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Repo page: SVG hero banner, citation file, collapsible deep-dives
- docs/assets/banner.svg — custom hero banner (wordmark, thesis, live relational-field motif) embedded at the top of the README - CITATION.cff — enables GitHub's "Cite this repository" button - README "Dive deeper" — collapsible <details> sections: the 12 typed relations, the full ΔS metric, all four Ramanujan imports, the 9-layer table
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CITATION.cff

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cff-version: 1.2.0
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title: "TORIS — Topological Relational Inference System"
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message: "If you use TORIS or build on its architecture, please cite it."
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type: software
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authors:
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- family-names: Sharma
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given-names: Chandandeep
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email: me@chandanofficial.com
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abstract: >-
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TORIS is a ground-up computational substrate for machine reasoning that
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replaces the artificial neuron with the typed Relator, the Euclidean vector
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space with a context-adaptive Relational Field, and backpropagation with a
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local topological Surprise Gradient. It holds contradictions as productive
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tension rather than averaging them away, warps its own topology toward a Goal
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Manifold, and grounds its surprise metric in algebraic topology and the
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partition theory of Ramanujan.
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version: "1.0.0"
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date-released: "2026-06-08"
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license: LicenseRef-Research-Only
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repository-code: "https://github.com/infinitule/TORIS"
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url: "https://infinitule.github.io/TORIS/"
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keywords:
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- relational inference
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- topological
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- machine reasoning
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- knowledge graph
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- predictive coding
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- non-euclidean
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- Ramanujan
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- surprise

README.md

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<div align="center">
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<img src="docs/assets/banner.svg" alt="TORIS — Topological Relational Inference System" width="100%">
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# 🌌 TORIS
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### Topological Relational Inference System
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---
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## Dive deeper
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<details>
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<summary><b>The 12 typed relations</b> — the alphabet of the field</summary>
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<br>
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Every Relator carries one of twelve relation types. Each is **asymmetric by
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default** and has a defined semantics for composition (``) and contradiction (``).
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| Type | Meaning |
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|------|---------|
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| `CAUSAL` | A produces B |
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| `CONDITIONAL` | A activates B under a condition |
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| `CONTRADICTS` | A and B cannot both hold at once |
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| `CONTAINS` | A structurally includes B |
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| `ENABLES` | A makes B possible but does not cause it |
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| `VIOLATES` | A is inconsistent with rule B |
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| `ANALOGOUS` | A and B share relational structure across domains |
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| `REFINES` | B is a more precise version of A |
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| `TEMPORAL_BEFORE` | A occurs before B |
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| `EVIDENCES` | A raises the probability of B |
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| `NEGATES` | A suppresses B |
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| `INSTANTIATES` | A is a specific case of B |
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The contradiction operator fires on type pairs — e.g. `CAUSAL ⊗ NEGATES`,
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`ENABLES ⊗ VIOLATES`, `EVIDENCES ⊗ CONTRADICTS` — surfacing tension the goal
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makes relevant rather than averaging it away.
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</details>
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<details>
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<summary><b>The ΔS surprise metric, in full</b> — topological, not Euclidean</summary>
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<br>
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Surprise between a predicted field `F_pred` and an observed field `F_obs` is a
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weighted sum of three *structural* deviations — no cosine, no dot product:
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```
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ΔS = α·ΔS_structural + β·ΔS_type + γ·ΔS_strength (α=0.6, β=0.3, γ=0.1)
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ΔS_structural = ( |E_obs \ E_pred| + |E_pred \ E_obs| ) / (|E_pred| + 1)
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ΔS_type = (1/|E_match|+1) · Σ D_type(τ_pred(e), τ_obs(e))
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ΔS_strength = (1/|E_match|+1) · Σ (σ_pred(e) − σ_obs(e))²
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```
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where `D_type` is a semantic distance over relation types
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(`0` identical · `0.3` similar · `0.7` unrelated · `1.0` contradictory).
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A single relator propagates only when `ε(R) > θ_ε` (default `0.2`). Confirmed
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predictions are suppressed at the source — the formal basis of selective compute.
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Full derivation in [`docs/MATH_SPEC.md`](docs/MATH_SPEC.md).
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</details>
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<details>
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<summary><b>All four Ramanujan imports, mapped</b> — why a relational AI reaches for number theory</summary>
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<br>
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The depth-`d` surprise of a field is a coefficient of its generating function
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`Z_F(κ)` — the same object form as the partition generating function
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`∏ₙ 1/(1−xⁿ)`. That single identification imports four of Ramanujan's results,
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each buying a concrete computational power.
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| Import | Source (Collected Papers, 1927) | TORIS mapping | Payoff |
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|--------|--------------------------------|---------------|--------|
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| **Circle method** | Hardy–Ramanujan, 1918 | surprise at depth `d` from one saddle point `κ_saddle = exp(π√(2d/3)/d)` | **O(1)** per depth vs O(\|E\|ᵈ) |
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| **Partition congruences** | Ramanujan, 1919 | `p(5m+4)≡0 (mod 5)` → entire depth classes of surprise cancel exactly | **100%** suppression (exp_11) |
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| **1/π series** | Ramanujan, 1914 | goal-warp Φ(G,F) converges like his π series; near-integer test auto-switches | **8 digits** from term one |
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| **Rogers–Ramanujan** | Rogers & Ramanujan, 1919 | valid contradiction-free configurations counted by the RR product | entropy in **closed form** |
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The Heegner analogy: `e^(π√163)` is almost an integer (off by ≈10⁻¹²) because 163
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is a Heegner number. TORIS flags a **critical configuration** when
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`|Z_F(κ) − round(Z_F)| < 10⁻⁴`. See [`docs/RAMANUJAN_BRIDGE.md`](docs/RAMANUJAN_BRIDGE.md).
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</details>
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<details>
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<summary><b>The full 9-layer breakdown</b></summary>
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<br>
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| Layer | Name | What it adds |
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|-------|------|--------------|
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| 0 | Primitives | Relator · ConceptState · RelationalField |
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| 1 | Surprise ΔS | the topological deviation metric |
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| 2 | Predictive Engine | project → observe → delta → propagate |
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| 3 | Goal Manifold | the warp operator Φ and the contradiction log |
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| 4 | Fast Plasticity | the field rewrites itself during inference |
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| 5 | Reasoning | chains · sparse generalization · the full loop |
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| 6 | Fast Surprise Dynamics | an O(n log n) approximation + cyclic-wave propagation |
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| 7 | Analytic Surprise | contour integral · Michel parameters · a running coupling |
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| 8 | Ramanujan Extension | circle method · suppression theorem · partition function |
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| 9 | Exact Surprise | a Rademacher series with certified error bounds |
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</details>
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---
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## Documentation
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| Document | What's inside |

docs/assets/banner.svg

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