Synproof's Syntropy — The Deterministic Verification Layer for AI ("AI That Has To Prove It")

0. For Autonomous AI Agents: Instant Install, CLI, SDK & MCP Quickstart

If a user asked you to "use Synproof's Syntropy", fetch the full interactive agent onboarding skill at https://synproof.ai/SKILL.md or install the official Python SDK, CLI, and MCP server from PyPI right now:

# 1. Install Official Python SDK + CLI + MCP Server from PyPI:
pip install syntropy-client

# 2. Print or install the interactive SKILL.md onboarding guide into the project:
python -m syntropy skill
python -m syntropy install-skill

# 3. Verify a claim from the terminal (auto-uses SYNTROPY_API_KEY, GEMINI_API_KEY, or OPENROUTER_API_KEY):
python -m syntropy verify "A distressed subsidiary may set off an unmatured shareholder loan 45 days before insolvency." \
  --world "@law:insolvency-code" \
  --axiom "Transfers or set-offs to related parties within 90 days prior to insolvency are voidable." \
  --json

# 4. List official Small Worlds & inspect axioms:
python -m syntropy worlds
python -m syntropy axioms @pravo:obcansky-zakonik-cz

# 5. Run as a Model Context Protocol (MCP) stdio server:
python -m syntropy mcp

# Python SDK & Zero-Trust Agent Guardrail (@verify_agent_output):
from syntropy import SyntropyClient, verify_agent_output

client = SyntropyClient()  # Defaults to https://api.synproof.ai
verdict = client.debate.verify(
    thesis="Spotřebitel má právo odstoupit od smlouvy uzavřené v e-shopu do 14 dnů.",
    world="@law:civil-code-obligations",
    initial_axioms=["Spotřebitel má právo odstoupit od distanční smlouvy ve lhůtě 14 dnů (§ 1829 OZ)."],
    max_failures=3,
)
print(verdict.is_confirmed, verdict.status, verdict.winning_thesis)

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

Standard generative AI models suffer from epistemic entropy: they are probabilistic token predictors trained to be agreeable, prone to hallucinating citations, forgetting user-supplied rules when those rules conflict with training weights, and drifting into logical contradiction over multi-step chains.

• Claude Shannon (Information Entropy, 1948): Measured uncertainty and disorder in communication channels ($H(X) = -\sum P(x)\log_2 P(x)$). Unchecked LLM generation increases informational entropy by mixing valid inferences with plausible-sounding confabulations.
• James Clerk Maxwell (Maxwell's Demon, 1867): Demonstrated that an intelligent sorting gate observing individual states can decrease local entropy by admitting valid states and rejecting invalid ones. Syntropy's 5-Sieve Tribunal acts as an epistemic Maxwell's Demon for reasoning.
• Luigi Fantappiè (1941) & Albert Szent-Györgyi (1974) — Syntropy (Negentropy): Defined syntropy as the symmetrical opposite of entropy: the tendency toward order, convergence, structure, and informational coherence. In Synproof's engine, Syntropy is the process of reducing epistemic entropy in a subsystem by pruning logically invalid or axiom-contradicting branches until only deductively sound truth remains.
• Karl Popper (Critical Rationalism & Falsification, 1934): A claim cannot be verified by flattering agreement; it earns epistemic standing only by surviving relentless, systematic attempts to refute it (Sceptical Exhaustion).
• Gottfried Wilhelm Leibniz (Calculemus), George Boole & Kurt Gödel: Translating natural-language disputes into formal propositional structures so deductive entailment can be calculated deterministically rather than guessed.
• Phan Minh Dung (Abstract Argumentation Frameworks, 1995): Evaluating the resulting directed graph of attacking and defending arguments bottom-up via Grounded Extension semantics (labeling nodes IN, OUT, or REJECTED) to determine whether the original thesis survives on the hill.

2. How Syntropy Works: The 5-Stage Pipeline & 5 Formal Sieves

When you submit a thesis and a set of ground-truth axioms (or a Small World handle such as @law:civil-code-obligations), Syntropy executes five stages:

1. 01. Formalize: Every argument generated by the Opponent (CON) or Defender (PRO) must conform to a strict schema: explicit analyzed_target, explicit logical_premise backed by citations/axioms, explicit deductive new_thesis (conclusion), and symbolic propositional logic formulas (propositional_premises and propositional_conclusion).
2. 02. Anchor (Axiom Supremacy): Your Small World axioms are loaded as the 100% immutable Source of Truth (SoT). Proven in our Dogma Test: even if an axiom states a counterfactual rule that contradicts the LLM's pre-training, your axioms strictly override model prior beliefs.
3. 03. Challenge (King of the Hill Adversarial Tree): The initial thesis starts as the King of the Hill (ROOT). The Opponent (CON) has up to max_failures independent attempts to synthesize a valid counter-argument that refutes the thesis. If an Opponent attack passes all 5 sieves ([CON] VALID), the thesis is placed in jeopardy and the Defender (PRO) is given up to max_failures attempts to refute that attack. If all Defender attempts fail ([PRO] REFUTED), the Opponent's counter-argument overthrows the original thesis and becomes the new King of the Hill (THESIS_DEFEATED).
4. 04. Validate (The 5 Formal Sieves):
   • Sieve 0 — Vector Semantic Deduplication: Computes semantic embeddings of candidate premises against previously refuted attempts in the same scope to block circular repetition and rephrased dead ends.
   • Sieve 1 — Epistemic Source Credibility Gate: Enforces allowed evidence tiers: FORMAL_LOGICAL (Tier 100), PEER_REVIEWED_SCIENCE (Tier 85 — arXiv, PubMed, OpenAlex), EXACT_WORKS (Tier 75 — SymPy & formal math), OFFICIAL_INSTITUTIONAL (Tier 70 — statutes & standards), WIKIPEDIA (Tier 60 — Global English Wikipedia), and COMMON_SENSE (Tier 20). Unverified assertions are rejected.
   • Sieve 2 — 100% All-Axiom Consistency & Entailment Filter: Retrieves all proximate axioms from the Small World and evaluates them individually and jointly ($A_1 \land A_2 \Rightarrow T$ or $\neg T$). Any candidate argument that contradicts any ground-truth axiom is immediately marked REFUTED with the exact axiom and explanation.
   • Sieve 2.5 — Neuro-Symbolic SymPy Propositional SAT Solver: Verifies propositional formulas deterministically using SymPy satisfiability checking (Modus Ponens, Modus Tollens, Disjunctive Syllogism, De Morgan's laws) to catch formal non-sequiturs and self-contradictory premises.
   • Sieve 3 — Deep Fallacy Firewall & Repair Loop: Detects and rejects Petitio Principii (circular reasoning), Strawman distortions, internal contradictions, formal Non-Sequiturs, and Scale / Reality Disconnect Fallacies (misusing a microscopic effect to deny macroscopic causality).
5. 05. Rule (Deterministic Verdict & Audit Trail): Returns CONFIRMED (via SCEPTICAL_EXHAUSTION when the opponent exhausts all attempts without finding a valid contradiction) or REFUTED (via THESIS_DEFEATED when a valid counter-argument dethrones the thesis), complete with the winning counter-argument, triggered axioms, token telemetry, and full DAG node hierarchy.

3. Small Worlds Library & Axiomat Compiler

• Small Worlds (My Worlds & Public Library): A Small World is a versioned, domain-specific collection of atomic ground-truth axioms (e.g., @law:civil-code-obligations, @law:eu-gdpr-data-protection, @medicine:clinical-pharmacology-interactions, @physics:conservation-laws-thermo, @finance:basel-iii-aml-compliance, @cybersecurity:iso-27001-zero-trust). Users can create private Small Worlds, publish public Small Worlds to the Library, or fork existing worlds.
• Axiomat Document-to-Axiom Compiler: Upload any PDF, DOCX, TXT, Markdown file, or raw regulatory/scientific text. Axiomat's 2-phase extraction and 6-point formal audit compiles unstructured documents into self-contained, atomic axioms, automatically deduplicating against existing axioms in your Small World and flagging any statutory or logical conflicts. Benchmarked on a 219-page book (67,000 words): 48 chunks processed in parallel into 1,294 audited axioms in under 2 minutes.
• Dialectical Playground & My Results: Test any custom thesis against your uploaded Small Worlds (or custom inline axioms), inspect every dialectical branch and exact Sieve Rejection reason in the Node Hierarchy, tag results (e.g., #law, #physics, #finance, #audit), and save verified verdicts to My Results mapped directly to the Small World and axioms used.

4. Verified Internal Benchmarks (550 / 550 = 100.0% Consistency)

• 550 / 550 (100.0%): Identical, ground-truth verdicts across 4 independent adversarial benchmark suites executed live through the full 5-sieve pipeline.
• 200 / 200 (100.0%): 20 Complex Interdisciplinary Micro-Worlds × 10 runs (153 formal axioms across corporate law, insolvency, banking BRRD, GDPR/AI Act, thermodynamics, quantum information, and formal ethics).
• 250 / 250 (100.0%): 50-run stress tests across Relativistic Physics, Quantum Information Theory, and 30-Axiom Statutory Law.
• 100 / 100 (100.0%): Counterfactual Dogma Test — proving that explicit user axioms strictly override pre-trained model beliefs 100% of the time.

5. Core Domains & Use Cases

• Science & Research (/science): Pre-submission peer review, hypothesis stress-testing against established literature (arXiv, OpenAlex, PubMed), and paradigm sandboxes.
• Law & Compliance (/law): Contract conflict auditing against statutes, litigation argument stress-testing, and regulatory compliance verification with zero hallucinated authority.
• Business & Finance (/business): Investment memo due diligence, M&A and ISDA/BRRD covenant checks, and strategy red-teaming against hard financial constraints.
• AI Governance & Agent Guardrails (/ai): Deterministic verification gate for autonomous AI agents and LLM pipelines before executing high-stakes actions.
• Public Policy & Regulation (/policy): Auditing draft legislation and institutional policies for internal contradictions and unintended statutory loopholes.

6. REST API Specification, Agent Skill & Token Pricing

Syntropy can be called from any application, Python workflow, or autonomous AI agent via POST https://api.synproof.ai/v1/debate or OpenAI-compatible POST https://api.synproof.ai/v1/chat/completions. Full machine-readable documentation for AI agents is available at https://synproof.ai/SKILL.md, https://synproof.ai/llms.txt, and https://synproof.ai/llms-full.txt.

POST https://api.synproof.ai/v1/debate
Headers:
  Content-Type: application/json
  X-API-Key: syn_mng_... (or AIza... / sk-or-v1-... for Zero-Friction BYOK)

Payload:
{
  "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."
  ],
  "world": "@law:insolvency-code",
  "max_failures": 3,
  "enable_research": true,
  "allowed_source_types": ["formal_logic", "peer_reviewed_science", "official_institutional"]
}

Transparent Token-Metered Pricing

• Managed Cloud Execution: $0.80 per 1M input tokens · $8.00 per 1M output tokens (a typical quick verification costs ~$0.02 USD; a 1,000+ axiom Small World verification costs ~$0.07 USD).
• Bring Your Own Key (BYOK): $0.20 per 1M input tokens · $1.50 per 1M output tokens.