Proof — Verse 1.59

वृद्धयादयो यथा शब्दाः स्वरूपोपनिबन्धनाः ।
आदैच्प्रत्यायितैः शब्दैः संबन्धं यान्ति संज्ञिभिः ॥ ५९ ॥

Words such as 'vrddhi', founded upon their own form, enter into relation with the words conveyed by 'at' and 'aic' as the things they name.

Endorsed axioms (each cite is verbatim commentary)

• {"kind": "relation", "name": "upanibandhana", "from": "vrddhi", "to": "svarupa"}“the word 'vrddhi' in that rule stands sva-rupa-upanibandhana, resting on its own form (this is Panini's own meta-rule svam rupam sabdasya, 1.1.68: a word in grammar denotes its own form unless it is a technical name)”
• {"kind": "relation", "name": "samjna", "from": "vrddhi", "to": "vowels"}“it relates as samjna, name, to the samjnins, the named items that 'adaic' conveys”
• {"kind": "relation", "name": "pratyayita", "from": "adaic", "to": "vowels"}“the vowels a, ai, au — given in the rule by the pratyahara 'adaic'”

Denials

• {"kind": "relation", "name": "samjna", "from": "vowels", "to": "vrddhi"}“it relates as samjna, name, to the samjnins, the named items that 'adaic' conveys”

Rejected readings (refuted by compiled theorems)

• “The term 'vrddhi' in Pāṇini's grammar denotes the process of vowel-lengthening itself, not the vowels a, ai, au.” — This misidentifies what vrddhi refers to. The commentary makes clear that vrddhi is the saṃjñā (name) for the vowels themselves: 'the vowels a, ai, au — given in the rule by the pratyahara adaic'. Vrddhi relates as a name to the named vowels, not to the process of lengthening.
• “The vowels a, ai, and au are the names that denote the technical term vrddhi.” — This reverses the saṃjñā (naming) relation. The commentary explicitly states 'it relates as samjna, name, to the samjnins, the named items' — vrddhi is the name (saṃjñā) and the vowels are what is named (saṃjñins). This reversed direction contradicts the verse's claim.
• “The term 'vrddhi' is simply another name for the pratyāhāra 'ādaic', both referring identically to the designation of vowels.” — This conflates two distinct linguistic roles. Vrddhi is the technical NAME (saṃjñā) that designates the vowels, while ādaic is the ABBREVIATION (pratyāhāra) mechanism that conveys them. The commentary distinguishes them: 'it relates as samjna, name, to the samjnins, the named items that adaic conveys.' They are related but not identical.

Lean module

/- Verse 1.59 — generated from data/contracts/1.59.json. DO NOT EDIT.
   Axiom cites are verbatim commentary quotations, validated by
   tests/test_contracts.py. -/
import VakyaVallari.Adequacy

namespace VakyaVallari.Verses.V1_59

open VakyaVallari

def vrddhi : Entity := ⟨"vṛddhi", Sorta.linguisticItem⟩
def svarupa : Entity := ⟨"svarūpa", Sorta.property⟩
def adaic : Entity := ⟨"ādaic", Sorta.linguisticItem⟩
def vowels : Entity := ⟨"the vowels (a, ai, au)", Sorta.linguisticItem⟩

def contract : Contract :=
  { axioms := [ Claim.relation "upanibandhana" (Node.ent vrddhi) (Node.ent svarupa)
    , Claim.relation "samjna" (Node.ent vrddhi) (Node.ent vowels)
    , Claim.relation "pratyayita" (Node.ent adaic) (Node.ent vowels) ]
  , denials := [ Claim.relation "samjna" (Node.ent vowels) (Node.ent vrddhi) ]
  , reported := [] }

def accepted : Reading :=
  { claims := [ Claim.relation "upanibandhana" (Node.ent vrddhi) (Node.ent svarupa)
    , Claim.relation "samjna" (Node.ent vrddhi) (Node.ent vowels) ] }

theorem accepted_adequate : contract.Adequate accepted := by decide

namespace Counterexamples

/- "The term 'vrddhi' in Pāṇini's grammar denotes the process of vowel-lengthening itself, not the vowels a, ai, au."
   Why rejected: This misidentifies what vrddhi refers to. The commentary makes clear that vrddhi is the saṃjñā (name) for the vowels themselves: 'the vowels a, ai, au — given in the rule by the pratyahara adaic'. Vrddhi relates as a name to the named vowels, not to the process of lengthening. -/
def lengthening_process : Entity := ⟨"vowel lengthening", Sorta.power⟩
def process_referent : Reading :=
  { claims := [ Claim.relation "samjna" (Node.ent vrddhi) (Node.ent lengthening_process) ] }
theorem process_referent_inadequate : ¬ contract.Adequate process_referent := by decide
#guard contract.licenses process_referent = false

/- 'The vowels a, ai, and au are the names that denote the technical term vrddhi.'
   Why rejected: This reverses the saṃjñā (naming) relation. The commentary explicitly states 'it relates as samjna, name, to the samjnins, the named items' — vrddhi is the name (saṃjñā) and the vowels are what is named (saṃjñins). This reversed direction contradicts the verse's claim. -/
def reversed_naming : Reading :=
  { claims := [ Claim.relation "samjna" (Node.ent vowels) (Node.ent vrddhi) ] }
theorem reversed_naming_inadequate : ¬ contract.Adequate reversed_naming := by decide
#guard contract.contradicts reversed_naming = true

/- "The term 'vrddhi' is simply another name for the pratyāhāra 'ādaic', both referring identically to the designation of vowels."
   Why rejected: This conflates two distinct linguistic roles. Vrddhi is the technical NAME (saṃjñā) that designates the vowels, while ādaic is the ABBREVIATION (pratyāhāra) mechanism that conveys them. The commentary distinguishes them: 'it relates as samjna, name, to the samjnins, the named items that adaic conveys.' They are related but not identical. -/
def merged_terms : Reading :=
  { claims := [ Claim.identity vrddhi adaic ] }
theorem merged_terms_inadequate : ¬ contract.Adequate merged_terms := by decide
#guard contract.licenses merged_terms = false

end Counterexamples

end VakyaVallari.Verses.V1_59