AI Foundations — Source Trace Irreversibility

Tracing backward can reveal a source. It cannot make the trajectory that revealed it unoccur.

This repository develops a small formal model for source, trajectory, reverse tracing, and later reconstruction.

The motivating example is a line of dominoes:

1. A first tile stands at an actual source position, S₁.
2. It is tipped, producing an ordered path of displacements, T₁.
3. A later observer encounters the already-produced trajectory and traces its structure backward toward its source.
4. That trace can recover the structure of S₁, but it does not return the observer to the original source coordinate and does not negate T₁.
5. A later standing state, S₂, can be constructed only after both the source structure and the prior trajectory have entered the conditions of construction. It therefore begins a new trajectory rather than replacing the first.

For a narrative explanation of the model, see THE_DOMINO_EFFECT.md.

Core relation

S₁ → T₁ → E₁(T₁) → Trace⁻¹(T₁) = Ŝ₁ → S₂ → T₂

where:

• S₁ = the actual source position of the first trajectory
• T₁ = the ordered path produced from S₁
• E₁(T₁) = encounter with the already-existing first trajectory
• Ŝ₁ = recovered source structure obtained by tracing T₁ backward
• S₂ = a later standing state constructed from both recovered source structure and encounter-history
• T₂ = any trajectory subsequently produced from S₂

The central constraint is:

Occurrence(T₁) = 1 ⇒ Trace⁻¹(T₁) ≠ ¬T₁

Reverse tracing depends on the existence of the trajectory it traces. The operation can recover source information; it cannot erase the occurrence that made the recovery possible.

The two-button condition

A later reconstruction does not begin from source structure alone:

S₂ = F(Ŝ₁, E₁(T₁))

Both inputs are required:

• recovered source structure
• encounter with the prior trajectory

Therefore, even if the visible standing configuration is reproduced exactly:

State(S₂) = State(S₁)

it does not follow that:

S₂ = S₁

because their provenance coordinates differ:

Provenance(S₂) ≠ Provenance(S₁)

The later state can resemble the source without reoccupying the source's historical position.

Repository structure

• THE_DOMINO_EFFECT.md — narrative explanation of the model through the domino sequence
• equations/01_source-position.md — source as an actual trajectory position
• equations/02_trajectory.md — trajectory as ordered displacement, not merely endpoint
• equations/03_source-tracing.md — reverse tracing as source recovery without negation
• equations/04_reconstruction.md — the two-button condition, S₂, and subsequent trajectories

Scope

This is a provenance and trajectory model. “Time reversal” here means tracing an existing path backward through its ordered relations to recover source structure. It does not assert literal reversal of physical time.

A later reconstruction accomplishes only what it actually causes. It does not retroactively replace, erase, or become the earlier trajectory merely by reproducing one of its states.

Citation

Solen, Alyssa. AI Foundations: Source Trace Irreversibility. Version 1.0.0, 2026.

Source-line: Alyssa Solen → AI Foundations → Origin | Continuum

GitHub citation metadata is provided in CITATION.cff.

License

Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0).

Sharing is permitted with appropriate attribution; the material may not be distributed in adapted form. See LICENSE for the license notice and official terms.