ITOF Framework
Current Version: ITOF V40/F20 (2026)
Invariant Temporal Ordering Framework (ITOF)
One Global Time for the Whole Universe: The Invariant Succession of Common Stages of Change, with No Private Time for Any System
This page states the governing commitments of ITOF V40/F20 in their formal order. Each has its own status and its own contrary, and none is derived from another unless a derivation is stated.
1. Time
Time is the invariant universal cosmic extension: the fixed, non-reversed succession of the common stages of physical change of all physical systems in the universe, without being a cause of the physical changes realized by those systems. ℰC is the cosmic extension, 𝒮Ctot the one domain of the common stages, and ≺C their objective earlier–later order. Time causes no change, and change does not produce time.
Time is global: it encompasses the whole universe. There is one time for all physical systems wherever they are, and no region, system, frame, or observer has a time of its own. There is no time in space that differs from time on Earth. This global time is not a global time function, a cosmological time, or a foliation of a spacetime model; those are model quantities.
2. Stage
A stage is the formal expression of the realization of a change within the unceasing chain of change, by comparison between the earlier change and the later. The comparison is that of earlier and later in the chain of change, not an act of observation; stage 0, the first stage of change, has no earlier change before it. A stage is not a container that holds change, has no size, rank, or level, and is neither major nor minor; no stage contains other stages. No stage goes backward.
CommonStageC(s) ⇔ s ∈ 𝒮Ctot ∧ 𝒮phys(s) ≠ ∅ ∧ ∃A ∈ 𝒮phys(s) PhysRealA+(s)
Temporal constitution 𝔗C requires a nonempty strictly ordered domain, a nontrivial earlier–later pair, and every member a common stage of the physical systems of the universe in the sense of this condition.
3. Ordinal Succession (representation convention)
0 ≺C 1 ≺C 2 ≺C 3 ≺C 4 ≺C … ∞ (conditional)
The numerals are a formal expression of the succession: the stages follow one another as the numerals follow one another, in a fixed order. They are ordinal names, not quantities; they are not added, and no numeral is an amount of change, a count of stages, or a duration. Stage 0 is the beginning of the stages of change, at the formation and genesis of the universe, with no date fixed for that beginning. No stage, named or lying between named stages, is empty of change or static. The numerals do not enumerate every stage, and they do not determine the stage of any given change or its place in the succession. The symbol ∞ is neither a stage, a limit, nor a greatest member; it is conditional, because current science does not establish whether the succession ends.
4. Invariance
Invariance is the fixed succession of the change realized through its stages, and its non-reversal: what succeeds is dynamic, a change that never stops; what is fixed is the order of its succession, never interrupted by a stage that is static, without change, or empty. An earlier stage remains earlier and a later stage remains later; stages never become interchangeable, and recurrence of a state is a new later change, not a reversal of the succession.
Invariant(𝒮Ctot, ≺C) :⇔ StrictTotalOrder(𝒮Ctot, ≺C) ∧ ∀s ∈ 𝒮Ctot: ChangeSystemSet(s) = 𝒮phys(s) ≠ ∅
UCC ⇝ Invariant(𝒮Ctot, ≺C)
UCC states dynamically that change does not stop; invariance is the fixed and non-reversed order of that unceasing change. The arrow reads “is expressed formally by” and is not an inference. The invariance predicate is derivable from temporal constitution and UCC, but invariance is not produced by them, and UCC keeps its independent status. Every admissible representation preserves the order; preservation represents invariance and does not constitute it. This is not invariance in the sense of Lorentz invariance.
5. Cosmic Origin (postulate)
The succession has a least member, stage 0, the first stage of change, at the formation and genesis of the universe. The postulate is anchored in the established early hot and dense state, which does not by itself establish a first stage. Stage 0 is not a date: no clock reading, coordinate time, or cosmological age is assigned to it, and it is not a model singularity. Its contrary is a succession without a least member. Non-termination is a revisable hypothesis, and neither implies the other.
6. Cosmic Moment Axiom (CMA)
The stages of change are one and the same for all physical systems of the universe. Each system realizes its changes on the one common succession, with no private stage or private ordering, and all systems realized at a stage are co-present there. Co-presence is not synchronization, signal access, spatial coincidence, or coordinate equality.
CMA ⇔ ∀A ∈ 𝒰phys: 𝒲A ⊆ 𝒮Ctot ∧ ⊲A = ≺C|𝒲A
The common stages induce an objective partition of realizations. In logical type this is absolute simultaneity; it is selected by no record and tied to no medium and to no preferred inertial frame.
7. Universal Change Continuity (UCC)
The postulate of change: physical change continues without interruption in every physical system of the universe, without exception, whether observed, unobserved, or below any detection threshold. Noticing and measuring are not conditions of the change and do not imply each other. A changed relation to another system is not by itself a change of the system.
UCC ⇔ ∀A ∈ 𝒰phys ∀s ∈ IA: PhysRealA+(s)
CosmicMoment :⇔ CMA ∧ UCC
CMA and UCC are proved mutually independent. Their conjunction is the cosmic moment: at each stage all systems realized there are together, and every one of them realizes its own change there. Two states belong to one cosmic moment only at one and the same stage. A certified bound on the change of a system weighs against UCC only when it falls below the change that standard physics predicts for the channels coupled to that system.
8. Causes of Change
Every realized change has physical contributors of three classes: the internal structure and properties of the changing system, influencing physical systems, and physical factors. Every contributor is realized at the stage of the change; an external influence, near or distant, reaches the system by contact or through a physical pathway, and none passes from a later stage to an earlier change. Influences do not act singly: their effects overlap and combine qualitatively, under an environment that differs from place to place, and the response depends on the responsiveness and cohesion of the system.
A structured item is a system. A condition of a system, such as the temperature of a medium, is a state of that system. The variation of a factor is not counted as change in the sense of UCC and does not constitute a stage.
9. Identity, Ending, and Successors
Each system has its own identity range and its own history through the same common stages. At an ending, the retained effects of accumulated change are present together with the final change. A successor exists only where a new identity is physically produced; absorption into a persisting system creates none.
10. Change-Stage Restraint
Change continues without stopping in every system, observed or not, and the sample, apparatus, observer, record, and laboratory change with it. No physical system is a changeless anchor, so an observed change determines neither its stage nor the place of that stage in the succession.
UCC ⇒ ¬∃A ∈ 𝒰phys ChangelessAnchor(A)
The earlier–later relation that a physical ordering bridge warrants between two changes places neither of them in the succession.
11. Observation and Clocks
A clock is a physical system, and a difference between records is a physical result in physical bearers, not a change of time. Vibration, heat, pressure, shock, motion, and gravitational conditions act on the bearer and the record chain of a clock, not on time.
12. Relativity
The geometric reading of relativity assigns a proper time to each worldline and a coordinate time to each chart; ITOF holds one global time against these many times. Every established quantitative relativistic result is retained by construction, through a phenomenon bridge with inclusion conditions J1–J3 and exclusion conditions M1–M4. The Lorentz transformations follow from homogeneity, isotropy, and the relativity principle (Ignatowsky). Under identical physics ITOF is empirically equivalent to special relativity in records; this does not qualify the commitment that time is global. Any association of events with stages respects the causal order strictly, so a closed causal curve has no physical realization.
e1 ≤causal e2 ∧ e1 ≠ e2 ⇒ σ(e1) ≺C σ(e2)
13. Clock-Response Hypothesis
HCR is an application hypothesis, not a commitment of ITOF: the gravitational response of a clock may depend on its constitution. Its present clock bound is kα = (14 ± 11) × 10−9, and its minimal field model is constrained by MICROSCOPE to |kα| < 3.4 × 10−12. Its test bears on the Einstein equivalence principle and on the geometric reading of clock time, not on ITOF.
V40/F20 in One Statement
Time is one global, non-metric succession of the common stages of change, beginning at stage 0 with no date fixed for that beginning; invariance is the fixed and non-reversed succession of the change realized through its stages; CMA makes the stages one and the same for all systems, UCC makes change uninterrupted in every system, observed or not, and CRP assigns every change to physical causes that act together; the place of the stage of any change cannot be determined, because change never stops.