# Synproof's Syntropy — The Deterministic Verification Layer for AI

> **Syntropy** (by **Synproof**, https://synproof.ai) is a neuro-symbolic, adversarial dialectical verification engine ("AI that has to prove it"). Instead of relying on probabilistic plausibility or agreeable chatbot prose, Syntropy puts any claim, legal clause, scientific hypothesis, financial strategy, or AI agent output on formal adversarial trial against explicit ground-truth rules called **Small Worlds** (sets of atomic, verified axioms).

Every claim is attacked and defended in a **King of the Hill** dialectical tree and filtered through **5 formal sieves** — including vector semantic deduplication, epistemic source-tier discipline, 100% axiom consistency checking, a deterministic **SymPy Propositional SAT Solver**, and **Phan Minh Dung's Grounded Extension semantics** — returning a binary, auditable verdict (`CONFIRMED` or `REFUTED`) with a complete DAG audit trail.

- **Website:** https://synproof.ai
- **API Base URL:** https://api.synproof.ai
- **Full Technical & API Reference for LLMs:** https://synproof.ai/llms-full.txt
- **Interactive Console & Dialectical Playground:** https://synproof.ai/#/app
- **Small Worlds Public Library:** https://synproof.ai/#/library

---

## 1. Theoretical Foundation: Why "Syntropy" vs. Information Entropy?

Standard generative language models exhibit **epistemic entropy**: they predict probable token sequences, flatter user biases, hallucinate nonexistent legal or scientific authorities, and silently allow pre-training priors to override explicit user constraints.

Synproof's **Syntropy** builds on six foundational pillars:
1. **Claude Shannon (Information Entropy, 1948):** $H(X) = -\sum P(x)\log_2 P(x)$. Unconstrained generation increases informational entropy by blending valid deductions with plausible confabulations.
2. **James Clerk Maxwell (Maxwell's Demon, 1867):** A selective sorting gate that decreases local entropy by admitting valid states and rejecting invalid ones. Syntropy's 5-Sieve Tribunal functions as an epistemic Maxwell's Demon for reasoning steps.
3. **Luigi Fantappiè (1941) & Albert Szent-Györgyi (1974) — Syntropy (Negentropy):** Syntropy is the symmetrical opposite of entropy: the convergence toward order, structure, and informational coherence. In Synproof, **Syntropy** is the deterministic reduction of epistemic entropy in a reasoning subsystem by pruning fallacious or axiom-contradicting branches until only deductively entailed truth survives.
4. **Karl Popper (Critical Rationalism & Falsification, 1934):** Claims earn epistemic standing not by agreement, but by surviving systematic, adversarial attempts to refute them (*Sceptical Exhaustion*).
5. **Leibniz (*Calculemus*), Boole & Gödel:** Translating natural-language claims into formal propositional logic so deductive validity is computed rather than guessed.
6. **Phan Minh Dung (Abstract Argumentation Frameworks, 1995):** Bottom-up graph evaluation via *Grounded Extension semantics* (`IN`, `OUT`, `REJECTED`) over the dialectical attack/defense tree.

---

## 2. How the 5-Sieve Dialectical Tribunal Works

When a thesis $T$ and a set of ground-truth axioms $\{A_1, \dots, A_n\}$ (or a Small World handle like `@law:insolvency-code`) are submitted:

1. **King of the Hill Adversarial Tree:**
   - The initial thesis $T$ starts at the root as the **King of the Hill**.
   - The **Opponent (`CON`)** has up to `max_failures` (default 6) attempts to synthesize a formally valid counter-argument that refutes $T$.
   - Every candidate argument must pass all **5 Sieves** before it is admitted into the dialectical graph.
   - If an Opponent attack passes all 5 Sieves (`[CON] VALID`), the root thesis is in jeopardy and the **Defender (`PRO`)** gets up to `max_failures` attempts to refute that specific `[CON]` attack.
   - If all Defender attempts fail (`[PRO] REFUTED`), the Opponent's attack prevails, overthrows the original thesis (`THESIS_DEFEATED`), and the verdict is **`REFUTED`**.
   - If the Opponent exhausts all allowed attempts without producing an undefeated valid attack (`SCEPTICAL_EXHAUSTION`), the verdict is **`CONFIRMED`**.

2. **The 5 Progressive Sieves:**
   - **Sieve 0 — Vector Semantic Deduplication:** Compares candidate premise embeddings against previously refuted attempts in the same scope to block circular repetition.
   - **Sieve 1 — Epistemic Source Credibility Gate:** Enforces allowed evidence tiers:
     - `formal_logic` (Tier 100 — Formal Deductive Inference)
     - `peer_reviewed_science` (Tier 85 — arXiv, PubMed, OpenAlex)
     - `exact_works` (Tier 75 — SymPy & Deterministic Math)
     - `official_institutional` (Tier 70 — Statutes, Standards, Official Records)
     - `wikipedia` (Tier 60 — Global English Wikipedia)
     - `common_sense` (Tier 20 — Empirical Domain Premise)
   - **Sieve 2 — 100% All-Axiom Consistency & Entailment Check:** Evaluates candidate arguments against all proximate Small World axioms individually and jointly ($A_1 \land A_2 \Rightarrow T$ or $\neg T$). Any argument contradicting any ground-truth axiom is immediately marked `REFUTED` with the exact axiom and explanation.
   - **Sieve 2.5 — Deterministic SymPy Propositional SAT Solver:** Verifies `propositional_premises` and `propositional_conclusion` via SymPy satisfiability checking (Modus Ponens, Modus Tollens, Disjunctive Syllogism, De Morgan's laws).
   - **Sieve 3 — Deep Fallacy Firewall & One-Shot Deductive Repair:** Rejects *Petitio Principii* (circularity), *Strawman* misrepresentations, internal contradictions, formal *Non-Sequiturs*, and *Scale / Reality Disconnect Fallacies*.

---

## 3. Small Worlds & Axiomat Compiler

- **Small Worlds (`My Worlds` & Public Library):** Domain-specific collections of atomic ground-truth axioms (statutes, contracts, corporate policies, scientific laws). Referenced via handle (e.g., `@law:insolvency-code`) or selected directly in the Dialectical Playground.
- **Axiomat Document-to-Axiom Compiler (`/v1/axiomat/extract`):** Converts uploaded PDFs, DOCX, TXT, Markdown files, or books into atomic, self-contained axioms using a 2-phase extraction and 6-point formal audit, with automatic semantic deduplication and conflict detection.
- **Verified Benchmarks:** **550 / 550 (100.0%)** ground-truth verdict consistency across 4 independent benchmark suites (20 Interdisciplinary Micro-Worlds × 10 runs, Relativistic Physics, Quantum Information, 30-Axiom Statutory Law, and the 100-run Counterfactual Dogma Test).

---

## 4. REST API Quickstart (`https://api.synproof.ai`)

### Start a Verification (`POST /v1/debate`)
```bash
curl -X POST https://api.synproof.ai/v1/debate \
  -H "Content-Type: application/json" \
  -H "X-API-Key: syn_mng_YOUR_KEY" \
  -d '{
    "thesis": "A distressed subsidiary may set off an unmatured shareholder loan 45 days before insolvency.",
    "initial_axioms": [
      "Transfers or set-offs to related parties within 90 days prior to insolvency are voidable.",
      "Shareholder loans are statutorily subordinated during the 90-day twilight period."
    ],
    "max_failures": 6,
    "enable_research": true,
    "allowed_source_types": ["formal_logic", "peer_reviewed_science", "official_institutional"]
  }'
```

### Poll Verification Result (`GET /v1/debate/{job_id}`)
Returns `status: "completed"` with `result`:
- `original_thesis_status`: `"CONFIRMED"` | `"REFUTED"`
- `stopping_reason`: `"SCEPTICAL_EXHAUSTION"` | `"THESIS_DEFEATED"`
- `winning_thesis`: Surviving thesis text
- `refuting_argument`: Decisive winning counter-argument (when `REFUTED`)
- `argumentation_tree`: Full hierarchical Dung Grounded Extension tree (`children`, `role`, `status`, `rejection_reason`, `anchored_axiom`)
- `archive_of_paths`: All root-to-leaf dialectical branch paths
- `verdict_report`: Structured explanation, `decisive_axioms_triggered`, and `defeated_arguments`
- `total_steps`: Total dialectical attempts evaluated
- `telemetry`: Exact `prompt_tokens`, `completion_tokens`, `total_tokens`, and `estimated_cost_usd`

---

## 5. Navigation & Documentation Links

- [Home — Synproof's Syntropy](https://synproof.ai/)
- [How It Works — 5-Sieve Pipeline & Benchmarks](https://synproof.ai/#/how-it-works)
- [For Science & Peer Review](https://synproof.ai/#/science)
- [For Law & Compliance](https://synproof.ai/#/law)
- [For Business & Finance](https://synproof.ai/#/business)
- [For AI Governance & Agent Guardrails](https://synproof.ai/#/ai)
- [For Public Policy](https://synproof.ai/#/policy)
- [Token-Metered Pricing ($0.80 / $8.00 per 1M Managed; $0.20 / $1.50 BYOK)](https://synproof.ai/#/pricing)
- [API & SDK Documentation](https://synproof.ai/#/docs)
- [Autonomous Agent Skill (`SKILL.md`)](https://synproof.ai/#/skill)
- [Small Worlds Public Library & Axiomat](https://synproof.ai/#/library)
- [Dialectical Console & Playground](https://synproof.ai/#/app)
- [Full Technical Specification (`/llms-full.txt`)](https://synproof.ai/llms-full.txt)