Local O049 witnessfinite domain
Mathematically well defined
A specific witness on an explicitly bounded local domain; no global existence proof.
Public research site
APEIRON
Mathematically Tested Model
Local AP1 scientific feasibility established for a bounded mathematical witness — not a full cosmological validation.
A medium without end.
Broader Apeiron interpretation · Post-AP1 hypothesis
Apeiron explores one fundamental carrier whose states and forms of organisation might describe space, gravity and cosmic structure. Ordinary matter is understood as an organised Apeiron manifestation. The bounded local AP1 core is tested; the comprehensive single-carrier picture remains a hypothesis.
AP1_GO_SCIENTIFIC_FEASIBILITY_FIRSTOne fundamental Apeiron carrier: ordinary matter as an organised manifestation, dark matter as a possible state, and dark energy as a possible state or dynamical form of that same carrier. This identification remains empirically open.
Conceptual visualization · not observational data
A · AP1-tested core
What the local AP1 core supports
AP1_GO_SCIENTIFIC_FEASIBILITY_FIRST applies to the bounded O049 witness on the explicitly finite local domain. The A–F gates document mathematical well-definedness, gravitational consistency, minimum stability in the claimed domain, a nontrivial Apeiron contribution and a quantitative internal model benchmark.
The bound local domain
The bounded O049 witness · τ ∈ [0,1/125], η = −τ, fixed conformal Planck units with Mpl_ren = 1. The status applies to the bound compatible linear scalar/TT response class with k ∈ [5/8,5/4]. The full technical identity and source bindings are retained in the methods and Technical Evidence Index.
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.
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.
Gravity and dynamicslocal scope
Consistency · minimum stability
Gravitational consistency, the bound minimum stability and a nontrivial Apeiron contribution within the specified response class.
Quantitative internal model benchmarknumerically testable
H_cosmic(τ_star) = 2 × 10⁻⁶
Exactly one event in the bound interval; its existence, uniqueness and bounded location are reproducibly specified, numerically testable and falsifiable in principle within the model. This does not claim completed independent reproduction and is not yet an astronomical observable directly mapped to observations.
τ_star is the event time and H_star the value of the cosmic Hubble rate: H_cosmic(τ_star) = H_star = 2 × 10⁻⁶. The time satisfies H0/(2 Mpl_ren²) < τ_star < 1/125; no precise event time is claimed. H0 ≈ 5.9044051867 × 10⁻⁶¹ is the bound initial value in the same units, not an observed Hubble measurement.
Audit 079 · Analytic buffer confirmed
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 lower bound itself comes from the bound earlier E14/E15/O029 proof records. Audit 079 checks the inherited evidence, arithmetic and resulting margin; it is not a new physics proof of this bound.
E14 · E15 · O029 (E26)
How the AP1-GO decision was reached
077 defined the scientific-feasibility scope prospectively after earlier O049 calculations were known. 078 performed no new physics calculation: it bound and audited the existing evidence under that scope and recorded the formal GO. AP1_GO is therefore a scientific-feasibility milestone; neither independent external validation nor historical preregistration. Earlier findings are not reinterpreted retrospectively.
!
AP1_GO is not a full cosmological demonstration, a complete last-scattering-to-present connection, a complete DM/DE demonstration, an overall astronomical fit, a global existence proof or a complete long-term stability proof. Apeiron is neither experimentally confirmed nor fully empirically validated; it is not a completed cosmological theory.
Post-AP1 / Validation Priorities — open
Independent reproduction of the bounded O049 witness and the H_star benchmark using an independent implementation or analyst. This is scientifically desirable Post-AP1 work, not a retrospectively introduced prerequisite for the already recorded AP1-GO.
Research history · earlier results unchanged
The 077 definition was introduced after earlier O049 results were known and applies from 077. Earlier findings are not reinterpreted retrospectively. v7.13, its open reproduction questions, the restricted configuration exclusion and earlier methodological limits remain in place.
v7.13 HARD-PASS · Published computation · limited scope. The frozen discrete gate result remains valid within its original scope; it does not establish a complete Apeiron theory.
STOP · configuration 013 · AP1-M1 configuration · excluded. For the exact frozen model with state 007, the common Cauchy set is empty. Other states or models are not excluded.
B · Broader Apeiron research programme / Post-AP1
Genesis, a cosmic cycle, return through black holes, full DM/DE interpretation, filaments and structure formation, complete cosmology and observational comparison are further hypotheses or research goals. O049 has not derived them as consequences or empirically confirmed them. This also applies to the open AP2/AP3 phases.
Broader Apeiron interpretation · Post-AP1 hypothesis
One carrier, different manifestations
The binding Apeiron single-carrier principle postulates one fundamental carrier. Ordinary matter belongs to it as an organised manifestation. Condensations, filaments, cosmic genesis and reconversion are investigated as possible processes within this carrier. A complete microphysical derivation and empirical tests remain outstanding.
One carrier
Ordinary matter is an organised Apeiron manifestation.
Genesis
A possible local phase transition within the same carrier.
Reconversion
Organised manifestations might transition to more fundamental Apeiron states.
Possible states of the same carrier
Dark matter and dark energy
Within the Apeiron model, dark matter denotes a possible manifestation or state of the same fundamental carrier. It is not postulated as separate fundamental matter alongside Apeiron.
Dark energy is investigated as a possible state or dynamical form of this carrier. This does not yet provide a quantitative explanation of cosmic acceleration or an observationally confirmed account of dark matter and dark energy.
Possible new particles would be interpreted within this model as Apeiron manifestations. Compatibility with future observations must be tested; the single-carrier principle does not replace measurement.
Quantitative attribution to rotation curves, lensing, CMB, BAO, Bullet-Cluster-like systems and structure formation remains Post-AP1/AP2/AP3 work. The local AP1 result does not identify observed dark matter or dark energy.
QCD and Higgs in the single-carrier picture
QCD and Higgs phenomena are interpreted as possible organised manifestations of the same Apeiron carrier. The Standard Model and QCD, their equations and established results remain unchanged. A derivation of these structures from Apeiron has not been demonstrated; the connection remains a hypothesis to be tested.
Broader Apeiron interpretation · Post-AP1 hypothesis
The Apeiron cycle
A qualitative illustration of a hypothesis: every stage belongs to the same fundamental carrier. Arrows show possible internal transitions, not an established cosmic history.
Concept illustration · no observational confirmation. BH reconversion: FEASIBILITY GO; empirically open.
Apeiron carrier
one fundamental carrier
Organisation
possible filaments and nodes
Genesis
possible internal phase transition
Universe
organised Apeiron manifestations
Black holes
possible conversion regions
Reconversion
to more fundamental states of the same carrier
Conceptual visualization · not observational data
Broader Apeiron interpretation · Post-AP1 hypothesis
A universe forms locally
As a broader hypothesis, Apeiron considers a local phase transition within a larger medium as a possible cosmic origin. The bubble image is an illustrative analogy only. Such a genesis is neither derived by the bounded O049 witness nor empirically confirmed.
BH reconversion · theoretical feasibility
Reconversion within the same carrier
Organised matter is already an Apeiron manifestation. Extreme black-hole regions might enable an internal transition to more fundamental Apeiron states. The project status is FEASIBILITY GO for the investigated effective feasibility class. This is not empirical confirmation or a derivation from the local O049 witness.
BH RECONVERSION · FEASIBILITY GO
The microscopic final state, a unique fundamental action, quantitative reconversion rates and observational evidence remain open. The transition postulates neither a separate Apeiron substance nor destruction of energy.
Conceptual visualization · not observational data
Public research record
Current Apeiron documents
Single-carrier principle · 14 September 2026. Each download states its document language and version.
PDF reader editions include a dated editorial notice; original pages are retained.
Historical / frozen · AP1 evidence
AP1-GO preprint · decision 078
APEIRON · Mathematically Tested Model · Local Scientific Feasibility of an Apeiron Realization
Historical / frozen · v1.1 · 11 September 2026 · A079/H1 · English · not peer-reviewed
The AP1 preprint v1.1/A079 and its evidence remain available unchanged as a historical/frozen computational and audit record. The documents listed above provide the current single-carrier interpretation. Earlier wording in the archives is historical.
The downloads provide current research documents and clearly labelled historical evidence. Later archiving on an established scientific platform with a DOI is intended; no such deposit or peer review is claimed here.
AI was used as a tool for source auditing, consolidation and drafting. Josip Fellner is responsible for the scientific claims and their approval; AI use does not replace independent validation.