Research Notes
Research Notes
These notes give a compact reference to the V40/F20 commitments, their statuses and contraries, and the open research questions. They do not replace the governing preprint.
Formal Core
TITOF := ℰC := (𝒮Ctot, ≺C)
CommonStageC(s) ⇔ s ∈ 𝒮Ctot ∧ 𝒮phys(s) ≠ ∅ ∧ ∃A ∈ 𝒮phys(s) PhysRealA+(s)
Invariant(𝒮Ctot, ≺C) :⇔ StrictTotalOrder(𝒮Ctot, ≺C) ∧ ∀s ∈ 𝒮Ctot: ChangeSystemSet(s) = 𝒮phys(s) ≠ ∅
UCC ⇝ Invariant(𝒮Ctot, ≺C)
CMA ⇔ ∀A ∈ 𝒰phys: 𝒲A ⊆ 𝒮Ctot ∧ ⊲A = ≺C|𝒲A
UCC ⇔ ∀A ∈ 𝒰phys ∀s ∈ IA: PhysRealA+(s)
CosmicMoment :⇔ CMA ∧ UCC
𝔗C(𝒮Ctot, ≺C) ∧ UCC ⇒ ∀s ∈ 𝒮Ctot: RealizedChangeStageC(s)
UCC ⇒ ¬∃A ∈ 𝒰phys ChangelessAnchor(A)
e1 ≤causal e2 ∧ e1 ≠ e2 ⇒ σ(e1) ≺C σ(e2)
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.
Status of Each Commitment
- Definitions: time, extension, invariance, cosmic stage, the common-stage condition, temporal constitution, the cosmic moment.
- Representation convention: the Ordinal Succession 0 ≺C 1 ≺C 2 ≺C … ∞ (conditional); its numerals determine the stage of no given change.
- Axioms and postulates: Strict Cosmic Ordering, CMA, UCC, CRP, Identity-Realization Convexity, the Actual Formation Boundary, PIECP, and the Cosmic Origin postulate.
- Principles: Change-Stage Restraint, Non-Transfer, and the Foundational Empirical Attribution Principle.
- Revisable hypothesis: non-termination of the succession.
- Optional: universal eventual identity ending.
- Application hypothesis: the clock-response hypothesis HCR, not a commitment of ITOF.
- Derived results: the theorem of stages of change, uninterrupted change, independence of CMA and UCC, stage-local causation, strict causal monotonicity of any association of events with stages, non-admission of temporal geometry, prediction non-separation.
Stated Contraries
- CMA: a physical system with a private stage or a private ordering of stages.
- UCC: warranted complete physical non-change of a system; a certified bound counts against UCC only when it falls below the change that standard physics predicts for the coupled channels.
- Strict order: a physical causal loop, in which a system contributes to a change of its own that is earlier than the contribution.
- Cosmic Origin: established evidence of physical systems realized before the first stage, that is, a succession without a least member.
- HCR (application level, not ITOF): refuted by a constitution-dependent clock response that violates its predicted pattern; restricted when clock comparisons establish |kα| < 1 × 10−9, and withdrawn in the electromagnetic sector at |kα| < 1 × 10−10. The present clock bound is kα = (14 ± 11) × 10−9; the MICROSCOPE bound |kα| < 3.4 × 10−12 places its minimal field model below the withdrawal threshold, so HCR remains open only as a phenomenological hypothesis about the response of clocks.
Relativity in Brief
- One global time against the many proper and coordinate times of the geometric reading.
- Every established quantitative result retained through the phenomenon bridge, with inclusion conditions J1–J3 and exclusion conditions M1–M4.
- Lorentz transformations from homogeneity, isotropy, and the relativity principle (Ignatowsky).
- Objective co-presence: in logical type absolute simultaneity, selected by no record, with no medium and no preferred frame; empirical equivalence with special relativity concerns records only.
Open Research Questions
- Engagement with causal set theory, where an order of elements is taken as basic.
- Engagement with the problem of time in canonical quantum gravity.
- Comparison with neo-Lorentzian readings of relativity, which also hold an objective simultaneity, but through a preferred frame or medium that ITOF does not posit.
- Experimental programs on certified isolated ground states, separating physical isolation from model-based subtraction.
- Clock comparisons under declared vibration, thermal, and gravitational conditions, using the vibration-condition protocol.
- Clock-ratio and equivalence-principle tests bearing on HCR.
- Evidence bearing on the first stage and on the end of the succession.
Project Records
Zenodo Archive — DOI 10.5281/zenodo.19542538