MathOS Registry — Binds v0.1 (Prereq Edges • Confusion Edges • Method Edges)Version: v0.1 (LOCK)

“`yaml id=”b8r2qm”
PAGE_START
PageID: EDUKATE::MATHOS::REG_BINDS_01
Slug: /mathos-registry-binds-v0-1/
Title: MathOS Registry — Binds v0.1 (Prereq Edges • Confusion Edges • Method Edges)
Version: v0.1 (LOCK)
Parent: /mathos-runtime-control-tower-v0-1/
Intent:

  • Provide the Bind graph that makes MathOS machine-runnable
  • 3 edge types:
    PREREQ (capability dependency)
    CONFUSE (common misbinding / misconception)
    METHOD (canonical corridor edge)
  • Each bind is a record with stable ID; never renamed
    GrammarLock:
    Place×Lane×Zoom×Role×Type×ID
    Lane: MATH

============================================================

BLOCK_01_DEFINITION_LOCK
Bind :=
a directed edge between nodes (ConceptNodes or SkillNodes) with a declared type and meaning.

BindTypes:
PREREQ:
NodeA required before NodeB is stable
CONFUSE:
NodeA is often mistaken for NodeB OR a misconception link
METHOD:
NodeA uses MethodCorridor to reach NodeB or solve NodeB family

BindContract:

  • BindIDs are immutable
  • New binds are appended; never delete, only deprecate with flag
  • Every bind includes:
    from_node
    to_node
    type
    rationale
    detection signature (optional)
    repair corridor (optional)

============================================================

REGISTRY::BINDS (CORE SET v0.1)

# PREREQ BINDS (Skill chain)

BIND_START
BindID: EDUKATE::MATHOS::BIND::PREREQ_001
type: PREREQ
from_node: EDUKATE::MATHOS::SKILL::SML_01
to_node: EDUKATE::MATHOS::SKILL::EQ_01
rationale:

  • equivalence cannot be preserved if symbol meaning is unstable
    repair_corridor:
  • RC_002

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::PREREQ_002
type: PREREQ
from_node: EDUKATE::MATHOS::SKILL::EQ_01
to_node: EDUKATE::MATHOS::SKILL::TR_01
rationale:

  • transfer requires stable legal moves across skins
    repair_corridor:
  • RC_003

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::PREREQ_003
type: PREREQ
from_node: EDUKATE::MATHOS::SKILL::TR_01
to_node: EDUKATE::MATHOS::SKILL::LS_01
rationale:

  • timing stability only makes sense after transfer is stable; otherwise LS spikes
    repair_corridor:
  • RC_004 then RC_009

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::PREREQ_004
type: PREREQ
from_node: EDUKATE::MATHOS::SKILL::ORA_01
to_node: EDUKATE::MATHOS::SKILL::ARCH_VALID_01
rationale:

  • Architect corridors require Oracle audit to avoid novelty noise
    repair_corridor:
  • RC_007

BIND_END

# PREREQ BINDS (Concept chain)

BIND_START
BindID: EDUKATE::MATHOS::BIND::PREREQ_101
type: PREREQ
from_node: EDUKATE::MATHOS::CONCEPT::NUM_QUANTITY_01
to_node: EDUKATE::MATHOS::CONCEPT::ARITHMETIC_OPS_01
rationale:

  • operations require magnitude sense and units intuition

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::PREREQ_102
type: PREREQ
from_node: EDUKATE::MATHOS::CONCEPT::ARITHMETIC_OPS_01
to_node: EDUKATE::MATHOS::CONCEPT::EQUIVALENCE_REWRITE_01
rationale:

  • algebra rewrites depend on stable arithmetic and representation conversion

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::PREREQ_103
type: PREREQ
from_node: EDUKATE::MATHOS::CONCEPT::EQUIVALENCE_REWRITE_01
to_node: EDUKATE::MATHOS::CONCEPT::EQUATIONS_LINEAR_01
rationale:

  • linear solving is a specific corridor built on equivalence rewrites

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::PREREQ_104
type: PREREQ
from_node: EDUKATE::MATHOS::CONCEPT::EQUATIONS_LINEAR_01
to_node: EDUKATE::MATHOS::CONCEPT::FUNCTIONS_01
rationale:

  • function notation and evaluation depends on equation/variable discipline

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::PREREQ_105
type: PREREQ
from_node: EDUKATE::MATHOS::CONCEPT::FUNCTIONS_01
to_node: EDUKATE::MATHOS::CONCEPT::GRAPHS_MODELS_01
rationale:

  • graphs are function representations; models require mapping variables to axes

BIND_END

# CONFUSION BINDS (misbindings to guard)

BIND_START
BindID: EDUKATE::MATHOS::BIND::CONFUSE_201
type: CONFUSE
from_node: EDUKATE::MATHOS::CONCEPT::ARITHMETIC_OPS_01
to_node: EDUKATE::MATHOS::CONCEPT::EQUIVALENCE_REWRITE_01
rationale:

  • students treat algebra rewrites like “do anything to move terms” (illegal move risk)
    detection_signature:
  • illegal cancellation; moving terms without equivalence
    repair_corridor:
  • RC_003

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::CONFUSE_202
type: CONFUSE
from_node: EDUKATE::MATHOS::SKILL::TR_01
to_node: EDUKATE::MATHOS::SKILL::LS_01
rationale:

  • students think timing practice creates transfer; it usually amplifies collapse if TR is weak
    detection_signature:
  • LS spikes while TR < 0.7
    repair_corridor:
  • RC_004 then RC_009

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::CONFUSE_203
type: CONFUSE
from_node: EDUKATE::MATHOS::SKILL::ORA_01
to_node: EDUKATE::MATHOS::SKILL::E4_EXECUTION_SLIP # NOTE: reserved alias; see error registry
rationale:

  • students confuse “checking” with “redoing everything”; checks must be fast invariants
    detection_signature:
  • checking takes too long; increases time bleed
    repair_corridor:
  • RC_007 + RC_008

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::CONFUSE_204
type: CONFUSE
from_node: EDUKATE::MATHOS::CONCEPT::PROBABILITY_EXPECTATION_01
to_node: EDUKATE::MATHOS::CONCEPT::ARITHMETIC_OPS_01
rationale:

  • students treat probability as arithmetic without meaning lock (events/sample space)
    detection_signature:
  • answers >1 or negative probabilities; wrong base events
    repair_corridor:
  • RC_002 + MF rebuild (future probability corridor)

BIND_END

# METHOD BINDS (corridor edges; placeholder IDs link to method registry later)

BIND_START
BindID: EDUKATE::MATHOS::BIND::METHOD_301
type: METHOD
from_node: EDUKATE::MATHOS::CONCEPT::EQUATIONS_LINEAR_01
to_node: EDUKATE::MATHOS::SKILL::TR_01
rationale:

  • linear family is best trained via 3-skin packs (structure invariant)
    linked_method_corridor:
    EDUKATE::MATHOS::METHOD::LINEAR_ISOLATE_01 # to be defined in method registry
    linked_transfer_pack:
    EDUKATE::MATHOS::TPACK::LINEAR_FAMILY_01 # to be defined in transfer packs registry

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::METHOD_302
type: METHOD
from_node: EDUKATE::MATHOS::CONCEPT::GRAPHS_MODELS_01
to_node: EDUKATE::MATHOS::SKILL::MF_01
rationale:

  • modeling tasks demand variable/units mapping and representation choice
    linked_method_corridor:
    EDUKATE::MATHOS::METHOD::MODEL_Y_MX_C_01

BIND_END

BIND_START
BindID: EDUKATE::MATHOS::BIND::METHOD_303
type: METHOD
from_node: EDUKATE::MATHOS::CONCEPT::SIMULATION_STATE_TRANSITION_01
to_node: EDUKATE::MATHOS::CONCEPT::OPTIMIZATION_CONSTRAINTS_01
rationale:

  • simulation templates require explicit objective/constraints to evaluate policies
    linked_method_corridor:
    EDUKATE::MATHOS::METHOD::SIM_TEMPLATE_01

BIND_END

============================================================

BLOCK_02_BIND HEALTH CHECKS (runtime diagnostics)
BindHealth:

  • If PREREQ violated (timing before transfer):
    expect LS spikes + panic patterns
  • If CONFUSE edges fire frequently:
    publish a clinic satellite page and link repair corridor
  • If METHOD edges missing:
    add method corridor registry records (next step)

============================================================

KNOWN_ISSUE (v0.1 placeholder)
Issue_001:
Bind CONFUSE_203 references a reserved alias “E4_EXECUTION_SLIP” as a skill node.
Correction plan:
– keep bind ID, update to reference ErrorTaxonomy E4 record only in v0.2
– do not rename bind.

============================================================

RELATED_PAGES
Links:

  • /mathos-runtime-control-tower-v0-1/
  • /mathos-registry-concept-nodes-v0-1/
  • /mathos-registry-skill-nodes-v0-1/
  • /mathos-registry-error-taxonomy-v0-1/
  • /mathos-sensors-pack-v0-1/
  • /mathos-fenceos-threshold-table-v0-1/
  • /mathos-data-adapter-spec-v0-1/

NEXT_OUTPUT (if you say “Next”)
PageID: EDUKATE::MATHOS::REG_METHODS_01
slug: /mathos-registry-method-corridors-v0-1/
(canonical method corridors as records: LINEAR_ISOLATE, FACTOR_ZERO, RATIO_TABLE, etc.)

PAGE_END
“`

Start Here For Mathematics OS Articles:

Start Here for Lattice Infrastructure Connectors

eduKateSG Learning Systems: