Canonical · Autocatalytic Constraints

The Three Autocatalytic Constraints

Tier-0A Substrate of Principia Attractum

The three autocatalytic constraints are the additional admissibility conditions that must hold for a recursive system to qualify as autocatalytic. They presuppose that recursion is already admissible; they add what autocatalysis specifically requires beyond that.

A quick way in

Before the formal statements, a dirty little cheat to carry in your pocket. The old line says the only things you can count on in life are death and taxes. Add one more, being born, and you have a rough feel for all three constraints at once:

To be born is Non-Free Restart. Nothing here resumes; anything that comes back has to start over, pay its way in, and become itself again from scratch.
Death is Irreversible Loss. Some losses do not reverse; when identity's boundary breaks past recovery, that instance is over.
Taxes are the running cost of staying admissible. To keep existing across time, an autocatalytic system pays a continual toll; stop paying and you drift toward the first item on the list.

So: a start you cannot skip, an end you cannot undo, and a toll in between you cannot stop paying. That is the shape of the three. It is a mnemonic, not a definition, and it is lossy on purpose; the exact conditions are below.

Not primitives

A Tier-0R primitive is ontic, universal, and pre-recursive. It restricts what the substrate is allowed to do before recursion has a chance to happen. The six ontic primitives are of this kind.

A Tier-0A constraint is derived, domain-restricted, and presupposes that recursion is already admissible. It applies only to the autocatalytic case. It does not restrict the substrate. It restricts what counts as autocatalytic behavior on top of it.

Three earlier candidates for this tier were promoted out during the framework's version-two audit because they turned out to be true of all recursion, not just autocatalysis. What remains here are the three items that are genuinely autocatalysis-specific.

The three

βIrreversible Loss Classification

A loss event in an autocatalytic system is classified as β when all three of the following hold:

  1. A boundary defining recursive identity is violated.
  2. The prior recursive configuration cannot be restored under transitions the system permits.
  3. Re-establishment of the configuration would require re-ignition, not continuation.

β is a classification outcome, not an agent, force, or process. It marks the structural status of a loss event. It does not cause the loss; it labels its irreversibility.

ADM-AUTOAutocatalytic Application of Admissibility

All six admissibility forms remain in force, but for autocatalytic recursive systems they are not equally weighted. Three forms govern the autocatalytic case, in a specific order of priority:

  1. Trajectory admissibility is the primary condition. An autocatalytic system stands or falls on whether its trajectory remains admissible over time.
  2. Transition admissibility is the per-update gate. Each state change must preserve recursive identity.
  3. Structural admissibility is the necessary precondition. Without it, no trajectory or transition question arises.

The remaining three forms — parametric, state, and asymptotic admissibility — stay in force but are subordinate: relevant to the analysis, but not the forms by which an autocatalytic instance stands or falls.

ADM-AUTO is a prioritization construct, not a new decomposition. It adds no admissibility forms; it specifies which of the existing six govern in the autocatalytic case.

Failure linkage:

trajectory-admissibility loss + boundary failure + irreversibility ⇒ β

NFRNon-Free Restart

After β-classified loss in an autocatalytic system, recursion may not resume freely. Any subsequent autocatalytic recursion in the same substrate must:

  1. Re-satisfy the conditions for recursive admissibility.
  2. Re-pay the initiation cost.
  3. Re-establish recursive identity.

The new recursion is a new autocatalytic instance, not a resumption of the lost one. Identity is not inherited across β. History matters in autocatalysis: a system that has undergone β-loss cannot proceed as if the loss did not occur.

What sits nearby but is not one of the three

Downstream of β and non-free restart, the framework carries a further Tier-0A pack governing the degradation-to-residue-to-restoration sequence. That pack is a classification-constraint set of seven sub-rules, not a fourth constraint. The three named on this page are what the framework's audit identifies as the genuinely autocatalysis-specific admissibility conditions.

The three-item scope of this tier is a v2 Principia Attractum result. In v2's internal-consistency audit, three conditions previously grouped here were promoted out of this tier because they hold for all recursion, not autocatalysis alone; β irreversible loss, non-free restart, and the autocatalytic application of admissibility are what the audit leaves as genuinely autocatalysis-specific. The constraint content is preserved from v1; the three-item boundary is v2.

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