Proof — Verse 1.87

यथाद्यसंख्याग्रहणमुपायः प्रतिपत्तये ।
संख्यान्तराणां भेदेऽपि तथा शब्दान्तरश्रुतिः ॥ ८७ ॥

As the grasp of the first number is a means to the cognition of further numbers even though they differ, so is the hearing of one word a means to the cognition of another.

Endorsed axioms (each cite is verbatim commentary)

• {"kind": "relation", "name": "upaya", "from": "adya_samkhya_grahanam", "to": "samkhya_antara_pratipatti"}“The grasp of adya-samkhya, the first number, is the upaya through which the numbers beyond it — genuinely different items — become cognizable”
• {"kind": "relation", "name": "upaya", "from": "sabdantara_sruti", "to": "sabda_antara_pratipatti"}“hearing one word opens cognitive access to other words not yet heard”
• {"kind": "relation", "name": "hetu", "from": "sabdantara_sruti", "to": "samskara"}“mastering some words confers a capacity for the rest, as mastering early numbers confers the number-series”
• {"kind": "predication", "name": "vivartamana", "of": "sabda_tattva"}“all words are variously-manifested configurations of one underlying word-nature (and ultimately of the one sabda-tattva)”

Rejected readings (refuted by compiled theorems)

• “The means by which one grasps numbers operates only in arithmetic, not in linguistic learning.” — Contradicts the verse's explicit parallelism. The verse states 'so too' (tathā) for words, establishing that the systematic means applies equally to linguistic and numerical domains. Reading it as number-exclusive denies the verse's central argumentative structure.
• “Word-learning and number-learning are completely independent intellectual capacities with no systematic connection.” — Contradicts the verse's yathā-tathā (as...so) structure, which establishes an explicit systematic analogy. The commentary emphasizes that 'mastering some words confers a capacity for the rest, as mastering early numbers confers the number-series,' showing they share a unified structure of acquisition. Treating them as isolated denies this systematic unity.

Lean module

/- Verse 1.87 — generated from data/contracts/1.87.json. DO NOT EDIT.
   Axiom cites are verbatim commentary quotations, validated by
   tests/test_contracts.py. -/
import VakyaVallari.Adequacy

namespace VakyaVallari.Verses.V1_87

open VakyaVallari

def adya_samkhya_grahanam : Entity := ⟨"ādya-saṃkhyā-grahaṇam", Sorta.cognition⟩
def samkhya_antara_pratipatti : Entity := ⟨"saṃkhyāntara-pratipatti", Sorta.cognition⟩
def sabdantara_sruti : Entity := ⟨"śabdāntara-śruti", Sorta.power⟩
def sabda_antara_pratipatti : Entity := ⟨"śabda-antara-pratipatti", Sorta.cognition⟩
def upaya : Entity := ⟨"upāya", Sorta.power⟩
def sabda_tattva : Entity := ⟨"śabda-tattva", Sorta.absolute⟩
def samskara : Entity := ⟨"saṃskāra", Sorta.power⟩

def contract : Contract :=
  { axioms := [ Claim.relation "upaya" (Node.ent adya_samkhya_grahanam) (Node.ent samkhya_antara_pratipatti)
    , Claim.relation "upaya" (Node.ent sabdantara_sruti) (Node.ent sabda_antara_pratipatti)
    , Claim.relation "hetu" (Node.ent sabdantara_sruti) (Node.ent samskara)
    , Claim.predication "vivartamana" sabda_tattva ]
  , denials := []
  , reported := [] }

def accepted : Reading :=
  { claims := [ Claim.relation "upaya" (Node.ent adya_samkhya_grahanam) (Node.ent samkhya_antara_pratipatti)
    , Claim.relation "upaya" (Node.ent sabdantara_sruti) (Node.ent sabda_antara_pratipatti) ] }

theorem accepted_adequate : contract.Adequate accepted := by decide

namespace Counterexamples

/- 'The means by which one grasps numbers operates only in arithmetic, not in linguistic learning.'
   Why rejected: Contradicts the verse's explicit parallelism. The verse states 'so too' (tathā) for words, establishing that the systematic means applies equally to linguistic and numerical domains. Reading it as number-exclusive denies the verse's central argumentative structure. -/
def exclusive_arithmetic : Reading :=
  { claims := [ Claim.predication "arithmetic_only" upaya ] }
theorem exclusive_arithmetic_inadequate : ¬ contract.Adequate exclusive_arithmetic := by decide
#guard contract.licenses exclusive_arithmetic = false

/- 'Word-learning and number-learning are completely independent intellectual capacities with no systematic connection.'
   Why rejected: Contradicts the verse's yathā-tathā (as...so) structure, which establishes an explicit systematic analogy. The commentary emphasizes that 'mastering some words confers a capacity for the rest, as mastering early numbers confers the number-series,' showing they share a unified structure of acquisition. Treating them as isolated denies this systematic unity. -/
def independent_competences : Reading :=
  { claims := [ Claim.predication "systematically_isolated" upaya ] }
theorem independent_competences_inadequate : ¬ contract.Adequate independent_competences := by decide
#guard contract.licenses independent_competences = false

end Counterexamples

end VakyaVallari.Verses.V1_87