Why we built the 777 network value model

Every product decision the protocol will ever make is downstream of a value model. Who do we admit? Which triples surface first? How do we price the matching engine? When is the network “full”? Without a written-down model, those answers are vibes. With one, they become consistent, auditable, and improvable. The 777 network preview is the public face of that spec; the same math drives admission and matching internally.

People who can stress-test the assumptions and either find them sound or improve them are the people we want as founding members. The page is a screening tool. If your reaction to the sliders is “where did the complementarity multiplier come from and is it endogenous to skill diversity?” you are who we built this for. If your reaction is “wow, big number,” you are not. The 777 is forming around people who think in models, not people who consume them.

The default for “what is a network of 777 ambitious people worth” is either silence (intuited but unstated) or hype (asserted without math). Both are worse than a transparent illustrative model with visitor-controlled assumptions. We would rather be wrong on a stated number than vague on an unstated one. The sliders are the apology in advance: change the inputs, watch the outputs move; you do not need to trust us, you need to be able to falsify us.

VCs invest in companies. Talent networks broker contracts. Time banks barter hours. Mastermind groups exchange advice. None of these compute the marginal coordinated productive capacity unlocked by complementarity-matched triples spanning direction-aligned humans. The methodology is the proof that Rhiz is a distinct category, not a re-skinning of an existing one. Replacing the 2.2 constant with an endogenous complementarity function, replacing additive matching yield with marginal lift plus overlap decay, swapping flat year-1 for a Bass S-curve, and adding a random-matching counterfactual: each move tightens the category boundary the protocol sits inside.

777 is the test fixture, not the product. The model has to survive at member 778, member 7,777, and member 77,700. Three things change as N grows.

Member valuation becomes marginal, not absolute.

For prospective member N+1, the right question is not “what is this person worth” but what is ΔV(N+1), the increase in coordinated value from adding them. That equals their own latent capacity plus their expected triple uplift. The page exposes this directly: it computes ΔV(778) under N log N scaling and shows the breakdown. The protocol’s admission threshold becomes “ΔV(prospect) > engine cost,” which is a quantitative bar instead of a judgment call.

Existing members compound, not depreciate.

Under Briscoe-Odlyzko-Tilly N log N scaling, every new admission ticks up the matching surface for every existing member by log(N+1)/log(N). Going from 777 to 7,778 multiplies the existing members’ surface by ~1.34. The scaling curve on the preview page renders this directly. This is the actual investment case: your seat appreciates as we grow because every later member becomes a potential triple-partner for you.

Saturation matters more than headcount.

The 201st US climate-builder adds less marginal value than the 1st Lagos climate-builder. The model already has direction × skill × geography cells; the missing piece is a saturation map that surfaces “open seats” the network is structurally short on. That tool stays internal (it is an admission targeting tool, not a public claim), but it follows from the same math the preview exposes.

Personalized expected value at the point of join.

The strongest use of this work is per-prospect. A candidate should see “given your direction profile and skill set, the current network has 14 high-value triples that include you, with an expected marginal yield of $X over your remaining career, at a Y% matching-intensity assumption.” That converts the population-level page into a personalized acceptance letter, and it falls out of running the same complementarity math against the prospect’s vector.

1. Marginal matching yield with overlap decay. The prior version summed full triple value on top of latent, which double-counted each member’s baseline up to 6×. Matching yield now sums only the lift (complementarity − 1) × alignment × baseCapacity, with a 1/(1+k) decay per member to attenuate repeated credit across the multiple triples one member can sit in.
2. Endogenous complementarity. The 2.2× constant becomes 1 + 1.5 × skill_entropy × direction_coherence. Range now [1.0, 2.5], varying per triple, calibrated against Hoogendoorn (2013) and Wennberg (2010) founding-team complementarity studies.
3. Counterfactual: random matching baseline. The page now shows scattered vs. random matched vs. Rhiz matched. The gap between random and Rhiz is the actual product claim; without it, random clustering takes credit for what we attribute to the engine.
4. Bass S-curve + Year 3 view. Year 1 / Year 2 / Year 3 / Year 4 / Year 5 = 10% / 30% / 55% / 75% / 90%. Year 3 is the new default mid-horizon view, since it is the timeframe investors actually evaluate against.
5. Discount rate sensitivity (3 / 5 / 7%). Lifetime NPV is no longer asserted at a single rate. Annual flow is invariant of discount rate (it is the contractually equivalent constant payment); lifetime is rediscounted at the visitor’s chosen rate.
6. Future-member ΔV(N+1) and N log N scaling curve. The page now extrapolates beyond N=777 using Briscoe-Odlyzko-Tilly scaling, calibrated against current observed values. Marginal-member breakdown shows what the next admission contributes and how much existing seats compound.

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