The Holographic Circlette: Part 13 — Chiral Symmetry Breaking and the Pion Mass from Discrete Topological Screening

Audit note. This paper predates the framework's methodology audit of 2026-05-30. The headline ``no free parameters at any stage'' framing is read in the post-audit sense at §16.3 search-space classification: the structural mechanism (f_π as bridge-to-bulk interface condition; GMOR from 2-step walk; chiral-log screening from 2D Pólya recurrence) survives at Proposition tier; the precise numerical matches (f_π at 0.7%, m_π at 1%) are class-2 tight matches whose formula-freedom (the √4π normalisation choice, the specific 1-loop screening form) has not yet undergone item-by-item audit. The pion-mass framework remains one of the cleaner Target-B candidates in canon, with several anchored open items (ANCHOR §15 items 69--71 on discrete-vs-continuum Green's function, item 72 HQET kaon framework) marking the substrate-level derivation steps that still need rigorising. We derive f_pi=Lambda_QCD/sqrt(4*pi)~93.66 MeV (0.7% from experiment). The GMOR relation follows from a 2-step quantum walk, yielding a bare mass of 169 MeV. The 1-loop self-energy via the 2D lattice Green's function screens the mass to m_pi=136.1 MeV (1% of the neutral pion). Zero free parameters at any stage. 2026-06-20 legacy erratum: This version adds a canon erratum note to the legacy paper. Pion derivation mostly held; update status The body is preserved as a historical derivation trail; the erratum note identifies the current ANCHOR/DRIFT status and superseded claims. 2026-06-21 canon refresh: This version incorporates the 2026-06-21 ANCHOR/DRIFT/PTMS canon refresh and rebuilt local PDF.