A registered result in its source context
Original ledger classification: Identity [I] (inventory + relocation arithmetic) + typing contract (gap completeness)
Recorded statement: THE RESIDUAL INVENTORY (one constant, one anchor, one clock to find; the COMPLETE machine-pinned gap list): (A) ONE-CONSTANT INVENTORY [I] - 2/3 = |Z2|/N_fam appears exactly in seven independent places across both sectors (flavor: Koide…
Statement, assumptions and sources
Paper context: TFPT — Introduction and reading guide
The exact identifier, original classification and full claim are available below.
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Read the exact registered claim and its dependencies
SYNTH.INVENTORY.01
Original ledger classification: Identity [I] (inventory + relocation arithmetic) + typing contract (gap completeness)
Original claim text
THE RESIDUAL INVENTORY (one constant, one anchor, one clock to find; the COMPLETE machine-pinned gap list): (A) ONE-CONSTANT INVENTORY [I] - 2/3 = |Z2|/N_fam appears exactly in seven independent places across both sectors (flavor: Koide branch point, transfer-gap base (2/3)^6, attractor inside the physical basin; gravity: Nariai entropy bound, SdS branch separation, canonical amplitude+frequency, canonical curvature base (2/3)^N_fam); ANCHOR TRIPTYCH [I]: configuration chi_a = (t-1)^2(t-2), Nariai cubic (t-1)^2(t+2) = traceless anchor, clock quadratic (lam-1)(lam+2); Nariai = (t-1) x clock; a = e2+e3. (B) RELOCATION THEOREM [I]+[P]: the cosmological one-loop clock correction eps = (c/24pi) Lambda/Mbar^2 = 7.6e-122 (c = 8 = the seam central charge, frozen rho_L) is deficient by 121.5 orders against the needed O(1) gap, and the deficit IS the Lambda hierarchy 2 alpha^-1/ln10 = 119.0 (+2.5 prefactors, the v60 split) => the seam clock must live at the SEAM scale, where the only gapped generator is the established boundary transfer operator; the bridge reaches its final form: ONE [P] identification 'transfer operator = seam Nariai clock'. (C) RESIDUAL TABLE (typing contract): exactly FIVE structural objects remain - R1 seam quantum clock [P] (HOR.CLOCK.01), R2 seam net holomorphic + c=8 [P]/[A] (GATE.METRIC.05/06/07), R3 seam determinant => EH form [A] (SEAM.AREACOEFF.03 residual), R4 H2 dictionary [A]/[P] (GATE.RU.01/CONTRACT.U.01), R5 parabolic realisation of Q carrying P1 [P] (GATE.QGEO.01/FLAV.SHEET.03) - plus the two irreducibles (one scale v_geo by dimensional analysis v78; the primitive pi) and the frozen data surfaces (gamma_CP, n_s/A_s, theta13, m_tau, r). COMPLETENESS is itself the claim: a sixth structural gap would FAIL v105. Nothing closed here; everything that remains is named, typed and counted
Original classification detail
Residual inventory: 5 named structural objects + 1 scale + pi; completeness machine-pinned
Dependencies as recorded
HOR.CLOCK.01; HOR.TRISECT.01; HOR.NARIAI.01; HOR.ORIENT.01; FR.KOIDE.04/05/06; GATE.METRIC.05-07; GATE.RU.01; GATE.QGEO.01; ANCHOR.VGEO.01; REG.FREEZE.01
Open the original ledger source, row 188Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- TFPT — Introduction and reading guide
- Origin Theory
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.
- Honest statusinput 4 origin theory
- Honest statusorigin theory
- Honest statusOrigin Theory
- 2026-06-12 (origin_theory style alignment + box reduction)Research changelog; TFPT — Introduction and reading guide
- 2026-06-13 (terminal residual inventory: (A) no longer a structural class; one hinge + F_transfer + irreducible core, v167)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Honest statusinput 4 origin theory
Registered verification modules
- v105_residual_inventory.pyRegistered verification module · registry
Read the description recorded in the module registry
THE RESIDUAL INVENTORY — one constant, one anchor, one clock to find, and the COMPLETE machine-pinned gap list: (A) 2/3 = |ℤ₂|/N_fam appears EXACTLY in seven independent places across both sectors (Koide branch point, gap base (2/3)⁶, basin attractor; Nariai bound, branch separation, canonical amplitude+frequency, curvature base (2/3)^N_fam) + the anchor triptych (configuration / Nariai roots / clock spectrum); (B) RELOCATION THEOREM: the cosmological one-loop clock correction ε = (c/24π)·Λ/M̄² = 7.6×10⁻¹²² (c = 8) is deficient by 121.5 orders — the deficit IS the Λ hierarchy 2α⁻¹/ln10 = 119.0 ⇒ the clock must live at the seam scale: ONE [P] identification 'transfer operator = seam Nariai clock'; (C) RESIDUAL TABLE: exactly FIVE structural objects remain (clock, holomorphy+c8, seam-det⇒EH, H2 dictionary, Q-realisation) + one scale + π — a sixth structural gap would FAIL this script
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