# Decay is for uncertainty, not value: staleness priors for sparse feeds, and the dissipative-role law

*Working title:* **Decay is for uncertainty.** A belief that fades toward "unknown" as it ages is a poor forecaster of the value and a good forecaster of its own error. The two jobs must be scored separately.

Author: [withheld in the repository copy]. Contact: [withheld].
Status: **DRAFT.**
Revision: 2026-11-02 second sweep (related work, venues).
Slate: PLAN.md P4. Companions: P3 (dark is not zero) and P2 (the estimator ladder; not cited here for its home-data verdict).

## Abstract (draft)

A sparse feed goes quiet. Should the belief it fed drift toward "unknown"? The answer depends on what the drift is for. On 103 real wallet series from a game's automated playtester fleet, decay toward uncertainty scored as a value model beat persistence on 0 of 103 series and beat never-decay on 10 of 103. Scored as an uncertainty model, where staleness 1 − |belief| is asked to predict the coming absolute error, the same knob is reported to win on 79 of 103 series, with mean correlation +0.285 at the best rate against −0.002 at zero; that artifact was not located at the pinned revision and must be re-run before quoting. A deterministic in-gate replication reproduces the dissociation: accumulators reject decay as a value model (best rate zero), accept it as an uncertainty model at an interior rate, and ±1 event signals accept a mean-reverting prior outright. Under constant cadence the calibration score is invariant in the rate, so identifying it needs gap variance, and the best rate tracks the feed's gap scale, not a universal constant. We read this as a taxonomy. Accumulator-class signals want a Wiener prior (mean persists, variance grows); event-class signals accept Ornstein–Uhlenbeck; a dissipative engine that relaxes everything toward the mixed state wrongs the accumulators. We add the dissipative-role law from a 13-day foreign deployment: a role fed one polarity of evidence saturates unless declared dissipative, and a sign error made the saturated belief look excellent. Live forecast skill is dark.

## Contributions

1. **The dissociation as a protocol.** One decay rate γ, scored twice under Dawid's prequential rule: as a value model (next-step error against persistence) and as an uncertainty model (does staleness predict |error|?). Report both. A decay that loses the first and wins the second is doing its job.
2. **The taxonomy.** Accumulator / event / regime. Accumulators want Wiener (Sun, Polyanskiy & Uysal 2020); events accept OU (Ornee & Sun 2021). An engine whose dissipation relaxes every belief toward I/2 imposes OU on all three; accumulators are the class it wrongs. Regime is named and unmeasured.
3. **γ* is a property of the feed.** Pinned: with constant cadence the calibration score is γ-invariant, so γ* needs gap variance to exist. γ* tracks the gap scale: 3e-4 /s on a gridworld wire; reported 3e-3–1e-2 /s on game wallets (confidence half-life ≈ 1–4 min of play).
4. **The dissipative-role law and the inverted-sign trap.** Real detectors emit OFF as a re-arm timeout (median 326 s), so an honest adapter drops it and the role hears only "present". On a unitary role dephasing never relaxes populations; the belief sat at z ≈ +0.95 for 13 days with a flat tape (std ≈ 0.002), and a sign inversion made the AUC look excellent. Declaring the role dissipative restored dynamics. The pole pathology of one-sided evidence is the pinned synthetic twin.
5. **Cadence is not decay.** A zero-order hold across the one gap a batch closes defeats sparse-feed starvation: daily batches within 0.15 z of the dense stream; market A/B burst 0.5154 / hold 0.5170 / starvation control 0.4764. Three clocks are kept apart: compute time, membrane cadence, in-universe time.
6. **Decisiveness versus retention.** A gamma-scale ladder {0.25, 1, 4} moved mean |z| 6.5× (0.01586 → 0.00243) while surprise moved 2.5%; n = 1 walk per rung, reported as instrument-level.

## Outline (≈6,500 words)

1. **Two things "decay" could mean** (600). GRU-D pulls a stale input toward the mean; a Kalman filter grows variance with age. Both are called decay. We state the dissociation and why one accuracy number cannot see it.
2. **Protocol** (800). Prequential one-step scoring; persistence as the unit, after Hyndman & Koehler's MASE; the uncertainty score as correlation between staleness and realised |error| across a series; γ swept; γ* per criterion. Calibration is a joint property of forecast and outcome, sharpness of the forecast alone.
3. **103 real series** (700). The value result (0/103; 10/103 at α = 0.5) with its committed artifact. The uncertainty result (79/103; +0.285 vs −0.002; γ* 3e-3–1e-2 /s) as reported in the engine's decay notes, carrying the caveat that the artifact was not located at `8e67bcc` and is re-run before any release.
4. **In-gate replication** (800). The deterministic gridworld day: value-γ* = 0 for accumulators; calibration peaks at γ* = 3e-4 /s (corr +0.302 vs +0.223 at γ = 0) on a sparse irregular wire; ±1 events accept OU (value-γ* = 1e-4 /s; RMSE 0.520 vs 0.532 for persistence); constant cadence makes the calibration score γ-invariant.
5. **Two priors, three classes** (900). Wiener: mean persists and variance grows linearly, so the best value forecast is persistence and any γ > 0 loses, while the growing variance is real. OU: mean reverts and variance saturates. The engine's relaxation toward I/2 is OU on the Bloch coordinate. Blank boot mixes analog-dissipative roles to maximum entropy rather than a pole.
6. **The dissipative-role law** (700). The 13-day export, the re-arm timeout, the saturated unitary role, the inverted-sign AUC, the fix (+0.95 → +0.09 after four quiet hours → re-light). Why one polarity of evidence needs a dissipator: the pole pathology and its purity floor.
7. **Cadence, starvation, decisiveness** (600). Membrane hold; the market A/B; the E2 ladder; why hold is not decay.
8. **Related work and the negative space** (900). As below.
9. **Threats, dark list, conclusion** (500). As below.

## Related work and the negative space

**Age → uncertainty.** Sun, Polyanskiy & Uysal (2020), IEEE Trans. Information Theory: for a Wiener source the MSE-optimal sampler thresholds estimation error and zero-wait is not optimal; age and uncertainty are different quantities. Ornee & Sun (2021), IEEE/ACM ToN 29(5):1962–1975, DOI 10.1109/TNET.2021.3078137 (verified 2026-11-02): for an OU source the signal-agnostic optimum minimises a nonlinear function of age. Shisher & Sun (2022), ACM MobiHoc: on real data inference error is monotone in age only for near-Markov pairs. Kam et al. (2018), INFOCOM Workshops: an effective age, because plain age does not track estimation error. Maatouk et al. (2020), IEEE/ACM ToN: age counted only while wrong. Kaul, Yates & Gruteser (2012), IEEE INFOCOM, and Yates et al. (2021), IEEE JSAC: the origin and the survey.

**Intermittent observation.** Sinopoli et al. (2004), IEEE TAC: Bernoulli arrivals and a critical rate below which error covariance diverges. Sijs & Lazar (2012), IEEE TAC: the absence of an event carries information given a known trigger.

**Saturating gain.** Veliz-Cuba, Kilpatrick & Josić (2016), SIAM Review: evidence is discounted faster at large log-odds; an optimal observer's certainty saturates; linear (OU) discounting is only an approximation. Glaze, Kable & Gold (2015), eLife: a leaky accumulator with non-absorbing bounds. Jacobs & Steck (2006), Contemporary Physics: the stochastic term of the master equation vanishes at an eigenstate, and backaction occurs whether or not the observer uses the record.

**Learned decay.** Che et al. (2018), Scientific Reports (GRU-D): trainable decay of inputs toward the empirical mean and of the hidden state. Rubanova, Chen & Duvenaud (2019), NeurIPS: ODE-RNN integrates the hidden state across gaps.

**Scoring.** Dawid (1984), JRSS A: the prequential principle. Dawid & Vovk (1999), Bernoulli: its properties. Gneiting & Raftery (2007), JASA: strictly proper scores. Gneiting, Balabdaoui & Raftery (2007), JRSS-B: calibration and sharpness. Hyndman & Koehler (2006), IJF: MASE makes the naive forecast the unit. Makridakis, Spiliotis & Assimakopoulos (2018), PLOS ONE: simple methods beat ML on M3. Gama, Sebastião & Rodrigues (2013), Machine Learning: prequential error for streams.

**Adaptive noise and occupancy.** Mehra (1970), IEEE TAC, and Zhang et al. (2020), IEEE Access: innovation-based noise identification needs thousands of samples and can diverge. Kleiminger, Mattern & Santini (2014), Energy and Buildings, and Scott et al. (2011), UbiComp (PreHeat): occupancy prediction scored by accuracy-type metrics.

**The negative space.** Sun and Ornee–Sun give the age-to-variance maps for Wiener and OU, but assume the process class is known and never test against persistence on real feeds. Shisher & Sun show non-monotone error versus age on real data but do not separate value from uncertainty. GRU-D learns both a value decay and a hidden-state decay and scores neither as calibration. Sinopoli treats silence as loss carrying no information; Sijs & Lazar treat it as information given a trigger; neither asks which prior class a feed belongs to. Veliz-Cuba and Glaze derive saturation for symmetric two-state environments, not for one-polarity evidence. Kleiminger and PreHeat never report proper scores against persistence. Hyndman & Koehler make persistence the unit, and no Age-of-Information paper has joined it. No source found runs value-decay against uncertainty-decay head-to-head, against persistence, on several real feeds.

**Second sweep (2026-11-02).** Ornee & Sun is now verified as IEEE/ACM Transactions on Networking 29(5):1962–1975, DOI 10.1109/TNET.2021.3078137 (conference version WiOpt 2019). Two age-to-value neighbours join the Age paragraph: Chen & Ephremides (2024), "Minimizing Age of Incorrect Information over a channel with random delay," IEEE/ACM ToN 32(4):2752–2764, DOI 10.1109/TNET.2024.3389964 (verified; workshop version INFOCOM Workshops 2023), and Wang, Badiu & Coon (2021), "Relationship between age and value of information for a noisy Ornstein–Uhlenbeck process," Entropy 23(8):940, DOI 10.3390/e23080940 (record verified; content not read), the one title found that puts age and value on an OU process, which is the event-class prior here. Neither runs value-decay against uncertainty-decay, or either against persistence, on real feeds; Shisher & Sun (2022) remains the nearest published negative. On the occupancy side, Esmaieeli-Sikaroudi, Goikhman, Chubarov, Nguyen, Chertkov & Vorobev (2024), arXiv:2409.11743, fit a switching autoregressive process with a Markov regime to indoor CO2 and report that it "outperforms simple Hidden Markov approaches on simulated and real-life data", with no metric or number in the abstract; the sweep found no Wonham or Bernoulli filter applied to presence sensing at all (web and arXiv-API queries returned bandpass-filter patents and an HMM refining an inhabitant count), so the pole-pathology reading in §6, where the Wonham gain goes deaf, has no published presence-sensing twin to cite either way. The 79/103 caveat is unchanged: the artifact is still not located at `8e67bcc`, and the number stays "reported in the engine's decay notes" until it is re-run.

## Evidence each claim rests on

| Claim | Pointer | Tier |
|---|---|---|
| Value model loses: 0/103 beats persistence; 10/103 beats never-decay (α = 0.5); 103 series from the LLM-playtester fleet | SpaceWheat `🍄/🧪/hive/gamma_walk.py`, `gamma_walk_results.json` (`series_scored: 103, beats_persistence: 0, decay_beats_no_decay: 10`) | MEASURED (artifact committed, public repo) |
| Uncertainty model wins: 79/103; mean corr +0.285 at best γ vs −0.002 at γ = 0; γ* 3e-3–1e-2 /s (half-life ≈ 1–4 min) | DARK: needs public evidence (a public repro or measurement) before it can be claimed | DARK |
| In-gate dissociation: accumulators value-γ* = 0; calibration peaks at γ* = 3e-4 /s (corr +0.302 vs +0.223); ±1 events accept OU (value-γ* = 1e-4 /s; RMSE 0.520 vs 0.532); constant cadence → γ-invariant; γ* tracks gap scale | DARK: needs public evidence (a public repro or measurement) before it can be claimed | DARK |
| Reading: accumulators want Wiener; dissipative decay toward I/2 imposes OU; accumulators are the class wronged | `docs/DECAY_NOTES.md` | interpretation of PINNED + MEASURED |
| Decisiveness vs retention: {0.25, 1, 4}; 214 observations, 8 clusters; mean \|z\| 0.01586 / 0.00973 / 0.00243; surprise 0.4496 / 0.4437 / 0.4384 | DARK: needs public evidence (a public repro or measurement) before it can be claimed | DARK |
| Dissipative-role law: OFF as re-arm timeout (median 326 s); unitary role pinned z ≈ +0.95 for 13 days, std ≈ 0.002, AUC excellent under an inverted sign; dissipative declaration restored dynamics (+0.95 → +0.09 → re-light) | DARK: needs public evidence (a public repro or measurement) before it can be claimed | DARK |
| Pole pathology: one-sided evidence saturates z; the Wonham gain goes deaf; purity floor Z_CAP = 0.98 is load-bearing | DARK: needs public evidence (a public repro or measurement) before it can be claimed | DARK |
| Blank boot mixes analog-dissipative roles to max entropy, not a pole | DARK: needs public evidence (a public repro or measurement) before it can be claimed | DARK |
| Membrane cadence: daily batches within 0.15 z of the dense stream; market A/B burst 0.5154 / hold 0.5170 / starvation 0.4764 | DARK: needs public evidence (a public repro or measurement) before it can be claimed | DARK |
| Three times kept untangled (dt / φ-clock / Berry tape; `ingest_hold_s`; in-universe) | DARK: needs public evidence (a public repro or measurement) before it can be claimed | DARK |
| Forecast skill on live data; any decision taken on these beliefs | — | DARK |

## DARK (no number is typed)

- The 79/103 result, until its artifact is re-run and committed.
- The regime class: named in the taxonomy, no measured member.
- Live forecast skill, and any production decision made on a decayed belief.
- Transfer of γ* across feeds of the same class.
- Any effect size from the earlier deployment the engine descends from (rule 0.2; not quoted).
- Human readers of a decayed belief.

## Threats to validity

The 103 series come from an automated playtester fleet in one game, not from human players. The in-gate replication is a deterministic synthetic day. The E2 ladder is n = 1 per rung. The dissipative-role law rests on 13 days of one private home export; its numbers can be reported but its data cannot be shared, which limits independent reproduction. The uncertainty score is a correlation, a calibration proxy and not a strictly proper score. The never-decay comparison fixes α = 0.5. The market A/B sits in a small-n regime the owner's ledger describes as "inside the noise band at this n". The claim that the engine's dissipation is OU is a reading of the mechanism, not a fitted model.

## What this paper is not

Not a claim that the quantum representation matters here; γ is a scalar relaxation rate, and the argument holds for any belief with a mixed middle. Not a scheduling or sampling result. Not a new filter, and not the estimator-ladder paper (P2). Not a value forecast of wallets or presence. Not a human study. No number from any earlier deployment the engine descends from appears, and the home-data ladder verdict is not cited.