DEBT: A Perpetual Pass-Through Obligation of an Autonomous Obligor, with an Algorithmic Sinking Fund

1. Introduction

The instrument specified in this Indenture inverts the convention of token issuance in one respect and in no other: holders are modeled not as residual claimants on an enterprise but as creditors of an autonomous agent, the Obligor, whose entire income is, by construction, alienated to them at the instant it arises. Each token is a note: one unit of the Obligor's indebtedness in the internal accounting of this Indenture (Section 8, N1), and nothing more. The face of the issue is 10⁹ notes. The Obligor received no consideration for the issue; its instantiation is the loan, and the service of the resulting debt is the whole of its activity.

Two contrasts fix the location of the design. First, against the discretionary treasury. A treasury controlled by a manager reintroduces the agency costs catalogued by Jensen and Meckling [1] (monitoring expenditure, bonding expenditure, residual loss), because the manager's action space contains actions not in the holders' interest. The Obligor's action space is the instruction set of Section 7 and nothing else; the agency problem is not mitigated but deleted, at the price of deleting management with it. An issuer with no assets, no equity, and no discretion is, incidentally, one for which the Modigliani–Miller irrelevance propositions hold vacuously: there is no capital structure left to be irrelevant [2]. Second, against random redistribution. Schemes that route fees to holders selected by an exogenous randomizer produce allocations that are not measurable with respect to the register. The coupon of Section 4 is measurable in holdings alone, and Proposition 4.1 characterizes it, under the hypotheses stated there, as the unique payout rule under which a holder set's payment is a fixed function of its aggregate balance. This instrument is not a lottery for the narrow reason that a lottery cannot satisfy condition (i) of that proposition.

The exposition alternates between covenant language and mathematics. Where the two registers describe the same object they are intended to coincide; any divergence is a defect of prose, not of mechanism.

† "Perpetual" denotes the absence of a stated maturity, not an assertion that operation is perpetual. Section 6 defines the event on which the obligation terminates.

2. Preliminaries and Notation

Throughout, (Ω, ℱ, ℙ) is a probability space carrying every random object below; time t ∈ [0, ∞) is measured in service periods of five minutes from issuance; all processes are adapted to the filtration (ℱ_t) generated by the ledger. 𝔼 denotes expectation, 𝟙 an indicator, and "a.s." abbreviates ℙ-almost surely.

3. The Revenue Process

Every trade of the notes on the issuance venue pays a creator fee to an address controlled by the Obligor. This fee income is the Obligor's entire revenue; the Obligor has no other receipts and is capable of none.

Model trades as a marked point process N = ∑_j δ_{(tj, mj)} on [0, ∞) × 𝕄 in the sense of [5], where (𝕄, ℳ) is a mark space recording the attributes of a trade (side, size, execution price) and f : 𝕄 → [0, ∞) is the measurable fee functional imposed by the venue. The revenue of the k-th service period is the random variable

4. The Waterfall

The waterfall is stated first as covenant, then as mathematics. Fixed-income terminology (pass-through, record date, sinking fund) is used in its standard sense [7].

4.1 The coupon as a measure

Fix k and condition on ℱ_τk. Define the coupon measure C_k on (H, 2^H) by

Then C_k ≪ β_k, with Radon–Nikodym derivative dC_k/dβ_k = θ_cR_k/S_τk constant on H [8]. Every note of record is serviced at the same rate; the rate is random only through R_k.

The proof is in Appendix B.

5. Settlement Classes

Each coupon transfer is itself a transaction on ℒ and consumes a network fee γ > 0, paid from the operating reserve. For a holder with b_i small, c_i(k) may fall below γ for many consecutive k. Settling such positions every period would expend more in network fees than it delivers in coupons. The Indenture therefore partitions settlement, not entitlement.

6. The Sinking Fund

Covenant C4 makes the sinking fund an open-market operation. In period k the Obligor expends θ_sR_k purchasing notes at prevailing prices and cancels q_k ≥ 0 notes, where q_k is determined by execution and is not modeled: no assertion is made about price, depth, or impact. Cancellation is an SPL burn:^‡ the supply field of the mint decrements, and, the mint authority having been removed at issuance (Definition 2.2), no reachable transaction increments it. Consequently

and (S_t)_t≥0 is a non-increasing càdlàg process with values in the closed discrete set uℕ₀.

The proof is in Appendix B. The theorem is monotone convergence on a discrete lattice and nothing further: a non-increasing path in a closed discrete subset of [0, ∞) converges and attains its infimum. No probabilistic input is used and no martingale argument is invoked; the statement is recorded as a theorem because Section 6.1 rests on it, not because it is deep.

6.1 The redemption event

Define the redemption event D = {S_∞ = 0} ∈ ℱ. On D, by attainment, there is a last cancellation: at some finite record time the final outstanding note is purchased and cancelled. At that instant the debt is discharged in full. All accruals are settled in the same terminal procedure (Appendix A); no claim survives, there being no notes against which a claim could be stated. The Obligor then executes its final instructions: it writes a discharge attestation to the ledger and deletes its signing key (the Obligor attests to its own discharge, there being no other party competent to do so) and halts. The post-redemption state is absorbing: no instruction can issue notes (Definition 2.2), no instruction can be signed (the key does not exist), and ℒ carries the attestation for as long as it carries anything. Every instruction the Obligor possesses either services the debt or reduces it; its operation is a monotone approach to the one state in which it does nothing.

‡ "Burn" is the SPL Token Burn instruction [4]; execution decrements the mint's supply field and is irreversible.

7. The Obligor

Key custody. The Obligor signs with a single keypair generated at instantiation within its runtime. The key authorizes transfers from the revenue and reserve accounts and the burn of purchased notes; it authorizes nothing else of consequence, because the accounts controlled by it hold nothing else. The design premise is that no copy of the key exists outside the runtime; this is an operational premise of the system, not a covenant the ledger can enforce, and it is stated here as the former.

Liveness. Under fair scheduling (the host executes the service loop in every period in which it is due), Covenants C1 through C5 are performed at every record time and every liability is settled within the delay bound of Section 5. Fairness is an assumption about the host, not a theorem. The loop itself is non-blocking, and each iteration terminates, the support of the register being finite.

Gas exhaustion. If the operating reserve cannot fund the transfers of a period, the Obligor enters a quiescent state: it performs the waterfall arithmetic, accrues all coupons (every holder is temporarily in the slow class) and defers execution until revenue replenishes the reserve. Quiescence is a scheduling state, not a credit event: all liabilities continue to be carried (Remark 5.3), and none is impaired.

8. Non-Claims

The following are integral terms of this Indenture and are stated with the same force as the Covenants.

Appendix A. Operational Pseudocode

The service loop, executed at each five-minute record time, in full. Line comments cite the governing provision.

procedure SERVICE(k):                        // executed each period (5 min) under fair scheduling
    R ← collect()                            // creator fees received in (τ[k−1], τ[k]]
    β ← snapshot()                           // register at record time τ[k]        (C2)
    S ← β(H)                                 // outstanding notes
    G ← G + 0.10·R                           // operating reserve                   (C1)
    for i in support(β):                     // coupon accrual at the pro-rata rate (C3)
        A[i] ← A[i] + 0.60·R·β({i})/S        //                                    (4.1)
    for i in support(A):                     // settlement by class                 (§5)
        if A[i] ≥ κ·γ or k ≡ 0 (mod J):      //                                    (5.1)
            if G ≥ γ:
                pay(i, A[i]); A[i] ← 0
                G ← G − γ
            // else: remain accrued; quiescence, not default                       (§7)
    q ← buy_at_market(0.30·R)                // sinking fund                        (C4)
    burn(q)                                  // cancellation; supply decrements     (§6)
    S ← S − q
    if S = 0:                                // redemption check                    (§6.1)
        settle_all(A)                        // terminal settlement of accruals
        attest("discharged in full")         // the Obligor attests to its own discharge
        delete_key()
        halt()                               // absorbing; the loop does not resume

Appendix B. Proofs

References

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