Proof — Verse 1.45

आत्मभेदस्तयोः केचिदस्तीत्याहुः पुराणगाः ।
बुद्धिभेदादभिन्नस्य भेदमेके प्रचक्षते ॥ ४५ ॥

Some who follow the ancient way say there is a difference of essence between the two; others declare that the difference of what is in fact undivided arises from a difference in cognition.

Endorsed axioms (each cite is verbatim commentary)

• {"kind": "predication", "name": "abhinna", "of": "sphota"}“The eke, the others, hold that the sphota is abhinna, undivided, and that duality is buddhibheda-ja, born of a difference in the apprehending cognition”
• {"kind": "relation", "name": "buddhibheda", "from": "sabda", "to": "sphota"}“The eke, the others, hold that the sphota is abhinna, undivided, and that duality is buddhibheda-ja, born of a difference in the apprehending cognition”
• {"kind": "predication", "name": "vivarta_compatible", "of": "sphota"}“The second position is the one that coheres with the vivarta metaphysics of 1.1-2, where all plurality is appearance riding on the one”

Denials

• {"kind": "relation", "name": "atmabheda", "from": "sabda", "to": "sphota"}“The puranagas, followers of the old doctrine, hold atmabheda: sound and sphota are two in essence, really distinct items.”

Rejected readings (refuted by compiled theorems)

• “Sound and sphota are fundamentally different entities in essence.” — The commentary attributes atmabheda to puranagas but the endorsed position (buddhibheda) contradicts this. The verse makes clear that sphota is abhinna with only cognitive difference, not essential difference.
• “Sphota is merely a manifestation or appearance of sound itself.” — The commentary emphasizes sphota as abhinna (undivided/independent), suggesting it transcends or equals sound ontologically, not as a derivative manifestation. Treating it as a manifestation demotes its status incorrectly.
• “Sound and sphota are identical without any cognitive difference whatsoever.” — The verse explicitly states that difference arises from cognitive variation (buddhibheda). Asserting identity without cognitive differentiation contradicts the buddhibheda relation.

Lean module

/- Verse 1.45 — generated from data/contracts/1.45.json. DO NOT EDIT.
   Axiom cites are verbatim commentary quotations, validated by
   tests/test_contracts.py. -/
import VakyaVallari.Adequacy

namespace VakyaVallari.Verses.V1_45

open VakyaVallari

def sabda : Entity := ⟨"śabda", Sorta.linguisticItem⟩
def sphota : Entity := ⟨"sphota", Sorta.linguisticItem⟩
def buddhi : Entity := ⟨"buddhi", Sorta.cognition⟩

def contract : Contract :=
  { axioms := [ Claim.predication "abhinna" sphota
    , Claim.relation "buddhibheda" (Node.ent sabda) (Node.ent sphota)
    , Claim.predication "vivarta_compatible" sphota ]
  , denials := [ Claim.relation "atmabheda" (Node.ent sabda) (Node.ent sphota) ]
  , reported := [] }

def accepted : Reading :=
  { claims := [ Claim.predication "abhinna" sphota
    , Claim.relation "buddhibheda" (Node.ent sabda) (Node.ent sphota) ] }

theorem accepted_adequate : contract.Adequate accepted := by decide

namespace Counterexamples

/- 'Sound and sphota are fundamentally different entities in essence.'
   Why rejected: The commentary attributes atmabheda to puranagas but the endorsed position (buddhibheda) contradicts this. The verse makes clear that sphota is abhinna with only cognitive difference, not essential difference. -/
def atmabheda_doctrine : Reading :=
  { claims := [ Claim.relation "atmabheda" (Node.ent sabda) (Node.ent sphota) ] }
theorem atmabheda_doctrine_inadequate : ¬ contract.Adequate atmabheda_doctrine := by decide
#guard contract.contradicts atmabheda_doctrine = true

/- 'Sphota is merely a manifestation or appearance of sound itself.'
   Why rejected: The commentary emphasizes sphota as abhinna (undivided/independent), suggesting it transcends or equals sound ontologically, not as a derivative manifestation. Treating it as a manifestation demotes its status incorrectly. -/
def sphota_wrong : Entity := ⟨"sphota", Sorta.manifestation⟩
def sphota_manifestation : Reading :=
  { claims := [ Claim.relation "vivartate" (Node.ent sabda) (Node.ent sphota_wrong) ] }
theorem sphota_manifestation_inadequate : ¬ contract.Adequate sphota_manifestation := by decide
#guard contract.licenses sphota_manifestation = false
theorem sphota_manifestation_sort_error : sphota_wrong ≠ sphota := by decide

/- 'Sound and sphota are identical without any cognitive difference whatsoever.'
   Why rejected: The verse explicitly states that difference arises from cognitive variation (buddhibheda). Asserting identity without cognitive differentiation contradicts the buddhibheda relation. -/
def no_cognitive_variation : Reading :=
  { claims := [ Claim.identity sabda sphota ] }
theorem no_cognitive_variation_inadequate : ¬ contract.Adequate no_cognitive_variation := by decide
#guard contract.licenses no_cognitive_variation = false

end Counterexamples

end VakyaVallari.Verses.V1_45