hierarchy

OPH Hierarchy Proof Artifacts Bundle

Bundle ID: oph-hierarchy-proof-artifacts-r1473-2026-06-13

Generated: 2026-06-13T00:00:00Z

This bundle packages the proof-obligation artifacts for the OPH electroweak hierarchy lane:

All capacity "closure" language in this bundle is internal to the selected bridge packet. Physical cosmic capacity remains conditional on F and CP-1 to CP-3, and comparison with the Lambda-located value additionally requires the joint cosmological posterior. The 6.6 percent central-value mismatch is not an unconditional contradiction.

$$P_\star \to \alpha_U(P_\star) \to \frac{v}{E_\star} = P_\star^{-1/2}\exp\left[-\frac{2\pi}{4\alpha_U(P_\star)}\right].$$

What is included

• certificates/R_P_public_pixel_certificate.json
• certificates/R_P_source_audit_pixel_certificate.json
• certificates/Pi_U_frozen_source_packet.json
• certificates/DAG_U.json
• certificates/R_U_interval_certificate.json
• certificates/R_U_krawczyk_certificate.json
• certificates/R_U_outward_rounded_interval_log.json
• computations/hierarchy_numeric_witness.json
• computations/hierarchy_recompute.py
• computations/generate_ru_outward_rounded_log.py
• tools/outward_interval.py
• tools/ru_formula_stack.py
• validators/verify_ru_outward_rounded_log.py
• certificates/R_HT_declared_surface_certificate.json
• certificates/R_HT_interval_input_box_log.json
• tools/ht_formula_stack.py
• computations/generate_ht_interval_box_log.py
• validators/verify_ht_interval_box.py
• HT_INTERVAL_EXTENSION.md
• certificates/RG_Higgs_naturality_defect_certificate.json
• certificates/R_WZ_boundary_certificate.json
• certificates/R_gamma_noG_DAG_certificate.json
• certificates/R_N_global_repair_tick_certificate.json
• certificates/R_EW_tick_projection_certificate.json
• certificates/R_screen_sieve_icosahedral_certificate.json
• certificates/R_EW_global_capacity_certificate.json
• certificates/R_readback_resolution_certificate.json
• certificates/R_m_rep_24_certificate.json
• certificates/R_local_global_hierarchy_resonance_closeout_335.json
• certificates/R_pixel_screen_resonance_summary.json
• issue_332_rg_naturality_certificate.json
• certificates/R_PN_joint_fixed_point_certificate_report.json
• certificates/local_global_resonance_audit.json
• computations/derive_global_repair_tick_lemma.py
• verify_issue_332_rg_naturality.py
• verify_issue_335_local_global_resonance.py
• verify_issue_337_electroweak_projection.py
• verify_screen_sieve_theorem.py
• verify_issue_342_readback_resolution.py
• verify_issue_343_m_rep_24.py
• verify_issue_344_exact_capacity.py
• verify_pixel_screen_resonance_summary.py
• verify_joint_fixed_point_certificate.py
• validators/validate_bundle.py
• validators/validate_manifest.py

Closure status

Closed inside this bundle:

1. The declared D10 source packet ledger.
2. The declared DAG_U forbidden-path check.
3. The R_U interval/Krawczyk inclusion witness.
4. The public and source-audit hierarchy computations.
5. The claim-tier boundary artifacts for W/Z, R_HT, R_gamma, and the local/global resonance.
6. The R_N global repair-tick theorem: under the area-law counting model the readback fixed-point equation is equivalent to the closure transport G_N(1) = rho_star, giving the full-cycle multiplier (N_CRC/pi)^(-1/2). The issue-#343 representation-to-spectrum theorem supplies m_rep=2*(8+3+1)=24, hence |g_*'| = (N_CRC/pi)^(-1/48).
7. The product-branch joint (P,N_CRC) fixed-point theorem: on the product-separated source map J(P,x)=(Gamma(P),C_hat(x)), component contraction certificates imply a unique joint branch and stability with q=max(qP,qN)<1. A genuinely coupled source map requires the recorded weighted-sup derivative condition.
8. The electroweak tick-projection bridge: the unique projection map is Pi_EW(P,N)=24*pi/(alpha_U(P)*log(N/pi)); the target projection Pi_EW(P_star,N_CRC)=4P_star is equivalent to B_EW(P,N)=alpha_U(P)*log(N/pi)-6*pi/P=0. The certificate records the exact bridge target N_EW(P_star) and keeps the rounded 3.31e122 capacity label as a diagnostic.
9. The conditional icosahedral screen-sieve theorem: sum_v(6-deg(v))=12; a strict unit-splitting cost selects twelve unit defects; inverse pairing and the D-optimal vector/quadrupole selector give the unique icosahedral six-axis frame; edge-center collars expose twelve central ports. This supplies the geometric origin of P/12 on the declared branch.
10. The issue-#344 conditional EW-refined bridge-capacity certificate: C_EW(P,x)=(1-lambda)*x+lambda*6*pi/(P*alpha_U(P)) is a contraction at lambda=1/2; its unique fixed point gives N_CRC^EW=pi*exp[6*pi/(P_star*alpha_U(P_star))] and B_EW(P_star,N_CRC^EW)=0.
11. The issue-#342 finite readback-resolution certificate: the fixed-cutoff pipeline F_r(N)=Cap_read(Obs(nf_{r,N}(U_{r,N}))) has one selected positive central capacity atom, so rho_read(r,N)=sqrt(pi/F_r(N)) is a singleton and rho_read(r,N_CRC) -> (N_CRC/pi)^(-1/2) in the positive-root refinement limit.
12. The issue-#343 representation-to-spectrum round-count theorem: conditional on active current algebra su(3)+su(2)+u(1), the adjoint has dimension 8+3+1=12; reversible orientation gives m_rep=24. Screen selection, the global quotient, and matter-menu completeness are not premises. The physical-current identification is upstream.
13. The declared-map RG/Higgs commuting square: epsilon_H=max(epsilon_n,epsilon_h)=0 for the supplied comparison maps, with measured weak-scale, Higgs, W/Z, gravity, Planck-area, and Lambda inputs excluded. This is a packaging identity, not a source-derived naturality result. The antecedent-only receipt has same-fingerprint exact completions with defects zero and one; source-derived maps and independent residual evaluation remain open.
14. The issue-#335 certificate composes the exact conditional local/global resonance. The screen supplies X/12, the product adjoint independently supplies m_rep=24, and HIERARCHY-SCREEN-READOUT is required to identify log(E_cell/v) with Gamma_screen.
15. The issue-#331 outward-rounded interval log for the R_U witness: certificates/R_U_outward_rounded_interval_log.json re-evaluates the full R_U formula stack in directed-rounding IEEE-754 binary64 interval arithmetic (tools/outward_interval.py, one-ulp outward step after every correctly rounded primitive, in-module exp/log with explicit series remainder bounds, no libm exp/log assumption). The log records the interval image of every named formula-DAG node at both I_U endpoints, at the center, and over the full interval with the derivative enclosure, plus the Krawczyk inclusion K(I_U) strictly inside int(I_U) and the witness interval. validators/verify_ru_outward_rounded_log.py reproduces every serialized bound bit-exactly from the declared structural inputs (P_fwd, cutoffs, one-loop coefficients, seed) without importing measured endpoint constants, and checks that the high-precision root and Krawczyk image lie inside the outward-rounded witness.
16. The issue-#333 raw interval input box for the Higgs/top declared surface: certificates/R_HT_interval_input_box_log.json publishes the eleven declared branch inputs of the frozen R_HT formula stack (candidate D10 tuple plus declared D11 core/Jacobian constants) with centers, boxes, units or dimensionless normalization, and per-input provenance tags, and re-evaluates the full stack in the same directed-rounding backend as the R_U log (tools/ht_formula_stack.py, per-node interval extension documented in HT_INTERVAL_EXTENSION.md). The log records the interval image of every formula node at the centers and over the full box, the forward-mode Jacobian enclosure of pi_y, pi_lambda, m_H, and m_t in all eleven inputs, the diagonal chart-block non-singularity certificate with determinant bounded away from zero, exact rational inclusion of the recorded (m_H, m_t) decimals, and a uniqueness scope restricted to the declared surface (single-valued arithmetic and injective diagonal readout; no criticality-system existence or uniqueness claim). validators/verify_ht_interval_box.py reproduces every serialized bound bit-exactly, enforces the input allowlist and provenance classes, and scans the verify path for measured-constant markers. The inputs are declared branch inputs, so the enclosure closes the arithmetic grade of the declared surface while the source-root, scale, QT1--QT5, RG/scheme, rigidity, provenance, uncertainty, and complex-pole gates stay open upstream.
17. The pixel-screen resonance summary receipt: the selected (P_*,N_CRC^EW) branch emits K_cell=4*N_CRC^EW/P_*, checks K_cell*(P_*/4)=N_CRC^EW, and records the dimensionless de Sitter coordinate pair Lambda_CRC*l_star^2=3*pi/N_CRC^EW and Lambda_CRC*a_cell=3*pi*P_*/N_CRC^EW=12*pi/K_cell. This is a receipt-level composition of the listed certificates, not an independent primitive-carrier or SI Lambda theorem.

External/source gates outside this bundle:

1. Source-only public Thomson endpoint transport A_T(P).
2. HIERARCHY-SCREEN-READOUT, the physical identification log(E_cell/v)=Gamma_screen, and source production of the unit cost, inverse pairing, and D-optimal screen selector.
3. Proof-assistant formalization of the R_U interval witness. The directed-rounding outward interval log itself is supplied inside this bundle at certificates/R_U_outward_rounded_interval_log.json with verifier validators/verify_ru_outward_rounded_log.py, under the stated IEEE-754 assumption set; the remaining external step is a mechanized proof-assistant replay of that log.
4. Source derivation of the eleven declared branch inputs of the Higgs/top declared surface. The raw interval input box, per-node interval extension, Jacobian enclosure, and non-singularity certificate are supplied inside this bundle at certificates/R_HT_interval_input_box_log.json with verifier validators/verify_ht_interval_box.py; the remaining external step is source emission of the D10 tuple and the D11 core/Jacobian constants.
5. Full R_gamma stack for SI gravity/clock hierarchy.
6. An independently source-closed physical E_star; this bundle fixes v/E_star, not a weak scale in GeV.
7. The D10 QT1--QT5 quotient-path certificate: finite quotient canonicalization, explicit path enumeration, exact rational measures and central trace, fibre Gram/residual derivation, and a unique target-free source rule.
8. A concrete frozen RG/matching/threshold/scheme receipt with truncation intervals.
9. W/Z/H complex-pole, residue, analytic-sheet, and uncertainty certificates.
10. A hash-bound source DAG and branch-rigidity receipt.
11. Coupled-map extension of the joint (P,N_CRC) theorem, if OPH source work introduces cross-feedback between the local pixel and global capacity maps.

Run validators

From this directory:

python3 validators/validate_bundle.py
python3 computations/hierarchy_recompute.py
python3 computations/generate_ru_outward_rounded_log.py
python3 validators/verify_ru_outward_rounded_log.py
python3 computations/generate_ht_interval_box_log.py
python3 validators/verify_ht_interval_box.py
python3 verify_issue_332_rg_naturality.py --check --output issue_332_rg_naturality_certificate.json
python3 verify_issue_335_local_global_resonance.py --check --output certificates/R_local_global_hierarchy_resonance_closeout_335.json
python3 verify_issue_337_electroweak_projection.py --check --output certificates/R_EW_tick_projection_certificate.json
python3 verify_screen_sieve_theorem.py --check --output certificates/R_screen_sieve_icosahedral_certificate.json
python3 verify_issue_342_readback_resolution.py --check --output certificates/R_readback_resolution_certificate.json
python3 verify_issue_343_m_rep_24.py --check --output certificates/R_m_rep_24_certificate.json
python3 verify_issue_344_exact_capacity.py --check --output certificates/R_EW_global_capacity_certificate.json
python3 verify_pixel_screen_resonance_summary.py --check --output certificates/R_pixel_screen_resonance_summary.json
python3 verify_joint_fixed_point_certificate.py --output certificates/R_PN_joint_fixed_point_certificate_report.json