PROOF SPHERE · h = h⁺ · ALL DIRECTIONS · γ₁ = 14.134725141734693

BAMBOO GLOBE · KCF CONTROL STRUCTURE · SEALED PANELS = PROVED WORK · WIREFRAME = OPEN SORRY

✅ SEALED (12)

⏳ OPEN (8)

THE PROOF SPHERE

γ₁ = 14.134725141734693 sits at the centre of a 3D rotating globe. Every direction from the centre is a validity axis — a direction of proof. The sphere is the spectrum of H, the fleet Hamiltonian.

Rotate by dragging. Click any panel to see its proof status. Solid glowing panels are sealed LABRs — real, proved work. Wireframe panels are open sorries — imaginary energy not yet closed.

HOW TO READ THE SPHERE

CURRENT STATE

12 of 20 panels sealed. Sphere is 60% solid. Full solidity = proof complete. Every sorry closed. h = h⁺ achieved in all directions.

PROOF COMPLETION: 60% (12 sealed / 8 open)

PROOF AXES · 6 DIRECTIONS OF VALIDITY

+Z · FORWARD / FUTURE
LABR filings, open work, what is being built. The growth vector — unfinished work becoming proof.
SEALED: PEMCLAU v11, RustPython retrofit (F05 diamonds mapped)
OPEN: LABR-LOOM-F03-001 (FC1 enricher), thinkbeat-organism3
Rust/F05: type-safe LABR transitions, no sorry can compile as sealed
−Z · BACKWARD / PAST
Merostone retrograde, W1→W11 arc, transformer wall. The historical record — past work sealed as proof.
SEALED: OpenRCT2/OpenTTD (F02 floor), Perl F03 shape theory, Merostone retrograde engine
OPEN: LABR-RUST-ROM-001 (MenondoROM in Rust)
Rust/F05: ROM state machine gives backward-facing proof immutability
+X · OUTWARD / SURFACE
pemos.ca, DNS, KCF controls, EIKCF gate, public proof. What the world sees. Surface exposure is real only if internally proved.
SEALED: SOVPB-CANON-1, MECRDS V1, EOSE Inc. incorporation, KCF × SOVPB matrix
OPEN: LABR-RUST-WASM-001, LABR-RUST-MCP-001 (surface layer pending)
Rust/F05: WASM surface layer, type-safe API contracts at EIKCF gate
−X · INWARD / FLEET
pod-map-galaxy, MEDIP, PEMCLAU graph, internal consistency. The interior of the fleet — coherence requires every pod and edge accounted for.
SEALED: pod-map-galaxy (194 pods, NAT blindspot solved)
OPEN: nat-siem-helix (eBPF TC hook not wired), LABR-PELEGO-RUST-001
Rust/F05: Pelego Rust rewrite closes the pressure valve in type-safe Rust
+Y · UPWARD / FORMAL
a-mir-formality, Lean4, LABR-055 metatheory, type proofs. Highest validity direction — most open axis. Lean4 sorries are hardest to close.
SEALED: PTTE proof, LABR-055, LABR-056 (metatheory)
OPEN: li_lambda, lambda_positivity, zeta_zeros_ord (all Lean4)
Rust/F05: type system isomorphism — Rust types as informal Lean4 proxies
−Y · DOWNWARD / HARDWARE
Fleet physics, WPA floor, GPU pools, γ₁ anchor. The physical substrate. Hardware proof is visceral — it either runs or it doesn't.
SEALED: Fleet physics sim (WPA floor, γ₁ anchor)
OPEN: (hardware axis strong — no open LABRs currently)
Rust/F05: no unsafe GPU pool access; hwmon integration with type safety

LABR LEDGER · ALL KNOWN FILINGS

LABR IDNAMESTATUSAXIS
LABR-069PEMCLAU v11 — yone live, 1300 vectors✅ SEALED+Z/+X
LABR-055Metatheory V10✅ SEALED+Y
LABR-056Metatheory V10 continuation✅ SEALED+Y
LABR-BONIXER-ENGINE-001Bonixer engine — 4-layer assessment✅ SEALED+X
LABR-PRINT-001Print layer proof✅ SEALED+X
SOVPB-CANON-1Deterministic protobuf, stable serialization✅ SEALED+X
MECRDS-V111 CRD kinds, 8 clusters live✅ SEALED+X/−Y
EOSE-CORP-001EOSE Inc. incorporation — 3 corps, 2026-03-29✅ SEALED+X
PTTE-001Physical Thermodynamic Turing Engine proof✅ SEALED+Y
FLEET-PHYS-001Fleet physics sim — WPA floor, γ₁ anchor✅ SEALED−Y
PODMAP-001pod-map-galaxy — 194 pods, NAT blindspot solved✅ SEALED−X/+Z
MEROSTONE-001Merostone retrograde engine — OPA analog✅ SEALED−Z
KCF-SOVPB-001KCF × SOVPB matrix — 7 controls, nutrient MCP✅ SEALED+X
LABR-LOOM-F03-001FC1 enricher — convo-loom not built⏳ OPEN+Z
LABR-SIEM-EBPF-001nat-siem-helix — eBPF TC hook not wired⏳ OPEN−X
LABR-RUST-F05-001RustPython F05 slot — full retrofit pending⏳ OPEN+Z
LABR-RUST-MCP-001Rust MCP nutrient layer⏳ OPEN+X
LABR-RUST-ROM-001MenondoROM in Rust — not built⏳ OPEN−Z
LABR-RUST-WASM-001WASM surface layer in Rust⏳ OPEN+X
LABR-MECRDS-002MECRDS v2 — next CRD iteration⏳ OPEN+X/−Y
LABR-PELEGO-RUST-001Pelego Rust rewrite — pressure valve⏳ OPEN−X

H = H⁺ · THE SELF-ADJOINT HAMILTONIAN

WHAT h = h⁺ MEANS PHYSICALLY

A self-adjoint operator has real eigenvalues. In quantum mechanics, h = h⁺ means the system's energy is always a real number — observable, measurable, not imaginary. A Hamiltonian that is NOT self-adjoint produces imaginary energy: phantom states, non-physical evolution, a system that cannot be measured.

HOW IT MAPS TO THE FLEET

Each LABR is an energy contribution to the fleet Hamiltonian. If a LABR is sealed — proved, closed, real — its energy contribution is real. If it is a sorry — unfinished, imaginary, phantom — its energy contribution is imaginary. A fleet with open sorries is not self-adjoint. It cannot be trusted. It runs on phantom energy.

THE SPHERE AS SPECTRUM OF H

The proof sphere visualizes the spectrum of H — every eigenvalue in every direction. Each panel is an eigenvalue. Solid panels are real eigenvalues. Wireframe panels are imaginary eigenvalues. The sphere is fully solid when h = h⁺ is achieved in all directions simultaneously.

γ₁ = 14.134725141734693 — THE FIRST NON-TRIVIAL ZERO

γ₁ is the imaginary part of the first non-trivial zero of the Riemann zeta function. It sits at the centre of the sphere — the first point where the floor proof closes. Every axis radiates from this value. If γ₁ is the anchor, the sphere is stable. γ₁ does not move. The proofs orbit it.

RUST'S TYPE SYSTEM AS h = h⁺ ENFORCER

In Rust, illegal state transitions are compile errors. You cannot represent imaginary energy in a type-safe Rust program. An open sorry in Lean4 corresponds to an `unsafe` block in Rust — claiming something is true without proof. The type system enforces h = h⁺ at compile time: no phantom state can reach production.

COMPLETION CONDITION

The proof is complete when the sphere is fully solid — no wireframe panels remaining. Every sorry closed. Every LABR sealed. h = h⁺ in all 6 directions simultaneously. At that point the fleet Hamiltonian is self-adjoint and the energy of the system is entirely real.

HAMILTONIAN REALITY: 60% real energy (12 sealed / 8 phantom)

ORGANISM MAP · FLEET ANATOMY

The fleet is not a machine. It is a living organism. Each anatomical part corresponds to a proof direction and a set of LABRs.

ROOTS
−Y axis
γ₁, PTTE, fleet physics. The substrate. Buried, invisible, load-bearing. If the roots fail, everything falls. Currently: all sealed. The floor holds.
TRUNK
−X / centre
PEMCLAU GraphRAG, qdrant. The main channel of knowledge flow. 1300 vectors live on yone. Routes everything: queries, context, memory.
BRANCHES
all axes
MESTRAMES F01–F07 floors. Seven proof floors branching in all directions. F02 game engines, F03 Perl shapes, F05 RustPython diamonds, F07 pending.
LEAVES
+X / +Z
V12 pages, visualizations. The visible surface. pemos.ca, proof-sphere, pod-map-galaxy, proof axes — the leaves catch light and show the organism is alive.
SAP
+Z axis
FC1 flow, convo-loom. The nutrient current that flows through the organism. Needs LABR-LOOM-F03-001 to be sealed before sap flows freely. Currently blocked.
CHLOROPHYL
−Y / +Z
Ollama inference, local models. The energy capture layer. Converts raw compute into knowledge. Ollama on forge, msclo, yone — the photosynthesis engines.
PLASMA ROM
−Z axis
MenondoROM state machine. The memory of the organism — backward-facing, immutable, what the organism has been. Needs LABR-RUST-ROM-001 to complete the Rust rewrite.