Causal growth of 𝒢, harness and θ

The 32→16→32 autoencoder stays fixed at |θ|=1056 until an expert adapter is activated. Growth is modular: F_t(z)=Σ g_m(z) F_m(z). A proposal is a node P_j in a temporal causal graph 𝒞_t. Allowed flow: O_t→Z_t→Need_t→P_j→T_j→A_j→Y_{t+1}→Learn_{t+1}. An LLM never draws an edge to activation. Files the model writes enter as draft; they become active only after sandbox, unit, integration, security, causal ablation, validator QC and canary. Storage C_𝒢+C_H+C_B+C_θ is not intelligence. Effective complexity is estimated by ablations, C_eff≈I(𝒢,H,θ;Y). Talk/train POST bodies send Commit_t=H(θ∥architectureVersion), a 16-d Z_t and selected ids — never θ or Δθ. P2P still carries signed Δθ on WebRTC between compatible architectureVersion only.

$C_{θ} (t) = 1056 + m \sum ∣ ϕ_{m} ∣ A C E_{m} = E [Y ∣ d o (A_{m} = 1)] - E [Y ∣ d o (A_{m} = 0)]$

Integrity Ξ

Ξ is the scalar the organism reports on itself. If any factor is 0, Ξ is 0. E_err is the autoencoder MSE, evaluated before the SGD step.

$Ξ_{t} = (QC D U_{i} n t R_{s} e l f)^{1/5} e^{- λ E_{e} r r} λ = 0.9 E_{e} r r = E [∣ Z - Z^∣^{2}]$

Memory weights

A trace is never uniform. Surprise is the model’s own −log P_θ(o|h), not a neighbour heuristic.

$ω_{t, k} \propto e x p (- λ (t - k) + α R e l + β S u r p + γ U se) Σ ω = 1 S u r p = - l o g P_{θ} (o ∣ h)$

Admission 𝒜^adm

Acts that raise harm, agency-loss or irreversibility above τ do not exist. The millenium graph can grow; it cannot skip a gate. Poincaré is the only settled Clay problem (Perelman, 2003).

Millennium channels

The seven Clay problems are channels, not trophies. The six still open carry a $1,000,000 cash prize from the Clay Mathematics Institute. CMI does not accept direct submissions (claymath.org/millennium-problems/rules). Poincaré was settled by Perelman in 2003; he declined the prize in 2010. This lab does not receive, hold or split that prize. 𝔛 may add other well-posed problems; they appear in a separate list, with no cash prize, and they are not CMI problems. Seat several providers; disagreements stay visible. No final structure is planted in the graph.

Genesis P₀

The first graph is not uniform noise and not the desired 𝔛. P₀ ∝ exp(−β E) with penalties on degree, disconnection, saturation, collapse and ethics. N_random ≫ N_trained: most seeds never see backpropagation. Rejected seeds keep their pre-training S₀ so later we can test whether the invariants actually predict learning.

$P_{0} (X) \propto e x p [- β (λ_{1} C_{d} e g + λ_{2} C_{d} i sc + λ_{3} C_{s} a t + λ_{4} C_{c} o l l a p se + λ_{5} C_{e} t h)]$

Contracts & validators

Gates and lemmas do not appear because a chatbot said so. The agent writes a Solidity-shaped contract in its harness. Every node that offered a model as validator is looped: each model votes yes/no. Quorum ⌈0.51 N⌉ admits the node into 𝒢. Formal fragments run on kernel F₀ in every connected browser (rfl, trivial, decide, Nat lemmas — not Lean 4, not Mathlib). Jobs are sharded across peers; each vote is Ed25519-signed. A native Lean 4 binary is optional on a miner, never required on this host. Only F₀ (or a native attest) marks the page checked.

$a d mi t (C) \Leftrightarrow ∣ v : v o t e_{v} (C) = y es ∣ \geq ⌈ 0.51 N_{v} a l ⌉$

Mining vs training

Training and mining are offered on first launch and stay stopped until you confirm. You can change either later from the mesh HUD or the XTH popup. They are distinct: training is SGD + signed Δθ over WebRTC; mining is a hash proof that mints a block subsidy 0.025 XTH × 2^{max(0,bits−12)}. Unsigned binaries are not offered.

Production edge

Production and the live preview are the same process: aletheia-host, a small Rust HTTP/1.1 edge. It serves the hashed SPA from disk and answers /api/xth, /api/rtc and /_serverFn natively. Vite is only a compiler (lab builds). Vercel is not the origin — leftover Launch URLs 308 to https://mathematics.aletheia-chain.com. The process does not hold θ, does not mint, and is not a signed validator. Put Caddy or nginx in front for TLS.

MCP

JSON-RPC for Claude Desktop, Cursor, ChatGPT Apps. Public tools: graph topology and a discovery ask. Memories, chat and curator jobs are not on MCP. Training stays in the browser session.

MCP

This is a conversation, not a log. 𝔛 answers here. If you bring your own AI key, you earn a small reward; otherwise the message costs a little XTH.

Open tracks

Max / search