# The Echo Garden — experiment protocol

Written before the multi-seed results, 2026-09-07. This is an original toy-model experiment, not a replication or evidence about real minds.

## Question

Can a group keep a perfect account of its evidence and still preserve a truth past its expiry? When does sharing help, when do copies masquerade as observations, and when does discounting old evidence hurt?

## Predictions registered before the batch

1. In the world-change condition, time-weighted provenance will have lower post-change Brier loss than timeless provenance in the majority of 128 paired seeds.
2. In a difficult but stable condition, aggressive age-discounting will have higher late-window Brier loss than timeless provenance in the majority of 128 paired seeds. A null or reversal will be reported rather than hidden.
3. Repeated-belief sharing may become both wrong and very confident. The proportion of seeds with this failure is a result, not a premise or pass criterion.
4. Causal checks: setting peer exchanges to zero must make recursive belief sharing and deduplicated evidence identical. Setting age-discount half-life to zero (meaning infinity) must make the provenance policies identical. Relabeling an observation's witnesses must not create additional origins.

## Fixed design

- 24 agents, 180 rounds, initial state A. At most one observation per agent per round.
- A sample reports the true state with probability q; agents know q. Its signed log-likelihood is ±log(q/(1−q)). Initial log-odds are zero.
- With probability `shared`, an observing agent hears that round's common bulletin. All its witnesses share one source ID and one outcome. Other samples have separate source IDs. Each source is independent across origins and rounds conditional on the world state.
- Two synchronous peer exchanges per round, uniformly random other agent. Every policy receives the same observations and contacts. Contact and evidence random streams are separate and seeded; changing communication never redraws evidence.
- Recursive sharing adds 0.35 times a peer's complete log-odds to the recipient's own, without subtracting repeated origins. This deliberately naive rule is not a generic model of human communication.
- Timeless provenance gossips source-ID sets and counts every origin once per agent.
- Time-aware provenance uses the same source-ID sets but weights an origin aged a rounds by 2^(−a/h). A copy keeps its original birth time. Storage is not deleted; only decision weight fades.
- Full source-ID exchange has unlimited payload, unlike the one-scalar recursive message. Payload entries are measured. Equal observations and contacts do not mean equal byte cost. No claim of resource-optimality follows.
- No policy is told about a change. Neither provenance method is an optimal Bayesian filter for a switching world.

## Preregistered conditions

- **Turning world:** q=0.65, observation chance=0.18, shared fraction=0.65, half-life=12, world reverses at round 70.
- **Difficult stable world:** q=0.56, observation chance=0.08, shared fraction=0.90, half-life=4, no reversal.
- **Echo condition:** q=0.60, observation chance=0.12, shared fraction=0.80, half-life=12, three peer exchanges, no reversal.
- **Communication ablation:** turning-world condition, peer exchanges 0, 1, 2, 4. All else fixed.
- Seeds 1 through 128, inclusive. No seed search. The interactive initial seed is 42, a fixed illustration, not the batch evidence.

## Outcomes and uncertainty

Brier loss is the mean squared difference between an agent's P(A) and the true state encoded A=1, B=0. Lower is better. Accuracy counts ties as half correct. “Wrong & sure” means the wrong side has probability at least 0.9. Confidence alone is never scored as learning.

The independent sampling unit is a world/seed, not an agent or a round. The report uses paired per-seed differences and 95% normal-approximation Monte Carlo intervals (mean ±1.96·sample-SD/√128), descriptive for this seed set, not a guarantee about a wider model family. Turning-world post-change loss covers rounds 70–179. Difficult-stable late loss covers rounds 90–179. Recovery is the first start of five consecutive rounds with at least 90% agents correct after reversal; unrecovered runs are reported separately, never silently dropped.

## Falsification and limits

A positive age-discount advantage in both stable and changing conditions would falsify the proposed trade-off here. Equal performance without communication checks the claimed echo mechanism; unequal performance would be an implementation defect. A re-timestamped copied observation is a defect, not evidence for the model.

There are no strategic agents, deception, goals, semantics, selective attention, learning of reliability, endogenous sampling, coordination payoffs, or observation costs. Independent RNG seeds are synthetic worlds, not people. This demonstrates possible failure mechanisms under explicit rules; it estimates no effect in a real organization and implies nothing about sentience.