Heat & Decay¶

Every cognitive chain carries a heat score: a number in \([0, 1]\) that decays with neglect and recovers with use. Heat is the single signal that drives the memory lifecycle: hot chains get promoted to the knowledge graph, cold chains get archived.

The model is a direct implementation of the Ebbinghaus forgetting curve with spaced-repetition reinforcement.

The formula¶

\[ H(t) \;=\; I_{\text{base}} \times e^{-\Delta T \,/\, (\tau \cdot S)} \]

Symbol	Meaning	Source
\(H(t)\)	Heat now	computed on every promoter pass
\(I_{\text{base}}\)	Base importance of the chain	see below
\(\Delta T\)	Hours since the chain was last accessed	`last_accessed_at`, falling back to `max(last_event_at, started_at)`; clamped ≥ 0
\(\tau\)	Decay constant, hours	`HEAT_DECAY_TAU_HOURS` (default 24)
\(S\)	Recall strength (the spaced-repetition multiplier)	grows with well-spaced accesses

Base importance¶

\[ I_{\text{base}} = \min\bigl(1.0,\;\; w_1 \cdot \text{Intrinsic} + w_2 \cdot \text{Density}\bigr) \]

with \(w_1 =\) HEAT_WEIGHT_INTRINSIC (default 0.7) and \(w_2 =\) HEAT_WEIGHT_DENSITY (default 0.3).

Intrinsic is the LLM's judgment of the chain's importance (\(0\)–\(1\)), produced during chain formation.

Density rewards structurally rich segments, accumulated additively and capped at 1.0:

Signal	Bonus
Entities present	+0.15
Contains a `thought` or `action` event	+0.20
Observation with `workflow_id` / `execution_id` / blob	+0.25
Each distinct `origin_service` (capped)	+0.15
More than one turn	+0.05

A multi-service automation trace with entities and reasoning scores far higher density than two lines of chit-chat. That is by design.

Recall strength: memories that are used, harden¶

\(S\) starts at 1.0 and never drops below it. When a chain is accessed (retrieved by search or context blending), RecordAccess applies:

if hours since previous access > HEAT_COOLDOWN_HOURS (12):
    S ×= HEAT_RECALL_GROWTH (1.5)

The 12-hour cooldown is what makes this spaced repetition: ten retrievals in one afternoon count once, but returning to a topic across days multiplies \(S\). And since \(S\) divides \(\Delta T\) in the exponent, a hardened memory cools dramatically slower.

The reference curve¶

With \(\tau = 24h\) and \(S = 1\): heat falls to \(e^{-1} \approx 36.8\%\) of \(I_{\text{base}}\) after 24 hours.

Chain (\(I_{base}=0.8\))	After 12h	24h	48h	7d
Never re-accessed (\(S=1\))	0.49	0.29	0.11	0.0007
Recalled twice, spaced (\(S=2.25\))	0.64	0.51	0.33	0.036

The two thresholds¶

Heat is compared against two gates, creating three lifecycle bands:

H ≥ 0.3   → PROMOTE     knowledge extracted into the LTM graph
0.1–0.3   → DORMANT     stays searchable in MTM, keeps decaying
H < 0.1   → FREEZE      archiver candidate ("freezing point")

Promotion threshold: MEMORY_OS_MTM_HEAT_THRESHOLD, pipeline default 0.3 (the .env.example ships 0.8 for conservative production promotion)
Freezing point: MTM_FREEZING_POINT (default 0.1), evaluated by the archiver only for chains idle longer than MTM_ARCHIVE_SCAN_DAYS (default 7 days)

The promoter recomputes every active chain's heat on each pass (30-minute ticker), so heat is never stored stale for the promotion decision; the persisted heat_score is a snapshot for observability and archiving.

Tuning intuition

Raise HEAT_DECAY_TAU_HOURS to make all memory stickier; raise the promotion threshold to make the graph more selective. They pull in opposite directions on graph write volume.
HEAT_WEIGHT_INTRINSIC vs HEAT_WEIGHT_DENSITY trades the LLM's semantic judgment against structural evidence. Automation-heavy tenants often deserve more density weight.
Watch the memos_heat_score_distribution histogram before and after any change (Metrics).