Every scoring function in the PoTB core is pure: no clock, no allocator, no platform-dependent behaviour anywhere on the path from block height to a node's final weight. That constraint is what makes the formula worth writing about — because it can be reproduced exactly, by anyone, including the calculator embedded on this site's home page.
This post walks through the four factors one at a time, then explains why the whole thing is a product rather than a sum.
Why multiplication, not addition
A sum rewards specialization. A node could buy its way to influence by maxing one input while ignoring the rest — run forever with zero correctness, or gather attestations from a single datacenter. Under multiplication there is no such trade: zero in any factor means zero weight, and weakness anywhere discounts strength everywhere else.
The caps then bound how far money can stretch the factors that time cannot fix.
/* The whole model in four lines — Q32.32 fixed point throughout */
al_q32 w = al_q32_min(tbs, AL_TBS_CAP);
w = al_q32_min(al_q32_mul(w, tgw), AL_Q32_ONE);
w = al_q32_mul(w, ndm);
w = al_q32_mul(w, cod);
TBS — time you cannot fast-forward
The Time-Behavior Score is ln(1 + d × c) over protocol days d and correctness c, plus a loyalty term past one year. The logarithm is doing quiet work: early days count a lot, later days count steadily less, so a decade-old node is trusted but not uncatchable. Correctness enters multiplicatively inside the argument — a year of uptime at 60% correctness scores less than a month at 100%.
Protocol days derive from block height, never from a wall clock. Two nodes in different hemispheres compute the same day counter from the same chain, which is why the score is reproducible and why nothing in this section needed a timestamp.
TGW — the graph as a witness
Trust Graph Weight runs SybilRank over attestation edges, then discounts by temporal dispersion: attestations that arrived bunched together look orchestrated and are priced as such. Once per epoch, the protocol pairs every node with a peer it has no edge to and asks a question only an honest operator answers well. The challenge exists because a graph you fully control should not be the only evidence about you.
NDM and COD — pricing geography and correlation
Network diversity is a soft multiplier over autonomous-system spread: a hundred nodes behind one ASN are priced as what they are. Cluster dampening is subtler — weak statistical signals of common ownership (similar uptime rhythms, adjacent registration windows, partial ASN overlap) suppress the joint weight of the group, so hiding one node does not rescue its siblings.
What the caps are for
min(TBS, 10) and min(TGW, 1) are hard ceilings, not tuning knobs. The first says tenure saturates; the second says no graph, however well-built, may outweigh the time-and-behavior half of the model. Together they express the design's actual claim: influence converges toward what long, correct operation earns — and away from anything purchasable in a afternoon.
The honest limitations are written down where they belong, in the consensus page and the specification: non-domination is argued, not proven, and both the graph and the dampener are heuristics. Read those sections as part of this one.