This report evaluates a reference-enhanced public measurement rule for Total Stake Inference (TSI). Under the candidate rule, settled canonical blocks may carry bounded references to validated non-ancestor blocks selected from the producer’s local block tree. These references preserve active-slot evidence that would otherwise be absent from the settled canonical view. They are measurement metadata only: they do not alter fork choice, ledger-state transitions, eligibility proofs, or block weight.
The proposed change leaves the baseline TSI update unchanged and modifies only the public occupied-slot measurement supplied to that update. The baseline chain_only mode forms its measurement from settled canonical-chain blocks. The candidate chain_plus_resolved_refs mode additionally incorporates resolved, measurement-eligible one-hop references carried by settled canonical blocks. Both modes deduplicate block identifiers and then binarize by slot, so multiple counted blocks from the same slot contribute only one occupied-slot observation.
The report uses two complementary evidence layers. The primary TSI-feedback evaluation feeds each measurement rule’s occupied-slot count into the baseline TSI update and uses the resulting denominator in subsequent leader election. These experiments measure the protocol-level effect of recovering off-branch evidence. Separate known-denominator experiments freeze the true denominator to isolate the measurement mechanism, study the reference window (W) and per-block budget $m_{\max}$, and evaluate omission, resolution, fetch, and metadata-exposure diagnostics.
The primary feedback experiments use the mainnet observation period (T=388800), target activation rate (f=1/30), learning rate $\beta=1$, (N=80), and matched-Poisson delay. The principal outcome is the normalized denominator $D_\ell/D_{\mathrm{true}}$. Candidate-block emission, canonical growth, block survival, and the ground-truth counting factors $q_{\mathrm{chain}}$ and $q_{\mathrm{refs}}$ are reported as mechanism diagnostics. The selected mainnet-parameter configurations use three external seeds and configuration-dependent update horizons, so the reported values are finite-horizon readouts rather than general equilibrium or convergence claims.
At mean delays 10, 20, and 29, the median finite-horizon normalized denominator is approximately 0.705, 0.399, and 0.168 under chain-only TSI, compared with 0.959, 0.882, and 0.759 under references with $(W,m_{\max})=(60,2)$. The corresponding median pre-fork candidate-block rates are approximately 0.0476, 0.0840, and 0.1983 blocks per slot under chain-only TSI, compared with 0.0356, 0.0395, and 0.0453 under reference-enhanced TSI. References therefore keep the inferred denominator substantially closer to the true stake and sharply reduce feedback-driven over-emission as delay increases.
The delay-40 stress comparison shows severe chain-only degradation and a strong joint W–$m_{\max}$ effect. After five updates, the chain-only denominator has fallen to approximately 0.101 and remains under continued collapse-bound descent, with candidate emission approximately 0.2574 blocks per slot. The corresponding reference-enhanced finite-horizon readouts are approximately 0.525, 0.852, and 0.986 for $(W,m_{\max})=(60,2)$, $(240,2)$, and $(240,4)$, with candidate rates approximately 0.0646, 0.0396, and 0.0342. Together with the known-denominator parameter sweeps, these results show that the reference window and per-block carrying capacity should be treated as a joint, delay-regime-dependent parameter choice.
The results clarify the relationship between denominator accuracy and canonical growth. Chain-only TSI can keep its canonical counted rate near the target by depressing the inferred denominator and generating many additional candidate blocks. Reference-enhanced TSI instead recovers part of the missing occupied-slot evidence, maintains a more accurate denominator, improves block survival, and reduces fork waste. Its canonical-only growth need not equal $f$, because its controller input is the slot-binarized union of canonical and eligible referenced evidence rather than canonical occupancy alone. The relevant distinction is therefore denominator accuracy versus over-emission-based canonical-growth compensation, not a general trade-off between inference accuracy and protocol performance.
Local fixed-response scans provide an additional consistency check. At the selected delay and reference configurations, the empirical response crossings are close to the corresponding dynamic finite-horizon denominator readouts. These checks support the local update direction around the observed regions, but they do not establish uniqueness, global convergence, or infinite-horizon stability. Near mean delay 29, the full simulator’s empirical chain-only crossing also differs substantially from the simplified analytical prediction. The analytical formulas are therefore retained as simplified comparators rather than treated as exact full-simulator fixed-point predictions.
Specification-arithmetic checks show that integer staging with an exact representation of $f=1/30$ closely matches the real-valued update used in the primary experiments. The literal PRECISION = 1000 rule quantizes the target to 0.033 and produces a modest calibration shift, but it does not change the severe chain-only degradation classification, the benefit of references, or the ordering of the tested delay-40 reference configurations.
The combined evidence supports chain_plus_resolved_refs as a candidate TSI measurement mode for an RFC and subsequent construction-specification work. It does not by itself constitute a final construction specification, a general convergence proof, a complete incentive or privacy analysis, or a topology-aware network evaluation. The earlier $T=2500,\beta=0.8$ feedback experiments are retained in Appendix A as exploratory diagnostics and analytical comparisons; their numerical operating levels are not used as the report’s primary specification-facing results.
Total Stake Inference estimates the active-stake denominator from publicly observable occupied-slot evidence. Under network delay and forks, the settled canonical chain may omit valid blocks from truly active slots. Chain-only measurement therefore under-counts public activity and may depress the inferred denominator.
This report evaluates chain_plus_resolved_refs as a candidate TSI measurement mode. Settled canonical blocks may carry bounded references to validated non-ancestor blocks, and the estimator may count resolved, measurement-eligible references when constructing the epoch occupancy measurement. The baseline TSI update itself remains unchanged.
The report separates two evidence layers. Section 3 evaluates the TSI-feedback process, in which each observation period’s measured occupancy updates the denominator used in subsequent leader election. Sections 4 and 5 use a known true denominator to isolate measurement visibility, parameter calibration, and deployment robustness. Section 6 summarizes specification implications and limitations.
The earlier T=2500 exploratory feedback experiments are retained in Appendix A and are not used as the primary specification-facing numerical results.
The TSI-feedback hypothesis is: