Treasury Proof Ledger (TPL)

• TPL is a cryptographic auditing framework that models institutional treasuries as conserved, multi-domain state machines using proof-of-reserves and proof-of-transit logs.
• It employs hash-chained receipts, Bitcoin-anchored commitments, and policy-based disclosure views to ensure transparency, security, and auditability.
• TPL overcomes conventional proof-of-reserves limitations by enabling cross-domain, multi-period trails and stakeholder-specific, privacy-compatible disclosures.

The Treasury Proof Ledger (TPL) is a cryptographic auditing framework designed to provide accountable, policy-driven transparency for institutional Bitcoin treasuries across multiple domains—including on-chain wallets, off-chain custodians, derivatives, and fee sinks—without disclosing sensitive operational details. TPL models the treasury as a conserved multi-domain state machine, with verifiable append-only logs of proof-of-reserves snapshots, proof-of-transit receipts for inter-domain transfers, and policy-driven, stakeholder-specific disclosure views. Security guarantees, including exposure soundness, policy completeness, non-equivocation, and privacy-compatible policy views, are obtained using standard cryptographic primitives and Bitcoin-anchored commitments, conditional on minimal non-collusion assumptions and explicit governance boundaries (Puente et al., 3 Dec 2025).

1. Motivation: Shortcomings of Conventional Proof-of-Reserves

Conventional point-in-time proof-of-reserves (PoR) protocols—such as Merkle-tree attestations of visible UTXOs—do not meet the escrow, risk management, and regulatory requirements of institutional treasuries. Specifically, typical PoR approaches:

• Expose live wallet addresses: Compromising operational privacy.
• Fail to model liabilities or encumbrances: Neglecting derivatives, collateral, or borrowed assets.
• Lack cross-domain auditability: Omit off-chain, custodial, or synthetic exposures.
• Do not yield replayable multi-period trails: Hindering dynamic and historical auditability.

Current practice is thus inadequate for ecosystems involving complex internal transfers, policy-driven disclosures, or the separation of duty among various stakeholders (e.g., public investors, auditors, regulators). TPL is introduced to reconcile these requirements by treating exposures as conserved cryptographic state, rather than a sequence of isolated PoR claims (Puente et al., 3 Dec 2025).

2. Idealised Model: Multi-Domain State Machine and Ledger Construction

Multi-Domain Exposure Vector

Let $\mathcal{D} = \{d_1, d_2, \ldots, d_m\}$ be a set of treasury domains (e.g., cold storage, exchanges, custody, derivatives, explicit fee sinks $d_{\mathsf{fee}}$). At time $t$, each domain $d \in \mathcal{D}$ has an exposure $B_d(t) \in \mathbb{Z}$, capturing net Bitcoin holdings (including negative/externalized or encumbered exposures). The collective treasury state is $\mathbf{B}(t) = (B_d(t))_{d \in \mathcal{D}}$.

Balance-Update Rule and Fee Sink

Treasury events $$e_k = (t_k, d_{\mathrm{src}}, d_{\mathrm{dst}}, v_k, \mathsf{evid}_k, m_k)$$—with $v_k$ the value in BTC, $\mathsf{evid}_k$ evidence (transaction IDs or attestations), and $m_k$ policy metadata—are handled as a totally ordered sequence. The state transition for all $d \neq d_{\mathsf{fee}}$ is:

$$B_d(t_k^+) = \begin{cases} B_d(t_k^-) - v_k & \text{if}\ d = d_{\mathrm{src}}\ B_d(t_k^-) + v_k & \text{if}\ d = d_{\mathrm{dst}}\ B_d(t_k^-) & \text{otherwise} \end{cases}$$

Transfers to/from $d_{\mathsf{fee}}$ represent explicit network fees or unmodeled outflows.

Conservation Theorem

Defining total non-fee exposure $$S(t) = \sum_{d \in \mathcal{D} \setminus \{d_{\mathsf{fee}}\}} B_d(t)$$, the update rule ensures:

$S(t_{i+1}) = S(t_i)$

for any event interval without external flows beyond the fee sink. This guarantees an auditable, closed-system model where fee drains and asset flows are accounted for explicitly.

TPL Ledger Abstraction

TPL is instantiated as an append-only ledger sequence $$\mathrm{TPL}_0 \preceq \mathrm{TPL}_1 \preceq \ldots$$ with:

• $\mathcal{R}_i$: Hash-chained PoT receipts linking event logs.
• $\mathcal{S}_i$: PoR snapshots (e.g., Merkle roots per domain).
• $M_i$: Policy metadata.

Ledger prefixes are committed by $C_i = H(\mathrm{TPL}_i)$ (with $H$ collision-resistant), then anchored onto the Bitcoin blockchain (e.g., via OP_RETURN or Taproot). Core algorithms include $\mathsf{Setup}$, $\mathsf{AppendEvent}$, $\mathsf{Snapshot}$, $\mathsf{Anchor}$, $\mathsf{GenView}$, and $\mathsf{VerifyView}$, supporting append-only progress, policy-based disclosures, and verifiability by external parties (Puente et al., 3 Dec 2025).

3. Security and Correctness Notions

TPL's guarantees are formalized using cryptographic reductions and adversarial models:

Exposure Soundness

No adversary $\mathcal{A}$ can produce an alternative TPL prefix that overstates total Bitcoin exposure in any in-scope domain set, conditioned on PoR and PoT soundness and the absence of hash collisions. Formally, if $$\sum_{d \in \mathcal{D}} B^\star_d(t_i) > \sum_{d \in \mathcal{D}} B_d(t_i)$$ for validly presented views, $\mathcal{A}$ breaks a standard cryptographic assumption.

Policy Completeness

For any stakeholder policy $V_\alpha$ formalized as a predicate $P(e, t, \alpha)$, TPL ensures that any event designated as "must be disclosed" appears in the generated view. If omitted but $\mathsf{VerifyView}$ still accepts, this constitutes a cryptographic break.

Non-Equivocation

Once a prefix is anchored, it is computationally infeasible for the treasury to produce a distinct, valid prefix (consistent with anchors) leading to different stakeholder views. This ensures forward integrity.

Privacy-Compatible Views

Stakeholder-specific leakage profiles $L_\alpha$ define maximal information exposure. The framework can instantiate views that leak no more than $L_\alpha$ under witness-indistinguishability or zero-knowledge assumptions for underlying PoR/PoT proofs. The public policy analyzed allows exposure of only aggregate and encumbered positions, not internal wallet structures.

4. Construction and Deployment: Real-World Instantiation

TPL's security properties are realized by composing known cryptographic tools:

• Proof-of-Reserves (PoR) Snapshots: Periodic, per-domain attestations built from Merkle commitments or similar constructs.
• Proof-of-Transit (PoT) Hash Chains: Each event $e_i$ is incorporated into a hash-chained receipt

$$R_i = H(R_{i-1} \| h_i \| d_{\mathrm{src}} \| \ldots),\quad h_i = H(\mathsf{evid}_i \| v_i \| m_i)$$

• On-chain Anchoring: Commitments $C_i$ are embedded into the Bitcoin blockchain, ensuring public immutability.
• Policy-Based Views: $\mathsf{GenView}$ generates stakeholder-specific logs; $\mathsf{VerifyView}$ allows independent validation.

The system depends on a "minimal non-collusion" condition—per domain, at least one party serves honestly in some security-relevant role (PoR provider, PoT relayer, anchor keyholder, or auditor).

A standard deployment streams events into a TPL engine, periodically recomputes $C_i$, anchors it, and disseminates proofs to stakeholders, who independently verify their designated policy-compliant view.

5. Illustrative Example: Corporate Treasury Workflow

A stylized TPL instance partitions a treasury into domains:

$$\mathcal{D} = \{\text{ColdStorage}, \text{Exchange}, \text{Collateral}, d_{\mathsf{fee}}\}$$

Event sequence:

1. $e_1$: external $\rightarrow$ ColdStorage, $v = 100$ BTC
2. $e_2$: ColdStorage $\rightarrow$ Exchange, $v = 40$
3. $e_3$: Exchange $\rightarrow$ Collateral, $v = 30$
4. $e_4$: Collateral $\rightarrow$ Exchange, $v = 10$
5. $e_5$: Exchange $\rightarrow d_{\mathsf{fee}}$, $v = 0.0001$

Exposures evolve as:

$B_{\mathit{Cold}}: 100 \rightarrow 60$, $$B_{\mathit{Exch}}: 0 \rightarrow 40 \rightarrow 10 \rightarrow 9.9999$$, $B_{\mathit{Coll}}: 0 \rightarrow 30 \rightarrow 20$, $B_{d_{\mathsf{fee}}}: 0 \rightarrow 0.0001$

Resulting snapshot: $(60, 9.9999, 20)$. Distinct policies determine disclosure granularity:

• Public investors: total, aggregated exposures (e.g., $100$ BTC, $20$ BTC encumbered).
• Regulators: per-domain disclosures, encumbrance flags.
• Auditors: broad disclosure, with minimal redaction.

Cross-institutional aggregation is feasible: e.g., three treasuries each exposing $\leq 6$ million BTC sum to $\leq 18$ million BTC, within Bitcoin's $21$ million cap (Puente et al., 3 Dec 2025).

6. Limitations, Assumptions, and Non-Goals

Cryptographic Assumptions

• Collision-resistant hash function $H$
• EUF-CMA digital signatures
• Secure, existence/ownership-sound PoR and unforgeable PoT constructions
• Zero-knowledge or witness-indistinguishability for privacy, as needed

Systemic Assumptions

• Bitcoin's append-only ledger and sufficient finality (no deep reorganizations)
• Timeliness: bounded liveness for events, snapshots, and anchors

Governance and Modelling

• Per-domain minimal non-collusion: at least one honest security-role holder
• Domain completeness: all positions are assigned within $\mathcal{D}$
• Policy faithfulness: views determined by visible event subsequences

Non-Goals

• No fiat valuation or market-risk analytics
• No full differential-privacy for arbitrary policies
• No defense against full internal/external collusion

TPL does not introduce novel cryptographic primitives but composes standard mechanisms under explicit operational, adversarial, and policy assumptions to offer machine-verifiable, policy-aware transparency and auditability for multi-domain Bitcoin treasuries (Puente et al., 3 Dec 2025).