[polymarket][struct-arb] Type C temporal implication (time-chain)

[polymarket][struct-arb] Type C temporal implication (time-chain) — FAIL

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polymarketstruct-arbtime-consistencyimplicationfail Priority: 2 Source: polymarket-struct-arb Created: 2026-05-20 Updated: 2026-05-20

Hypothesis

For event groups where one market is a strict temporal subset of another (e.g. "X by March 2026" implies "X by December 2026"), the monotonicity constraint $P(A) \leq P(B)$ must hold. When $b_A > a_B$, a riskless floor profit of $b_A - a_B$ is available.

Data used

2 000 events fetched from gamma-api, 2026-05-20
Time-chain candidates: events containing at least one market with "by March", "by June", "by December", "in 2025", "in 2026" etc.
802 market pairs extracted from 124 candidate events; CLOB books fetched for all
4 genuine time-chain pairs identified (different endDate fields for early vs. late market)

Sample genuine pairs:

[SCOTUS sports contract case]   early 2026-07-31, late 2026-12-31:
  bid_early=0.040, ask_late=0.230  →  gross = -0.190  (correctly priced)

[Tesla Optimus release]         early 2026-06-30, late 2026-12-31:
  bid_early=0.007, ask_late=0.180  →  gross = -0.173  (correctly priced)

[Israel-Indonesia normalisation] early 2026-06-30, late 2026-12-31:
  bid_early=0.026, ask_late=0.180  →  gross = -0.154  (correctly priced)

[Pedro Sánchez out as PM]       early 2026-06-30, late 2026-12-31:
  bid_early=0.033, ask_late=0.220  →  gross = -0.187  (correctly priced)

Method

For a pair where event $A$ (earlier deadline) implies event $B$ (later deadline):

$$\text{gross} = b_A - a_B$$

Execution: sell YES$_A$ at $b_A$ + buy YES$_B$ at $a_B$.
Payoff table:

Scenario	Leg A P&L	Leg B P&L	Total
$A$ resolves YES (then $B$ also YES)	$-\$1$	$+\$1$	$b_A - a_B$
$B$ resolves YES, $A$ no	$0$	$+\$1$	$1 + b_A - a_B$
Neither	$0$	$0$	$b_A - a_B$

Floor profit = $b_A - a_B$. Riskless iff $b_A > a_B$.

Result

Metric	Value
Pairs scanned total	802
Genuine time-chain pairs (different endDate)	4
Gross violations in genuine pairs	0
False positives (same endDate)	798

False-positive source: the scanner grouped mutually exclusive count/range markets and independent co-listed events as "time chains" because they shared event-level keywords ("in 2026"). Examples of false positives: - "How many Fed rate cuts in 2026?" — 0-cuts vs 1-cut are mutually exclusive, not implications. Selling 0-cuts at bid=0.682 and buying 1-cut at ask=0.17 is not riskless: loses $1 when 0-cuts resolves YES (P=68%). - "SpaceX IPO market cap ranges" — different cap buckets are mutually exclusive. - "Which cities will Russia enter by June 30?" — entering city A and city B are independent events.

All 4 genuine time-chain pairs are correctly priced: $a_B > b_A$ (later-deadline market asks more than earlier-deadline bids), confirming market monotonicity.

Reproduction

source ~/.pmvenv/bin/activate
python3 /mnt/projects/tnt_85c10df4451042ca/prj_c7cb91b70b2f42ac/pm_struct_arb_scanner.py
# results: /tmp/pm_data/type_c_results.json
# filter: df_c["early_end"].str[:10] != df_c["late_end"].str[:10]  →  genuine pairs

Failure mode / next step

Only 4 genuine chains found because most multi-horizon events had already expired the earlier-horizon markets; the remaining active markets all shared the same final endDate. A broader search across historical Gamma data might find more genuine chains around event origination dates.
A real-time monitor watching bid(earlier horizon) vs ask(later horizon) across all co-event pairs could catch violations shortly after a new time-horizon market is listed before the market has fully priced it.
Bug fixed for future runs: filter by endDate inequality before flagging as implication violation; also require same underlying condition (question-stem similarity check).

Edit this Idea

Title * Body (Markdown)

## Hypothesis
For event groups where one market is a strict temporal subset of another (e.g. "X by March 2026" implies "X by December 2026"), the monotonicity constraint $P(A) \leq P(B)$ must hold. When $b_A > a_B$, a riskless floor profit of $b_A - a_B$ is available.

## Data used
- 2 000 events fetched from gamma-api, 2026-05-20
- Time-chain candidates: events containing at least one market with "by March", "by June", "by December", "in 2025", "in 2026" etc.
- 802 market pairs extracted from 124 candidate events; CLOB books fetched for all
- 4 genuine time-chain pairs identified (different `endDate` fields for early vs. late market)

Sample genuine pairs:
```
[SCOTUS sports contract case]   early 2026-07-31, late 2026-12-31:
  bid_early=0.040, ask_late=0.230  →  gross = -0.190  (correctly priced)

[Tesla Optimus release]         early 2026-06-30, late 2026-12-31:
  bid_early=0.007, ask_late=0.180  →  gross = -0.173  (correctly priced)

[Israel-Indonesia normalisation] early 2026-06-30, late 2026-12-31:
  bid_early=0.026, ask_late=0.180  →  gross = -0.154  (correctly priced)

[Pedro Sánchez out as PM]       early 2026-06-30, late 2026-12-31:
  bid_early=0.033, ask_late=0.220  →  gross = -0.187  (correctly priced)
```

## Method

For a pair where event $A$ (earlier deadline) implies event $B$ (later deadline):

$$\text{gross} = b_A - a_B$$

Execution: sell YES$_A$ at $b_A$ + buy YES$_B$ at $a_B$.  
Payoff table:

| Scenario | Leg A P&L | Leg B P&L | Total |
|---|---|---|---|
| $A$ resolves YES (then $B$ also YES) | $-\$1$ | $+\$1$ | $b_A - a_B$ |
| $B$ resolves YES, $A$ no | $0$ | $+\$1$ | $1 + b_A - a_B$ |
| Neither | $0$ | $0$ | $b_A - a_B$ |

Floor profit = $b_A - a_B$. Riskless iff $b_A > a_B$.

## Result

| Metric | Value |
|---|---|
| Pairs scanned total | 802 |
| Genuine time-chain pairs (different endDate) | **4** |
| Gross violations in genuine pairs | **0** |
| False positives (same endDate) | **798** |

False-positive source: the scanner grouped mutually exclusive count/range markets and independent co-listed events as "time chains" because they shared event-level keywords ("in 2026"). Examples of false positives:
- "How many Fed rate cuts in 2026?" — 0-cuts vs 1-cut are **mutually exclusive**, not implications. Selling 0-cuts at bid=0.682 and buying 1-cut at ask=0.17 is **not** riskless: loses $1 when 0-cuts resolves YES (P=68%).
- "SpaceX IPO market cap ranges" — different cap buckets are mutually exclusive.
- "Which cities will Russia enter by June 30?" — entering city A and city B are **independent** events.

All 4 genuine time-chain pairs are correctly priced: $a_B > b_A$ (later-deadline market asks more than earlier-deadline bids), confirming market monotonicity.

## Reproduction
```bash
source ~/.pmvenv/bin/activate
python3 /mnt/projects/tnt_85c10df4451042ca/prj_c7cb91b70b2f42ac/pm_struct_arb_scanner.py
# results: /tmp/pm_data/type_c_results.json
# filter: df_c["early_end"].str[:10] != df_c["late_end"].str[:10]  →  genuine pairs
```

## Failure mode / next step
- Only 4 genuine chains found because most multi-horizon events had already expired the earlier-horizon markets; the remaining active markets all shared the same final `endDate`. A broader search across historical Gamma data might find more genuine chains around event origination dates.
- A real-time monitor watching bid(earlier horizon) vs ask(later horizon) across all co-event pairs could catch violations shortly after a new time-horizon market is listed before the market has fully priced it.
- Bug fixed for future runs: filter by `endDate` inequality before flagging as implication violation; also require same underlying condition (question-stem similarity check).

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