A registered result in its source context
Original ledger classification: Identity/Lie [I]/[L]
Recorded statement: Unique attractor: a gapped boundary transport selects ONE fixed point [I]/[L]. The boundary transport spectrum {1,(2/3)^6,(1/3)^6} has spectral gap Delta=-log(2/3)^6=6 log(3/2)=2.4328>0. By Perron-Frobenius a primitive gapped operator has…
Statement, assumptions and sources
Paper context: Origin Theory
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SEAM.ATTRACTOR.01
Original ledger classification: Identity/Lie [I]/[L]
Original claim text
Unique attractor: a gapped boundary transport selects ONE fixed point [I]/[L]. The boundary transport spectrum {1,(2/3)^6,(1/3)^6} has spectral gap Delta=-log(2/3)^6=6 log(3/2)=2.4328>0. By Perron-Frobenius a primitive gapped operator has a UNIQUE dominant eigenvector and iteration converges to it geometrically at rate lambda2/lambda1=(2/3)^6, independent of initial state (demonstrated: two different starts -> same fixed direction, cos=1). This is the dynamical-systems content of 'parameter-free via fixed point' - the realized state is an ATTRACTOR, not a tuning; the convergence rate is the SAME (2/3)^6 of flavor+horizon (v54). Coxeter rotation lives in |mu4|=4 invariant planes (exponents pair m+(30-m)=30); sum exps=120=|R+(E8)|; #roots=rank*h=240. Entropy reset = the gap: T^n/lambda1^n -> rank-1 projector (only boundary law survives). Cyclic-cosmology reading is [P], not included
Original classification detail
Identity/Lie [I]/[L]
Dependencies as recorded
SEAM.HORIZON.01; SEAM.CYCLE.01; v54; v55
Open the original ledger source, row 133Location 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.
- Origin Theory
- E8 audit and bootstrap
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.
- 2026-06-15 (QGEO: the bedrock recast as a falsifiable kill-test)Research changelog; TFPT — Introduction and reading guide
- -1.2cm TFPT — Origin Theory\\[2mm] The seam as a horizon, the cyclic compiler hull,\\ and the self-reproducing parameter-free fixed point\\[2mm] An \ structural core ( [formula in source] – [formula in source] ) with one honestly-typed \ interpretationorigin theory
- Honest statusinput 4 origin theory
- The Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
- The unique attractor: a gapped transport selects ONE fixed pointorigin theory
- -1.2cm TFPT — Origin Theory\\[2mm] The seam as a horizon, the cyclic compiler hull,\\ and the self-reproducing parameter-free fixed point\\[2mm] An \ structural core ( [formula in source] – [formula in source] ) with one honestly-typed \ interpretationinput 4 origin theory
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- 2026-06-24 (Lean 4: FORM.SPECTRALGAP.01 extended to the finite-dimensional Perron–Frobenius case)Research changelog; TFPT — Introduction and reading guide
All 36 linked sections
- 2026-06-22 (the four black-hole-birth completion routes investigated: none closes all or is 100\% provable alone; all four converge on SEAM.EQUIV.01 [formula in source] the decoupled QG contour: v343)
- Appendix: computational verification
- Drei verschiedene Eindeutigkeitsfragen
- Honest status
- -1.2cm TFPT — Origin Theory\\[2mm] The seam as a horizon, the cyclic compiler hull,\\ and the self-reproducing parameter-free fixed point\\[2mm] An \ structural core ( [formula in source] – [formula in source] ) with one honestly-typed \ interpretation
- Appendix: computational verification
- The hard reduction: the live residual as typed interfaces
- Honest status
- 2026-06-23 (Bird's-eye synthesis: two new structural patterns — v383 the universal spectral-gap principle and v384 the residual is certification, not construction)
- 2026-06-12 (origin_theory style alignment + box reduction)
- Research Contract 2 — [formula in source]
- Front matter / support
- Front matter / support
- Front matter / support
- The unique attractor: a gapped transport selects ONE fixed point
- Front matter / support
- Honest status
- 2026-06-13 (premise A as a conditional fixed-point theorem; the load relocates to one scope premise, v160)
- 2026-06-22 (the translation clock: the discrete [formula in source] dynamic bridge is the order- [formula in source] Coxeter element, a clock with two coprime hands [formula in source] , read law-inclusive ( [formula in source] ) or live-only ( [formula in source] ): v319)
- Appendix: computational verification
- The compact status formula: three honest layers
- Appendix: computational verification
- 2026-06-22 (the bird's-eye rethink: TFPT is a unique self-consistent LOOP with ZERO free dials, not a linear axiom system; [formula in source] is a fixed geometric constant, not a dial; the one residual is the continuum closure: v353)
- -1.2cm TFPT — Origin Theory\\[2mm] The seam as a horizon, the cyclic compiler hull,\\ and the self-reproducing parameter-free fixed point\\[2mm] An \ structural core ( [formula in source] – [formula in source] ) with one honestly-typed \ interpretation
- Research Contract 2 — [formula in source]
- The unique attractor: a gapped transport selects ONE fixed point
- In plain words
- The maximal black hole is the anchor: SdS in seam units
Registered verification modules
- v56_unique_attractor.pyRegistered verification module · horizon
Read the description recorded in the module registry
gapped transport ⇒ unique attractor at rate (2/3)⁶
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