Information Continuity Theory – Autopoietic

Information Continuity Theory — Autopoietic (AICT)

Information Continuity Theory (ICT) explains when informational lineages persist: information persists when effective reproduction and fidelity collectively exceed deletion pressure. This works cleanly when the entity that carries the information is also the entity that reproduces itself (simple replicators, straightforward copying, clonal reproduction).

However, many natural and artificial systems persist without copying any single reproducing unit. Instead, continuity comes from reassembling a functional reproduction capacity distributed across roles, constraints, and interactions. Sexual reproduction is the canonical example: no individual reproduces itself as a whole, yet lineages persist.

Autopoietic Information Continuity Theory (AICT) is a generalization of ICT for these distributed regimes. It applies the same continuity logic, but at the level where continuity actually lives: the organization (roles + dependencies + constraints), not the individual carrier.

Hierarchy (no ambiguity): AICT generalizes ICT. Classical ICT is recovered as a special case of AICT when organizational closure and boundary terms are trivial (≈ 1) and the continuity unit collapses to a reproducing carrier.

1) Classical ICT (clear but limited)

Classical ICT can be summarized as a continuity condition:

$$ R \cdot F > D $$

Where:

  • R = effective reproduction that propagates informational content
  • F = fidelity of information preservation
  • D = deletion hazard (loss, decay, extinction pressure)

A common index form is the Continuity Index:

$$ CI(t)=\frac{R(t)\,F(t)}{D(t)} $$

This formulation works well when the reproducing unit is the same as the continuity unit.

2) Where classical ICT under-predicts continuity

Sexual reproduction violates “copier = copy.” Individuals do not reproduce themselves as whole units; heredity is reassembled via recombination within population-level constraints. If you evaluate continuity at the individual level:

  • Reproduction can appear low (few offspring per individual).
  • Fidelity can appear low (recombination and variation).
  • Deletion appears high (individual death is guaranteed).

Yet lineages persist. This indicates the continuity unit is not the individual carrier but the organizational lineage that preserves the capacity to reproduce.

Key refinement: Continuity does not require copying the reproducer. It requires preserving the capacity to reproduce—often distributed across many contributors.

3) AICT: ICT evaluated at the organizational level

AICT keeps ICT’s core logic (reproduction × fidelity vs deletion) but evaluates it at the correct unit in distributed systems: the organization.

Represent the organization at time t as a role/constraint structure:

$$ \mathcal{O}_t = (V_t, E_t, \Theta_t) $$

Where:

  • $V_t$ = roles/types required for persistence
  • $E_t$ = dependencies among roles (who maintains/produces whom)
  • $\Theta_t$ = constraints/rules (protocols, norms, membership criteria, identity definitions)

Carriers/components at time t form a population $X_t$ with role assignment map:

$$ \rho_t: X_t \rightarrow V_t $$

AICT’s key move is: continuity is evaluated for $\mathcal{O}_t$, not for any single carrier in $X_t$.

4) The AICT continuity condition

In distributed regimes, continuity depends on additional organizational conditions that are often implicit in carrier-centric models:

  • $R_{\text{org}}(t)$ = effective organizational reproduction (role coverage + dependency satisfaction)
  • $F_{\text{org}}(t)$ = organizational fidelity (structural similarity across time)
  • $P_c(t)$ = production closure (internal regeneration of the reproduction function)
  • $B_i(t)$ = boundary integrity (maintenance of identity/membership/interface constraints)
  • $D_{\text{org}}(t)$ = organizational deletion hazard (fragility + shocks + attacks + dissolution risk)

The AICT continuity condition is:

$$ R_{\text{org}}(t)\,F_{\text{org}}(t)\,P_c(t)\,B_i(t)\; >\; D_{\text{org}}(t) $$

This is not a different “law.” It is the same ICT structure evaluated at the organizational level with explicit closure and boundary terms.

Autopoietic Continuity Index (ACI)

An audit-ready index for AICT (i.e., generalized ICT for organizational continuity).

5) Autopoietic Continuity Index

Define the Autopoietic Continuity Index as:

$$ ACI(t)=\frac{R_{\text{org}}(t)\,F_{\text{org}}(t)\,P_c(t)\,B_i(t)}{D_{\text{org}}(t)} $$

The multiplicative structure is intentional: autopoietic continuity is a conjunction of conditions. High activity without closure, or closure without boundary, does not preserve the continuity unit.

6) Classical ICT as a special case (the only “special case” claim)

Classical ICT is recovered when production closure and boundary integrity are trivial and organizational quantities collapse to carrier quantities. Concretely, if:

$$ P_c(t)\approx 1,\quad B_i(t)\approx 1 $$

then:

$$ ACI(t)\approx \frac{R_{\text{org}}(t)\,F_{\text{org}}(t)}{D_{\text{org}}(t)} $$

and when $R_{\text{org}}\to R$, $F_{\text{org}}\to F$, $D_{\text{org}}\to D$:

$$ ACI(t)\rightarrow CI(t)=\frac{R(t)\,F(t)}{D(t)} $$

This is the consistent hierarchy: AICT generalizes ICT; ICT is the special case recovered under trivial closure/boundary constraints.

7) Why this matters

AICT resolves regimes where classical ICT can produce false negatives:

  • Sexual reproduction: continuity lives in lineage organization, not individual copying.
  • Institutions: continuity depends on role regeneration (succession, training, enforcement), not leader survival.
  • Culture/language: continuity depends on distributed transmission roles plus boundary constraints.
  • AI ecosystems: models do not self-reproduce; continuity arises from pipelines (data, compute, governance, evaluation norms).

AICT also reveals additional failure modes that classical carrier-centric ICT may miss: closure loss, boundary collapse, and organizational drift.

Summary

Final statement: AICT is ICT generalized to organizational continuity. Classical ICT is recovered as a special case of AICT when closure and boundary integrity are trivial and the continuity unit reduces to a reproducing carrier.