The Social Tier: Remembering Who Said What · Pentad Labs Research Notes

The Social Tier: Remembering Who Said What

Kendall Clark · Pentad Labs · 6 July 2026 · PLRN-017

Abstract

PLRN-013 argued that an enterprise has no record of a matter that<br>is true from no perspective, only many situated accounts that disagree, and that<br>an agentic memory system worth the name keeps them rather than flattening them.<br>That note made the case. This one shows the details. For each piece of<br>WunderOS’s social memory tier, including the opinion, its fusion, the trust<br>placed in a source, the “case file” the various perspectives live in, and the<br>sense in which one agent knows what another has done, I give the mathematics it<br>rests on and, in a few cases, some code.

1. Three tiers the standard picture leaves out

Almost every account of memory for agents begins from the same taxonomy taken<br>over from mid-century cognitive psychology: working, episodic, procedural,<br>semantic. It is a good taxonomy and I keep it. But it carries two silent<br>assumptions. The first is that memory belongs to an individual: one mind, one<br>store, one vantage. The second is that agentic memory should be modeled on human<br>memory at all. I will not argue against either; both are plainly wrong in my<br>view. But the remedy is to add a social memory tier. The four standard tiers<br>are less wrong than incomplete. They are simply not enough for an enterprise,<br>which, legal personhood aside, isn’t really an individual. So WunderOS adds<br>three tiers:

a compliance tier (what was permitted, by whom, provable after the fact),

an institutional tier (what the organization knows as a whole without<br>collapse-by-integration), and

a social tier (who said what, from which vantage, and how far to trust<br>it).

2. The opinion

A confidence between zero and one cannot separate two cases a decision must<br>separate: first, a source examined and found evenly balanced; and, second, a<br>source about which nothing is yet known. Both read one-half; only the second<br>should move under a little evidence. What the scalar omits is how much is<br>unknown. So the unit of the social tier is not a probability but a Subjective<br>Logic opinion (after Jøsang), which carries uncertainty as its own mass:

pub type SLOpinion {<br>SLOpinion(belief: Float, disbelief: Float, uncertainty: Float)

with \(b + d + u = 1\) and a base rate \(a\) fixing the prior expectation. A<br>decision still reads a number off it—the projected probability, \(P(x) = b +<br>a\,u\)—but the number is no longer all there is. The move that makes the next<br>section work is that an opinion is equivalently a quantity of evidence under a<br>non-informative Beta prior of weight \(W\) (here \(W=2\)):

\[r = \frac{W\,b}{u}, \qquad s = \frac{W\,d}{u}, \qquad<br>b = \frac{r}{r+s+W},\; d = \frac{s}{r+s+W},\; u = \frac{W}{r+s+W}.\]

3. Fusion that does not depend on the order it arrives in

Agentic accounts of real-world facts like human gossip do not arrive in a<br>canonical order, nor do they arrive bidden, that is, gossip and opinion<br>confront you in the daily grind of life, whether or not one also happens to<br>seek it out, for whatever motivation.

In WunderOS, inspired as it is in part by Linda tuplespaces, opinions come over<br>Gerede, the substrate’s gossip protocol, which promises nothing about sequence<br>and, after a partition, reconciles the two sides by exchanging what each is<br>missing rather than replaying a log.

Two nodes will see the same accounts in different orders. If the combined<br>result depended on order, the two nodes would hold two different memories of the<br>same events.

In evidence form the fix is immediate. Jøsang’s cumulative fusion is addition of<br>evidence,

\[\omega_1 \oplus \omega_2 \;=\; \big(r_1 + r_2,\; s_1 + s_2\big),\]

Addition is commutative and associative. WunderOS carries the counts in a wide<br>fixed-point integer accumulator—a quire, which does not round between<br>operations—so the addition is exact, and “commutative and associative” becomes<br>not an approximation that holds on the cases tested but bit-for-bit identity.

The fusion kernel (zig/sl_ops.zig) folds any number of opinions through one<br>accumulation and one conversion, and the property is asserted directly:

test "accumulate: fold is byte-identical under any permutation (associativity)" {<br>const a = OpinionTuple{ .b = 0.6, .d = 0.2, .u = 0.2, .a = 0.5 };<br>const b = OpinionTuple{ .b = 0.1, .d = 0.7, .u = 0.2, .a = 0.5 };<br>const c = OpinionTuple{ .b = 0.3, .d = 0.3, .u = 0.4, .a = 0.5 };<br>// accumulate over every permutation of {a,b,c} — all bits_equal

That the substrate’s arithmetic is deterministic in this sense is the subject of<br>PLRN-002; here it does one specific job, which is to make gossiped<br>belief safe to hold.

4. Trust as a rating

Fusion assumes the accounts are worth pooling; discounting adjusts for the fact<br>that some sources are worth more than others, and discounting needs a number.

WunderOS does not hand-set a weight. It carries a source’s standing as a<br>Glicko-2 rating—an estimated...