is the observation that a small set of mathematical structures — linear algebra, calculus, graph theory, information theory — suffices to describe phenomena spanning 60+ orders of magnitude in scale, across domains with no known causal connection. Falsifier of the sharpened claim: A world (or substantial domain within it) whose regularities require a mathematical framework with no overlap with any other domain’s framework — complete incompressibility of descriptive apparatus across domain boundaries. Rival: The shared mathematical framework is a selection effect — we (human observers) can only perceive what our cognitive and mathematical tools can represent; the apparent convergence is an artifact of our representational limitations (cf. C24, observer bias). ## 0.3 Audit Findings Summary: v1 → Encyclopedia A citation audit of the v1 spine (25 nodes) found a 25% defect rate. The following corrections have been applied in this version: Node-Level Corrections Node v1 Error Correction C04 Anderson “More Is Different” (1972) cited as symmetry-breaking source Corrected: Anderson 1963 “Plasmons, Gauge Invariance, and Mass” Phys. Rev. 130:439 is the symmetry-breaking paper. 1972 is the emergence paper (now C21). C05 Single citation for SOC Corrected: Split into Bak-Tang-Wiesenfeld 1987 PRL 59:381 (1/f noise) and 1988 PRA 38:364 (full SOC theory). Both cited. C12 Autopoiesis dated 1972 Corrected: Maturana & Varela 1980, D. Reidel, Boston Studies in the Philosophy of Science vol. 42. The 1972 text was a preprint; 1980 is the canonical publication. C18 “Waves” treated as single node Corrected: Split into C18a (linear wave equation, T0) and C18b (excitable media / limit cycles, T1). These share the word “wave” but not mathematics. C18a obeys ∂²u/∂t² = c²∇²u; C18b is nonlinear threshold dynamics. C16 Branching treated as single scale field Corrected: Murray’s law (r₀³=r₁³+r₂³, laminar viscous flow), Horton’s laws (river networks, different exponents), and Bejan’s constructal law (engineering optimization) are three different results. Do not claim all branching instances share Murray scaling. C17 Golden angle formula imprecise Corrected: Formula is 2π(1−1/φ) ≈ 137.5°, equivalently 360°/φ². Lindstedt 1984 FLAGGED UNVERIFIED — source could not be independently confirmed. Structural Corrections Issue Correction Independence tags Re-tagged post-Macy/variational analysis. Nodes C06, C07 now carry explicit flags for Macy Conference cross-pollination. C02 critical note Added honest flag: variational principles are definitional universality (almost any smooth law can be written as extremum), not substantive universality. This is a known limitation, not hidden. T2+ uncertainty flags All T2 nodes (C12, C13, C19) now carry explicit uncertainty flags in F1 (Tier facet). C05 critics Clauset, Shalizi & Newman 2009 and Mitchell, Crutchfield & Hraber 1993 both cited as rivals. C11 critics Clauset et al. 2009 caution on scale-free claims cited as rival. C24 edge Explicit IN-TENSION-WITH edge to C06 declared. C25 typing Fault line between metaphysics and mechanism explicitly typed; no blurring. Receipt Standards Applied • Every T0–T3 claim carries a named falsifier • Every T1–T2 claim carries a rival in strongest form • Every convergence claim carries an independence check • No receipt, no claim. No rival, no load. No falsifier, no science. --- ## Corpus map - Next: [Convergence Encyclopedia — C01](/a/convergence-encyclopedia-c01) - Encyclopedia start: [The Schema](/a/convergence-encyclopedia-schema) - Kin corpora: [Total Structure](/a/oip-total-structure) · [Signature of the Grain](/a/oip-sog-preamble-axioms)