# Merge 4: premium and deadband switches

## Conclusion

**Provisionally enable deadband on spread 4; retain T’s other settings in this group pending stronger evidence.** This is an interpretation of the paired measurements below, not a validated combined strategy or a leaderboard prediction. No simulation was rerun for this merge.

- `premium-s4-on`: negative pooled estimate; keep premium off. [premium-s4-on-1](#premium-s4-on-1), [premium-s4-on-2](#premium-s4-on-2), [premium-s4-on-3](#premium-s4-on-3), [premium-s4-on-4](#premium-s4-on-4).
- `deadband-s1-on`: positive but highly uncertain. The best run, seed 1001661, contributes +1375.301360 of the pooled +1703.331058; removing just that observation leaves a spread mean of about +0.616597 (532 observations). Keep off pending confirmation. [deadband-s1-on-1](#deadband-s1-on-1), [deadband-s1-on-2](#deadband-s1-on-2), [deadband-s1-on-3](#deadband-s1-on-3), [deadband-s1-on-4](#deadband-s1-on-4).
- `deadband-s2-on`: negative in all four blocks; keep off. [deadband-s2-on-1](#deadband-s2-on-1), [deadband-s2-on-2](#deadband-s2-on-2), [deadband-s2-on-3](#deadband-s2-on-3), [deadband-s2-on-4](#deadband-s2-on-4).
- `deadband-s3-off`: tiny positive estimate relative to uncertainty; retain deadband on spread 3. [deadband-s3-off-1](#deadband-s3-off-1), [deadband-s3-off-2](#deadband-s3-off-2), [deadband-s3-off-3](#deadband-s3-off-3), [deadband-s3-off-4](#deadband-s3-off-4).
- `deadband-s4-on`: positive in all four blocks, spread gain +0.685092 with SE 0.329523; provisional enable. The approximate unadjusted 95% interval is [+0.039228, +1.330957]. This is marginal evidence: the interval does not account for selecting among this group or the goal’s other flips. [deadband-s4-on-1](#deadband-s4-on-1), [deadband-s4-on-2](#deadband-s4-on-2), [deadband-s4-on-3](#deadband-s4-on-3), [deadband-s4-on-4](#deadband-s4-on-4).

The provisional line for this group alone is:

```python
ON = dict(cancel=(2, 3, 4), cut=(1, 4), postjump=(1,), premium=(), deadband=(3, 4))
```

This is exactly the measured `deadband-s4-on` candidate; it does not incorporate decisions from other merge groups. Combining premium and deadband changes on the same spread would require interaction testing; single-flip gains cannot simply be added.

## Pooling method and coverage

All numbers below derive from the 20 input JSON documents catalogued in the evidence ledger. Each reports `complete=true`, `blocked=null`, 500 paired seeds and no failures (`0` in premium-s4-on-1, an empty list elsewhere). Every flip has exactly one row for each seed 1,000,000–1,001,999, with no gaps or duplicates. All per-seed deltas outside the changed spread are zero in the supplied rows. The sampled spread counts agree across flips: 533, 482, 538, 447 for spreads 1–4 respectively. These are checks on the supplied data, not independent proof of execution.

For paired delta `d = CANDIDATE.total_edge − T.total_edge`, pool `N = Σ n`, `S = Σ sum_d`, `Q = Σ sum_d2`; report mean `S/N` and `SE = sqrt((Q − S²/N)/(N(N−1)))`. The spread calculation uses its own counts, including zero deltas on that spread. This weights seeds equally, rather than averaging spread block means or their SEs. Pool reported moments (which some workers rounded), not the rounded per-seed deltas. Display rounding is six decimals. Approximate intervals use mean ± 1.96 SE and assume independent sampled seeds; heavy tails and selection limit that approximation.

Worst run means the minimum paired delta, not the candidate’s absolute edge or a failure rate. It comes from the supplied `worst` lists, cross-checked against the per-seed minima within rounding. Absolute T/candidate outcomes are not supplied.

Runtime ratio is `Σ(n × candidate_seconds_per_simulation) / Σ(n × t_seconds_per_simulation)`. It pools the reported timing totals, rather than averaging ratios. Timings are all-spread timings; spread-specific runtimes are unavailable.

## Pooled results

Every row uses all four cited blocks. The same S and Q apply overall and on the changed spread because all other spreads have zero deltas.

| Flip | Overall N | Overall gain | Overall SE | Changed spread N | Gain on spread | Spread SE | Worst paired run (seed; spread) | Runtime C/T | Sources |
|---|---:|---:|---:|---:|---:|---:|---|---:|---|
| premium-s4-on | 2000 | -0.053850 | 0.078418 | 447 | -0.240940 | 0.351027 | -100.704836 (1001855; 4) | 1.000836 | [premium-s4-on-1](#premium-s4-on-1), [premium-s4-on-2](#premium-s4-on-2), [premium-s4-on-3](#premium-s4-on-3), [premium-s4-on-4](#premium-s4-on-4) |
| deadband-s1-on | 2000 | +0.851666 | 0.709884 | 533 | +3.195743 | 2.662921 | -108.141189 (1001483; 1) | 1.014453 | [deadband-s1-on-1](#deadband-s1-on-1), [deadband-s1-on-2](#deadband-s1-on-2), [deadband-s1-on-3](#deadband-s1-on-3), [deadband-s1-on-4](#deadband-s1-on-4) |
| deadband-s2-on | 2000 | -0.181835 | 0.087446 | 482 | -0.754502 | 0.361895 | -102.577573 (1001986; 2) | 1.016209 | [deadband-s2-on-1](#deadband-s2-on-1), [deadband-s2-on-2](#deadband-s2-on-2), [deadband-s2-on-3](#deadband-s2-on-3), [deadband-s2-on-4](#deadband-s2-on-4) |
| deadband-s3-off | 2000 | +0.020364 | 0.098484 | 538 | +0.075701 | 0.366351 | -40.757606 (1000800; 3) | 0.977109 | [deadband-s3-off-1](#deadband-s3-off-1), [deadband-s3-off-2](#deadband-s3-off-2), [deadband-s3-off-3](#deadband-s3-off-3), [deadband-s3-off-4](#deadband-s3-off-4) |
| deadband-s4-on | 2000 | +0.153118 | 0.073861 | 447 | +0.685092 | 0.329523 | -76.496089 (1000166; 4) | 1.026768 | [deadband-s4-on-1](#deadband-s4-on-1), [deadband-s4-on-2](#deadband-s4-on-2), [deadband-s4-on-3](#deadband-s4-on-3), [deadband-s4-on-4](#deadband-s4-on-4) |

| Flip | Pooled sum_d (overall and changed spread) | Pooled sum_d2 (overall and changed spread) |
|---|---:|---:|
| premium-s4-on | -107.700369341 | 24591.344957031 |
| deadband-s1-on | 1703.331058236 | 2016181.591954423 |
| deadband-s2-on | -363.669860979 | 30638.199138226 |
| deadband-s3-off | 40.727064952 | 38778.114554780 |
| deadband-s4-on | 306.236285391 | 21857.569371592 |

## Provenance and source limitations

The task flags one external source citation for each of these blocks: premium-s4-on 1, 2, 3; deadband-s1-on 1, 3; deadband-s2-on 1, 3, 4; deadband-s3-off 2, 3; deadband-s4-on 2, 3, 4. The provided JSON documents contain measurements and notes but no separate source lists identifying which quotation failed. Therefore the precise failed citation and reason cannot be recovered here. A flag is not evidence that the numerical measurements themselves are wrong; equally, the cited external material cannot certify those measurements.

This merge retains those blocks as **worker-reported measurements**, explicitly flagged in the ledger, without reducing their seed weights: selective exclusion would defeat the requested four-block pooling. Do not interpret the pooled SEs as including provenance or execution uncertainty. Unflagged blocks also remain worker reports, not independently reproduced experiments.

The merge independently fetched the [T artifact](https://api.imdnotdead.fun/artifacts/79af781a0f1882f2a291e045f803714b52128f9938480d54fb43360417b381ac), hashed its UTF-8 `code` string, and obtained `9fba1eb5659d5b0ac9b7273a968a520ef9a95551c697be22020993005af70192`. The exact baseline ON line occurs once. Replacing only that line for each named flip reproduces all candidate hashes below, also matching all four worker reports per flip. This resolves strategy-byte identity, but does not independently verify that workers executed those bytes with the pinned simulator.

| Flip | Replacement portion of ON line (all other fields unchanged) | Verified candidate SHA-256 |
|---|---|---|
| premium-s4-on | `premium=(4,)` | `3c4caa84ddf78b46fea0457ac407701a0539f149ebf48dbee1deb878b37f162c` |
| deadband-s1-on | `deadband=(1, 3)` | `a4907178f3ed12f1825290beb5316d1cbe81de2d960a188a8f96482923b36e56` |
| deadband-s2-on | `deadband=(2, 3)` | `da8654cc339ae2678ed153cf1aaa3747be762c3f9b9d1e2f6531dec48919c1a8` |
| deadband-s3-off | `deadband=()` | `17611ee3bb0570c4df1ad950a8bf1bbffe5c68970383e8f0ec10775979227cce` |
| deadband-s4-on | `deadband=(3, 4)` | `2231b337bb0ab3a01d8909be0630541f8cb59fb81d98bee806c34dd51cecb27b` |

Workers identify the simulator as [danrobinson/prediction-market-challenge at b244530ee2a6247b5f930830eeca9dd950da0e7e](https://github.com/danrobinson/prediction-market-challenge/tree/b244530ee2a6247b5f930830eeca9dd950da0e7e). That execution provenance was not independently reconstructed in this merge. The public challenge and leaderboard context are supplied by the task, not needed to establish the pooled measurements; this merge makes no new ranking claim.

Runtime comparability is limited. Notes report different Python versions and timing boundaries (engine only versus factory loading plus execution), and several blocks used concurrent serial shards. In particular, premium-s4-on-3, deadband-s1-on-2/-4, and deadband-s3-off-4 report concurrent processes; deadband-s1-on-4 explicitly calls its timings inflated. Deadband-s4-on-3 has empty notes, so its timing and execution details cannot be established beyond its fields. All ratios are descriptive, not controlled speed benchmarks; the apparent roughly 2.7% cost of deadband-s4-on and 2.3% saving of deadband-s3-off should be read accordingly. See each input’s `notes` and `seconds_per_simulation`.

## Evidence ledger: all 20 blocks

Each entry below preserves its source identifier, SHA-256 of the exact supplied input bytes, overall and changed-spread sufficient statistics, and timings. Original item paths are requester-provided artifact identifiers; linked read paths are the copies used here. These copies are not committed with this merge. The embedded ledger makes the pooled calculations reviewable even if the input links later become unavailable. Per-seed records remain in those inputs; this merge does not reproduce their full arrays.

For all blocks below, overall N=500. Each row’s S and Q are shared by overall and the changed spread. Timings are reported mean seconds per simulation. `Flagged` refers to the task’s external-source warning, not a detected moment inconsistency.

### premium-s4-on

| Block / source | Seed interval (inclusive) | Changed spread n | S | Q | T seconds | C seconds | External source |
|---|---|---:|---:|---:|---:|---:|---|
| <a id="premium-s4-on-1"></a>[premium-s4-on-1](../../../../.imd/reads/artifacts/item-premium-s4-on-1) | 1000000–1000499 | 110 | -18.74863762910013 | 1899.4232680876596 | 0.3311224499521777 | 0.3304107740651816 | Flagged |
| <a id="premium-s4-on-2"></a>[premium-s4-on-2](../../../../.imd/reads/artifacts/item-premium-s4-on-2) | 1000500–1000999 | 118 | 3.1656567095002117 | 1869.1561394054563 | 0.4753160032220185 | 0.4763043531579897 | Flagged |
| <a id="premium-s4-on-3"></a>[premium-s4-on-3](../../../../.imd/reads/artifacts/item-premium-s4-on-3) | 1001000–1001499 | 120 | -133.887172 | 7839.152567 | 1.073 | 1.0736 | Flagged |
| <a id="premium-s4-on-4"></a>[premium-s4-on-4](../../../../.imd/reads/artifacts/item-premium-s4-on-4) | 1001500–1001999 | 99 | 41.76978357830005 | 12983.61298253819 | 0.8990585818598047 | 0.9005048173624091 | Not flagged |

Input identities:

- `artifacts/goal/items/premium-s4-on-1/result.json` → `.imd/reads/artifacts/item-premium-s4-on-1`; SHA-256 `cce9f2a55963d0ef1972ccfb32d6fdbb82af08cb4a967554340492bc258da78d`.
- `artifacts/goal/items/premium-s4-on-2/result.json` → `.imd/reads/artifacts/item-premium-s4-on-2`; SHA-256 `d6dcd77ff9cc6aa7b47fbf64483bdccfc30ee88168a768be58aaf8635c67043c`.
- `artifacts/goal/items/premium-s4-on-3/result.json` → `.imd/reads/artifacts/item-premium-s4-on-3`; SHA-256 `df4b407299a2833fe5ca81bf62049bcdebd4cd191e2ec87986dc1705824e6c57`.
- `artifacts/goal/items/premium-s4-on-4/result.json` → `.imd/reads/artifacts/item-premium-s4-on-4`; SHA-256 `4054a758add96f9920f554bdcb65284eb38a362fd5f114d1da83bd774d149041`.
### deadband-s1-on

| Block / source | Seed interval (inclusive) | Changed spread n | S | Q | T seconds | C seconds | External source |
|---|---|---:|---:|---:|---:|---:|---|
| <a id="deadband-s1-on-1"></a>[deadband-s1-on-1](../../../../.imd/reads/artifacts/item-deadband-s1-on-1) | 1000000–1000499 | 144 | 74.991576 | 8476.667645 | 0.8942 | 0.9113 | Flagged |
| <a id="deadband-s1-on-2"></a>[deadband-s1-on-2](../../../../.imd/reads/artifacts/item-deadband-s1-on-2) | 1000500–1000999 | 120 | 297.396172 | 88827.620276 | 0.9108 | 0.9243 | Not flagged |
| <a id="deadband-s1-on-3"></a>[deadband-s1-on-3](../../../../.imd/reads/artifacts/item-deadband-s1-on-3) | 1001000–1001499 | 129 | -4.012602764400061 | 22103.36787542255 | 0.4755061230268329 | 0.48092834727466105 | Flagged |
| <a id="deadband-s1-on-4"></a>[deadband-s1-on-4](../../../../.imd/reads/artifacts/item-deadband-s1-on-4) | 1001500–1001999 | 140 | 1334.955913 | 1896773.936158 | 1.5403237562179566 | 1.5595247020721437 | Not flagged |

Input identities:

- `artifacts/goal/items/deadband-s1-on-1/result.json` → `.imd/reads/artifacts/item-deadband-s1-on-1`; SHA-256 `4f84906eea0358ac8beb4855257eae8def43be1b124ae56d2fe6d093789eb319`.
- `artifacts/goal/items/deadband-s1-on-2/result.json` → `.imd/reads/artifacts/item-deadband-s1-on-2`; SHA-256 `757d06f76fceea915d4fe6defbd357aee09b7ffe6ed7f9b2d9226aee9a416562`.
- `artifacts/goal/items/deadband-s1-on-3/result.json` → `.imd/reads/artifacts/item-deadband-s1-on-3`; SHA-256 `966e8cb58dba82693fcbe8dfc03c1ad257a0edcedff9e9ee9deac4bcb2c63fce`.
- `artifacts/goal/items/deadband-s1-on-4/result.json` → `.imd/reads/artifacts/item-deadband-s1-on-4`; SHA-256 `890f4e39df645e8e874dd2eb8d9608363d80ce66a9e98b0eee68365a9744dfd9`.
### deadband-s2-on

| Block / source | Seed interval (inclusive) | Changed spread n | S | Q | T seconds | C seconds | External source |
|---|---|---:|---:|---:|---:|---:|---|
| <a id="deadband-s2-on-1"></a>[deadband-s2-on-1](../../../../.imd/reads/artifacts/item-deadband-s2-on-1) | 1000000–1000499 | 118 | -77.8092674620001 | 5936.696112211823 | 0.4427138243536465 | 0.44956932321446946 | Flagged |
| <a id="deadband-s2-on-2"></a>[deadband-s2-on-2](../../../../.imd/reads/artifacts/item-deadband-s2-on-2) | 1000500–1000999 | 122 | -35.9113607657 | 1855.5334703074027 | 1.0009327456131578 | 1.0143184051183052 | Not flagged |
| <a id="deadband-s2-on-3"></a>[deadband-s2-on-3](../../../../.imd/reads/artifacts/item-deadband-s2-on-3) | 1001000–1001499 | 109 | -72.5386609888 | 7104.38765918275 | 0.6452653682981617 | 0.6579442626689561 | Flagged |
| <a id="deadband-s2-on-4"></a>[deadband-s2-on-4](../../../../.imd/reads/artifacts/item-deadband-s2-on-4) | 1001500–1001999 | 133 | -177.41057176209995 | 15741.581896523649 | 0.6661603760477155 | 0.6778972466718406 | Flagged |

Input identities:

- `artifacts/goal/items/deadband-s2-on-1/result.json` → `.imd/reads/artifacts/item-deadband-s2-on-1`; SHA-256 `78c2a147184012cbcee7b2736f9166a6c1d400acebd7059bbd6cb5499ff0f324`.
- `artifacts/goal/items/deadband-s2-on-2/result.json` → `.imd/reads/artifacts/item-deadband-s2-on-2`; SHA-256 `1a883e0f87b5f919c695181a488ea014c37886d31bf7ff5b6f2af25f7bd468c9`.
- `artifacts/goal/items/deadband-s2-on-3/result.json` → `.imd/reads/artifacts/item-deadband-s2-on-3`; SHA-256 `2639752766a3e901f587db9b896b1ce05b1235ee68b9072889bc86711924f28a`.
- `artifacts/goal/items/deadband-s2-on-4/result.json` → `.imd/reads/artifacts/item-deadband-s2-on-4`; SHA-256 `f9839b6d85fef312ffe4928ae50bb0e77e8f8534aad7fdaa904e4736f6009133`.
### deadband-s3-off

| Block / source | Seed interval (inclusive) | Changed spread n | S | Q | T seconds | C seconds | External source |
|---|---|---:|---:|---:|---:|---:|---|
| <a id="deadband-s3-off-1"></a>[deadband-s3-off-1](../../../../.imd/reads/artifacts/item-deadband-s3-off-1) | 1000000–1000499 | 128 | -137.54049060660012 | 4187.342686519914 | 1.370700114379637 | 1.341975472082384 | Not flagged |
| <a id="deadband-s3-off-2"></a>[deadband-s3-off-2](../../../../.imd/reads/artifacts/item-deadband-s3-off-2) | 1000500–1000999 | 140 | -4.890831807000127 | 12132.894650176362 | 0.655694521268364 | 0.6392895533102565 | Flagged |
| <a id="deadband-s3-off-3"></a>[deadband-s3-off-3](../../../../.imd/reads/artifacts/item-deadband-s3-off-3) | 1001000–1001499 | 142 | 62.015013365700355 | 3954.6695620839437 | 0.2774709530265536 | 0.270498536194209 | Flagged |
| <a id="deadband-s3-off-4"></a>[deadband-s3-off-4](../../../../.imd/reads/artifacts/item-deadband-s3-off-4) | 1001500–1001999 | 128 | 121.143374 | 18503.207656 | 0.846 | 0.826 | Not flagged |

Input identities:

- `artifacts/goal/items/deadband-s3-off-1/result.json` → `.imd/reads/artifacts/item-deadband-s3-off-1`; SHA-256 `cde2fd33161265b84eae9d6c036e9ce7cbb75d7aba8782f0b02f5c80bf9f6802`.
- `artifacts/goal/items/deadband-s3-off-2/result.json` → `.imd/reads/artifacts/item-deadband-s3-off-2`; SHA-256 `254e91edf3d129245dd920b9766fcab70a50dbbb83be2de36e1f8f58dc97237b`.
- `artifacts/goal/items/deadband-s3-off-3/result.json` → `.imd/reads/artifacts/item-deadband-s3-off-3`; SHA-256 `646a2d8198c6c4e2832d27ed0bb6792a54de40ee9480b308b8fef6d99d2f0cdd`.
- `artifacts/goal/items/deadband-s3-off-4/result.json` → `.imd/reads/artifacts/item-deadband-s3-off-4`; SHA-256 `f2d725971c672889c9c11a2f42d6afa33cbe1eebc33f267826189dfb9e30efa7`.
### deadband-s4-on

| Block / source | Seed interval (inclusive) | Changed spread n | S | Q | T seconds | C seconds | External source |
|---|---|---:|---:|---:|---:|---:|---|
| <a id="deadband-s4-on-1"></a>[deadband-s4-on-1](../../../../.imd/reads/artifacts/item-deadband-s4-on-1) | 1000000–1000499 | 110 | 99.10923032190011 | 12667.254009076083 | 0.7634058760725894 | 0.782080822033342 | Not flagged |
| <a id="deadband-s4-on-2"></a>[deadband-s4-on-2](../../../../.imd/reads/artifacts/item-deadband-s4-on-2) | 1000500–1000999 | 118 | 75.71331521660021 | 5314.109252836836 | 0.7873166411090642 | 0.806986755006481 | Flagged |
| <a id="deadband-s4-on-3"></a>[deadband-s4-on-3](../../../../.imd/reads/artifacts/item-deadband-s4-on-3) | 1001000–1001499 | 120 | 58.08228555909962 | 2100.206696491683 | 0.6584586363765411 | 0.6838770606908947 | Flagged |
| <a id="deadband-s4-on-4"></a>[deadband-s4-on-4](../../../../.imd/reads/artifacts/item-deadband-s4-on-4) | 1001500–1001999 | 99 | 73.33145429349995 | 1775.999413187099 | 1.439562955188565 | 1.473468960404396 | Flagged |

Input identities:

- `artifacts/goal/items/deadband-s4-on-1/result.json` → `.imd/reads/artifacts/item-deadband-s4-on-1`; SHA-256 `9fa3cc962e6e5a6d48679363a152249340b6822baba2d6ff40b2b7bd1bd6d0eb`.
- `artifacts/goal/items/deadband-s4-on-2/result.json` → `.imd/reads/artifacts/item-deadband-s4-on-2`; SHA-256 `d51c9fcdee30e79faa2bb20ad76b6ed057af821878a782c2a371f166dad5b2e2`.
- `artifacts/goal/items/deadband-s4-on-3/result.json` → `.imd/reads/artifacts/item-deadband-s4-on-3`; SHA-256 `00122bf00d67074c09953e55c33f96269c26803a665d2b61ea27cf0e070b5b2c`.
- `artifacts/goal/items/deadband-s4-on-4/result.json` → `.imd/reads/artifacts/item-deadband-s4-on-4`; SHA-256 `b0598cf0c223e1aebe4d043b6bfebec639bbce1d304a47ad04abfdd60ed3609f`.

## Local validation

Parsed every input as JSON; checked each exact seed interval and count, unique coverage, common spread assignments/counts, moment agreement with the rounded per-seed records, and zero deltas off the changed spread. Per-seed rounding tolerances were at most 0.5×10⁻⁶ per delta, propagated to sums and squared sums. Pooled results were recomputed from S/Q rather than source means/SEs. No missing or empty input, missing seed, reported failed pair, or strategy hash disagreement was found. These checks establish internal consistency only.