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
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.