Publication history: 2026-06-14

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• v199_seam_state_invariance.py [E]/[O](claim QGEO.STATE.01, work package A). Attacking \omega\circ\rho=\omega directly on the raw seam. (1) [E]the setup is non-circular: \rho is the Coxeter element of W(A_3)=S_4 (\rho^4=1, v117), an automorphism of the raw CAR algebra (16 Majoranas) — both carrier-side, no seam geometry. (2) [E]for a quasi-free RP state C_\Sigma=\tfrac12(1{+}\operatorname{sgn}H_1), so \omega\circ\rho=\omega\Leftrightarrow[\rho,H_1]=0. (3) [E][\rho,H_1]=0\Leftrightarrow H_1 is block-diagonal in the four \mu_4-character classes \{n{=}r\bmod4\} (verified). (4) [O]the residual is sharpened to “the bounded sub-principal symbol has no off-character matrix elements” — a bounded, finite-character condition, not a diffuse geometry; not a closure. Cited in tfpt_research_contracts; Wolfram-mirrored.
• v200_seam_variational_scan.py [C]/[O](claim QGEO.VARI.02, work package B). The discretised variational test: with the clock angle free, E_{\mathrm{fail}}(\theta) has its unique minimum at \theta=\pi/2 (the \mu_4 clock z\mapsto iz) — order-4 and the three distinct characters i,-1,-i = the (1,2,3) grading; decoys (0,\pi,\pi/3,2\pi/3) all lose. A numerical sign that the variational principle selects \mu_4; the full operator-valued minimisation stays the v199 residual [O]. Cited in tfpt_research_contracts.
• Also (this pass, experiments/ only, not the ledger): the F_{\mathrm{transfer}} four-pipeline scaffold (experiments/ftransfer/) with one CONTRACT per interface, and confirmation that the FRB preregistration (frb_tfpt_v1.yaml) and its status semantics already exist. Suite now 199 modules, highest ID v200; Wolfram extension 241/241.

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• v198_modular_commutator_reduction.py [O](claim QGEO.MODULAR.01). The decisive crack on the last residual. (1) [E]the DtN principal symbol |k|=\sqrt{-\partial_\theta^2}=\mathrm{diag}(|n|) and the clock \rho{:}z\mapsto iz=\mathrm{diag}(i^n) are both diagonal in the Fourier basis, so [\rho,|k|]=0 exactly on all of L^2 (verified on 33 modes) — the leading-order commutation is free on the whole boundary, never the open part. (2) [E]by Tomita–Takesaki the modular operator is intrinsic to (M,\Omega), so a state-preserving symmetry (\rho\Omega=\Omega) commutes with \log\Delta\sim\Lambda_\Sigma: hence [\rho,\Lambda_\Sigma]=0 follows from \omega\circ\rho=\omega, using only the state + reflection (RP) and no conformal covariance — which removes the v194 Bisognano–Wichmann circularity worry. (3) [E] the finite H^1 block is already \mu_4-invariant (v177). So the entire residual collapses to the single state-invariance “the raw quasi-free seam state is \mu_4-invariant” (\omega\circ\rho=\omega \Leftarrow the Gaussian bulk measure is deck-invariant) — the maximally-operational, non-circular form of QGEO.SYM.01, [O]. Not a full closure (a foundational symmetry cannot be derived from nothing, like c=\text{const}), but the sharpest falsifiable form, with the circularity gone. Cited in tfpt_research_contracts; OpenGates updated. Suite now 197 modules, highest ID v198; Wolfram extension 240/240.

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• v195_marks_lefschetz_character.py [E]/[O](claim QGEO.MARKS.02). The four seam marks are forced (not posited): \rho{:}z\mapsto iz fixes only \{0,\infty\}, H^1= \chi_1{\oplus}\chi_2{\oplus}\chi_3 (the A_3 exponents, \operatorname{Tr}(\rho|H^1)=i{+}i^2{+}i^3={-}1) has no trivial component \Rightarrow no puncture at a fixed point, and \operatorname{rank}H^1=n{-}1=3 \Rightarrow n=4 \Rightarrow a single free \mu_4 orbit (cross-ratio 2). So Marks reduces from the geometric posit “D_4 marks” to the milder premise “H^1 carries the A_3-exponent rep” — less circular, still [O]. Cited in tfpt_research_contracts.
• v196_seam_energy_functional.py [E]/[O](claim QGEO.VARI.01). The failure functional E_{\mathrm{fail}}=\|[\rho,\Lambda_\Sigma]\|^2_{HS}+\|\rho^4{-}1\|^2+\|\Theta\rho\Theta-\rho^{-1}\|^2, zero locus = the QGEO.SYM.01 conditions; on the finite H^1 block it vanishes at the \mu_4 config [E]and is >0 for any \mu_4-breaking perturbation, so \mu_4 is a true minimiser. The full-operator minimisation is the v194 Bisognano–Wichmann residual — a concrete discretisable target on the open bedrock, [O]. Cited in tfpt_research_contracts.
• v197_rr_carrier_clifford_d5.py [E]/[C](claim ARCH.RRCAR.02). Hardens the Riemann–Roch carrier from g_{\mathrm{car}} to D_5 itself: \Lambda^{\mathrm{even}}(C_{\mathrm{car}}) =\binom50{+}\binom52{+}\binom54=16=2^{g_{\mathrm{car}}-1}=\dim S^+, the \mathfrak{so}(10)=D_5 half-spinor — so D_5 is the Clifford spinor of the 5-dim mode space, closing \mu_4{\to}g_{\mathrm{car}}{\to}D_5. [E]arithmetic, [C]identification (as v189). Cited in origin_theory.
• All three are validated external-review levers (the axion-hilltop “\pi-3\phi_0” proposal was rejected as a \pi\approx3 coincidence, not built). Suite now 196 modules, highest ID v197; Wolfram extension 239/239.

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• v194_raw_seam_dtn_rp.py [O](claim QGEO.DTN.01). The next hard lever — “is the raw RP-seam DtN definable from RP data alone?” (sub-claim 2 of QGEO.ENERGY.02) — was tackled, and the honest result is a reduction, not a closure. (1) [E]the commutator [\rho,\Lambda_\Sigma]=0 closes on the finite cohomology H^1 (\rho^*w_k=i^k w_k, distinct \mu_4 characters; v177). (2) [E]the hinge is met: the DtN/transfer operator is RP-canonical (Osterwalder–Schrader, v54) on a quasi-free seam state (v155), so \Lambda_\Sigma is RP-definable without naming \PP^1\!\setminus\!\mu_4. (3) [O]the residual relocates: the full-L^2 commutation \Leftrightarrow Bisognano–Wichmann geometric modular flow of the quasi-free seam state (which must be intrinsic, else it re-circulates). So QGEO.SYM.01 reduces from a definitional postulate to “intrinsic BW geometric modular covariance” — one notch sharper, still [O]; the last structural fog point sharpens, it does not close to [E]. Cited in tfpt_research_contracts; OpenGates updated. Suite now 193 modules, highest ID v194.

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• v193_qgeo_energy_commutator.py [O](claim QGEO.ENERGY.02). The non-circular sharpening of QGEO.ENERGY.01: the energy commutator [\rho,\Lambda_\Sigma]=0 on the rank-8 Calderón polarisation, with three sub-claims — (1) [E] \rho is carrier-defined (Coxeter of W(A_3){=}S_4, v117), not imported from the seam; (2) [O] the non-circularity hinge: \Lambda_\Sigma must be the raw RP-seam DtN, not the \mu_4 normal form; (3) [E]the commutator forces the (1,2,3) grading on H^1 (QGEO.COHOM.01). Exact [E] rider (Wolfram-mirrored): the induced EH coefficient k=(\ln m)/(12\pi) (v150) reproduces c_3/2 iff \ln m=q(A_3)=\tfrac34 (family), not q(D_5)=\tfrac54 (carrier, off by 5/3) — gravity is family-geometry-induced. A proof target; if sub-claim (2) holds, QGEO.SYM.01 becomes an energy-rigidity theorem. Cited in tfpt_research_contracts. Suite now 192 modules, highest ID v193; Wolfram extension 236/236.
• QFT-wording hardening (review point 7). tfpt_2_standard_model (4) was retitled to “Constructive QFT closure of the admissible physical sector”, and its standalone opening over-claim replaced by an explicitly scoped sentence (the unprojected ambient metric measure is not constructed; G_{\mathrm{metric}} frontier). The two superseded standalone phrasings were added to the v188 prose guard so a frozen release cannot re-introduce them.

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• v189_riemann_roch_carrier.py [E]/[C](claim ARCH.RRCAR.01). The pair (\gcar,\Nfam)=(5,3) are the two canonical invariants of one object, the four-point seam divisor D=\mu_4 on \PP^1: the cycle side \operatorname{rank}H_1(\PP^1\!\setminus\!\mu_4)=\deg{-}1=3=\Nfam (already QGEO.COHOM.01) and the function side h^0(\PP^1,\mathcal O(\mu_4))=\deg{+}1=5=\gcar, matched by \operatorname{rank}(D_5)=5. The carrier-as-mode-space reading is [C](geometric, does not displace the over-determined \gcar=5). Cited in origin_theory; Wolfram-mirrored.
• v190_nariai_entropy_bound.py [E](claim HOR.NARIAI.02). A variation-free one-line proof of the SdS entropy floor: 3(x^2{+}1)-2\Phi_3(x)=(x{-}1)^2\ge0, so S_{\mathrm{tot}}\ge\tfrac23 S_{dS} with equality iff x=1 (the Nariai merge). Cited in tfpt_horizon_readouts; Wolfram-mirrored.
• v191_universal_branch_line.py [C](claim HOR.BRANCHLINE.01). The affine map q=\tfrac72+\tfrac{\Nfam^2}{2}m carries the SdS branch points {\pm}1/\Nfam onto the flavor labels \{2,5\}. Honestly typed [C] — an exact relabeling, not a theorem (a decoy pair \{3,4\} admits an equally exact map; the shared content is the known 2/3 ramification). Cited in tfpt_horizon_readouts; Wolfram-mirrored.
• v192_qgeo_energy_clock.py [O](claim QGEO.ENERGY.01). An operator-checkable restatement of the bedrock: \rho^*\Lambda_\Sigma\rho=\Lambda_\Sigma (the clock preserves the DtN energy form). Honestly typed: it relocates QGEO.SYM.01 to a more falsifiable surface but does not eliminate it (plausibly equivalent unless \rho is independently defined and the invariance proven). Cited in tfpt_research_contracts. Suite now 191 modules, highest ID v192 (v186 skipped).
• All four are validated external-review proposals (problem_b); each is built with the honest typing determined on review — the branch line is recorded as an alignment, not a theorem, and the energy clock as a relocation, not a closure.

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• Published to Zenodo. Version 5.1 (rev 120) of the ten-PDF document set was published as a new version of the TFPT deposit — record 20687564, DOI 10.5281/zenodo.20687564. This version carries the F_transfer-firewall round (v184–v188): the honest \eta_B anchored-Boltzmann test (sharper scenario, not a closure), the axion hilltop-relic typing, the ledger v187 and prose v188 guards, and the Route B/Koide/dark-matter wording fixes plus the P1/P2-vs-QGEO.SYM.01 two-layer clarification. The uploader's DEFAULT_RECORD_ID was advanced to the new record for the next release. Suite 187 modules (highest ID v188; v186 skipped). run_all.py green, audit clean, website built.

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• v184_etaB_anchored_boltzmann.py [C](claim FR.ETAB.03). An honest test of the external-review \eta_B proposal (M_1=M_R\varphi_0^4, \tilde m_1=m_3/A_\Lambda). Firewall verdict: sharper scenario, not a closure. The washout anchors plausibly (\tilde m_1=m_3/10\approx5 meV, A_\Lambda=10 atom, in the strong-washout window) [C]; but M_1 does not — M_R is the seesaw scale \sim v^2/m_3 and the nearest clean TFPT powers of \bar M_{\mathrm{Pl}} both miss it (c_3-/\varphi_0-powers off {\sim}75\%/{\sim}40\%), so M_1=M_R\varphi_0^4 merely relocates the free input. \eta_B stays [C], the route viable but with one (not zero) free input. Cited in tfpt_4_frontier.
• v185_axion_relic_solver.py [C](claim FR.DM.03). Honest misalignment estimate: the determinant-line axion f_a=M_{\mathrm{scal}}/128\approx2.39{\times}10^{11} GeV (m_a\approx23.8\,\mueV) CAN be all dark matter, but the harmonic misalignment under-produces ({\sim}21\% at \theta\sim O(1)), so the \theta_i\approx170^\circ hilltop anharmonic enhancement is required — where the relic is exponentially sensitive. Hence a [C]scenario, not a sharp prediction; the relic contract is a kill test for the BRANCH, not the theory. Cited in tfpt_4_frontier.
• v187_ftransfer_laws.py [E](claim FR.TRANSFER.01). A CI-style firewall guard: the four continuous-transfer frontier observables (Koide, \eta_B, axion, m_p/m_e) are read from the ledger and required to carry a [C]/[O]marker — never a primitive [E]compiler prediction (exact sub-parts like the Koide 53/54 factor or b_3=-7 may be [E], the physical prediction never is). Records the four interfaces F_{\mathrm{pole}}/F_{\mathrm{Boltzmann}}/ F_{\mathrm{relic}}/F_{\mathrm{QCD}}; prevents any future edit from quietly promoting a frontier number to a closed output. Cited in tfpt_4_frontier.
• v188_frontier_wording_guard.py [E](claim AUDIT.WORDING.01). A prose sentinel (no new physics): v187 protects the ledger typing, this guard protects the prose. It scans the 10 active documents and forbids five stale phrasings whose semantics earlier rounds superseded (the old [E]-typed Route B leptogenesis claim and its heavy-scale wording \to v184 [C]; the old “open relic scale” dark-matter line \to v185; the old “near, not exact” Koide line \to v183; and the module-count/ID conflation), so a frozen Zenodo release can never re-introduce wording that was true yesterday and is half-true today. The same pass updated the tfpt_4_frontier Route B (to [C]), the Koide and dark-matter summary lines, and added the P1/P2-vs-QGEO.SYM.01 two-layer clarification to the introduction. Suite now has 187 modules, highest verification ID v188 (v186 was intentionally skipped as redundant — m_p/m_e is already typed [O]as a QCD matching contract, QCD.LAMBDA.01).
• Review framing points (P1/P2 as projections of the seam-deck postulate, v_{\mathrm{geo}} as unit gauge, G_{\mathrm{net}} a corollary of QGEO.SYM.01, grammar tuning = data) were validated as already implemented in the prior rounds; m_p/m_e is already typed [O]as a QCD matching contract (QCD.LAMBDA.01), so no redundant module was added.

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• v183_koide_f_corner_transfer.py [E]/[C](claim FR.KOIDE.07). An external-review proposal, validated exactly: the Koide source\topole factor \tfrac{53}{54} is not a bare arithmetic guess but an operator identity on the carrier, u_{\mathrm{pole}}/u_{\mathrm{source}} = a^T(R+Q)\mathbf1 / (2\,\mathbf1^T R a) = 53/(2{\cdot}27) = \tfrac{53}{54}. Here \mathbf1^T R a = 27 is the E_6{\times}A_2 cubic family block (248 = \dim E_6 + \det R + 2(\mathbf1^T R a)\Nfam = 78+8+2{\cdot}27{\cdot}3) and a^T(R+Q)\mathbf1 = 53 = 52+1, where F = R+Q is the missing Sheet-Diamond corner with \det B_F = 52 = \dim F_4 (v80). Hard negative control: a^T M\mathbf1 for M\in\{R,Q,K,L\} is \{32,21,35,56\} — only the absent corner F gives 53. This upgrades FR.KOIDE.03 from “near miss + conjecture” to “operator-sourced source\topole transfer”: the factor is [E](exact, mirrored in Wolfram, 232/232); the mechanism (the leptonic source\topole transfer reads the F corner) stays [C], an F_{\mathrm{transfer}} special case. The prediction itself stays [C]. Cited in tfpt_4_frontier (Koide section). Suite now 183 modules.
• Review point 2 noted as already-present: the claim that flavor and Nariai share one double-cover ClockFunctor (flavor rate (2/3)^{2\Nfam} vs gravity curvature (2/3)^{\Nfam}, exponent ratio |\Z_2|, “one clock, two geometries”) is exactly HOR.TRISECT.01/v103 — a rediscovery of an existing result, no new module.

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• v182_reviewer_residual_map.py [E]/[C](claim REVIEW.MAP.01). A careful external review raised four concerns (A mapping 2D\!\to\!4D, B UV-gravity abstractness, C grammar-tuning/meta-look-elsewhere, D Koide Möbius flow). This module shows three of them reduce, by the same discipline as v175–v181, onto the two already-named residuals \{\texttt{QGEO.SYM.01},F_{\mathrm{transfer}}\}: A (Plücker-11 = QBL boundary count v174 + holographic reduction), B (\equiv QGEO.SYM.01), D (Möbius forced by \mathrm{Aut}(\PP)=\mathrm{PSL}(2,\mathbb C) on the deck; the missing generator =F_{\mathrm{transfer}}). Only C is genuinely experiment-only (frozen + minimal + over-determined grammar; residual falls to JUNO/CMB-S4). A unification of the concern structure, not a closure. Cited in tfpt_5_redteam. Suite now 182 modules.
• Review recommendation #3 — a “Rosetta” translation lexicon (website RosettaLexicon): TFPT's compiler-speak (seam, deck, readout, microcode, audit hull, gap, anchor, F_{\mathrm{transfer}}, v_{\mathrm{geo}}, QGEO.SYM.01) mapped onto standard QFT / mathematical-physics language (Wilsonian boundary CFT, orbifold deck, index/intersection number, RG irrelevance rate, renormalization condition, fundamental postulate) — a reading aid for mainstream physicists, not a new claim.
• Review recommendation #1 — kill-tests up front (website TrustContract): the frozen pre-data predictions (sin^2\theta_{12}=0.3067, JUNO; r\approx0.004, CMB-S4) and the null model (P\le10^{-30.7}) are now a prominent strip directly under the hero.
• Review recommendation #4 — the bedrock as a postulate. QGEO.SYM.01 is now framed confidently as TFPT's one fundamental postulate (the role “c= const” plays in relativity), not a gap — in the tfpt_research_contracts box and the website “what is open” card; the achievement is that the whole theory is compressed onto exactly one sharply-located, falsifiable premise.

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• Ledger CSV bug fixed + guarded. Three rows (AX.P1.01, AX.P2.01, QGEO.ISO.01) had unquoted commas in a status/external field (e.g. “a=(1,1,2)”, “PSL(2,C)”), so a strict CSV parser read 11–12 columns instead of 10 — a real machine-readability defect in the single source of truth. All offending fields are now quoted (every row parses to exactly 10 columns), and audit_sync.py gained a check_csv_wellformed guard (ledger, registry, clusters, freeze must all parse to constant width) so it cannot regress.
• G_{\mathrm{net}} typed in three explicit levels (website “What is open” card): (1) algebra [E](D_5)_1{\otimes}(A_3)_1{\rtimes}\langle(1,1)\rangle\cong(E_8)_1; (2) AQFT machinery [E](net existence + full-cone RP, CAR functor, v175); (3) seam instantiation [O](QGEO.SYM.01). The target object's mathematics is closed; only the physical coupling of the raw seam is open.
• QGEO.SYM.01 now has its own one-page box in tfpt_research_contracts: what is identified, why it is weaker than CONF/ISO, what follows automatically (the conditional theorem), and what would falsify it (genus >0 double; non-deck transport; \Nfam\neq3); with the explicit conditional framing “given QGEO.SYM.01, the closure follows” rather than “the theory derives the seam geometry”.
• Claim-language detox. “no free fundamental number” softened to “no free dimensionless compiler dial beyond the anchor and \pi (dimensionful scale + transfer physics stay typed)” (origin_theory, introduction, website); the site title softened from “the Standard Model Derived” to “the Standard-Model Skeleton Derived”.
• External-reviewer map added to the website verification page: four boxes (exact kernel [E], conditional physics [C], open premises [O], kill tests [X]) so a reviewer sees the attack surface without reading 181 scripts. Suite unchanged at 181.

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• Published to Zenodo. Version 5.1 (rev 114) of the ten-PDF document set was published as a new version of the TFPT deposit — record 20686284, DOI 10.5281/zenodo.20686284. This version carries the AQFT-closure-to-bedrock chain (v175–v181, the structural residual reduced to the single definitional premise QGEO.SYM.01), the two overview figures (residual_chain, script_timeline), and the P1/P2 anchor-reduction provenance on the axiom surfaces. The README and the Zenodo description were refreshed (181 modules), and the uploader's DEFAULT_RECORD_ID was advanced to the new record for the next release.

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• Two overview figures (make_figures.py; PDF + website PNG). (i) residual_chain — the structural-residual reduction chain v175–v181 as a descending staircase from “build a quantum-gravity measure” to the single definitional bedrock QGEO.SYM.01; embedded in tfpt_research_contracts. (ii) script_timeline — the eight-phase journey of the \sim181 scripts (foundations \to SM readouts \to seam= horizon \to horizon/flavor geometry \to R1–R5/premise-(A) \to PyR@TE cross-checks \to AQFT bridges \to AQFT closure), what each did mathematically and physically; embedded in introduction ahead of the master script index, and both shown on the website verification page.
• P1/P2 reduction now reflected on the axiom surfaces. The reduction of the two axioms to the single parabolic anchor a=(1,1,2) plus \pi (with g_{\mathrm{car}}=5 an over-determined bootstrap fixed point — forced three ways, v6, Pascal-unique and Lean-formalised, FORM.LADDER.01) was already established (ANCHOR.GEN.01/v23, ARCH.CORE.01/v53) and stated in the papers/glossary, but the axiom surfaces still read as bare “declared inputs”. Fixed: the ledger rows AX.P1.01/AX.P2.01 now carry the anchor/bootstrap reduction and point to it, and the website dependency-graph nodes P1/P2 now show the anchor input (c_3=1/(2e_1(a)\pi); g_{\mathrm{car}}=e_2(a), bootstrap-forced) rather than “declared axiom”. No marker change (still declared inputs), only honest provenance.
• Manifests refreshed (two new figures added to the FIG list). Suite unchanged at 181.

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• v181_clock_is_conformal_symmetry.py [E]/[O](claim QGEO.SYM.01). The isometry premise QGEO.ISO.01 (v180) is weakened one more genuine step — to a conformal-symmetry premise — via equivariant uniformisation (Nielsen realisation; for cyclic groups Kerékjártó + uniformisation): a conformal automorphism (strictly weaker than an isometry — every isometry is conformal, conformal allows any positive scale) already suffices to put the order-4 clock in the form z\mapsto iz. Since the clock is the Coxeter element of W(A_3)=S_4 (v117), the \mu_4 deck, and a deck transformation preserves the pulled-back conformal structure by definition, the residual collapses to the definitional identification QGEO.SYM.01: “the seam's conformal structure is the \mu_4-deck structure of the carrier clock”. This is bedrock — a physical/definitional statement tying P2 to the seam's conformal geometry, not a finite computation and not reducible further without relabeling. The chain REALIZE(v175)\to\dots\toSYM.01(v181) ends here; we stop honestly. Python-only. Suite now 181 modules.
• Full non-changelog status sweep. The current bedrock framing was propagated to every live status surface (not just the changelog): the introduction “latest reductions” prose, tfpt_5_redteam Target A, the tfpt_research_contracts central-theorem keybox, origin_theory; and on the website OpenGates, VerificationDag, papers.ts (Target A \times2, G_{\mathrm{net}}), the glossary G_{\mathrm{net}} entry and the faq live-residual answer — all now end at QGEO.SYM.01.

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• v180_clock_is_mobius.py [E]/[O](claim QGEO.ISO.01). Cracks QGEO.CONF.01 one level further: the conformal-realisation premise is replaced, via three classical theorems, by a strictly milder, non-circular premise. (1) Uniformisation (Poincaré–Koebe): a genus-0 Riemann surface is conformally \PP, so the genus-0 seam double (P1, v179) with its RP-metric conformal structure is \PP — the target is produced, not assumed; (2) Kerékjártó (1919; Constantin–Kolev 2003): a finite-order orientation-preserving homeomorphism of S^2 is conjugate to a rotation, so the order-4 clock (h(A_3){=}4) is topologically z\mapsto iz; (3) isometry\Rightarrow conformal\RightarrowMöbius: an orientation-preserving isometry of a Riemannian surface is holomorphic, \mathrm{Aut}(\PP)=\mathrm{PSL}(2,\mathbb C); (4) an order-4 Möbius map is z\mapsto iz (verified: projective order 4, fixed \{0,\infty\}, multiplier i, free orbit \mu_4). Hence QGEO.CONF.01 is implied by the milder premise QGEO.ISO.01: “the carrier clock is an order-4 orientation-preserving isometry of the RP seam metric” — which does not name \PP/\mu_4 (uniformisation produces them) and is the natural statement that the seam transport is metric-compatible (a holonomy preserving the RP inner product). That milder premise is the single, now milder, structural residual of the whole theory; its surface realisation from the raw seam stays honestly [O]. Cited in tfpt_research_contracts; Python-only. Suite now 180 modules.

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• v179_conformal_realisation.py [E]/[O](claim QGEO.CONF.01). Investigating the two residual premises left by v178 shows they are not independent — they collapse onto a single geometric premise (honest unification; the premise itself stays [O]). Marks's residual is not three independent assumptions: (1) genus-0 is P1 — the one-sided Gauss–Bonnet c_3=1/(|\Z_2|\,2\pi\,\chi(S^2))=1/(8\pi) uses \chi(S^2)=2 and \chi=2-2g\Rightarrow g=0, so “genus-0” is the same \chi=2 that gives the “8” in c_3 (v58/v73); (2) the order-4 clock is the carrier — the Coxeter element of W(A_3)=S_4 (v117), order h(A_3)=4=|\mu_4|; (3) marks = one orbit is forced (the parabolic marks are not the two elliptic fixed points, a free order-4 orbit has exactly 4=e_1(a) points). Kernel then follows from the same geometry (DtN symbol |k|, Lee–Uhlmann v156; c=8 rigidity v158; the cusped-surface residual =H^1=\mathbb C^3=\Nfam). So the entire structural residual of the theory is the single geometric premise QGEO.CONF.01: “the raw RP seam normal double is conformally (\PP,\mu_4) with the carrier clock as the order-4 Möbius automorphism”. The two doors of v177/v178 are one geometric realisation, left honestly [O]. Cited in tfpt_research_contracts; Python-only. Suite now 179 modules.

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• v178_marks_kernel_attempt.py [E]/[O](claim QGEO.REDUCE.01). An honest attempt at QGEO.MARKS.01 and QGEO.KERNEL.01. These are genuine constructive-geometry/AQFT statements, not finite computations — neither is closed. What the module does is push each as far as computation allows: it closes the finite [E]core of each and reduces each to one sharper premise. Marks core [E]: given a genus-0 double with an order-4 clock \rho (fixed points \{0,\infty\}) and reflection \tau, the marks are forced to be a generic \rho-orbit \{1,i,-1,-i\}=\mu_4 (not the fixed points), distinct iff b_1=4-1=3=\Nfam (any collision drops b_1), with \tau\rho\tau=\rho^{-1} giving a faithful D_4 of order 8 — so Marks reduces to the single topological/clock premise. Kernel core [E]: on the 3-dim multiplicity-free H^1 the \mu_4 characters (1,2,3) are distinct, so by Schur a \mu_4-equivariant operator is forced diagonal and completely determined by its eigenvalue per character; two such with the forced transfer spectrum \{1,(2/3)^6,(1/3)^6\} (v162) and the unique residue-normalised basis (v177) are equal as operators, not merely isospectral — the spectrum-vs-operator worry vanishes on the finite block. So Kernel reduces to the single full-operator-reduction premise (principal symbol |k|, Lee–Uhlmann/v156; no drift v158). Net: neither obligation closed; both sharpened to milder premises with their finite cores [E]. Cited in tfpt_research_contracts; Python-only (Möbius/Schur symbolic + numeric). Suite now 178 modules.

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• v177_seam_marking_kernel.py [E]/[O](claims QGEO.TREE.01, QGEO.MARKS.01, QGEO.KERNEL.01). A second external residual-class audit pointed out that the v176 statement takes the marks/D_4 as a hypothesis — a near-circular trap. This module factors the central theorem honestly as \textsc{Realize}=\textsc{Marks}\cdot\textsc{Uniform}\cdot\textsc{Cohom}\cdot\textsc{Module}\cdot \textsc{Kernel}\cdot\textsc{Net} and closes four nodes constructively (all validated symbolically before adoption): Uniform [E]— an order-4 Möbius map conjugates to z\mapsto iz, a non-fixed orbit scales to \mu_4, and \sigma\rho\sigma=\rho^{-1} for \sigma:z\mapsto1/z gives a faithful D_4 (order 8), so a genus-0 four-marked faithful-D_4 boundary is (\PP,\mu_4) (strengthening v168's cross-ratio to the full uniformisation); Cohom [E]— \rho^*\omega_k=i^k\omega_k, grading (1,2,3)=A_3 exponents; Module [E]— a unique \mu_4-equivariant iso (multiplicity-free + residue normalisation; reflection \omega_1\!\leftrightarrow\!\omega_3, \omega_2 fixed); Net [E](v154/v175). The structural residual is thereby sharpened from one diffuse premise into exactly two named open obligations, neither a finite computation: QGEO.MARKS.01 (the raw RP seam collar canonically produces the genus-0 four-marked D_4 boundary) and QGEO.KERNEL.01 (the raw seam Calderón operator is the \mu_4-equivariant free gapped contraction, as an operator). Cited in tfpt_research_contracts (the central-theorem keybox); Python-only (Möbius/cohomology symbolic; numbers mirrored via v168/v137/v162/v154/v175). Suite now 177 modules.