Closed-form analysis of elfmem's long-term dynamics¶
Source: scripts/longitudinal_sim/closed_form.py — runnable derivations
Purpose: identify structural constraints that any architectural proposal must respect
Reproduces in: ~1 second, no DB, no LLM
Six analytical derivations of elfmem's dynamics. Each derives a constraint from
the actual production formulas in src/elfmem/scoring.py and
src/elfmem/operations/outcome.py. The numerical values use Dmitry's reported
4h/day usage rate.
D1 — Beta-Binomial inertness (signal saturation)¶
Marginal effect of one new outcome with signal s and weight w:
where N is the count of prior outcomes. At N=100, weight=1, discrepancy=0.4:
Δc ≈ 0.004. The block is asymptotically frozen.
| N | Δc at s−c=0.4, w=1.0 | Δc at rescore w=0.5 |
|---|---|---|
| 0 | 0.2000 | 0.1333 |
| 10 | 0.0333 | 0.0190 |
| 100 | 0.0040 | 0.0020 |
| 500 | 0.0008 | 0.0004 |
Implication: any mechanism that relies on accumulated outcomes to drive long-term identity change fails by year 1 of heavy usage. Additive rescore (v0.16, weight=0.5) protects evidence but cannot rescue ossified blocks.
D2 — Decay half-life by tier¶
At 4 active hours/day:
| Tier | λ | Half-life (hrs) | Half-life (days) | 10%-life (days) |
|---|---|---|---|---|
| PERMANENT | 0.00001 | 69,315 | 17,329 | 57,564 |
| DURABLE | 0.001 | 693 | 173 | 576 |
| STANDARD | 0.010 | 69 | 17 | 58 |
| EPHEMERAL | 0.050 | 14 | 3.5 | 12 |
Implication: a STANDARD block must be reinforced within ~17 days or its recency falls below 50%. The v0.15.3 cold-start floor extends only the first ~9 active days (D3 below). After that, blocks must accumulate edges or outcomes — or sink.
D3 — Cold-start floor active window¶
The v0.15.3 floor is active while recency > 0.70. For STANDARD tier:
| Tier | Floor active for |
|---|---|
| PERMANENT | 35,667 hours |
| DURABLE | 357 hours |
| STANDARD | 35.7 hours (8.9 days) |
| EPHEMERAL | 7.1 hours |
Implication: cold-start protection is real but brief. After ~9 days a STANDARD block must have earned edges or outcomes to survive.
D4 — Structural constitutional dominance in ATTENTION¶
ATTENTION_WEIGHTS: sim=0.35, conf=0.15, rec=0.25, cent=0.15, reinf=0.10.
Decomposing the bedrock-vs-new baseline (similarity excluded):
| Channel | Bedrock contrib | New-block contrib (with floor) | Δ |
|---|---|---|---|
| confidence | 0.15 × 1.0 = 0.150 | 0.15 × 1.0 = 0.150 | 0 |
| recency | 0.25 × 0.95 = 0.238 | 0.25 × 1.00 = 0.250 | +0.013 |
| centrality | 0.15 × 0.80 = 0.120 | 0.15 × 0.50 = 0.075 | -0.045 |
| reinforcement | 0.10 × 1.0 = 0.100 | 0.10 × 0.0 = 0.000 | -0.100 |
| non-similarity total | 0.608 | 0.475 | −0.133 |
A new block needs to beat the bedrock by 0.133 / 0.35 = 0.38 similarity to win on similarity alone. Realistic similarity gaps don't reach that.
Implication: in ATTENTION, constitutional bedrock with thematic overlap ≥ ~0.75 cannot be beaten by any new block under current weights. This is the "shadow hierarchy" Dmitry projected — and it's mathematically inevitable, not a tuning bug.
D5 — Constitutional permanence horizon¶
PERMANENT tier λ = 0.00001. At 4h/day:
recency=0.50 reached at 69,315 active hours = 47.5 years
recency=0.10 reached at 230,259 active hours = 158 years
Implication: PERMANENT blocks are immortal on any human timescale. Constitutional evolution cannot be driven by decay. It requires either (a) explicit user amendment, (b) a tier-demotion mechanism, or (c) excluding constitutional from ranking competition entirely.
D6 — Rescore power against ossified blocks¶
Block earned to c=0.85 over N outcomes. Rescore with α=0.55, weight=0.5:
| N | new c | Δc |
|---|---|---|
| 1 | 0.7900 | −0.060 |
| 10 | 0.8370 | −0.013 |
| 100 | 0.8485 | −0.0015 |
| 500 | 0.8497 | −0.0003 |
Implication: additive rescore protects evidence (~30× less destructive than overwriting) but cannot rescue ossified blocks. Once N>>100, rescore is bookkeeping. For an agent to evolve, a different mechanism is required: constitutional review cycles, tier demotion, or candidate-pool changes.
Summary — what the math constrains¶
| Finding | Constrains |
|---|---|
| D1 + D6 | No "more aggressive rescore" can fix ossification |
| D2 + D3 | Cold-start window is ~9 days at typical usage |
| D4 | Constitutional dominance is structural, not parametric |
| D5 | PERMANENT tier blocks need an evolution mechanism beyond decay |
These constraints informed every architectural proposal explored in this research directory. Any future proposal should be tested against the same formulas before being committed to.
Reproducing¶
Output is deterministic. The numerical values in this document are pinned by that script.