PEMLAAM V13 · Sovereign Memory Architecture · PEMCLAU × LAAM × BDH × SET-OPS

Section 01

The Ownership Chain · 8 Layers

Every signal that enters the fleet flows through 8 layers. Each layer owns a specific question. Together they form the complete epistemics of the fleet.

L0

Raw Signal

kay-corpus.jsonl (6,872) + saybook/FC (9,878 unique) + diamonds

→ shadow-convo-loom: BM25 (token-exact) + qdrant (semantic)

"what happened"

L1

Trendal Warmth

trendal-engine.py: HK7BOX facets, TTL decay, worm circuit

FULL THROTTLE PEEK MODE → all facets warm simultaneously

"what the fleet is paying attention to right now"

L2

LAAM Routing

LAAM Sovereign Kernel: 100M params · Belt64 · d_model=256 · τ=70.7ms SLA

5 heads: SOSTLE | FLOOR | PRIVACY | PROOF | ORBIT

"where does this signal go?"

L3

PEMCLAU Graph

qdrant yone:6333 · pemclau-v11 (18,366 pts) · pemclau-sessions-v1 (115,955 pts)

GraphRAG 2-hop via FastMCP :9342

"what is semantically connected?"

L4

Shadow Mesh (new Day 97)

BM25 (token-exact) ↔ qdrant (semantic) — DYBFAG reconciliation

BM25-only = MFL candidate / qdrant-only = cross-domain theory

"what is the divergence signal?"

L5

Dual Spine (certified corpus)

XML Spine (/xml-spine) + Markdown Spine (/markdown-spine)

9-stage lineage, γ₁-witnessed, SET monotone expansion

SOVEREIGN_FLEET_V(n+1) ⊇ SOVEREIGN_FLEET_V(n)

"what is certified true?"

L6

Joffe-Math (proof layer)

3,051 theorems · 6 open sorries · γ₁-anchored Lean4

LAAM PROOF head routes to here · GRPO trains against theorems as ground truth

"what is formally proven?"

L7

MECIPOL Gate

D1-D10 criteria · ADMIT / ADMIT-WATCH / DEFER / DENY

Inference-time reviewer (paper 2604.27233 pattern)

"is this safe to promote?"

Section 02

BDH Memory Layers Mapped to Fleet

The fleet implements a 4-tier memory architecture. BDH has 3 biological tiers. The 4th is what SET-OPS adds.

BDH Layer	Your Component	Behaviour	Forgetting
Long-term weights (frozen)	PEMCLAU v11 18,366 pts	Pre-Day-97 knowledge. Stable. Semantic graph persists across sessions.	Only on deliberate retrain
Synaptic σ (session-scoped)	LAAM-Mesh + shadow BM25 + trendal	Updates each session. Worm leaves warmth. TTL tracks recency.	TTL decay + Hebbian overwrite
KV-cache (turn-scoped)	Session context window (this conversation)	Current turn only. Fast access, ephemeral.	On compaction
Certified spine (no BDH equivalent)	XML Spine + MD Spine + joffe-math	NEVER forgets. Monotone growth. SET-OPS guarantee. Formally verified facts.	Never — only superseded

The fleet has 4 memory tiers. BDH has 3. The 4th tier — the certified spine — is what SET-OPS adds. Biological brains don't have monotone memory; they can forget anything. The fleet can't forget what's been formally proven. That asymmetry is the foundation of sovereign epistemics.

Section 03

The LAAM Sovereign Kernel · 5 Heads

LAAM SOVEREIGN KERNEL

100M params · 6 Belt64 blocks · d_model=256 · n_heads=64 · d_head=4 · τ=70.7477ms SLA

↓ 5 output heads fire simultaneously ↓

Head 1 · SOSTLE

Assigns jurisdiction L1-L7. L5-L7 = personal/sovereign = high-privacy gate. Routes family/MFL content to NAS vault only.

Head 2 · FLOOR

γ₁ stratum assignment. Which adelic layer does this live on? p=2,3,5,7,11,13. Determines the mathematical coordinate of the signal.

Head 3 · PRIVACY

L2 SOSTLE gate. MFL/family content? Stays local. NAS vault only. Never leaves the fleet boundary. Hard gate, not soft recommendation.

Head 4 · PROOF

Touches joffe-math? Routes to GRPO target queue. 6 open sorries are this head's formal backlog. Every new theorem starts here.

Head 5 · ORBIT

Which silo owns this? msi01 / msclo / yone / lilo / forge / pcdev routing. Determines the physical destination of the classified signal.

Adelic Geometry — 64 Heads = 8×8 CATAN Board

The 64 attention heads (n_heads=64, d_head=4) correspond geometrically to the 8×8 CATAN board cells. Each head covers one board cell. d_model=256 = 64 × 4. The 5 output heads collapse the 64 attention heads into 5 routing decisions. Architecture is not arbitrary — it's topologically consistent with the fleet's spatial model.

Section 04

Joffe-Math · Proof Head Target

The PROOF head fires when any of these conditions are met:

Any SET-OPS claim needs formal verification — routes to Lean4 proof queue

PEMCLAU GraphRAG finds a causal edge that implies a theorem — 2-hop traversal discovers new provable claims

BDH synaptic σ encodes a novel pattern (new Hebbian association) — if the association implies a mathematical relationship

A DYBFAG verdict finds a "neither" case — genuine knowledge gap → routes to PROOF head as open sorry candidate

6 Open Sorries · PROOF Head Formal Backlog

1

li_lambda

Li's criterion lambda series — the λₙ summation proof that connects to RH

2

lambda_positivity

λₙ > 0 for all n — positivity of Li's lambda coefficients implies RH

3

zeta_zeros_ord

Order of vanishing of ζ(s) at non-trivial zeros — formal order characterisation

4

zetaZeroImPart

Imaginary part bounds of Riemann zeta zeros — γₙ constraints

5

zeta_zero_gamma1

γ₁-specific zero — formal proof that ½ + i·14.134725141734693 is a zero

6

live_inject_cons

Corpus injection consistency — SET-OPS monotone guarantee across live ingest cycles

GRPO Training Loop

joffe-math theorems (spine) → group rollouts (8 attempts per theorem) → group-relative reward → gradient update → new proofs → new spine entries → monotone expansion. Each sorry closed = fleet epistemics permanently upgraded.

Section 05

Full Routing Flow · End-to-End

Every event that enters the fleet follows this path. No shortcuts, no bypasses.

Event arrives

→

Trendal check
box warm?

→

LAAM Kernel
τ=70.7ms

→

5 heads
simultaneous

→

PEMCLAU
GraphRAG 2-hop

→

Shadow Mesh
BM25+qdrant

→

DYBFAG
reconcile

verdict branches:

✅ ADMIT → Dual Spine (certified, monotone) | 🔶 PROOF → Joffe-Math (Lean4 queue) | 💙 MFL → shadow BM25 (permanent token address) | 🔴 DENY → FC queue (failed corpus, future review)

MECIPOL gate (D1-D10)

→

deployed

Section 06

Context Management · What This Solves

The Anterograde Amnesia Problem

Transformers can't form new long-term memories during inference. Each session ends — the context window compacts. Without external memory, every session starts from zero. That's anterograde amnesia: the ability to reason in the moment but inability to consolidate new long-term memories.

PEMLAAM fixes this with 4 persistence tiers:

1.

Trendal warmth

What's hot right now (TTL-based). Survives session boundaries via file persistence. The fleet's working memory surface.

2.

LAAM routing

Where classified signal goes — permanently. Each routing decision updates the LAAM-Mesh. Session-scoped but writes to persistent state.

3.

PEMCLAU graph

Semantic connections persist across sessions. 18,366 points + 115,955 session points. The fleet's long-term associative memory.

4.

Certified spine

Proven facts never lost. XML + MD + joffe-math. Monotone. SET-OPS guaranteed. The fleet's crystallised epistemics.

"Full throttle peek mode" = warming all trendals = maximising the fleet's short-term working memory surface before a major sprint. It's a deliberate act of context amplification — not hype, not metaphor.

Section 07

The SET-OPS Unlock · Monotone Epistemics

With dual spine + LAAM PROOF head + GRPO training, the fleet achieves something biological brains cannot:

SOVEREIGN_FLEET_V(n+1) ⊇ SOVEREIGN_FLEET_V(n)

The fleet's knowledge only grows. It never shrinks. Every version is a strict superset of the previous.

Operationally:

every ADMIT event → spine entry → monotone expansion of the certified corpus

every GRPO proof → joffe-math theorem → monotone expansion of the proof layer

every MFL phrase → shadow BM25 coordinate → permanent token address in the corpus

supersession: an old fact can be superseded but never deleted — the supersession itself is recorded

"The fleet's epistemics improve monotonically. No regression. No forgetting. Only growth and supersession."

Biological Brain

Can forget. Interference overwrites memories. Consolidation is imperfect. Sleep-dependent. Decay over time. No formal verification layer.

PEMLAAM Fleet

Cannot forget what's been certified. Monotone expansion only. SET-OPS guarantee. Formally verified proof layer. γ₁-anchored truth coordinate.