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BTT-EDUOS-ADDMATH-A0-A1-00 — ADD MATH A0 GATE IMPLEMENTATION NODE

Algebra Integrity Firewall (Code-Only v0.1)

0) METADATA

NODE.ID: BTT-EDUOS-ADDMATH-A0-A1-00
NODE.TYPE: place_implementation_child
PLACE.ID: SG-SGP-BUKITTIMAH
ORG.ID: BTT
PARENT.NODE: BTT-EDUOS-ADDMATH-A1-00
SUBOS: ADDMATHOS
STAGE: A0 (integrity_gate)
PURPOSE: eliminate_algebra_leaks_under_time_pressure_to_prevent_high_coupling_collapse
VERSION: v0.1

1) DEFINITION LOCK

DEF.BTT_ADDMATH_A0:
  A0 is the mandatory integrity gate for Add Math. BTT implements an algebra firewall
  that drives sign/term conservation, identity anchoring, and proof-like microchecks
  so small leaks cannot amplify into total collapse in long chains.

2) ENTRY CONDITIONS (WHEN THIS NODE IS ACTIVATED)

ENTRY:
  - algebra_leak_rate_under_pressure > threshold
  OR
  - repeated_sign_term_errors persist
  OR
  - student can follow worked solutions but fails independently
EXIT:
  - leak_rate -> near_zero under timed conditions
  - chain_integrity stable across variants

3) DOMINANT FAILURE MODES (A0)

FAIL.A0:
  A1: algebra_leak_amplification
  A7: verification_absence
  A8: time_pressure_chain_collapse

4) PROTOCOL SET (A0 FIREWALL)

PROTO.A0.1: sign_tracking (explicit negative markers)
PROTO.A0.2: term_conservation_check (no term disappears)
PROTO.A0.3: identity_anchoring (always reference canonical forms)
PROTO.A0.4: substitution_sanity_check (spot impossible results)
PROTO.A0.5: checkpoint_microchecks (after each high-risk transform)
PROTO.A0.6: timed_chain_drills (speed + accuracy)
PROTO.A0.7: spaced_retrieval_lock (BIOOS consolidation)

5) SENSOR TARGETS (A0)

SENSOR.A0.S1: sign_error_rate -> near_zero
SENSOR.A0.S2: term_loss_rate -> near_zero
SENSOR.A0.S3: transformation_accuracy -> high
SENSOR.A0.S4: microcheck_frequency -> stable
SENSOR.A0.S5: time_to_first_step -> low
SENSOR.A0.S6: variance_under_time -> low
SENSOR.A0.S7: retention_7d_14d -> stable

6) LOCK

LOCK:
  No A0 integrity, no Add Math.
  BTT enforces the algebra firewall until leaks are near zero under time pressure.

BTT-EDUOS-ADDMATH-A1-A1-00 — FUNCTION SYSTEMS IMPLEMENTATION NODE

Function Thinking + Composition/Inverse Protocol (Code-Only v0.1)

0) METADATA

NODE.ID: BTT-EDUOS-ADDMATH-A1-A1-00
NODE.TYPE: place_implementation_child
PLACE.ID: SG-SGP-BUKITTIMAH
ORG.ID: BTT
PARENT.NODE: BTT-EDUOS-ADDMATH-A1-00
SUBOS: ADDMATHOS
STAGE: A1 (functions)
PURPOSE: stabilise_function_thinking_composition_inverses_domain_range_and_mapping_accuracy
VERSION: v0.1

1) DEFINITION LOCK

DEF.BTT_ADDMATH_A1:
  Add Math functions are the modelling backbone. BTT implements a function-system protocol
  (mapping, composition, inverse validity, domain/range discipline) so students can move
  between forms without confusion and transfer to exam variants reliably.

2) DOMINANT FAILURE MODES (A1)

FAIL.A1:
  A3: function_system_misalignment
  A2: structure_blindness
  A7: verification_absence

3) PROTOCOL SET (FUNCTION SYSTEMS)

PROTO.A1.1: mapping_protocol (input->process->output)
PROTO.A1.2: domain_range_discipline (validity checks)
PROTO.A1.3: composition_template (f(g(x)) step rules)
PROTO.A1.4: inverse_validity_protocol (one-to-one + restrictions)
PROTO.A1.5: representation_switching (table<->graph<->equation)
PROTO.A1.6: verification_microchecks (plug-in tests)
PROTO.A1.7: interleaved_variants (transfer training)
PROTO.A1.8: spaced_retrieval_lock (BIOOS)

4) SENSOR TARGETS (A1)

SENSOR.A1.S1: composition_accuracy -> high
SENSOR.A1.S2: inverse_validity_accuracy -> high
SENSOR.A1.S3: domain_range_error_rate -> low
SENSOR.A1.S4: structure_recognition_latency -> low
SENSOR.A1.S5: transfer_to_variants -> high
SENSOR.A1.S6: retention_7d_14d -> stable

5) LOCK

LOCK:
  Function systems require discipline: mapping + validity + templates.
  BTT trains transfer by forcing correct domain/range and inverse checks under time.

BTT-EDUOS-ADDMATH-A2-A1-00 — LOGS/INDICES IMPLEMENTATION NODE

Growth/Decay Structure + Transform Templates (Code-Only v0.1)

0) METADATA

NODE.ID: BTT-EDUOS-ADDMATH-A2-A1-00
NODE.TYPE: place_implementation_child
PLACE.ID: SG-SGP-BUKITTIMAH
ORG.ID: BTT
PARENT.NODE: BTT-EDUOS-ADDMATH-A1-00
SUBOS: ADDMATHOS
STAGE: A2 (logs_indices)
PURPOSE: enforce_identity_templates_and_structure_recognition_for_exponential_logarithmic_modelling
VERSION: v0.1

1) DEFINITION LOCK

DEF.BTT_ADDMATH_A2:
  Logs/indices are structure-heavy and leak-sensitive. BTT implements identity-template
  libraries and transformation discipline to prevent freestyle manipulation and ensure
  modelling readiness for growth/decay questions.

2) DOMINANT FAILURE MODES (A2)

FAIL.A2:
  A4: transformation_errors
  A2: structure_blindness
  A1: algebra_leak_amplification

3) PROTOCOL SET (LOGS/INDICES)

PROTO.A2.1: identity_template_library (canonical forms)
PROTO.A2.2: transform_sequence_rules (no freestyle reorder)
PROTO.A2.3: base_tracking (keep base consistent)
PROTO.A2.4: restriction_checks (domain/validity)
PROTO.A2.5: substitution_sanity (spot impossible outputs)
PROTO.A2.6: mixed_variants (transfer training)
PROTO.A2.7: spaced_retrieval_lock (BIOOS)

4) SENSOR TARGETS (A2)

SENSOR.A2.S1: identity_application_accuracy -> high
SENSOR.A2.S2: base_tracking_error_rate -> low
SENSOR.A2.S3: transform_sequence_integrity -> high
SENSOR.A2.S4: restriction_check_rate -> stable
SENSOR.A2.S5: transfer_to_variants -> high
SENSOR.A2.S6: retention_7d_14d -> stable

5) LOCK

LOCK:
  Logs/indices succeed by template discipline.
  BTT prevents freestyle manipulation and forces structure recognition + validity checks.

BTT-EDUOS-ADDMATH-A3-A1-00 — TRIGONOMETRY STRUCTURE IMPLEMENTATION NODE

Periodic Modelling + Identity Discipline (Code-Only v0.1)

0) METADATA

NODE.ID: BTT-EDUOS-ADDMATH-A3-A1-00
NODE.TYPE: place_implementation_child
PLACE.ID: SG-SGP-BUKITTIMAH
ORG.ID: BTT
PARENT.NODE: BTT-EDUOS-ADDMATH-A1-00
SUBOS: ADDMATHOS
STAGE: A3 (trig_structure)
PURPOSE: stabilise_trig_identities_equations_and_periodic_modelling_with_transfer_to_variants
VERSION: v0.1

1) DEFINITION LOCK

DEF.BTT_ADDMATH_A3:
  Trigonometry is periodic structure plus identity discipline. BTT trains students to
  recognize trig families, apply identity templates correctly, and solve equations with
  domain/range awareness, maintaining accuracy under long chains.

2) DOMINANT FAILURE MODES (A3)

FAIL.A3:
  A4: identity_transformation_errors
  A2: structure_blindness
  A1: algebra_leak_amplification

3) PROTOCOL SET (TRIG STRUCTURE)

PROTO.A3.1: trig_family_classifier (equations/identities/graphs)
PROTO.A3.2: identity_template_library (canonical conversions)
PROTO.A3.3: domain_range_solution_protocol (principal + general solutions)
PROTO.A3.4: restriction_checks (validity, extraneous solutions)
PROTO.A3.5: microcheckpoints (after identity steps)
PROTO.A3.6: variation_wrappers (transfer training)
PROTO.A3.7: spaced_retrieval_lock (BIOOS)

4) SENSOR TARGETS (A3)

SENSOR.A3.S1: identity_accuracy -> high
SENSOR.A3.S2: general_solution_accuracy -> high
SENSOR.A3.S3: extraneous_solution_rate -> low
SENSOR.A3.S4: structure_recognition_latency -> low
SENSOR.A3.S5: transfer_to_variants -> high
SENSOR.A3.S6: retention_7d_14d -> stable

5) LOCK

LOCK:
  Trig success = structure recognition + identity discipline + validity checks.
  BTT trains general solutions and prevents extraneous answers under exam pressure.

Start Here:

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