12-Week Math Architect Training Program for AVOO to P3

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PageID: EDUKATE::MATHOS::AVOO_TRAINPACK_01
Slug: /math-architect-training-pack-12-week/
Title: Math Architect Training Pack (12 Weeks) — AVOO to P3 (Genius-Adjacent Corridor Training)
ParentHubs:

/avoo-mathematics-role-lattice/
/how-mathematics-works/
Version: v0.1 (LOCK)
Intent:
Provide: a repeatable 12-week training program for AVOO
Outcome: P2 stability for most; P3 Architect corridor behavior for top track
Controls: sandbox windows + rho (symmetry budget) to avoid collapse
TokenLock:
AVOO
transfer
interleaving
retrieval practice + feedback
worked examples
sandbox windows
CivOSOverlaysAllowed:
BOX_SANDBOX_CONTROL
BOX_NEG_VOID
SENSOR_PANEL_TRAINPACK

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BLOCK_01_QUICK_ANSWER (AboveTheFold; PAA-ready)
Answer_70_110w:
This is a 12-week Math Architect training program using the AVOO lattice (Operator, Oracle, Visionary, Architect). Weeks 1–4 build P2 stability (meaning-lock, equivalence, transfer, timed reliability). Weeks 5–8 train Oracle (validity audit) and Visionary (representation/model selection). Weeks 9–12 train Architect corridors (representation invention, invariants, reduction, duality, generalize→specialize) inside sandbox windows so exploration doesn’t collapse the base. Promotion is gate-based: Validity + Reuse + Transfer + rho safe band.
Bullets:

Build: P2 under load (transfer + timed stability)
Harden: Oracle + Visionary (truth + model choice)
Expand: Architect corridors (P3) with sandbox control
SeeAlso:
/avoo-mathematics-role-lattice/
/math-truncation-and-stitching-recovery-protocol/

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BLOCK_02_DEFINITION_LOCK (No drift)
AVOO:
Operator := executes correctly under load
Oracle := validates (find-first-illegal-step + counterexample habit)
Visionary:= selects representation/model/route
Architect:= creates new corridors (new representation/invariant/reduction/generalization)

P-levels:
P0 panic/guess
P1 template-only
P2 transfer-stable
P3 builder/corridor generator

Architect corridor families (C1–C5):
C1 Representation-Invention
C2 Invariant-Hunting
C3 Reduction/Compression
C4 Duality/Symmetry-Flips
C5 Generalize-Then-Specialize

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BOX_SANDBOX_CONTROL (critical safety mechanism)
SandboxControl:

80% Exploit (Operator/Oracle/Visionary stability)
20% Explore (Architect sandbox)
rho := ChoiceInjected / SymmetryCapacity
Fence:
if (rho high) OR (LS spikes) OR (SML drops) -> TRUNCATE exploration -> STITCH base binds
Rule:
Genius-adjacent training is NOT “harder problems”.
It is “corridor generation under audit” with rho kept safe.

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BLOCK_03_INPUTS (what student needs)
Inputs:

notebook (error log + corridor log)
timer
answer key source (textbook/teacher solution)
weekly mixed set (10–15 Q)
3-skin transfer packs (per topic)
worked examples for each broken step

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BLOCK_04_CORE METRICS (what we measure weekly)
Metrics:
TR (TransferRate):
– 3-skin pack correct/3
LS (LoadShear):
– timed accuracy / untimed accuracy ratio
SML (MeaningLock):
– can explain symbols/units in 10s
ORA (OracleHabit):
– first illegal step detection + sanity check presence
CHOICE (StrategySelection):
– can label structure before solving
NoveltyRate (Architect):
– # corridor attempts/session
ValidityRate (Architect):
– % corridor attempts that pass Oracle audit
ReuseScore (Architect):
– corridor works on 3 variants
CompressionGain (Architect):
– steps saved vs baseline method
rho (SymmetryBudget):
– choice intensity / capacity

Targets:

P2 target: TR >= 0.7, LS stable, SML stable
P3 Architect target: ValidityRate high + ReuseScore high + rho safe

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BLOCK_05_DAILY SCHEDULE (30 minutes/day; 5 days/week)
Daily_30min:
0-2 min: Meaning line (SML) + structure tag (CHOICE)
2-15 min: Core set (6 Q) (no solver)
15-20 min: Feedback check + mark FD (first divergence)
20-25 min: Repair rule (1 sentence) + re-attempt 1 Q (retrieval)
25-30 min: 1 skin-change variant (transfer)

Rules:

Solver only allowed after attempt (feedback stage)
If LS high -> remove timer; rebuild SML/EQ first
SeeAlso:
/math-fenceos-stop-loss-for-exam-mistakes/
/math-worksheets/

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BLOCK_06_WEEKLY STRUCTURE (1 cycle)
Weekly_Cycle:
Day1: Skill acquisition (worked example -> near copies -> independent)
Day2: Retrieval + feedback (same skill)
Day3: Transfer (3-skin pack)
Day4: Interleaved mixed set (3 types; strategy choice)
Day5: Mild timed re-entry (only if TR>=0.7)

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BLOCK_07_12-WEEK PLAN (the actual pack)

WEEKS_1_4 (Operator P2 Stabilization)
Goal:

build SML + EQ + TR + LS baseline
eliminate P1 template illusion
Week1: SML + Parsing stability
meaning line every question
bracket/precedence drills
end of week: TR test pack A
Week2: EQ (equivalence discipline)
rewrite forms; simplify/factor/expand; solve linear
end: TR test pack B
Week3: Transfer via 3-skin packs
2 packs/day (structure labels enforced)
end: TR target >= 0.7
Week4: Load stability ladder entry
Level1 timing only if TR>=0.7
end: LS stable + FENCEOS habits

Gate_W4_Promote:

TR >= 0.7
SML stable (10s meaning test passes)
ORA basic check used on >=70% questions

WEEKS_5_8 (Oracle + Visionary Upgrade)
Goal:

Oracle: validity audit becomes automatic
Visionary: representation and method-choice becomes automatic
Week5: Oracle Bootcamp
“find first illegal step” drills (5/day)
counterexample habit (2/day)
mandatory sanity check per question
Week6: Proof-lite & Justification
explain each step rule (1 sentence)
rewrite-based reasoning (equivalence justification)
Week7: Visionary Representation Drills
choose representation (table/diagram/equation/graph)
choose method from 3 cards before solving
Week8: Mixed Interleaved Sets (exam realism)
interleaving: ABCABC (3 types)
timed ladder Level2 allowed if LS stable

Gate_W8_Promote:

ORA strong (FD detection > 70%)
CHOICE strong (structure tag correct > 70%)
TR stable across 2 different structure families

WEEKS_9_12 (Architect Sandbox — Corridor Generator to P3)
Goal:

generate new corridors that pass audit and generalize
SandboxRatio:
80% exploit (standard practice)
20% explore (Architect tasks) Week9: C1 Representation-Invention Task:
- generate 3 representations for same problem family
- pick best by simplicity + generality
  Output:
- corridor template + conditions
  Week10: C2 Invariant-Hunting
  Task:
- propose 2 invariants/lemmas
- test on 3 variants
  Output:
- invariant statement + proof sketch
  Week11: C3 Reduction/Compression
  Task:
- map problem family -> simpler known family
- measure CompressionGain
  Output:
- reduction mapping + proof of correctness
  Week12: C4/C5 Duality + Generalize-Then-Specialize
  Task:
- flip viewpoint (direct/contrapositive, primal/dual, symmetry)
- generalize statement, prove, specialize back
  Output:
- reusable theorem template + example set

Gate_W12_P3_Architect:

ValidityRate high (Oracle audit passes)
ReuseScore high (works on 3 skins)
rho safe band maintained
LS does not spike during exploration weeks

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BLOCK_08_ARCHITECT TASK TEMPLATE (copy/paste daily)
Architect_Task_Template:
Step1: Generate 3 representations (R1,R2,R3)
Step2: Propose 2 invariants/lemmas (I1,I2)
Step3: Attempt 1 reduction mapping (Red1)
Step4: Produce proof-plan (lemmas + dependencies)
Step5: Test on 3 skin-changed variants (V1,V2,V3)
Step6: Oracle audit:
– locate first gap
– counterexample attempt
Step7: Finalize corridor:
– state conditions where it works
– compute CompressionGain
– compute ReuseScore

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BLOCK_09_PROMOTION TESTS (weekly; 20 minutes)
Weekly_Test:

TR Test: 1 pack (3 skins) -> record TR
LS Test: 6 Q mild timed -> record LS
ORA Test: 2 bug-hunt solutions -> record FD accuracy
CHOICE Test: label structure for 6 mixed Q before solving

PromotionRules:

If TR < 0.4 -> immediate Stitch protocol (no timing, no sandbox)
If LS spikes -> drop one timing level
If ORA weak -> add 10 min/day bug-hunt for next week
SeeAlso:
/math-transfer-test-same-structure-different-skin/
/math-phase-slip-why-students-panic/

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BLOCK_10_THE “NO GENIUS COLLAPSE” RULESET (safety)
SafetyRules:
SR1: No sandbox if TR < 0.7 SR2: No sandbox if LS unstable SR3: No sandbox if SML low SR4: Oracle audit required for every corridor claim SR5: If rho high -> reduce choices; return to exploitation week
SR6: Every new corridor must pass 3-variant reuse test

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BOX_NEG_VOID (Google-style: what goes wrong)
NegativeVoid:

student jumps to “hard problems” without P2 base
exploration increases choice beyond capacity (rho high)
proofs/validity ignored (Oracle absent)
Outcome:
phase slip under load (P2->P0)
false confidence then collapse
FailureTrace:
weak base -> high choice -> wrong corridor -> no audit -> error cascade -> panic -> avoidance

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SENSOR_PANEL_TRAINPACK (FenceOS-lite)
Sensors:
TR, LS, SML, ORA, CHOICE
NoveltyRate, ValidityRate, ReuseScore, CompressionGain, rho
Thresholds:
Fence_Base:
if (TR < 0.4) OR (SML low) -> TRUNCATE timing + sandbox -> stitch base
Fence_Load:
if (LS spikes) -> drop timing level + rebuild checks
Promote_P2:
if (TR >= 0.7) AND (LS stable) AND (ORA present) -> allow mixed timed sets
Promote_P3_Architect:
if (ValidityRate high) AND (ReuseScore high) AND (rho safe) -> expand sandbox

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FAQ_PACK (PAA-ready)

Q1: Can you train “Architect-level” thinking in math?
A_55_85w:
Yes, by training corridor generation, not by merely doing harder questions. Architect training means producing new representations, invariants, reductions, and generalizations that still pass validity audit and work across multiple variants. The program must control exploration with sandbox windows and promotion gates so choice doesn’t exceed capacity and cause phase slip.
Bullets:

Train corridors (representations/invariants/reductions)
Require Oracle audit + 3-variant reuse
Use sandbox control to prevent collapse
SeeAlso: /avoo-mathematics-role-lattice/

Q2: How long does it take to reach P2 or P3?
A_45_80w:
Many students can reach P2 (transfer-stable) within weeks if they train meaning-lock, equivalence, and transfer variants before heavy timing. P3 Architect behavior takes longer and depends on strong Oracle habits (validity) and controlled exploration. This pack uses 12 weeks as a structured ramp with gates—if gates fail, you stitch before proceeding.
Bullets:

P2: stabilize transfer + load first
P3: add corridor tasks only after base is stable
Gates decide pace; not calendar alone
SeeAlso: /math-truncation-and-stitching-recovery-protocol/

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RELATED_PAGES (internal sitelinks)
Links:

/avoo-mathematics-role-lattice/
/how-mathematics-works/
/math-transfer-test-same-structure-different-skin/
/math-fenceos-stop-loss-for-exam-mistakes/
/math-phase-slip-why-students-panic/
/math-truncation-and-stitching-recovery-protocol/
/symmetry-of-mathematics-genesis-selfie/

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Math Architect Training Pack (12 Weeks) — AVOO to P3 (Genius-Adjacent Corridor Training)

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