Mechanism: The Closed-Loop Re-Incorporation Cycle

The re-incorporation primitive defines a material flow in which carbon mass embodied in an end-of-life structural element is recovered, conditioned, and returned to the fabrication pipeline as feedstock for a subsequent structural element. The cycle comprises four distinguishable stages. First, an end-of-life structural element is taken out of service through a credentialed retirement event recorded in its lineage chain. Second, the element is processed through a recovery operation that liberates the carbon mass from the surrounding matrix, typically through controlled pyrolysis, solvent extraction, or mechanical comminution depending on the host material. Third, the recovered carbon is conditioned to feedstock specification, particle size, moisture content, residual ash, contaminant profile, and accepted into a credentialed feedstock inventory. Fourth, the conditioned recovered carbon is dispatched into a new fabrication batch, where it co-mingles with fresh biomass-derived carbon at a ratio dictated by recovery yield and project-level mass-balance accounting.

Each stage is associated with a credentialed event in the lineage chain. The retirement event records the identity of the retiring element, the time and location of retirement, and the authorized retirement actor. The recovery event records the recovery facility, recovery method, input mass, output mass, and recovery efficiency for the specific batch. The conditioning event records the feedstock specification achieved and any deviations. The re-incorporation event records the new element being fabricated, the mass fraction of recovered carbon entering the new element's matrix, and the link to the prior generation's lineage. These events together compose a multi-generation lineage that survives every material transformation in the cycle.

The credentialed admissibility profile of the new structural element thus records not just its own fabrication parameters but also the originating biomass capture event, every prior structural-element life through which its carbon has passed, every recovery and re-incorporation event in its history, and the cryptographic links binding these events into a tamper-evident chain. Verification of the chain at any future date establishes the carbon's complete trajectory from atmosphere through biomass through one or more structural-element lives to its current incorporation.

Mass-balance accounting at the re-incorporation event reconciles the recovered-carbon mass against the new element's design carbon inventory and resolves any shortfall with credentialed fresh-biomass top-up. The reconciliation is performed against the published feedstock specification: recovered carbon meeting the specification is admitted at full credit; recovered carbon failing the specification is rejected to a downgrade pathway (lower-grade structural product, soil amendment, or terminal sequestration) and replaced by additional fresh biomass in the new element's batch. Each reconciliation outcome is itself a credentialed event, so that the mass-balance ledger of the re-incorporation pipeline is continuously and independently auditable rather than periodically reported.

The chain construction admits branching where a single retired element's recovered carbon is dispatched into multiple new fabrication batches, and merging where a single new fabrication batch incorporates recovered carbon from multiple retired elements. Branching events fan out the lineage chain into multiple successor chains, each carrying a fractional mass-share credential of the parent element. Merging events fan in multiple parent chains into a single successor chain whose credential records the per-parent mass contributions. The chain topology is therefore a directed acyclic graph rather than a linear sequence, and per-atom-trajectory verification reduces to a graph traversal whose computational cost is bounded by the depth and fan-out of the relevant subgraph.

Operating Parameters and Engineering Envelope

Recovery efficiency, the ratio of recovered carbon mass to carbon mass present in the retired element, defines the dominant operating parameter. The disclosed embodiments target the range of 0.70 to 0.95, with the lower bound representative of mechanical-only recovery from heavily contaminated end-of-life streams and the upper bound representative of optimized pyrolytic recovery from clean, single-source streams. Recovery efficiency below 0.70 admits the cycle to operate but pushes the fresh-biomass top-up rate to levels that may erode the long-horizon carbon-stewardship case; efficiency above 0.95 is technically achievable but typically incurs energy and process-cost penalties that outweigh the marginal mass benefit.

Generation count, the number N of distinct structural-element lives a given carbon atom passes through before being lost from the loop, scales as 1 / (1 - efficiency) for a steady-state cycle. At efficiency 0.85, expected generation count is approximately 6.7; at efficiency 0.95, approximately 20. Long-horizon carbon stewardship cases are typically built around the upper end of this range, where individual carbon atoms remain in the loop for centuries of cumulative residence time before exiting.

Lineage-chain depth grows linearly with generation count and is bounded by storage and verification cost, both of which scale sub-linearly with depth under standard hash-chain constructions. A practical engineering envelope admits chains of hundreds of generations without verification cost growing prohibitively, which is comfortably above the depth implied by the recovery-efficiency ranges considered.

Fresh-biomass top-up rate equals (1 - efficiency) of throughput at steady state. The architecture admits the top-up to be drawn from any biomass source admissible to the originating-feedstock specification, including agricultural residues, dedicated energy crops, forestry residues, and direct-air-capture-coupled algal cultivation. The credentialed profile records the top-up source for each generation, admitting downstream auditors to characterize the cumulative biomass-source mix of any given carbon atom in the loop.

Alternative Embodiments

A first alternative embodiment realizes the recovery stage through pyrolytic conversion of retired elements to a carbon-rich solid intermediate (biochar-equivalent), which is then milled to feedstock specification. A second embodiment uses chemical depolymerization of polymeric host matrices, releasing carbon-bearing molecular fragments that are condensed and reformed into feedstock. A third embodiment uses bioreactive recovery, fungal or bacterial digestion of the host matrix, yielding a carbon-rich biological intermediate that itself enters the biomass-feedstock specification.

Lineage-chain embodiments range from lightweight Merkle-chain constructions (favoring storage compactness at the cost of slightly heavier verification computation) to full append-only ledgers replicated across multiple credentialed witnesses (favoring verification simplicity at the cost of higher per-event storage). Hybrid embodiments using compressed proofs over deep chains admit centuries of generation depth while preserving sub-second verification cost.

A further alternative embodiment co-locates the recovery operation with the fabrication facility so that retired elements arriving at the gate enter recovery, conditioning, and re-incorporation under a single facility credential. The co-located embodiment shortens the logistical chain between retirement and re-fabrication and reduces transport-emissions overhead in the lineage record, at the cost of confining facility throughput to a single combined process line. A complementary distributed embodiment routes retired elements through a network of regional recovery hubs feeding a smaller number of fabrication facilities, with the lineage chain absorbing a regional-routing event between recovery and re-incorporation.

Recovery-method-mixed embodiments admit a single recovery batch to be processed through more than one of the disclosed recovery techniques in series, for example, mechanical comminution followed by pyrolytic refinement, or chemical depolymerization followed by biological polishing, with each stage logged as a discrete credentialed event under the umbrella of the parent recovery operation. Mixed-method recovery is admissible whenever the host-matrix composition or the contamination profile demands it, and the lineage chain records the method sequence so that downstream audits can resolve the carbon trajectory through every transformation rather than through a single aggregated recovery event.

Composition with Adjacent Primitives

The closed-loop primitive composes with the originating-biomass attestation primitive disclosed in the parent provisional: the first generation's lineage roots in a credentialed biomass-capture event, and every subsequent generation in the loop inherits, by chain construction, an unbroken cryptographic linkage back to that root. A multi-generation element's environmental claims are thus grounded not in a self-attested fabrication record but in a chain of independently-verifiable events extending to atmospheric CO2 capture.

The primitive further composes with the per-element retirement attestation and the per-block fault-isolation primitive disclosed in companion filings: retirement events that drive elements into the recovery pipeline, and isolation events that terminate operational service prior to retirement, both feed the lineage chain that the re-incorporation event subsequently extends. The aggregate effect is a single coherent chain spanning fabrication, service, isolation, retirement, recovery, and re-fabrication across arbitrarily many generations.

Prior-Art Distinctions

Conventional recycling pipelines for carbon-containing materials, paper, plastics, certain construction-product streams, recover material mass but do not preserve cryptographically-verifiable lineage across the recovery transition. A second-generation paper or plastic typically loses any specific connection to its first-generation source; lineage if recorded at all is statistical and aggregate, not per-atom-trajectory. The disclosed primitive's preservation of per-element cryptographic continuity across the recovery boundary is, to the inventor's knowledge, without prior-art precedent in the carbon-stewardship literature.

Carbon-removal credit frameworks under voluntary and compliance markets typically attest to a single capture event and a single storage commitment, without provision for multi-generation re-incorporation or chained provenance across generations. Article 6.4 of the Paris Agreement establishes a long-term storage requirement but does not specify a chained-attestation mechanism for carbon that passes through multiple successive product lives. The disclosed primitive supplies precisely such a mechanism, structurally compatible with Article 6.4's long-horizon storage definition while admitting active material utility across the storage horizon.

Prior bio-based product LCAs (life-cycle analyses) treat material end-of-life as a terminal accounting event rather than as the entry to a subsequent generation, and consequently cannot represent the carbon-stewardship benefit of multi-generation re-incorporation. The present disclosure admits LCAs that treat each generation as an extended residence interval within a single chained carbon trajectory.

Disclosure Scope

The disclosure encompasses material flows in which carbon mass recovered from end-of-life structural elements re-enters a fabrication pipeline as feedstock for subsequent structural elements, where each transition (retirement, recovery, conditioning, re-incorporation) is recorded as a credentialed event in a tamper-evident lineage chain that extends across multiple structural-element generations and roots in a credentialed originating biomass capture event.

The scope is host-material-agnostic: any structural-element matrix from which carbon mass can be liberated and re-conditioned to feedstock specification is within scope, including but not limited to bio-derived polymers, lignin-bonded composites, carbonized cellulosic structures, and engineered biochar matrices. The scope is recovery-method-agnostic: pyrolytic, chemical, mechanical, biological, and hybrid recovery methods are all within scope where the recovery event is appropriately attested.

The scope further encompasses methods of accounting for carbon-stewardship benefit across multi-generation chains, including methods that allocate residence time, that compute generation-count expectations from recovery efficiency, that compose multi-generation chains with Article 6.4 long-term storage frameworks, and that admit independent verification of any claimed generation depth from the chain alone. Equivalents include any closed-loop carbon flow that achieves the disclosed combination of multi-generation cryptographic continuity, mass-balance conservation at the disclosed efficiency ranges, and auditable provenance from atmospheric capture forward, regardless of specific recovery technology or chain implementation.