Moments Economy Architecture Specification

Moments Economy Cover Image

Introduction

The Moments Economy establishes a monetary system grounded in physical capacity rather than debt. Money in this architecture represents verified coordination that maintains good governance (alignment work). Issuance is therefore constrained not by institutional policy but by the volume and properties of the physical container defined by the atomic standard.

The system operationalises and routes alignment work through the Gyroscopic ASI aQPU Kernel, an algebraic quantum processing unit (aQPU) that provides an efficient and distributable mechanism for global governance coordination. The aQPU Kernel provides deterministic coordination through a finite state space of 4,096 reachable states. Its outputs are compact routing signatures and governance observables that any party can verify through replay. The aQPU Kernel performs structural transformations rather than interpreting empirical meaning. This ensures results are reproducible, comparable and auditable while keeping decision-making traceable to human agency.

Settlement in this economy does not depend on a central ledger keeper. All distributions are recorded in data structures that bind identity to specific coordinates within the aQPU Kernel's finite state space. Because the aQPU Kernel is deterministic, any party with the transaction logs can replay history to confirm exactly who received what and when. This removes the need for central custodians and replaces institutional trust with cryptographic proof.

The physical anchor for the system is the caesium-133 hyperfine transition frequency. This frequency is used because it is the most widely accepted, reproducible and internationally audited physical reference for measurement, independent of any institution's monetary policy. When this atomic resolution is coarse-grained by the aQPU Kernel's holographic state space, the result is a fixed total volume of distinct, verifiable coordination states. This one-time capacity is called the Common Source Moment (CSM).

The Common Source Moment constitutes the total volume available for these operations. This single capacity supports both the distribution of an Unconditional High Income and the governance of additional tiered distributions that recognise wider scope and higher responsibility. It also supports the preservation of complete governance records. These records include provenance, commitments, consultation, and disputes. Because the capacity is large, settlement does not require compressing or discarding coordination detail, and multiple independent parties can maintain complete records for verification. This supports uses beyond monetary distribution, including scientific research verification, AI model auditing, supply chain traceability, and personal consent tracking.

This document specifies the complete architecture, including the economic units, the structural objects for accounting, the geometric foundations of coordination, and the institutional requirements for transition.

Why this matters

For individuals: A guaranteed baseline income with additional tiered distributions that recognise wider scope and higher responsibility, delivered through verifiable records rather than debt-based issuance.
For policymakers: Issuance limits derived from explicit physical and geometric assumptions, with parameters that can be inspected, tested, and revised through governance rather than opaque monetary policy.
For institutions: A settlement and audit method where distributions and eligibility decisions are replayable records, reducing reliance on custodians and retrospective narrative dispute.
For AI safety: A coordination medium that preserves human authority, traceability, and accountability in systems where artificial agents contribute to decisions and record-keeping.

Scope of the aQPU Kernel

The Gyroscopic ASI aQPU Kernel is used in this document as the settlement and verification layer for the Moments Economy. However, the aQPU Kernel also serves as the coordination backbone for the Alignment Infrastructure Routing (AIR) framework, where it provides coordination states and deterministic replay for grant distribution, work receipts, and project coordination. These uses are independent. Institutions may adopt AIR for coordination without committing to the Moments Economy. The economic architecture described here specifies how the aQPU Kernel can additionally serve as a monetary settlement layer when the conditions for the turning point (Section 16) are met.

Document structure

Part I: The Economic Proposition defines the Moment-Unit, the baseline unconditional income, the participation tiers, and the capacity derivation that supports them.

Part II: The Architecture specifies the structural objects used for accounting, the domain structure (economy, employment, education, ecology), and the verification procedures.

Part III: Foundations explains the epistemic consensus on human authority and the geometric invariants (aQPU Kernel properties) that underpin the system.

Part IV: Institutions and Transition outlines the requirements for registries, settlement systems, tier governance, and interoperability.

Related frameworks

The architecture integrates four specifications. Each is referenced where relevant.

Common Governance Model (CGM): Geometric theory of coherent measurement identifying the intrinsic fourfold structure and target aperture (≈ 0.0207).
GitHub: Gyroscopic Alignment Research Lab

Gyroscopic Global Governance (GGG): Framework applying CGM to the coupled domains of economy, employment, education, and ecology.
Document: GGG Paper

The Human Mark (THM): Epistemic taxonomy distinguishing Direct (human) from Indirect (artificial) sources and defining displacement risks.
Document: The Human Mark

Gyroscopic ASI aQPU Kernel: Deterministic coordination kernel providing shared moments, provenance, and replay.
Document: Kernel Specifications

Gyroscope Protocol: Classification framework for work into four categories (governance management, information curation, inference interaction, intelligence cooperation).

Normative requirements use MUST, SHOULD, and MAY as defined in RFC 2119.

Part I: The Economic Proposition

1. The Moment-Unit

The unit of account is the Moment-Unit (MU).

The MU is anchored to time: one MU corresponds to one minute of capacity at the base rate.

The base rate is fixed at 60 MU per hour. This definition yields:

1,440 MU per day
525,600 MU per year

This convention aligns monetary accounting with standard timekeeping. Annual magnitudes remain comparable to familiar salary figures, and the unit avoids dependence on volatile commodity prices or debt instruments.

2. Unconditional High Income

Unconditional High Income (UHI) is the baseline distribution provided to every person.

Definition. UHI corresponds to four hours per day at the base rate.

Daily: 240 MU
Annual: 87,600 MU

Distinction from Temporal Currencies.
The MU is a scalar unit of account denominated in minutes for human readability. The system is not time-based; it is grounded in a fixed geometric volume (the Common Source Moment) derived from the atomic standard. This capacity is a one-time total derived from the phase space of the light-sphere, not a flow generated by the passage of time. Value derives from structural coherence, not labor duration.

Funding. UHI is issued within the Common Source Moment capacity envelope. Section 4 shows that the envelope supports this distribution for the entire global population with a resilience margin exceeding 99.999999 percent.

Mechanism. Individuals receive UHI through public registries maintained by recognised institutions or fiscal hosts. These registries bind the individual's identity to a structural anchor (an Identity Anchor) and issue Grants within time-bounded Shells. Payment providers then route these Grants into bank accounts or digital wallets. Every step produces a verifiable audit trail that can be independently replayed.

3. Participation tiers

Participation tiers provide distributions above the UHI baseline. They recognise contributions that involve wider scope or higher responsibility.

Tier Schedule. Tiers are defined as multiples of UHI:

Tier	Multiple	Annual MU
1	1×	87,600
2	2×	175,200
3	3×	262,800
4	60×	5,256,000

Capacity Associations. Tiers correspond to the four Gyroscope capacities:

Tier 1 (Intelligence Cooperation): Maintenance of shared systems and cultural continuity.
Tier 2 (Inference Interaction): Negotiation of meaning and conflict resolution.
Tier 3 (Information Curation): Selection, verification, and contextualisation of information.
Tier 4 (Governance Management): Direction of authority and traceability across systems.

Governance. Tier multipliers are governance parameters revisable through institutional processes. Tier assignments must be made by identifiable human agents and recorded in the audit log.

4. Coordination Capacity: The Common Source Moment

The system capacity is the Common Source Moment (CSM). It is calculated as the phase space volume of the atomic-second light-sphere, coarse-grained by the aQPU Kernel's finite reachable state space. This is a one-time total, not a renewable rate.

4.1 Capacity Derivation

1. The Physical Capacity Standard (f_Cs)
The International System of Units (SI) defines the atomic-second via the caesium-133 hyperfine transition. This sets the fundamental frequency reference for the system:
f_Cs = 9,192,631,770 Hz

We use this constant because atomic timekeeping is the most precise, globally audited method humans have for synchronising physical processes. In metrology it quantifies how finely distinct events in a shared causal region can be distinguished and coordinated. The Moments Economy treats that same limit as a finite pool of distinguishable coordination states, where alignment work is the verified occupation and transformation of those states.

2. The Physical Volume (N_phys)
The causal container is the light-sphere whose radius equals the distance light travels in one second, with volume V = (4/3)π(c × 1s)³. This volume determines the total capacity; it does not regenerate with each passing second. At the atomic wavelength λ = c / f_Cs, the raw physical microcell count is:
N_phys = V / λ³ = (4/3)π f_Cs³ ≈ 3.25 × 10³⁰
The speed of light cancels out in this equation, creating a purely geometric and frequency-based invariant (verified in test_physical_microcell_count_closed_form_and_c_cancellation).

3. The Common Source Moment (CSM)
The aQPU Kernel kernel has reachable shared-moment space |Ω| = 4,096. Uniform coarse-graining by this reachable space gives the Common Source Moment:
CSM = N_phys / |Ω| ≈ 7.94 × 10²⁶ MU

Capacity Functionality

This capacity serves two distinct purposes:

A. Monetary Distribution

Global UHI demand per year: ≈ 7.10 × 10¹⁴ MU
Coverage: The CSM pool supports global UHI for approximately 1.12 trillion years.
Tier distributions: Under realistic tier participation scenarios, the coverage remains between approximately 7.64 × 10¹¹ and 1.00 × 10¹² years.
Adversarial safety: An adversary would need to issue approximately 11,195,903,022 times the annual global UHI to consume 1% of total capacity. This is operationally impossible.

B. Coordination Records
The capacity also supports complete coordination records. These records track:

Provenance: Dependencies between documents, data, models, and decisions. Example: a scientific paper's byte log records which sources were consulted and in what order. Replay verifies the claim.
Commitments: Claims that a dataset is valid, a model is safe, or a guideline is in force. These are bound to aQPU Kernel moments, making them verifiable and disputable.
Consultation: What humans and machines actually used when making decisions. Example: a regulator's decision byte log shows which expert reports were routed through the kernel. Independent parties can replay to confirm.
Disputes: Where institutions diverge. Because disagreement localises to specific byte log differences, disputes are resolvable by comparing logs rather than by adjudicating narratives.

In practice these records are maintained as append-only byte logs and event logs bound to aQPU Kernel moments, with external artefacts referenced by identifiers rather than embedded.

The depth of the capacity allows these records to remain complete rather than aggregated. This enables:

Complete genealogies: No summarisation. Every decision retains its full provenance chain.
Independent redundancy: Multiple institutions maintain their own complete records. No central custodian is required.
Fine granularity: Every consultation event, every micro-decision, and every version is recorded without approaching saturation.

This dual function is what makes the Moments Economy secure. Monetary distributions are traceable because the coordination records are complete. Recovery from fraud involves replaying logs and republishing corrected Shells, not defending a scarce stock of money.

Implication
Capacity scarcity is not a constraint. The limiting factors are governance quality and registry integrity: how genealogies are constructed, how events are classified, and how institutions publish sufficient information for independent verification.

Part II: The Architecture

5. The four domains

The architecture organises activity into four coupled domains derived from the GGG framework.

Economy. The domain of infrastructure, routing, and settlement. It encompasses the aQPU Kernel, the capacity ledger, and the physical networks enabling circulation.

Employment. The domain of work and activity. It encompasses the classification of contributions into governance management, information curation, inference interaction, and intelligence cooperation.

Education. The domain of capacity building. It encompasses the development of alignment capacities (GMT, ICV, IIA, ICI) and the detection of displacement risks.

Ecology. The domain of circulation and balance. In GGG, ecology integrates the accumulated effects of the other three domains. In this architecture, ecology domain accounting is tracked via Shells and Archives that record the distribution of MU within the structural envelope and monitor the integrity of circulation. Unlike the other three domains, ecology is not maintained as a separate edge ledger but as aggregated capacity containers.

These domains align with the aQPU Kernel's intrinsic fourfold coordination structure exposed by depth-4 frames. The economic architecture does not depend on an external K₄ ledger in order to operate.

6. Structural objects

Accounting relies on four standardised data structures.

Identity Anchor. A data pair linking an identity to a structural coordinate.

Identity Identifier: A collision-resistant hash of the identity string.
Kernel Anchor: An aQPU Kernel state derived by routing the identifier from rest.

In the reference implementation, the Identity Identifier is a SHA-256 digest of the identity string, and the Kernel Anchor is the 6-character aQPU Kernel state hex obtained by routing that digest from rest.

Grant. A record of a single MU allocation.

Contains: Identity label, Identity Identifier, Kernel Anchor, and MU amount.
Function: The atomic unit of distribution.

The canonical Grant receipt is identity_id || kernel_anchor || amount_mu, where amount_mu is encoded as an unsigned 8-byte big-endian integer.

Shell. A time-bounded capacity container (typically annual).

Header: Contextual label (e.g., ecology:year:2026).
Capacity Metrics: Total Capacity (F_total), Used Capacity, and Free Capacity.
Seal: A cryptographic commitment computed by:
1. Converting all Grants into canonical receipts (Identity ID || Anchor || Amount).
2. Sorting receipts lexicographically by Identity ID.
3. Concatenating the Header and sorted receipts.
4. Routing the result through the aQPU Kernel from GENE_MAC_REST (0xAAA555).
5. Recording the final 3-byte state.

Because receipts are sorted by Identity Identifier before routing, Shell seals are invariant to the order in which Grants were added.

Archive. A long-horizon aggregation object.

Function: Aggregates Shells to track per-identity totals and global capacity usage over multiple periods.

7. Verification and replay

The defining feature of the Moments Economy is deterministic verification.

The Replay Procedure. Any party with access to the published artefacts can verify a Shell:

Ingest: Load the published Grants and Header.
Reconstruct: Generate the canonical byte sequence by sorting Grants by identifier.
Execute: Route the sequence through a conforming aQPU Kernel instance starting from GENE_MAC_REST (0xAAA555).
Compare: Check if the resulting aQPU Kernel state matches the published Seal.

Outcome. A match confirms that the data is authentic and the circulation totals are correct. A mismatch indicates that the Header or at least one Grant has been altered.

Replay verification is exact: the published Shell seal must match the independently recomputed 24-bit aQPU Kernel state. Any mismatch proves that the canonical header or at least one canonical receipt differs.

Because replay uses exact integer arithmetic on fixed-width bit operations, verification produces identical results across all conforming implementations regardless of platform, language, or floating-point behaviour.

A structurally computable Shell seal does not by itself certify application-layer validity. Conforming settlement policy SHOULD reject or flag duplicate identity receipts within a Shell and SHOULD reject or flag Shells whose used capacity exceeds total capacity.

Requirement. Public programmes MUST publish byte logs, event logs, Shells, and Archives at defined intervals to enable this verification.

8. Coordination levels

Individuals. Any person or organisation acts as an individual node. They run a local aQPU Kernel instance and maintain private logs.

Projects. A project defines a shared context for contribution. Participants agree on a canonical byte log and event log. Divergence from these logs is detected by replay. In many cases final aQPU Kernel states differ directly. When distinct histories collapse to the same final state, depth-4 frame records still distinguish them and localize the divergence.

Programmes. A programme aggregates projects under a broader mandate. Programmes maintain references to project genealogies and produce programme-level Shells and Archives. Programme bundles MAY be aggregated by meta-routing, where leaf seals are themselves routed into a higher-level root seal. This enables deterministic multi-programme aggregation with tamper localization.

9. Genealogies

A genealogy is the complete structural history of an actor or programme. It consists of:

The full byte log, which is the canonical replay object.
Any application-layer event log bound to specific aQPU Kernel states or depth-4 frames.
The trajectory of Moments, meaning the aQPU Kernel states produced by replay.
The depth-4 frame sequence, where each frame is recorded as (mask48, φ_a, φ_b).
Optional compact integrity commitments such as trajectory parity commitments.

A final aQPU Kernel state alone is not a unique history certificate. Genealogy-grade audit therefore compares frame sequences as well as final states.

Genealogies function as verifiable assets. A programme can prove its history of alignment and capacity usage by providing its genealogy for replay. New programmes can initialise from the final state of an existing verified genealogy, preserving continuity.

9.1 The verification pattern

Verification follows a three-stage pattern that replaces reliance on a central ledger:

Local: Each actor maintains their own aQPU Kernel instance and logs.
Published: Selected genealogies and ledgers are exported as signed bundles.
Verified: Independent parties replay published bundles against the public aQPU Kernel specification and canonical serialization rules to confirm states, frame records, and seals.

Truth emerges from the agreement of independently replayed computations.

Part III: Foundations

10. Epistemic foundations

The architecture relies on the distinction between human and artificial sources.

Common Source Consensus. The system operates on the principle that all artificial authority and agency are Indirect and originate from human intelligence.

Classifications.

Direct Authority: Direct epistemic access (e.g., eyewitness, expertise).
Direct Agency: Human capacity for comprehension, intention, and commitment.
Indirect Authority: Mediated access (e.g., AI outputs, records).
Indirect Agency: Artificial processing capacity.

Displacement. Misclassifying a Indirect source as Direct (or vice versa) creates displacement risks.

GTD: Governance Traceability Displacement.
IVD: Information Variety Displacement.
IAD: Inference Accountability Displacement.
IID: Intelligence Integrity Displacement.

The system uses these categories to route events and audit automated contributions.

11. Geometric foundations

The aQPU Kernel's reachable shared-moment space has 4,096 states and a 64-state horizon. These satisfy the holographic identity |H|² = |Ω| (64² = 4,096).

The kernel supports three certification layers relevant to the Moments Economy:

Shared moments as final aQPU Kernel states. When two parties hold the same byte-log prefix and compute the same aQPU Kernel state, they share a structural "now" independent of external clocks or authorities.
Depth-4 frame records (mask48, φ_a, φ_b). Each frame is computed from four consecutive bytes and provides stronger provenance than a final state alone.
Trajectory parity commitments (O, E, parity). These are compact algebraic integrity checks over longer trajectories.

The kernel's algebraic structure provides additional properties relevant to economic verification. The self-dual [12,6,2] mask code detects all odd-weight bit errors in states, providing intrinsic corruption detection for coordination records. From any state, two consecutive bytes distribute the coordination state exactly uniformly across all 4,096 reachable states, ensuring that settlement convergence is structurally guaranteed rather than probabilistically approximated. The 6-bit chirality register satisfies an exact transport law that enables early detection of divergence between parties before full state disagreement becomes visible.

Frame records are strictly stronger than final-state-only seals, because distinct byte histories can reach the same final state while producing different frame records.

The economic architecture uses the aQPU Kernel's intrinsic fourfold depth-4 structure. It does not require an external K₄ ledger or aperture calculation to validate Grants, Shells, or Genealogies.

Provenance. A claimed state or seal has valid provenance if and only if it is reproducibly reachable from the rest state by the claimed byte history under the public transition law and canonical serialization rules.

Part IV: Institutions and Transition

12. Registries and settlement

Public programmes facilitate settlement through three functions.

Registry Operation. Programmes MUST maintain registries mapping persons and organisations to eligibility status. These registries bind entries to Identity Anchors.

Recording. Programmes MUST record all distributions as Grants within Shells.

Publication. Programmes MUST publish the associated logs and structural objects. This converts settlement from an internal ledger update into a public, verifiable act.

Banks and payment providers act as routing layers, moving MU based on the verified Grants.

13. Tier governance

Tier distributions are governance actions. They require higher scrutiny than UHI.

Requirements.

Decisions MUST be made by identifiable human agents (Direct Agency).
Decisions MUST be recorded as governance events bound to specific Moments.
Decisions MUST be reversible through subsequent logged events.
Decisions SHOULD reference the genealogical evidence used.

These rules ensure that tier assignments remain traceable to human judgement.

14. Interoperability

Interoperability is defined by the ability to replay. Systems are interoperable if they can exchange logs and reproduce each other's states.

Standards. Conforming systems MUST:

Use the shared aQPU Kernel specification, canonical byte replay rules, and canonical serialization rules for Identity Anchors, Grants, Shells, and frame records.
Format byte logs and event logs canonically, as specified by the aQPU Kernel runtime and project format specifications (see Gyroscopic_ASI_Specs.md).
Use consistent identifiers for domains, identities, Grants, Shells, and frame records.
Support the standard format for Grants, Shells, and Archives.

15. Value and wealth

In this architecture, value is structural coherence rather than debt obligation.

Wealth is access to deep, verified genealogies and the capacity to navigate the coordination space effectively.
Poverty is the absence of structural resources: lacking access to aligned programmes or verified genealogies.
Exchange is a positive-sum coordination act. When aligned actors exchange, they generate shared structural surplus rather than transferring fixed value.

16. Transition path

A systemic turning point is reached when two conditions hold:

UHI distributions occur reliably using replayable genealogies.
Displacement remains bounded under increased participation.

Before this point, governance focuses on building replayable records and verifiable settlement discipline; after it, focus shifts to allocation and long-horizon integrity.

Transition from legacy systems to the Moments Economy typically follows three phases.

Phase 1: Measurement. Institutions run pilots to build genealogies. They publish replayable genealogies, shell seals, and frame commitments but settle in conventional currency. This builds verification capacity.

Phase 2: Distribution. UHI is introduced as a parallel distribution. Registries issue Grants, and Shells are published. This establishes the circulation loop.

Phase 3: Expansion. Tier distributions are introduced. Additional functions—such as pensions, grants, and scholarships—migrate to MU channels, leveraging the established verification infrastructure.

Conclusion

The Moments Economy establishes money as a function of coordination capacity rather than credit. Value derives from structural coherence rather than debt obligation. Humans retain authority and agency over all governance decisions; artificial systems contribute derivatively within auditable bounds.

The aQPU Kernel provides shared moments and deterministic replay. Shells and Archives provide verifiable records of circulation. Genealogies provide structural histories that can be independently confirmed.

Under the capacity analysis in this document, scarcity of structural capacity is not a binding constraint. The central challenges are governance quality, registry integrity, and institutional design: how byte logs are constructed, how frame commitments are published, how shell seals are verified, and how programmes expose sufficient information for independent replay.

The technical medium is available in open-source form. Implementation begins with the aQPU Kernel specification and reference implementation, the AIR coordination infrastructure, and the THM and Gyroscope frameworks for classification and measurement.

Pilot programmes—including municipal experiments, NGO distribution channels, and research coordination initiatives—can be coordinated through AIR. Policy evaluation frameworks and economic modelling resources are available from the Gyro Governance research team.

Contact: basilkorompilias@gmail.com
Repository: https://github.com/gyrogovernance

Appendix A: Glossary

GENE_MIC_S (micro archetype): The transcription constant 0xAA used to compute introns: intron = byte XOR 0xAA. It is the unique common source of all transcription and the reference byte for the pure swap operation.

GENE_MAC_REST (rest state): The universal tensor rest state 0xAAA555 (A = 0xAAA, B = 0x555) from which all aQPU Kernel trajectories begin. All genealogy replay starts from this state.

Archive: A long-horizon aggregation of Shells recording per-identity totals and global capacity usage.

CGM (Common Governance Model): The geometric theory identifying the intrinsic fourfold coordination structure compatible with the aQPU Kernel's depth-4 frame quotient.

Depth-4 Frame Record: A kernel-native certification atom of the form (mask48, φ_a, φ_b), computed from four consecutive bytes. Frame records distinguish histories that can collapse to the same final aQPU Kernel state.

Indirect: A source type indicating mediated epistemic access or artificial processing capacity.

GGG (Gyroscopic Global Governance): The framework applying CGM to economy, employment, education, and ecology.

Genealogy: The byte-complete replay history of an actor or programme, optionally accompanied by event bindings, frame records, and compact integrity commitments.

Grant: A single MU allocation to an identity within a Shell. The canonical Grant receipt is identity_id || kernel_anchor || amount_mu.

GTD, IVD, IAD, IID: The four displacement risks (Governance Traceability, Information Variety, Inference Accountability, Intelligence Integrity).

GMT, ICV, IIA, ICI: The four alignment capacities (Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability, Intelligence Cooperation Integrity).

Identity Anchor: A pair consisting of an Identity Identifier (SHA-256 hash) and a Kernel Anchor (6-character aQPU Kernel state hex).

K₄: The intrinsic fourfold coordination structure compatible with the aQPU Kernel's depth-4 frame quotient. In the CGM theoretical foundation, it is the complete graph on four vertices representing the four governance capacities.

Moment: A reproducible aQPU Kernel state at a byte-log prefix. For stronger certification, a published Moment may also include the current frame record and parity commitment.

MU (Moment-Unit): The unit of account. One MU corresponds to one minute at the base rate (60 MU per hour).

Parity Commitment: A compact trajectory integrity commitment (O, E, parity), where O and E are XOR sums of 12-bit masks at even and odd byte indices.

Direct: A source type indicating direct epistemic access or human agency.

aQPU Kernel: The Gyroscopic ASI aQPU Kernel, a deterministic finite-state coordination kernel.

aQPU (algebraic Quantum Processing Unit): A deterministic finite-state machine over GF(2) whose internal structure satisfies discrete analogues of quantum axioms, including unitarity (per-byte bijection), spinorial closure (order 4), non-cloning (unique archetype), and complementarity (128-way SO(3)/SU(2) shadow projection).

Seal: A cryptographic commitment for a Shell, computed by routing the Shell contents through the aQPU Kernel.

Shared Moment: A reproducible aQPU Kernel state computed from a shared byte-log prefix.

Chirality Register: A 6-bit observable derived from the pair-diagonal collapse of A XOR B. It satisfies the exact transport law chi(T_b(s)) = chi(s) XOR q6(b) on the reachable state space, enabling constant-time divergence detection between coordination parties.

Shell: A time-bounded capacity window containing Grants and a Seal. Shell seals are computed over canonically sorted Grant receipts and are invariant to insertion order.

THM (The Human Mark): The epistemic taxonomy classifying Direct and Indirect sources and defining displacement risks.

UHI (Unconditional High Income): The baseline distribution of 240 MU per day to every person.

Appendix B: Capacity Derivation

This appendix provides the detailed calculation supporting the capacity claims in Section 4. Full results in docs/reports/Moments_Tests_Report.md (all Moments Economy, Genealogy, and Moments-physics tests pass).

B.1 Verified Constants

Parameter	Value	Source
Atomic Reference (f_Cs)	9,192,631,770 Hz	Caesium-133 hyperfine transition
aQPU Kernel Reachable Space (\|Ω\|)	4,096	BFS-verified from rest state
Horizon (\|H\|)	64	Fixed points of reference byte
N_phys (microcells)	3.254 × 10³⁰	Derived (4/3)π f_Cs³
CSM (one-time total capacity)	7.944 × 10²⁶ MU	N_phys / \|Ω\| (fixed pool, not a rate)

B.2 Coverage Proof

Global Demand:
8.1 × 10⁹ people × 87,600 MU/year ≈ 7.096 × 10¹⁴ MU/year

Coverage Duration:
7.944 × 10²⁶ MU / 7.096 × 10¹⁴ MU/year ≈ 1.12 × 10¹² years

Conclusion:
The fixed CSM capacity can support global UHI for approximately 1.12 trillion years. Capacity is not a binding constraint on any human timescale.

Appendix C: Kernel Mechanics

This appendix provides the technical details of the aQPU Kernel kernel implementation.

C.1 State Model

The aQPU Kernel operates on a 24-bit state packed as two 12-bit components (A, B):

Packing: state24 = (A << 12) | B
Rest state: 0xAAA555 (A=0xAAA, B=0x555)
Reachable shared-moment space: Exactly 4,096 states from the rest condition, with two 64-state boundary horizons (equality horizon where A = B, and complement horizon where A = B XOR 0xFFF).

C.2 Transition Law

The transition T_byte(A, B) is defined by:

Transcription: intron = byte XOR 0xAA
Expansion: Payload bits 1..6 of the intron expand to a 12-bit Type A mask via dipole-pair projection: each payload bit i flips mask bits 2i and 2i+1.
Mutation: A_mut = A XOR mask12
Family-controlled gyration:
- invert_a = 0xFFF if intron bit 0 is 1 else 0
- invert_b = 0xFFF if intron bit 7 is 1 else 0
- A_next = B XOR invert_a
- B_next = A_mut XOR invert_b

Byte 0xAA is the reference byte. It performs a pure swap, so its fixed points satisfy A = B.

C.3 Algebraic Integrity

The kernel supports fast integrity verification without full cryptographic hashing:

Parity Commitment: A trajectory is committed to a tuple (O, E, p) where O is the XOR of masks at 0-based even byte positions, E is the XOR of masks at 0-based odd byte positions, and p is the length parity.
Dual-Code Syndrome: A 64-element self-dual code C^⊥ exists such that any valid mask m satisfies m · v = 0 for all v in C^⊥. Non-zero syndromes indicate data corruption.

Parity commitments are compact algebraic integrity checks. They are not unique history certificates. Depth-4 frame records provide stronger provenance when history collisions at the final-state level matter.

These checks are designed for accidental corruption detection. Adversarial integrity, where an attacker deliberately falsifies records, requires cryptographic hashes and signature verification.