Project Turtle / settled postgame analysis / 2026-07-05

Mexico vs England

Final: England 3-2 Mexico. Turtle missed the four-score card, but the loss is useful: the 2-2 score 4 was real, while the low-total support layer contradicted that branch.

Lock: 2026-07-05 10:02 AM EDTFinal: Mexico 2-3 EnglandWorld Cup Round of 16Estadio Azteca, Mexico City

Pregame lock remains unchanged. Postgame corrections live only in the audit.

Locked four-score card

Settled miss: score 1-1, 0-1, 0-2, 2-2.

Card CSV

Prediction lock2026-07-05 10:02 AM EDT

Visible timestamp; the card cannot move after state changes.

Final2-3

Score convention: Mexico first, England second.

Four-score cardMISS

Actual score was not in 1-1, 0-1, 0-2.

Score-card resultMISS

2-2 was close, but England's third goal broke the score 4.

SCORE 1 1-1

B_draw_low | P=0.132877 | I=0.811527

SCORE 2 0-1

B_away_win | P=0.126278 | I=0.426089

SCORE 3 0-2

B_away_cushion | P=0.075513 | I=0.452771

SCORE 4 2-2

B_draw_high | P=0.041806 | I=0.413765

Pregame / postgame analysis

The proof stayed locked. The audit names the miss.

Pregame analysisProblem. Using only pre-cutoff data for Mexico and England, let G={0,...,7} x {0,...,7} and P_count(h,a)=Pois(h;1.0523)Pois(a;1.1960). Filter each ledger by the opponent's strength realm, build result/spread/total/BTTS-clean threads, then rank S10 by LL(s). Determine the unique four-score card C4.

Public pre-match context reports Mexico as home side at Azteca and England managing fitness questions. Those facts are bounded modifiers; exact score selection still comes from the thread model.

Market prices are excluded from this proof. Prices may size or reject a public card only after the score cloud is locked.

Postgame analysisFinal Mexico 2-3 England: four-score card miss.

England scored through Foden 14', Bellingham 18', and Kane 79' (pen). Mexico answered through Jimenez 26' and 84'. Quansah's red card at 44' made the match state volatile rather than slow, and the locked low-total posture did not survive.

What went right: England strength was a valid branch, Over 1.5 was true, and 2-2 was a real score 4 state. What failed: Turtle selected low-control England scores and then labelled Under 3.5 as support even though score 4 was 2-2. From now on, a support market that kills score 4 must be called partial-card support, not full-card support.

Postgame audit

The correction is mechanical, not emotional.

Audit MD

Four-score accuracyMISS

C4={1-1, 0-1, 0-2}; actual=2-3.

Score-card resultMISS

score 4 = 2-2 came close but did not contain the third England goal.

Goals floorCorrect

Over 1.5 and BTTS direction were true.

Low-total supportWrong

Under 2.5 and Under 3.5 both failed in a five-goal game.

Timeline Turtle must explain

England 1-0 Foden 14'; England 2-0 Bellingham 18'; Mexico 1-2 Jimenez 26'; England red card Quansah 44'; England 3-1 Kane penalty 79'; Mexico 2-3 Jimenez 84'.

Carry-forward rule

If score 4 has four or more total goals, Under 3.5 cannot be presented as support for the full four-score card. It may be listed only as partial-card support. Elite-favorite rescue and red-card volatility also need a bounded score-family modifier before the next lock.

Score cloud

S10 before branch proof.

Full grid

Rank	Score	Probability	Cumulative Probability	Total Goals	Btts
1	1-1	0.132877	0.132877	2	1
2	0-1	0.126278	0.259154	1	0
3	1-0	0.111103	0.370257	1	0
4	0-0	0.105585	0.475843	0	0
5	1-2	0.079459	0.555302	3	1
6	0-2	0.075513	0.630814	2	0
7	2-1	0.069910	0.700725	3	1
8	2-0	0.058454	0.759179	2	0
9	2-2	0.041806	0.800985	4	1
10	1-3	0.031677	0.832662	4	1

Mathematical model

Data ledgers become lambdas, then a theorem.

Model CSV

A_MEX1.528

Blended attack

D_MEX0.845

Blended defensive weakness

A_ENG1.768

Blended attack

D_ENG0.833

Blended defensive weakness

Formula. A_i=w50 GF50_i+w10 GF10_i+wWC GFWC_i and D_i=w50 GA50_i+w10 GA10_i+wWC GAWC_i. Then lambda_home_raw=(A_home+D_away)/2 and lambda_away_raw=(A_away+D_home)/2. Context gates are bounded and recorded in the CSV.

P (h, a) = Pois (h; λ_h) Pois (a; λ_a)

Opponent-threshold model

The last 50 is filtered by today's opponent realm.

Threshold ledger Realm summaries

A flat last-50 table asks how a team performs in general. Turtle now asks how Mexico performs against England-strength opponents, and how England performs against Mexico-strength opponents. Sparse samples are marked and shrunk toward the full ledger.

Team Code	Team	Team Rating	Target Opponent Code	Target Opponent	Target Rating	Epsilon Used	Raw Rows In Realm	Effective Rows	Readiness	Readiness Score	Shrinkage Alpha	Goals For Per Match	Goals Against Per Match	Scored Rate	Failed To Score Rate	Conceded Rate	Clean Sheet Rate	Btts Rate	Over 1 5 Rate	Over 2 5 Rate	Over 3 5 Rate	Win Rate	Draw Rate	Loss Rate	Win By 1 Rate	Win By 2 Plus Rate	Loss By 1 Rate	Loss By 2 Plus Rate	Draw Low Rate	Draw High Rate
MEX	Mexico	7.40	ENG	England	8.90	1.25	8	2.924	usable	0.780	6.0	1.2849	1.2006	0.6581	0.3419	0.5044	0.4956	0.3489	0.6927	0.4327	0.3520	0.3631	0.3542	0.2827	0.0000	0.0000	0.0734	0.0614	0.1504	0.0424
ENG	England	8.90	MEX	Mexico	7.40	0.75	14	9.228	strong	1.000	0.0	1.6182	0.9271	0.8490	0.1510	0.6369	0.3631	0.5723	0.8097	0.4429	0.2018	0.4163	0.3797	0.2040	0.0393	0.3770	0.1417	0.0623	0.3797	0.0000

Thread model

Result, spread, total, and clean-sheet evidence before scores.

Thread CSV

Thread	State	Probability	Model Component	Evidence	Rule Note
result	home	0.304088	grid=0.320876; evidence=0.283550	Poisson count grid blended with opponent-threshold W/D/L realm evidence.	Exact scores inherit this result mass before branch selection.
result	draw	0.322765	grid=0.286597; evidence=0.366950	Poisson count grid blended with opponent-threshold W/D/L realm evidence.	Exact scores inherit this result mass before branch selection.
result	away	0.373147	grid=0.392476; evidence=0.349500	Poisson count grid blended with opponent-threshold W/D/L realm evidence.	Exact scores inherit this result mass before branch selection.
spread	home_by_1	0.146244	grid=0.197315; evidence=0.095165	Spread family is built before exact-score disclosure.	The strongest spread family receives the first representative.
spread	home_by_2_plus	0.082703	grid=0.123561; evidence=0.041840	Spread family is built before exact-score disclosure.	The strongest spread family receives the first representative.
spread	draw	0.389749	grid=0.286597; evidence=0.492881	Spread family is built before exact-score disclosure.	The strongest spread family receives the first representative.
spread	away_by_1	0.149981	grid=0.224265; evidence=0.075688	Spread family is built before exact-score disclosure.	The strongest spread family receives the first representative.
spread	away_by_2_plus	0.231324	grid=0.168211; evidence=0.294426	Spread family is built before exact-score disclosure.	The strongest spread family receives the first representative.
total_btts_clean	over_1_5	0.694670	count grid plus opponent-threshold event rates	Support thread; it can protect or reject a branch but cannot create a score by itself.	Used inside LL(s), not as a standalone prediction.
total_btts_clean	over_2_5	0.409204	count grid plus opponent-threshold event rates	Support thread; it can protect or reject a branch but cannot create a score by itself.	Used inside LL(s), not as a standalone prediction.
total_btts_clean	over_3_5	0.224858	count grid plus opponent-threshold event rates	Support thread; it can protect or reject a branch but cannot create a score by itself.	Used inside LL(s), not as a standalone prediction.
total_btts_clean	btts_yes	0.456967	count grid plus opponent-threshold event rates	Support thread; it can protect or reject a branch but cannot create a score by itself.	Used inside LL(s), not as a standalone prediction.
total_btts_clean	home_clean_sheet	0.311807	count grid plus opponent-threshold event rates	Support thread; it can protect or reject a branch but cannot create a score by itself.	Used inside LL(s), not as a standalone prediction.
total_btts_clean	away_clean_sheet	0.350650	count grid plus opponent-threshold event rates	Support thread; it can protect or reject a branch but cannot create a score by itself.	Used inside LL(s), not as a standalone prediction.

Candidate table

Every S10 score receives one status.

Candidate CSV

Rank	Score	Poisson Probability	Result Thread Probability	Spread Thread Probability	Total Thread Probability	Btts Clean Thread Probability	Turtle Index	Status	Rule
1	1-1	0.132877	0.322765	0.389749	0.285466	0.456967	0.811527	SCORE	R2 spread-thread leader
2	0-1	0.126278	0.373147	0.149981	0.305330	0.350650	0.426089	SCORE	R3 exact-cell anchor
3	1-0	0.111103	0.304088	0.146244	0.305330	0.311807	0.395911	EXCLUDED_BY_SPREAD_THREAD	R4 spread-order comparison
4	0-0	0.105585	0.322765	0.389749	0.305330	0.331228	0.657986	EXCLUDED_BY_TOTAL_THREAD	R1 total gate
5	1-2	0.079459	0.373147	0.149981	0.184346	0.456967	0.326606	EXCLUDED_BY_SPREAD_THREAD	R2/R5 spread comparison
6	0-2	0.075513	0.373147	0.231324	0.285466	0.350650	0.452771	SCORE	R4 alternate-thread representative
7	2-1	0.069910	0.304088	0.146244	0.184346	0.456967	0.305342	EXCLUDED_BY_SPREAD_THREAD	R4 spread-order comparison
8	2-0	0.058454	0.304088	0.082703	0.285466	0.311807	0.236537	EXCLUDED_BY_SPREAD_THREAD	R4 spread-order comparison
9	2-2	0.041806	0.322765	0.389749	0.224858	0.456967	0.413765	SCORE_4	R5 fourth-score
10	1-3	0.031677	0.373147	0.231324	0.224858	0.456967	0.304265	EXCLUDED_BY_SPREAD_THREAD	R2/R5 spread comparison

Data analysis

Only computed evidence, not clutter.

MEX ledger ENG ledger

Team Code	Team	Sample	Matches	Wins	Draws	Losses	Goals For Per Match	Goals Against Per Match	Scored Rate	Conceded Rate	Clean Sheet Rate	Btts Rate	Over 1 5 Rate	Over 2 5 Rate	Over 3 5 Rate	Two Plus Scored Rate
MEX	Mexico	last_50	50	27	12	11	1.500	0.900	0.7400	0.4200	0.5800	0.2800	0.7000	0.3800	0.2600	0.5200
MEX	Mexico	last_10	10	8	2	0	2.100	0.200	0.9000	0.2000	0.8000	0.2000	0.7000	0.3000	0.2000	0.6000
MEX	Mexico	world_cup_2026	4	4	0	0	2.000	0.000	1.0000	0.0000	1.0000	0.0000	0.7500	0.2500	0.0000	0.7500
ENG	England	last_50	50	32	11	7	2.300	0.680	0.8800	0.4800	0.5200	0.4200	0.8000	0.5600	0.2800	0.6000
ENG	England	last_10	10	7	2	1	1.700	0.500	0.8000	0.4000	0.6000	0.3000	0.6000	0.4000	0.1000	0.5000
ENG	England	world_cup_2026	4	3	1	0	2.000	0.750	0.7500	0.5000	0.5000	0.5000	0.7500	0.5000	0.2500	0.7500

Win/draw/loss score modes

Team Code	Team	Bucket	Matches	Avg Goals For	Avg Goals Against	Avg Total Goals	Scoreline Modes
MEX	Mexico	Wins	27	2.111	0.185	2.296	2-0 (10/27); 1-0 (8/27); 3-0 (3/27); 4-0 (2/27); 2-1 (2/27)
MEX	Mexico	Draws	12	0.917	0.917	1.833	0-0 (6/12); 2-2 (3/12); 1-1 (2/12); 3-3 (1/12)
MEX	Mexico	Losses	11	0.636	2.636	3.273	0-2 (4/11); 2-3 (2/11); 0-4 (2/11); 0-1 (1/11); 2-4 (1/11)
ENG	England	Wins	32	3.125	0.344	3.469	3-0 (7/32); 2-0 (6/32); 2-1 (4/32); 1-0 (4/32); 5-0 (3/32)
ENG	England	Draws	11	1.000	1.000	2.000	1-1 (6/11); 0-0 (3/11); 3-3 (1/11); 2-2 (1/11)
ENG	England	Losses	7	0.571	1.714	2.286	1-2 (3/7); 0-1 (3/7); 1-3 (1/7)

Support market note

Totals/BTTS are support, not the prediction.

Support CSV

Market	Side	Model Probability	Fair Price	Max Entry Price	Suggested Stake Usd	Portfolio Role	Decision
Over 1.5 goals	YES	0.694670	0.69	0.63	0-5	Supports score clouds requiring at least two total goals.	coherent only when at least two score scores need 2+ goals
Over 2.5 goals	NO	0.590796	0.59	0.53	5-10	Protects low-total cards but can kill 2-1/1-2 branches.	use cautiously if a score score has three total goals
Over 3.5 goals	NO	0.775142	0.78	0.72	10-15	Protects every cloud that stays below four total goals.	default support when all C4 scores are below four total goals
Both teams to score	YES	0.456967	0.46	0.40	0-5	Only supports if the four-score card actually requires both teams scoring.	not a shortcut; compare to exact-score cloud first

Postgame settlement: Over 1.5 YES and BTTS YES were true; Over 2.5 NO and Over 3.5 NO were false. The public correction is that Under 3.5 only supported the four-score card, not the full four-score card, because score 4 = 2-2 requires four goals.

Aster proof board

Definitions, data, rules, lemmas, theorem.

Proof MD

01Definition 1
Let G={0,...,7} x {0,...,7}. S10 is the ten scores with largest P_count(s), tie-broken lexicographically by (home goals, away goals): {1-1, 0-1, 1-0, 0-0, 1-2, 0-2, 2-1, 2-0, 2-2, 1-3}. No exact score outside S10 can enter C4; it may enter only a named post-lock/live-state audit.
02Definition 2
For s=(h,a), P(s)=Pois(h;lambda_MEX) Pois(a;lambda_ENG), where lambda_MEX=1.0523 and lambda_ENG=1.1960.
03Definition 3
Let r_MEX=7.40 and r_ENG=8.90. MEX evidence is filtered to opponents within epsilon of r_ENG; ENG evidence is filtered to opponents within epsilon of r_MEX.
04Definition 4
Each historical row receives weight recency * competition * squad_overlap * exp(-distance^2/(2 sigma^2)), sigma=0.75. If the realm has fewer than five usable rows, epsilon widens to 1.25. If effective n still stays below five, the realm statistic is shrunk toward the last-50 statistic and readiness is marked weak.
05Definition 5
LL(s)=log P_count(s)+0.70 log P_result(s)+0.85 log P_spread(s)+0.45 log P_total(s)+0.45 log P_BTTS_clean(s). TurtleIndex normalizes exp(LL) and adds bucket, branch, form, readiness, and pressure support.
06Definition 6
C4 is the ordered set of four scores selected by R2-R6; score 4 is selected by R5 and graded inside C4.
07Data 1
Mexico last-50 W-D-L is 27-12-11; GF/M=1.500, GA/M=0.900.
08Data 2
England last-50 W-D-L is 32-11-7; GF/M=2.300, GA/M=0.680.
09Data 3
Opponent-threshold realm: Mexico vs England-realm has 8 raw rows, effective n=2.924, readiness=usable, GF/M=1.2849, GA/M=1.2006, scored=0.6581, clean-sheet=0.4956.
10Data 4
Opponent-threshold realm: England vs Mexico-realm has 14 raw rows, effective n=9.228, readiness=strong, GF/M=1.6182, GA/M=0.9271, scored=0.8490, clean-sheet=0.3631.
11Data 5
Result thread probabilities are MEX win=0.304, draw=0.323, ENG win=0.373.
12Data 6
Spread thread order is draw=0.390; away_by_2_plus=0.231; away_by_1=0.150; home_by_1=0.146; home_by_2_plus=0.083. Therefore the strongest spread before exact-score selection is draw.
13Data 7
Total and clean-sheet threads are over1.5=0.695, over2.5=0.409, over3.5=0.225, BTTS=0.457, MEX clean sheet=0.312, ENG clean sheet=0.351.
14Data 8
Recent scoring remains visible but cannot delete clean sheets by itself: Mexico scored in 90.0% of last ten; England scored in 80.0% of last ten. Current World Cup samples: 4 and 4.
15Data 9
Public pre-match context reports Mexico as home side at Azteca and England managing fitness questions. Those facts are bounded modifiers; exact score selection still comes from the thread model.
16Data 10
Manual 0-10 strength seeds: England 8.9, Mexico 7.4. Venue and tournament form narrow the effective match gap.
17Rule R1
The only hard pre-selection removal is 0-0 when P(over 1.5) >= 0.640000. Raw scoring rate alone cannot delete a clean-sheet score.
18Rule R2
Let B* be the spread state with maximum spread-thread probability. The first MAIN score is argmax TurtleIndex among eligible S10 scores with spread_key=B*.
19Rule R3
After R2, the exact-cell anchor is the remaining eligible S10 score with maximum P_count(s).
20Rule R4
After R2 and R3, scan spread states by descending spread-thread mass and skip already represented states. The first unrepresented spread whose representative has spread mass >=0.140000 or TurtleIndex >=0.280000 enters C4.
21Rule R5
The fourth score is the remaining eligible score maximizing 0.35*P_spread + 0.25*form + 0.25*I + 0.15*P_BTTS_clean. It is part of C4, not a separate containment grade.
22Rule R6
If fewer than three score scores survive, fill by highest remaining eligible I(s).
23Inclusion Lemma 1
1-1 is in C4 by R2 spread-thread leader: P_count=0.132877, result=0.322765, spread=0.389749, total=0.285466, BTTS/clean=0.456967, I=0.811527. 1-1 maximizes I(s) inside the strongest spread thread draw=0.3897 and beats 2-2 by I=0.811527 > 0.413765.
24Inclusion Lemma 2
0-1 is in C4 by R3 exact-cell anchor: P_count=0.126278, result=0.373147, spread=0.149981, total=0.305330, BTTS/clean=0.350650, I=0.426089. 0-1 is the exact-cell anchor after the spread leader and beats the next remaining count cell 1-0 by P_count=0.126278 > 0.111103.
25Inclusion Lemma 3
0-2 is in C4 by R4 alternate-thread representative: P_count=0.075513, result=0.373147, spread=0.231324, total=0.285466, BTTS/clean=0.350650, I=0.452771. 0-2 represents the strongest unrepresented spread thread away_by_2_plus with mass 0.2313 >= 0.1400 and beats 1-3 by I=0.452771 > 0.304265.
26Fourth Score Lemma
2-2 is score 4 by R5: spread=0.389749, form=0.527500, I=0.413765, BTTS/clean=0.456967. 2-2 is the best excluded thesis-compatible branch by spread/form/index/BTTS-clean comparator and beats 1-3 by score 4 0.440274 > 0.357450.
27Exclusion Lemma
1-0 has status EXCLUDED_BY_SPREAD_THREAD by R4 spread-order comparison: 1-0 belongs to home_by_1, but R4 selected 0-2 from away_by_2_plus because P_spread(away_by_2_plus)=0.231324 > P_spread(home_by_1)=0.146244.
28Exclusion Lemma
0-0 has status EXCLUDED_BY_TOTAL_THREAD by R1 total gate: 0-0 fails R1 because P(over 1.5)=0.694670 >= 0.640000, so the no-goal cell is removed before branch selection.
29Exclusion Lemma
1-2 has status EXCLUDED_BY_SPREAD_THREAD by R2/R5 spread comparison: 1-2 shares away_by_1 with 0-1 and loses I=0.326606 < 0.426089.
30Exclusion Lemma
2-1 has status EXCLUDED_BY_SPREAD_THREAD by R4 spread-order comparison: 2-1 belongs to home_by_1, but R4 selected 0-2 from away_by_2_plus because P_spread(away_by_2_plus)=0.231324 > P_spread(home_by_1)=0.146244.
31Exclusion Lemma
2-0 has status EXCLUDED_BY_SPREAD_THREAD by R4 spread-order comparison: 2-0 belongs to home_by_2_plus, but R4 selected 0-2 from away_by_2_plus because P_spread(away_by_2_plus)=0.231324 > P_spread(home_by_2_plus)=0.082703.
32Exclusion Lemma
1-3 has status EXCLUDED_BY_SPREAD_THREAD by R2/R5 spread comparison: 1-3 shares away_by_2_plus with 0-2 and loses I=0.304265 < 0.452771.
33Theorem
Under Definitions 1-6, Data 1-10, and Rules R1-R6, the unique disclosed four-score card is C4={1-1, 0-1, 0-2, 2-2}.

Data room

Artifacts for audit.

Audit note

Strength ratings Threshold ledger Realm summaries Thread table Candidate table Proof ledger Prediction lock

Public sources used.