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1 | 1 | <div align="center"> |
2 | 2 |
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| 3 | +<img src="docs/assets/banner.svg" alt="TORIS — Topological Relational Inference System" width="100%"> |
| 4 | + |
3 | 5 | # 🌌 TORIS |
4 | 6 | ### Topological Relational Inference System |
5 | 7 |
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@@ -327,6 +329,107 @@ docs/ MATH_SPEC · ARCHITECTURE · DEVIATIONS · RAMANUJAN_BRIDGE |
327 | 329 |
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328 | 330 | --- |
329 | 331 |
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| 332 | +## Dive deeper |
| 333 | + |
| 334 | +<details> |
| 335 | +<summary><b>The 12 typed relations</b> — the alphabet of the field</summary> |
| 336 | + |
| 337 | +<br> |
| 338 | + |
| 339 | +Every Relator carries one of twelve relation types. Each is **asymmetric by |
| 340 | +default** and has a defined semantics for composition (`∘`) and contradiction (`⊗`). |
| 341 | + |
| 342 | +| Type | Meaning | |
| 343 | +|------|---------| |
| 344 | +| `CAUSAL` | A produces B | |
| 345 | +| `CONDITIONAL` | A activates B under a condition | |
| 346 | +| `CONTRADICTS` | A and B cannot both hold at once | |
| 347 | +| `CONTAINS` | A structurally includes B | |
| 348 | +| `ENABLES` | A makes B possible but does not cause it | |
| 349 | +| `VIOLATES` | A is inconsistent with rule B | |
| 350 | +| `ANALOGOUS` | A and B share relational structure across domains | |
| 351 | +| `REFINES` | B is a more precise version of A | |
| 352 | +| `TEMPORAL_BEFORE` | A occurs before B | |
| 353 | +| `EVIDENCES` | A raises the probability of B | |
| 354 | +| `NEGATES` | A suppresses B | |
| 355 | +| `INSTANTIATES` | A is a specific case of B | |
| 356 | + |
| 357 | +The contradiction operator fires on type pairs — e.g. `CAUSAL ⊗ NEGATES`, |
| 358 | +`ENABLES ⊗ VIOLATES`, `EVIDENCES ⊗ CONTRADICTS` — surfacing tension the goal |
| 359 | +makes relevant rather than averaging it away. |
| 360 | + |
| 361 | +</details> |
| 362 | + |
| 363 | +<details> |
| 364 | +<summary><b>The ΔS surprise metric, in full</b> — topological, not Euclidean</summary> |
| 365 | + |
| 366 | +<br> |
| 367 | + |
| 368 | +Surprise between a predicted field `F_pred` and an observed field `F_obs` is a |
| 369 | +weighted sum of three *structural* deviations — no cosine, no dot product: |
| 370 | + |
| 371 | +``` |
| 372 | +ΔS = α·ΔS_structural + β·ΔS_type + γ·ΔS_strength (α=0.6, β=0.3, γ=0.1) |
| 373 | +
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| 374 | +ΔS_structural = ( |E_obs \ E_pred| + |E_pred \ E_obs| ) / (|E_pred| + 1) |
| 375 | +ΔS_type = (1/|E_match|+1) · Σ D_type(τ_pred(e), τ_obs(e)) |
| 376 | +ΔS_strength = (1/|E_match|+1) · Σ (σ_pred(e) − σ_obs(e))² |
| 377 | +``` |
| 378 | + |
| 379 | +where `D_type` is a semantic distance over relation types |
| 380 | +(`0` identical · `0.3` similar · `0.7` unrelated · `1.0` contradictory). |
| 381 | + |
| 382 | +A single relator propagates only when `ε(R) > θ_ε` (default `0.2`). Confirmed |
| 383 | +predictions are suppressed at the source — the formal basis of selective compute. |
| 384 | +Full derivation in [`docs/MATH_SPEC.md`](docs/MATH_SPEC.md). |
| 385 | + |
| 386 | +</details> |
| 387 | + |
| 388 | +<details> |
| 389 | +<summary><b>All four Ramanujan imports, mapped</b> — why a relational AI reaches for number theory</summary> |
| 390 | + |
| 391 | +<br> |
| 392 | + |
| 393 | +The depth-`d` surprise of a field is a coefficient of its generating function |
| 394 | +`Z_F(κ)` — the same object form as the partition generating function |
| 395 | +`∏ₙ 1/(1−xⁿ)`. That single identification imports four of Ramanujan's results, |
| 396 | +each buying a concrete computational power. |
| 397 | + |
| 398 | +| Import | Source (Collected Papers, 1927) | TORIS mapping | Payoff | |
| 399 | +|--------|--------------------------------|---------------|--------| |
| 400 | +| **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) | |
| 401 | +| **Partition congruences** | Ramanujan, 1919 | `p(5m+4)≡0 (mod 5)` → entire depth classes of surprise cancel exactly | **100%** suppression (exp_11) | |
| 402 | +| **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 | |
| 403 | +| **Rogers–Ramanujan** | Rogers & Ramanujan, 1919 | valid contradiction-free configurations counted by the RR product | entropy in **closed form** | |
| 404 | + |
| 405 | +The Heegner analogy: `e^(π√163)` is almost an integer (off by ≈10⁻¹²) because 163 |
| 406 | +is a Heegner number. TORIS flags a **critical configuration** when |
| 407 | +`|Z_F(κ) − round(Z_F)| < 10⁻⁴`. See [`docs/RAMANUJAN_BRIDGE.md`](docs/RAMANUJAN_BRIDGE.md). |
| 408 | + |
| 409 | +</details> |
| 410 | + |
| 411 | +<details> |
| 412 | +<summary><b>The full 9-layer breakdown</b></summary> |
| 413 | + |
| 414 | +<br> |
| 415 | + |
| 416 | +| Layer | Name | What it adds | |
| 417 | +|-------|------|--------------| |
| 418 | +| 0 | Primitives | Relator · ConceptState · RelationalField | |
| 419 | +| 1 | Surprise ΔS | the topological deviation metric | |
| 420 | +| 2 | Predictive Engine | project → observe → delta → propagate | |
| 421 | +| 3 | Goal Manifold | the warp operator Φ and the contradiction log | |
| 422 | +| 4 | Fast Plasticity | the field rewrites itself during inference | |
| 423 | +| 5 | Reasoning | chains · sparse generalization · the full loop | |
| 424 | +| 6 | Fast Surprise Dynamics | an O(n log n) approximation + cyclic-wave propagation | |
| 425 | +| 7 | Analytic Surprise | contour integral · Michel parameters · a running coupling | |
| 426 | +| 8 | Ramanujan Extension | circle method · suppression theorem · partition function | |
| 427 | +| 9 | Exact Surprise | a Rademacher series with certified error bounds | |
| 428 | + |
| 429 | +</details> |
| 430 | + |
| 431 | +--- |
| 432 | + |
330 | 433 | ## Documentation |
331 | 434 |
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332 | 435 | | Document | What's inside | |
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