Verifiable Carbon Accounting (VCA)

The term is Heiss et al.’s (2023): carbon accounting in which the report carries its own proof of correctness, so that a recipient can check a figure without a trusted verification body and without seeing the data behind it. This page holds the joint reading of the two papers in sources/ that build it out — Heiss, Oegel, Shakeri & Tai (2023) and Man & Kleppmann (2026) — assessed against ICC’s eight decision-grade criteria.

Why one page for two papers. Martin Pompéry, 2026-08-17: “Du musst zwingend beide Papiere (Kleppmann, Heiss) zusammen betrachten.” Each paper was read individually and in full — no batch reading — and each has its own summary page with its own source attribution. The joint analysis lives here. They are not two parallel efforts: Man & Kleppmann §6 states the advance over Heiss et al. explicitly, and thanks Jonathan Heiß for feedback on the paper. One research strand, two stations.

The shared architecture

Both papers build the same three-part machine:

1. A trusted edge. Physical quantities enter through a digitally signing device — a meter with a tamper-proof hardware element (Kleppmann) or a sensor with a two-level PKI device/certificate attestation (Heiss). The trust anchor is the device, not the reporting company.
2. A zero-knowledge circuit that recomputes the emissions figure from the signed inputs according to a fixed, published method, and emits a proof that the recomputation was done correctly — while revealing nothing but the result.
3. A commitment that cannot be retracted, so the company cannot show different numbers to different counterparties.

Where they differ is instructive, and the differences are all in part 3 and in what the circuit is asked to prove.

	Heiss et al. (2023)	Man & Kleppmann (2026)
Unit of account	product carbon footprint, per product instance, across supply-chain tiers	per-customer share of a data centre’s emissions, per billing period
Proof system	zkSNARKs via ZoKrates; trusted setup, CRS disposed as “toxic waste”	o1js (Kimchi/Pickles, Pasta curves); no trusted setup; recursion
Commitment	Ethereum smart contract; on-chain verification (verifier.sol, Truffle/Ganache)	one hash per accounting period on a blockchain or a transparency log
Method governance	an accredited auditor signs off the MR-Schema before it becomes an MRV-Schema	the method is fixed in the circuit; only total revenue needs an auditor
Cross-tier link	upstream zkPCF is the authenticity input to the downstream proof	recursive composition of a totals proof and an allocation proof
Allocation	not addressed	the core contribution — proved fair against revenue share

Against the eight ICC criteria

⟨Inference throughout this section: the criteria are ICC’s, the papers do not use them, and the mapping is mine.⟩

A — Accuracy. Answered between the meter and the circuit. Both prove that the published figure is what the audited calculation yields on the attested inputs. Neither proves the calculation is the right one; that stays a human judgement, made once (Heiss’s accredited compliance check on the MR-Schema) rather than per report. Cryptography does not make accuracy unnecessary — it collapses accuracy into two questions, is the meter honest and is the circuit the agreed method, and answers everything in between.

B — Verifiability. Answered, and this is the direct hit. ICC states confidentiality as part of verifiability’s design and then supplies no mechanism — see the confidentiality gap. These two papers are the mechanism. Kleppmann’s abstract states the requirement in ICC’s own terms: proofs “to each customer that the emissions reported to that customer are accurate, without the customer being able to learn sensitive information about the data centre operator or other customers.”

C — Comparability. Partly, and as a side effect neither paper claims. ⟨Inference: a proof is always a proof against a specific circuit. Two reports carrying proofs against the same MRV-Schema or the same circuit are comparable by construction, because the method is not merely disclosed but enforced. Heiss’s MRV-Schema, anchored on-chain by an auditor, is a machine-readable methodology statement that a reader can bind a number to. That is a stronger form of comparability than a PDF methodology annex — and it is exactly what ICC says the exchange layer lacks.⟩

D — Representational faithfulness. Only as far as the meter, and both papers say so. Kleppmann, §1: “The key insight of this paper is how to ensure that the cryptographically verified data is an accurate reflection of the physical world.” Their two answers are trusted signing devices and — the novel one — coupling carbon accounting to financial accounting: “In order to lie about its emissions, the company would then also have to lie about its finances, which raises the stakes by making misreporting a crime.” The residual assumption is stated plainly in their conclusion: “We assume, however, that the company will not commit financial fraud.”

E — Fungibility. Untouched. Neither paper produces a transferable accountable quantity with legal title. A zkPCF is a commitment to a number, not an asset that moves. This is where the ledger architecture has something the cryptography does not.

F — Conservation across entities. Yes, but only inside a closing constraint. Heiss conserves along the chain: the upstream supplier’s committed zkPCF is the authenticity input to the downstream proof, so a tier cannot silently restate what it received. Kleppmann conserves across recipients: the Merkle commitment plus recursion means the allocations shown to different customers are provably the same allocation, and it sums to 100 %.

G — Completeness of scope. Not answered. Reduced. ⟨Inference, sharpened 2026-08-17 in discussion with Martin Pompéry, who pressed on exactly this and was right to.⟩ A zero-knowledge proof is a statement about a computation: that a published figure is the correct output of an agreed method on a set of attested inputs. “Nothing was left out” is not a statement about the computation but about the world, and it is unreachable from inside the circuit. It becomes provable only where a quantity exists that is (a) independently attested, (b) outside the reporter’s control, and (c) demonstrably covers the boundary.

Kleppmann has (a) and (b): the meter signs its own readings and the per-customer shares must reconcile, recursively, to exactly that sum — which is why the paper can invoke the GHG Protocol’s Completeness Principle at all. He does not have (c), and says so twice. In the conclusion: “Along with the assumption of a single electricity meter, this allowed us to side-step the problem of ensuring that all sources of emissions have been accounted for.” And in §5, on the attack that matters:

“If a data centre operator has multiple smart meters, perhaps in different DC buildings, it could omit some of these meters from the accounting, or use data from the wrong meters. […] In future work, we plan to make this aspect more robust by cross-referencing the DC operator’s electricity consumption data with bills from their electricity supplier; thus, a DC operator that wants to fake their consumption would also have to collude with their electricity supplier.”

⟨Inference: note what his own repair for (c) is — importing a second, independent attestation of the same aggregate. That is the closing constraint, arrived at from the other direction. So the honest statement is that G is not solved but reduced: from “is everything captured?” to “does an independently attested aggregate covering this boundary exist, and does the report reconcile to it?” For a data centre on grid electricity, nearly yes. For a supply chain, no — there is no meter and no party entitled to see the whole.⟩

The same assumption carries twice. ⟨Inference: the trusted meter is load-bearing for D as integrity (the device does not lie) and for G as boundary (the device is all there is to count). Different criteria, one piece of hardware, and in both places an assumption rather than a proof. This is one continuum with the M5 tension below, not two separate observations.⟩

H — Operability. Not decided by these papers, and the harder problem is inside ICC’s own definition. ⟨Inference, revised 2026-08-17 after Martin Pompéry’s objection that proof cost is not a fundamental limit and does not bear on the ICC document.⟩ Verification cost is a property of a deployment, not of the approach: Heiss’s 602,461 Gas is a fact about Ethereum in 2023 (it belongs on his paper’s page, not in a criterion assessment), and the 2026 paper takes the chain off the critical path entirely. Kleppmann’s figures — roughly $150/month for a data centre with a million customers, $0.01 per report requested, sub-second verification — are worth keeping for one reason only: they are a first indication from an operationalised environment, which is more than the criterion has had from anyone else.

The substantive problem under H is not cost. It is that ICC’s own definition of H demands transaction-level, near-real-time records while its Criterion C demands comparability, and period-averaging is how the LCA tradition achieves C — see temporal resolution and the service case. Neither paper engages this; both work on a boundary where the tension does not bite.

The closing-constraint thesis

⟨Inference: mine, 2026-08-17, developed in discussion with Martin Pompéry after he caught an earlier and wrong claim of mine that completeness is structurally unprovable in zero knowledge. It is not. It is provable under a condition, and naming the condition is the useful move.⟩

What cryptography proves is reconciliation against an independently attested closing aggregate. It cannot supply the aggregate. So completeness is not solved but reduced — to the question of whether such an aggregate exists and covers the boundary.

Kleppmann has a closing constraint and it is a physical object: one electricity meter, signing its own readings, whose total is not the reporting company’s to choose. Everything downstream of it — the allocation across a million customers, the fairness check against revenue share, the recursion — is reconciliation to that total. Remove the meter and the proof still shows the shares sum to 100 %, of a number the company invented.

A supply chain has no meter. There is no device that measures the emissions of a product as it crosses four firms, and no single party entitled to observe the whole of it. This is the reason Heiss’s paper conserves along the chain without ever asserting completeness of scope, and it is the reason ICC wants a ledger: the conservation rule of a double-entry system is an institutional closing constraint, manufactured where no physical one exists. ⟨Inference: the ledger’s balance identity and the data centre’s electricity meter are the same device, built out of different materials. That is the sentence the ICC response should turn on.⟩

Read this way, cryptography and the ledger are not rivals. The ledger supplies the closing constraint across entity boundaries; the proofs let firms satisfy it without opening their books. Neither does the other’s job.

Where SINE’s own commitments are in tension

• Trusted hardware. Both papers assume a signing meter or sensor that cannot be tampered with. CCTI’s stated policy is to minimise dependency on trusted hardware over time, and M5 makes removing the trusted-hardware assumption a gate criterion — see the CCTI stack. Contradiction recorded, not resolved: the papers’ architecture is what CCTI’s gate is designed to grow out of. ⟨Inference: this is a genuine research question, not a defect — the honest reading is that D (representational faithfulness) is where CCTI’s WP-A and this line of work meet, and that no one has removed the trusted edge yet.⟩
• Blockchain. The 2022 Data Commons whitepaper prefers peer-to-peer architectures over ledgers; Heiss’s design verifies proofs in an Ethereum smart contract. Man & Kleppmann defuse this, explicitly: “Our proposal does not depend on a blockchain or distributed ledger, except for publishing a single hash commitment per accounting period – a task that can also be fulfilled by a simpler system such as a transparency log.” The requirement is a public, append-only, non-retractable commitment; a blockchain is one implementation of it, certificate-transparency-style logs another. See Data Commons.

What is still missing

⟨Inference.⟩

1. The closing constraint across firms. Above. Unsolved by either paper, and the reason the ICC ledger question stays live.
2. Who audits the circuit. Heiss puts an accredited auditor on the MR-Schema and calls the check “essential”; Kleppmann’s method lives in the circuit with no equivalent gate. Neither addresses what happens when the audited method itself is the object of methodology arbitrage.
3. Allocation beyond revenue proportionality. Kleppmann’s fairness test is that each customer’s emission share is within fixed bounds of their revenue share — an economic allocation, which the PACT and ISO hierarchies rank below physical allocation. Defensible for a data centre; a live methodological fight anywhere else. See PACT PCF calculation methodology.
4. Demand. The wiki’s standing caveat applies: PACT succeeded as coordination work in which “the cryptography was not load-bearing.” Feasibility at $0.01 per report is not the same as a buyer.

Hitachi as a worked gap case ⟨added 2026-10-15⟩

The Hitachi Integrated Report 2026 is the first corporate disclosure in the wiki that can be read against this architecture end to end. It is useful because Hitachi is a strong reporter — the gap it leaves is therefore structural, not negligence.

What Hitachi reports (Integrated Report 2026, pp. 28, 42):

• Scope 1 + 2 market-based, FY2025: 460 kt-CO₂e — down from 3,412 kt in FY2021, partly through divestment. Some environmental data carries third-party limited assurance (EY ShinNihon).
• No Scope 3 figure anywhere in the Integrated Report’s ESG data. ⟨The Sustainability Report 2026 does carry a full Scope 3 inventory — 209.18 Mt-CO₂e for FY2025, 99.8 % of the footprint. See Hitachi, Ltd..⟩
• Compensation-linked supply-chain KPI: “number of procurement partners taking action on environment and human rights” (vs FY2024) — FY2027 target 1.5× (6,000+), FY2025 result 5,232. ⟨Corrected 2026-10-29: this slot previously held the “set GHG reduction plans and targets” KPI (700 / 428), which is not in the report’s compensation table (p. 29).⟩
• Headline environmental claim: 280 Mt/yr avoided emissions from products and services (FY25–27 forecast average), against a 100 Mt/yr target.

Three observations:

1. The assured number is ~600× smaller than the headline number. 460 kt measured and partly assured; 280 Mt claimed, forecast and counterfactual. ⟨Inference: this is the confidentiality gap seen from the issuer’s side — the quantities a company can prove are the ones it controls directly, and those are the small ones. Everything that depends on counterparties, or on a counterfactual, is asserted.⟩
2. The incentive is attached to engagement, not to evidence. A KPI counting partners who are taking action is satisfiable without a single verified emissions figure changing hands. ⟨Inference: this is precisely the substitution the bargaining-failure diagnosis predicts — when data cannot be extracted, the metric migrates to something that can be. See coordination vs. bargaining failure.⟩
3. Avoided emissions are the hardest case for this architecture, and the most commercially attractive. Heiss and Man/Kleppmann both prove that a figure was computed correctly from committed signed inputs; neither proves a counterfactual baseline. ⟨Inference: a proof regime could constrain the computation and the input provenance of an avoided-emissions claim while leaving the baseline a declared assumption — which would be a real improvement over an unqualified 280 Mt, and is a sharper research question than the completeness limit the wiki already records.⟩

Why this matters for the engagement. The sourced argument for SINE at Hitachi does not need Rail’s unverified 14.93% figure. It is visible in Hitachi’s own group reporting: the disclosure is strong where Hitachi controls the meter and silent where it does not, and the one compensation lever points at supplier engagement rather than supplier data. The entry route is Customer Zero — Hitachi’s own doctrine of validating a solution on its own sites first, where the counterparty problem is internal and the data is already Hitachi’s.

Cross-references

• Heiss et al., Verifiable Carbon Accounting in Supply Chains (2023)
• Man & Kleppmann, Emission Impossible (2026)
• The confidentiality gap — the thesis these papers answer
• The eight decision-grade criteria — the grid used above
• Ledger-based carbon accounting — the rival/complementary architecture
• Cryptographic trust infrastructure (CCTI stack) — where this sits in SINE’s own stack
• CCTI — both papers’ authors are inside it
• Jonathan Heiss, Martin Kleppmann
• Coordination failure vs. bargaining failure — VCA as a bargaining-side instrument
• Customer Zero and Hitachi, Ltd. — the worked gap case above
• Adtech as a regulatory precedent — the completeness limit recurs independently in the verifiable-auction literature (VEX 2013, Addax 2023): both prove correct rule application to the committed inputs, neither proves the committed set is complete. ⟨Inference: this looks like a domain-independent boundary of cryptographic verification, not an artefact of the single-electricity-meter assumption.⟩

Sources

• sources/whitepapers/2026-08-17-verifiable-carbon-accounting-in-supply-chains.md
• sources/whitepapers/2026-08-17-emission-impossible-verifiable-cloud-emissions/2026-08-17-emission-impossible-verifiable-cloud-emissions.md
• sources/whitepapers/2026-08-17-icc-carbon-accounting-landscape-review/2026-08-17-icc-carbon-accounting-landscape-review.md (the criteria)
• sources/proposals/2026-06-17-aria-ccti-proposal-draft-2.md (M5, trusted-hardware policy)
• sources/hitachi/2026-10-15-hitachi-integrated-annual-report-2026.md (the Hitachi gap case)