A registered result in its source context
Original ledger classification: Identity [I] (atom identities + new closure) + [P] (the one lift map)
Recorded statement: PAIRING VALUES ARE ATOM IDENTITIES (R4' collapses from two values to ONE map): given the lift n = w0(sigma) + |mu4| e3 (the v139 audit identity read structurally: w0 = the A3 EXPONENT DUALITY m <-> h-m = 4-m, an established Lie involution;…
Statement, assumptions and sources
Paper context: Research contracts
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GATE.UWALL.13
Original ledger classification: Identity [I] (atom identities + new closure) + [P] (the one lift map)
Original claim text
PAIRING VALUES ARE ATOM IDENTITIES (R4' collapses from two values to ONE map): given the lift n = w0(sigma) + |mu4| e3 (the v139 audit identity read structurally: w0 = the A3 EXPONENT DUALITY m <-> h-m = 4-m, an established Lie involution; lift slot = the top-exponent line, lift size = the glue order), ALL THREE pairings are atom arithmetic: (1) n.1 = sigma.1 + |mu4| = -|Z2|+|mu4| = |Z2| (<=> |mu4| = 2|Z2|); (2) NEW ATOM CLOSURE sigma.w0(a) = 2|Z2| - N_fam^2 + g_car = 0 <=> |mu4| + g_car = N_fam^2 (4+5=9), then n.a = |mu4| a3 = 8 = rank E8; (3) ||sigma||^2 = |Z2|^2+N_fam^4+g_car^2 = 110 = |Z2| g_car ||Pl(K)||_1 and n.sigma = 110 - 9 + 20 = 121 = ||Pl(K)||_1^2. STATUS: R4' = derive the ONE map n = w0(sigma)+|mu4|e3; no independent number remains
Original classification detail
Identity [I]: pairing values = atom identities; R4' = one lift map
Dependencies as recorded
GATE.UWALL.12; GATE.UWALL.11; v136; v139; v142
Open the original ledger source, row 230Location recorded in the ledger
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- Research contracts
Sections that explicitly cite this claim
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- 2026-06-12 (R1–R5 second round: every class at its floor, v145– v148)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Glue-norm arithmetic, and three readings of [formula in source] , [formula in source] , [formula in source]Architecture, E8 and the electromagnetic fixed point
- Glue-norm arithmetic, and three readings of [formula in source] , [formula in source] , [formula in source]tfpt 1 architecture e8
- Research Contract 1 — [formula in source]tfpt research contracts
- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v145_pairing_atoms.pyRegistered verification module · registry
Read the description recorded in the module registry
R4′ values = ATOM IDENTITIES: given the lift n = w₀(σ)+|μ₄|e₃ (w₀ = A₃ exponent duality), n·1 = |μ₄|−|ℤ₂| = 2, n·a = |μ₄|·a₃ = 8 via the new closure |μ₄|+g_car = N_fam² (4+5=9, σ⊥w₀(a)), n·σ = ‖σ‖²−N²+|μ₄|g = 121 — residue = derive the ONE map
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