**APEIRON**

**Mathematically Tested Model**

Local AP1 scientific feasibility established for a bounded mathematical witness — not a full cosmological validation.

# Audit 079 supplement

Josip Fellner · Version 1.1 · 11 September 2026 · Correction snapshot A079

HSTAR_E14_BUFFER_AUDIT_PASS. AP1_GO = TRUE. AP1_GO_SCIENTIFIC_FEASIBILITY_FIRST. This supplement presents the already decided audit for public reading; it does not rerun the audit or perform new physics.

## Certified bound and endpoint margin

HSTAR_E14_BUFFER_AUDIT_PASS: H_,τ > 2.6 × 10⁻⁴ is a conservative analytic, error-covered lower bound on [t_b,1/125]. The initial layer is controlled separately. It implies a guaranteed endpoint margin of about 4% above H_star = 2 × 10⁻⁶. Evidence chain: E14/E15 → O029/N029. The audit checked existing evidence and bound numbers; it supplies no new physics proof, solver run or AP1 gate decision.

Precisely: H(1/125) − H_star > 8 × 10⁻⁸ − 1.3 × 10⁻⁴ H0 > 8 × 10⁻⁸ − 7.8 × 10⁻⁶⁵. The relative lower bound is 0.04 − 65 H0; “about 4%” must not be rounded up to an exact guarantee of at least 4%.

The exact relation retained from 079 is H(1/125) > 2.6 × 10⁻⁴ (1/125 − t_b), with t_b = H0/(2 Mpl_ren²). In the bound units t_b = H0/2 < 3 × 10⁻⁶¹. Positivity of H(t_b), smoothness and the uniform derivative bound justify the endpoint inequality. On [0,t_b], a separate existing estimate gives H < 10⁻⁶⁰ < H_star. The derivative bound is not extended to τ = 0.

## Analytic provenance and error coverage

The number 2.6 × 10⁻⁴ is the conservative analytic lower bound inherited through E14 from O029.O10/O15. E15 supplies the bound intervals and the historical instantiation/identity records apply them to the same complete O049 witness. O029/N029 explicitly carry the geometric, massive-kernel, nonlinear source, initial-coordinate, free-state and resolvent remainders. Outer interval endpoints and conservative constants cover rounding in this derivation. Discretization, a numerical solver trajectory and interpolation are not used to establish it. This does not certify an arbitrary separately implemented numerical solver.

E18 supplies the full source bookkeeping and its standard-density majorant; it does not convert a computational profile into the exact history or provide the derivative certificate.

## H0 and source notation

H0 retains its historical meaning as the O049 initial/reference Hubble parameter, H₀⁽ᴼ⁰⁴⁹⁾ ≈ 5.9044051867 × 10⁻⁶¹, not a fit to the observed present-day H₀(obs). H_cosmic here denotes the model-internal Hubble rate defined with respect to cosmic time.

Within the bound model, ρ_nonstd = ρ_cl + ρ_ref + ρ_fin = 3H_star² − ρ_std ≈ 1.2 × 10⁻¹¹. E18 binds |ρ_std(a=1)| < 1 × 10⁻¹¹⁰ (1e-110). At the benchmark the carried envelope is |ρ_std(τ_star)| < (1e-110)/a_star⁴, with a_star > 0.997479. The initial-point bound is not transferred unchanged to the event slice.

The nonstandard sector therefore supplies practically the entire Friedmann source within this local model benchmark. This is not a DM/DE fit or a statement about the observed cosmological matter fraction; additional unknown particles remain possible.

The AP1 domain is a local mathematical feasibility domain, not a reconstruction of a physical cosmological epoch or an observational H(z) trajectory. The benchmark is not a direct H(z) prediction.

## Original audit records

- [Audit 079 report in German](evidence/audit_079/AUDIT_079.md)
- [Audit 079 decision](evidence/audit_079/DECISION_079.json)
- [Original audit manifest](evidence/audit_079/MANIFEST_079.json)
- [Original audit checksums](evidence/audit_079/SHA256SUMS)

These records describe the completed audit before this publication step. Their statement that no new publication was performed belongs to that earlier audit and remains historically intact. This supplement is the subsequently authorized public incorporation.

The benchmark is reproducibly specified, numerically testable and falsifiable within the model. It is not a completed independent reproduction, an astronomical observation or a direct H(z) prediction. No independent external validation or new physical proof is claimed.


## Public hygiene H1

**Source of the inherited lower bound.** The bound H_,τ > 2.6 × 10⁻⁴ comes from the bound earlier proof records: [E14](https://apeiron-field.info523741.chatgpt.site/downloads/ap1-go-078-v1.1-2026-09-11-audit079-hygiene/evidence/VARIANT_B_019/AP1_PROSPECTIVE_SELECTION_047/OWN_HSTAR_EVENT_047.md), [E15](https://apeiron-field.info523741.chatgpt.site/downloads/ap1-go-078-v1.1-2026-09-11-audit079-hygiene/evidence/VARIANT_B_019/AP1_PROSPECTIVE_SELECTION_047/RESULT_047_OWN_PREFIX_QUERY.json), [O029 (E26)](https://apeiron-field.info523741.chatgpt.site/downloads/ap1-go-078-v1.1-2026-09-11-audit079-hygiene/evidence/VARIANT_B_019/AP1_FEASIBILITY_BLOCK_029/O029_PRUEFBELEG_POSITIVE_EXPANSION_UNTERKLASSE.md). E14 states the event argument, E15 binds the witness input intervals, and O029 supplies the inherited positive-expansion bounds. Audit 079 checks the inherited evidence, arithmetic and resulting margin; it is not a new physics proof of this lower bound.