Publication history: 2026-07-14

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• v485_contact_diagonal_closed.py (SEAM.CONTACT.UNIT.02). The v484 merge left one analytic step: the diagonal (self-energy) zeta-renormalisation at the marks + the multiplicity matching. Settled at the computable level: [E]DIAGONAL ZERO AT THE KMS SCALE — the renormalised coincident-point Green function of |D| on circumference \ell is G_{\mathrm{reg}}(0;\ell)=\tfrac1\pi\ln(\ell/2\pi) EXACTLY (symbolic limit + 30-digit checks); it vanishes iff \ell=2\pi=1/(4\cthree), the v239 KMS seam circumference — the seam scale is the unique zero-self-energy scheme point, and the log is the pure SCALE channel (matching the structure: F_{U(1)} carries exactly ONE log term, the transport 8b_1\cthree^6\ln(1/\varphi_{\mathrm{seam}}), while the \phiz split is log-free). [E]CLOSED-FORM RESUMMATION (the BFK/gluing route already in the suite, v151): with the diagonal zero, the finite-rank mark determinant resums exactly — \det(I-uC)=(1-4u)(1+2u)^2, u=\varepsilon\cthree\ln2, all orders, the linear term ABSENT precisely because the diagonal vanishes (\operatorname{Tr}C=0); the series matches v484's \operatorname{Tr}(C^k)=4^k+2(-2)^k term by term. [E]WEIGHT DICHOTOMY: the SAME 48=3\times16 admissible states carry BOTH multiplicities — counted flat they give the \phiz puncture count 48=\Oadm; Y^2/loop/GUT-weighted they give the alpha budget 41=10b_1=40+1 (\operatorname{Tr}_{16}Y^2=\tfrac{10}3 exact, \nu^c=0; Ginsparg (3/5)(41/6)=41/10, v470) — one state set, two response weights, no new number. [C]/[O]CONSEQUENCE: with v484 EVERY finite/computable piece of the merged ALPHA.QUILLEN.EXACT.01 + HYP.PHI0.PUNCTURE.01 target is proven; the single remaining [O]is the identification of the abstract seam \zeta-det with this glued mark determinant — a face of SEAM.EQUIV.01, exactly the v382 typing, now substantiated computationally. Integrated in tfpt_1_architecture_e8 (eighth step of the ALPHA.QUILLEN arc) and origin_theory; ledger rows SEAM.CONTACT.UNIT.02 + update notes on .01 and both targets; Python-only by nature, flagged in the Wolfram README.

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• v484_seam_contact_unit.py (SEAM.CONTACT.UNIT.01). The v483 round left the two analytic targets sharing one rule (“weight \cthree per boundary contact insertion”: the F_{U(1)} ladder \{0,3,6\}, the \phiz puncture \{1,4\}). This module shows the shared rule is NOT a new unknown: [E]the unit chain \tfrac1{2\pi}=4\cthree=|\mu_4|\cthree=|\Z_2|\chi(S^2)\cthree — one bare boundary insertion divided by the orbit order |\mu_4|{=}4 is exactly \cthree; this is the v239 KMS seam unit and the v58/v73 one-sided Gauss–Bonnet in a single identity. [E]the mechanism is DERIVED on the actual seam circle for the finite cycle sector: the bare Green function G(d)=-\tfrac1\pi\ln|2\sin(d/2)| (polylog identity, 40 digits) takes INTEGER multiples of \cthree\ln2 at the \mu_4 separations (G(\pi/2)=-4\cthree\ln2, G(\pi)=-8\cthree\ln2; mark matrix -4\cthree\ln2\cdot\mathrm{circ}(0,1,2,1), spectrum \{4,-2,0,-2\}), so the \mu_4-invariant (orbit-averaged) insertion carries -(\cthree\ln2)C exactly and the log-det contact expansion is exactly graded in \cthree per insertion (\operatorname{Tr}C^k=4^k+2(-2)^k). [E]the grammar is suite-wide: the \Lambda prefactor \tfrac{3}{4\pi^2}=(8\pi)^2 d_{\mathrm{top}}=48\cthree^2 (v60) carries the SAME multiplicity \Oadm{=}48 as the \phiz puncture at TWO insertions; the g{-}2 seam loop divides by the same 2\pi=1/(4\cthree). [C]/[O]THE MERGE: the two tracked [O]targets collapse into ONE named analytic step — the diagonal (self-energy) zeta-renormalisation at the marks + the state-multiplicity matching (48=\Oadm, 41=10b_1); the finite half is proven, no target coefficient is claimed (the integers are forced by the square configuration, v354/v355-clean). Integrated in tfpt_1_architecture_e8 (seventh step of the ALPHA.QUILLEN arc) and origin_theory (\phiz split paragraph); ledger rows SEAM.CONTACT.UNIT.01 + update notes on both targets; Python-only by nature (mpmath polylog), exact identities flagged in the Wolfram README.

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• v482_seesaw_rung_decision.py (FLAV.NUSCALE.03). The decision computation NAMED by v481 is EXECUTED in bracketed (assumption-robust) form: the integer rung M_R=\cthree^3\Mbar needs a rescue factor \times1.670 in m_3 (0.0301 vs 0.0503 eV), while m_t(\overline{\mathrm{MS}})\pm3 GeV (>3\sigma), \alpha_3^{-1}\mp0.10 (>3\sigma), a \pm10\% band on the ADKLR \kappa run-down and a PS-leg Yukawa-beta envelope \times[0.5,1.5] move it by at most \times1.10 singly and \times1.165 ALL-favourably combined — the unstructured rung is EXCLUDED conditional on the carrier premise y_\nu{=}y_t (the v481 1-loop miss is not an RG artifact; no exact higher-loop coefficients trusted, pure envelope argument). [C]The only escape is a third-generation Majorana STRUCTURE factor r\sim1.67; its post-hoc 0.18\% proximity to \gcar/\Nfam=5/3 is recorded and DECLINED per v354/v355 (no forcing mechanism; the t_0{\sim}30 discipline of v478). [O]the v481 one-parameter window candidate (NO floor \Sigma m_\nu{=}0.059 eV) never used the integer rung and STANDS. Integrated in tfpt_2_standard_model (\nu-scale paragraph) and tfpt_5_redteam; ledger rows FLAV.NUSCALE.03 + .02 update note; Python-only by nature.
• v483_pillowcase_exact_traces.py (HYP.PHI0.GEOM.01). The GEOMETRIC side of the \phiz puncture target (HYP.PHI0.PUNCTURE.01/v408) is EXACT: every twisted/orbifold heat trace of the flat \tau{=}i pillowcase is a t-INDEPENDENT RATIONAL — \operatorname{Tr}(\gamma e^{t\Delta})=1 for \gamma=\sigma,\rho,\rho^3 at every tested t (position-space Gaussian image sums <10^{-9}; mode-space proof: only n{=}0 is \gamma-diagonal), matching the Atiyah–Bott fixed-point counts 4{\times}\tfrac14 (\det=4{=}|\mu_4|) and 2{\times}\tfrac12 (\det=2{=}|\Z_2|); the pillowcase contact term is EXACTLY \tfrac12=4\times\tfrac18 per mark and the clock-equivariant trace exactly 1, for all t. THEREFORE the \pi^{-4} in d_{\mathrm{top}}=48\cthree^4=\tfrac{3}{256\pi^4} cannot come from flat orbifold geometry at ANY order: it must sit in the per-insertion COUPLING normalisation (4{=}|\mu_4| marks of weight \cthree give \cthree^4, multiplicity \Oadm{=}48; the bare 1/(2\pi)-propagator 4-cycle differs by the exact rational \tfrac{3}{16}). The target NARROWS from “derive the term” to ONE rule — “per-mark insertion weight =\cthree” (the same residual class as the EM-Ward \cthree-ladder, EM.WARD.02) — and stays [O]. Complements the experiments-side Donnelly probe (honest negative). Integrated in origin_theory (\phiz split paragraph); ledger rows HYP.PHI0.GEOM.01 + HYP.PHI0.PUNCTURE.01 update note; Python-only by nature (quadrature verification of exact statements).

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• Website /verification: live journey views. The static script_timeline.png and residual_chain.png images (stale at the v303–v407 figure state, with alt text and captions still describing the old eleven-phase/v237 state) are replaced by two interactive components, SuiteTimeline.tsx (17 phases, v1–v481) and ResidualChain.tsx (the reduction chain through the certification round to the bedrock): every phase/step lists representative vN scripts that run live in the browser via the existing Pyodide reproducer, exactly like the dependency graph. Stale counts fixed (“\sim295-script journey”, “260 scripts” \to the generated suite total). The dependency graph itself was verified current (v479–v481 present; all 288 referenced scripts exist in the registry and the website mirror).
• Prediction surface: the empirical-audit narrative restructured. The single \sim13 000-character audit paragraph in lib/predictions.ts is split into twelve dated, verdict-badged rounds (AuditRound: date, title, verdict, two-sentence summary, full unabridged record on expand) plus a domain-chip row and the anti-double-counting note — same content, readable surface. Long-token overflow fixed (break-words) in the dependency-graph detail panel and the universal-gap-lab residual cards; the over-long ALPHA.QUILLEN residual note tightened to its current state (v470/v472, residual unchanged).
• Generated figures + captions synced. make_figures.py: the script timeline gains the v408–v481 certification-round phase (title now \sim475 scripts) and the residual chain gains the v458–v480 certification step (Kronheimer v479, four-interval v480, crossed-product v469) with sub-text wrapping fixed; figures regenerated (PDF + website PNG). The stale figure captions updated: introduction (timeline caption now spans the full arc), tfpt_research_contracts (residual-chain caption now states the SEAM.EQUIV.01 bedrock and certification round; QFT-skeleton caption now names the one [O]residual instead of the outdated “two open items”). No numbers, statuses or claims change anywhere.
• KaTeX macro fix (broken formula rendering). Formulas copied from the document set that use the shared TeX macros (\gcar, \Nfam, \cthree, …) rendered as red KaTeX errors on the site (e.g. the \varphi_0^{\mathrm{tree}} icosahedral-combinatorics formula on the Origin-Theory page). A shared macro map (lib/katex-macros.ts, mirroring the changelog.tex preamble) is now passed to every KaTeX render; an automated scan of all 19 site routes finds zero katex-error nodes.
• Readability pass (text walls clamped, content unchanged). A reusable Expandable component clamps long mirror prose with a fade + “Show more” toggle — applied to the paper-section bodies and front-box bullet lists (PaperSection.tsx, the home set pages and /papers/[slug]), the dependency-graph node summaries and the prediction-card descriptions. Nothing is deleted; the full text expands in place.
• Hylaean ecosystem card corrected. The hylaean.ai card spoke of “Field AI” with structure tags that did not describe the project. It now speaks consistently of Hylaean and is grounded in the project documentation (_documentation/core-physics/big-picture.md) and the site's own status log: one cognitive substrate behaving like a physical material, knowledge = attractor valleys, question = boundary condition, answers committed only on physical landing, capability claims gate-checked against a machine-checked claim registry (honest negatives published) — borrowing TFPT's structural discipline, not its physics predictions. The Agentic-Commerce card reference updated accordingly.
• Live-site correctness pass (counts + reading order). Sitewide audit against the deployed page found stale counts and fixed them: the document set is stated everywhere as 10 documents = 1 reading guide + 5 numbered papers + 4 companions (the safeguards companion was missing from the papers/downloads headers, the JSON-LD collection and the tfpt_docset.tex box, which still said “three companions” next to “four”); the stale “23 falsifiable predictions” claims (site metadata, OG image, llms.txt) now state the live count of the prediction surface (25 test surfaces, sourced from predictions.length where possible), while the interactive compiler page is honestly labelled as its own 23-readout prediction board (the standalone app's board genuinely has 23 entries; the intro film keeps its spoken “twenty-three”); and the /orientation reading-order lists are fixed to the canonical numbering (Red Team = Doc 5 added, Appendix H = 6, Origin = 7, contracts = 8, safeguards = 9 — the old list mislabelled 6/7 and omitted three documents). Presentation/consistency only; no physics content changes.

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• v479_kronheimer_quiver_bridge.py (SEAM.KRONHEIMER.01). The R3 residual of the \det K{=}1 keystone (v344: “the rewrite attractor graph IS the du Val singularity”) is an ESTABLISHED THEOREM — Kronheimer's ALE hyper-Kähler quotient construction + Torelli classification (J. Diff. Geom. 29 (1989) 665 and 685) — with all finite input data already compiler outputs, machine-checked [E]: the Kac marks \{1,2,2,3,3,4,4,5,6\} are the null vector of the affine-E_8 Cartan matrix AND the Perron vector A\delta{=}2\delta of the rewrite attractor (v312); the hyper-Kähler quotient dimension count lands exactly on 4 (the \mathbb{C}^2/\Gamma geometry; \sum_{\mathrm{edges}}d_id_j{=}\sum d_i^2{=}120 forced by the null identity); the gauge datum is |2I|{=}120{=}|\mu_4|h(E_8), h(E_8){=}30{=}2\cdot3\cdot5; the resolution carries the unimodular -E_8 form (\det{=}1, SNF = identity — the Poincaré link) with 3\cdot8{=}24 deformation parameters. [C] the theorems are cited, not re-proved (import class of NPW26/MMST/AGT); [O]the residual premise transforms to “the raw seam supplies ALE hyper-Kähler data asymptotic to the (2,3,5) cone” — the same single arrow as SEAM.EQUIV.01 (v346 L2). Integrated in origin_theory (R3 keybox + new Kronheimer paragraph) and tfpt_research_contracts (Kummer/du Val); ledger rows SEAM.KRONHEIMER.01 + SEAM.DETK.01 update note; Wolfram mirror added to the extension file (+2 exact checks, counted with the next verified engine run — the local engine is currently unactivated; the identical statements are sympy-exact in v479). LEAN: the finite input data are kernel-checked in TfptCarrier/KronheimerMarks.lean (marks = null/Perron vector over \Z, \sum\delta_i^2{=}120{=}4\cdot30, 30{=}2\cdot3\cdot5, dimension count =4; lake build clean, #print axioms = the three standard kernel axioms only).
• v480_multilocal_four_interval.py (QGEO.MULTILOCAL.01). The seam circle minus its four marks IS the n{=}4 multi-interval region of a chiral free fermion — the class whose multi-interval modular theory is exactly known (Casini–Huerta mixing term; Longo–Xu; Rehren–Tedesco multilocal fermions; KLM: holomorphic \Leftrightarrow trivial multi-interval inclusion, \mu{=}1 — the same one bit as \det K{=}1); until now the suite used only the single-ball CHM boost (v358). On the exactly solvable antiperiodic critical ring: [E]the quarter-turn clock is a signed permutation with \rho^4{=}{-}1 EXACTLY (the fermionic \mu_4 clock is the order-8 double-cover lift — the same \Z_2-lift pattern as 2I over I); [E]its primitive-8th-root character projectors decouple the 4-interval covariance at 10^{-15}, each sector a single-interval quarter-ring kernel with boundary twist (10^{-14} spectra); [E]\rho C\rho^{-1}{=}C at 10^{-14}, so \omega\circ\rho{=}\omega holds manifestly at the 4-interval state level, and a one-site displacement re-couples the sectors at 10^{-2} (negative control); [E]the cross-interval modular coupling peaks on the conjugate-point diagonal (the Casini–Huerta mixing shadow). [C]continuum theory cited; [O]the raw-seam premise (QGEO.SYM.01/SEAM.EQUIV.01) unchanged. Integrated in tfpt_research_contracts (marks keybox + rigidity contract + v478 leg A), origin_theory (BW paragraph), tfpt_4_frontier (v358 companion note); Python-only by nature.
• v481_seesaw_carrier_ladder.py (FLAV.NUSCALE.02, CANDIDATE class, genre v467/v468). FLAV.NUSCALE.01's y_\nu{=}1 probe was not the carrier normalisation: one SO(10) \mathbf{16} per family + the minimal Yukawa sector (\mathbf{10}_H / PS (1,2,2)) forces y_\nu{=}y_t at the matching scale (named premise). With explicit 1-loop RG (gauge/y_t/\lambda up; ADKLR Weinberg-operator running down, hep-ph/0108005) the (y_\nu,M_R) trade-off collapses to M_R alone: the observed m_3{=}0.0503 eV demands M_R{=}9.3{\times}10^{13} GeV — INSIDE the PS window [4.2{\times}10^{13},2.4{\times}10^{15}] (v249) at \log_{\cthree}(\Mbar/M_R){=}3.15 (the y_\nu{=}1 inversion gives the structureless 2.58). [X]honesty gate: the integer rung M_R{=}\cthree^3\Mbar predicts m_3{=}0.030 eV — 40\% low at 1-loop (\kappa run-down 0.794) — the ladder pin is DECLINED per v354/v355; the decision computation is named (2-loop SM + explicit PS thresholds). What survives: a one-parameter, window-bracketed [O]candidate with the falsifiable band m_3\in[0.002,0.115] eV and the NO floor \Sigma m_\nu{=}0.059 eV; frozen record untouched. Integrated in tfpt_2_standard_model (new paragraph after v272), introduction status card (third named candidate), tfpt_5_redteam; ledger rows FLAV.NUSCALE.02 + FLAV.NUSCALE.01 update note; Python-only by nature.
• Honest negative (experiments-only, no promotion): the Donnelly/Atiyah–Bott equivariant heat-kernel route for the \phi_0 puncture target (HYP.PHI0.PUNCTURE.01) types the KIND of term (order-4 equivariant contact datum; the exact weights \sum_{k=1}^{n-1}\tfrac1{4\sin^2(\pi k/n)} {=}\tfrac{n^2-1}{12} verified) but does NOT force the value 48\cthree^4 (pure rationals vs \pi^{-4}) — recorded in experiments/theory-contracts/phi0_donnelly_equivariant_probe.py; the target stays [O].