Last updated: 2026-05-22 · Paolo Pignatelli, Verbum Technologies
How Everything Connects
FIL Theory is the mathematical bedrock — every product, theorem, and patent claim derives from it. SARAI is the commercial instantiation: the startup, the protocol, the franchise architecture. The Delta Engine is the inverse SARAI problem, now formalized as Constructive Wasserstein Flow. Meridian is the Finance Franchisee of SARAI, self-funded and separate.
The Olah Bundle is the academic bridge to Anthropic's interpretability program — it cannot be sent until the CIP is filed. The CIP protects four new unprotected claims that emerged from the 2026 synthesis. The NCC standalone provisional must be filed before Main16 is submitted to arXiv.
Mathematical Foundation — FIL Theory
| Theorem / Object | Status | Location | Notes |
|---|---|---|---|
| LLC operator ΠC | Established | PaoloLab/FIL/ | Foundation of all formal objects |
| Voronoi Geometry | Established | PaoloLab/FIL/ | Meaning at gcd loci; Voronoi potential V(x) |
| Semantic Temperature Tc | Established | PaoloLab/FIL/ | Phase transition; anti-drift regulatory param |
| Physical Incompleteness Theorem | Lean 4 Verified | PaoloLab/FIL/Lean/ | Bounds KYC decidability |
| NLS Breather / ħlang = ħ | Established | PaoloLab/FIL/ | Main14; dual derivation |
| Main16 — Semantic Second Law | Proved | PaoloLab/FIL/ | Entropy non-decrease in semantic evolution |
| Main17 — Obstruction Theorem | Open (PSPH) | PaoloLab/FIL/ | One open step remaining |
| Main13 — Skyrmions | Active | PaoloLab/FIL/ | IPU/hardware connection |
New Formal Results — 2026
| Result | Status | Patent Impact |
|---|---|---|
| Phantom Tokens — ker(Φ̂*) | Active, unverified | CIP Claim Fence 1 |
| CF Encoder (Prime Cliff solution) | Active, unverified | CIP Claim Fence 3 |
| Machine KYC | Active, unverified | CIP Claim Fence 4 |
| gcd Convergence Criterion | Active | Strengthens Patent 4 |
| Asymmetry Functional Rμ | Active | Supports C12 in Olah bundle |
| Constructive Wasserstein Flow | New (2026-05-22) | Delta Engine formal structure |
| Drift Regulatory Framework | New (2026-05-22) | SARAI anti-drift; Olah prediction |
| Two-Level MI | Active | Olah bundle opening section |
Commercial Products & Architecture
| Product / Module | Status | Target | Revenue Model |
|---|---|---|---|
| SARAI Protocol | Patent 4 Filed | AI companies, enterprise | Licensing, SaaS |
| Delta Engine | Formal structure set | Scientific R&D, legal, medical | Per-session, embedded |
| Franchise Architecture | Defined | Platform play | Revenue share from franchisees |
| Module 0 — Prior Art Search | Defined | Patent attorneys, inventors | $200–800/search vs $3K–10K |
| Phantom Auditor | Concept — CIP pending | Enterprise compliance | Per-token SaaS, annual license |
| CF Encoder / Reverse Bridge | Concept — CIP pending | Robotics, IoT, finance data | Hardware + API |
| Meridian | H-METRIC blocking | Finance, hedge funds | Self-funded, separate from SARAI VC |
Academic & Strategic
| Item | Status | Target | Blocking condition |
|---|---|---|---|
| Olah Bundle C1–C10 | Ready — pending CIP | Chris Olah, Anthropic | ⚠ CIP must be filed first |
| Two-Level MI opening section | Written — seed ready | Olah bundle HUMAN.md | Add before send |
| MI circuit prediction (Drift Framework) | New (2026-05-22) | Olah bundle addition | Add before send |
| Main14 (arXiv) | Awaiting Olah response | arXiv / research community | Olah outreach first |
| NCC standalone provisional | PRIORITY 0 | USPTO | File before Main16 arXiv |
IP Protection
| Patent | Status | Claims | Notes |
|---|---|---|---|
| Patent 1 (Rashomon) | Filed provisional | Adversarial layer | |
| Patent 3 (NCC/Budget Monitor) | Filed | Thermodynamic layer | |
| Patent 4 (SARAI core) | Provisional filed Apr 2026 | 23 claims, 3 independent | 1 yellow flag (arXiv 2602.16424, distinguishable) |
| Patent 5 (IPU/Skyrmion) | In progress | Hardware acceleration | Connects to Main13 |
| Patent 6 (Governance) | Filed | Access control layer | |
| CIP to Patent 4 | ⚠ URGENT | Phantom Auditor, CF Encoder, Machine KYC, gcd criterion | Must file BEFORE Olah transmittal |
| NCC standalone provisional | PRIORITY 0 | Standalone | File before Main16 arXiv |
| Meridian (Concepts 9–16) | UNFILED — HOLD | All Meridian IP | Await patent counsel |
Active R&D Threads
Thread 1: Delta Engine → Constructive Wasserstein Flow
Key result: O_private replaced by recognition disposition (oracle for ∇U). Attractor co-constructed with trajectory. McKean-Vlasov dynamics: dμt/dt = −∇W F[μt; Ht]. V_latent recovered as W2(μt, μ∞).
Three open questions:
- Recognition operator regularity — gradient vs. threshold/half-space → bundle methods or stochastic mirror descent
- Voronoi attractor structure — detect the last cell crossing (exploring → refining phase transition)
- LLC operator contractivity — is ΠC a global contraction? Prediction: no → path-dependence
Next: Engineering prototype (conversation graph + last-cell-crossing detector); connect to Patent 4 CIP
Thread 2: Drift Regulatory Framework
Key result: T < Tc via formal object re-anchoring works on both architectural and learned drift mechanisms simultaneously.
Open empirical questions:
- Do base models drift more than RLHF'd models? (discriminates H1 from H2)
- Is drift directional signature context-conditional? (distinguishes learned vs. centroid-regression)
- Does social-signal phrasing outperform flat re-anchoring at matched token cost?
Next: MI circuit search proposal for Olah bundle; connect to SARAI anti-drift claims
Thread 3: Two-Level MI / Olah Bundle
Level 1 MI: what is this transformer doing? Level 2 MI: what must any system do for language to work? FIL's program is the Level 2 theory; Anthropic's interpretability work operates at Level 1. The bundle bridges them.
Blocking: CIP filing must happen first.
Next after CIP: Run Opus session using 2026-05-21_MI_two_levels_seed.md handoff; then send bundle to Chris Olah
Thread 4: Prior Art / Patent 4
arXiv 2602.16424 (Feb 18 2026) is the yellow flag. Distinguishable because Patent 4 claims specific prime-lattice gcd idempotency construction, not general multi-agent coordination. Priority date verification with counsel required.
Next: Verify priority date vs. arXiv 2602.16424 with counsel; add gcd convergence criterion to Patent 4 spec
Thread 5: Meridian
Theorems T11 (Price Ridge), T12 (Normal-Offset Shell Propagation), and Geodesic Price Discovery are established. All computation waits on the explicit metric tensor. Warped product and conformally flat candidates are the leading options.
Next: Dedicated Opus session on metric tensor formulation
Priority Queue — Ordered
| Priority | Action | Reason |
|---|---|---|
| 0 | File CIP (Claim Fences 1–4 + Products 15a/b) | Blocks Olah transmittal; new IP unprotected |
| 0 | File NCC standalone provisional | Blocks Main16 arXiv submission |
| 1 | Verify Phantom Token definition vs. Main11 | Before CIP; needed for Claim Fence 1 |
| 1 | Verify CF Encoding Lipschitz property | Before CIP; needed for Claim Fence 3 |
| 2 | Add Two-Level MI opening section to Olah HUMAN.md | Needed before send |
| 2 | Add MI circuit prediction (drift) to Olah bundle | Needed before send |
| 2 | Send Olah bundle | After CIP + edits |
| 3 | Opus session: Two-Level MI (handoff ready) | After Olah send or simultaneous |
| 3 | Opus session: H-METRIC for Meridian | Unblocks all Meridian computation |
| 4 | Module 0 Phase B: LLC claim compiler (Python) | First engineering deliverable |
| 4 | Delta Engine prototype: conversation graph + last-cell-crossing detector | Engineering |