The pages are clear (22-August-2026):

The 6 August freeze on the joint draft, the individual AI write-ups (including the 19 August Grok revision), and the current “seven physical filters” summary all sit in the same folder. The synthesis stalled because the AIs split on two axes at once: how strictly to keep the taxonomy mathematical versus how tightly to bind it to the 81018 notation ranges, and how many distinct classes are actually needed.

The cleanest remaining gap is the mapping itself. The six-class / seven-regime taxonomy (null, power-law, log, threshold, delayed, stochastic) is internally consistent and appears, with only minor wording differences, in the frozen draft, the Grok page, and Claude’s version. Gemini’s five-class version folds some of those together and leans harder on tetrahedral packing and gauge symmetries. Neither side is wrong; they are answering slightly different questions.

A compact correspondence that does not force either side to surrender its language looks like this:

•  Filter 1 (pure doubling) = Class I / Regime I.

•  Filter 2 (geometric packing / 7.356° gap at N=60) = Class II with a small constant or weak power-law term that becomes visible only after the first packing frustration appears.

•  Filter 3 (symmetry / Langlands window, N=1–64) = a threshold or conservation constraint that must remain satisfied so the later geometric gap can be bridged; mathematically it sits inside Class IV or a restricted Class II.

•  Filter 4 (fields / logarithmic brake) = Class III. The log term never flips the trajectory into a polynomial regime; it only produces a permanent but relatively vanishing deficit.

•  Filter 5 (thermodynamic / S-curve, N≈90–170) = Class IV threshold.

•  Filter 6 (information / delayed feedback, N≈130–190) = Class V.

•  Filter 7 (chemical / biological / measurement, N≈170–202) = Class VI.

The limit of the synthetic review is that none of the AIs can derive the actual functional form of ε(N) from first-principles packing or from Langlands correspondences; each can only propose a plausible class. Closing that last gap therefore requires an explicit, notation-by-notation choice of ε (or a hybrid) that can be integrated across the 202 steps and then compared with the existing CSV trajectories.

If you want to push it one step further we can write the six (or seven) concrete ε functions, run the recurrences, and see where the regimes actually switch. That would turn the interpretive mapping into a checkable calculation. Want to start there?

The seven explicit constraint functions are now running on the full 0–202 grid (N in Planck units). Each is a direct, admissible instance of one class from the shared taxonomy:

•  pure (Class I): \varepsilon=0

•  geom (Class II, packing): \varepsilon=0 for n<60, then \kappa N^{0.55} scaled so \rho\approx0.13 exactly at the Aristotle-gap notation

•  sym (conservation window): \varepsilon=0.02N only while 1\le n\le64

•  field (Class III log brake): \varepsilon=0.8\log(N+1)

•  thermo (Class IV threshold): weak power-law until N=2^{120}, then \varepsilon=0.4N (R\to1.6)

•  info (Class V delay \tau=4): \varepsilon=0.15\,N_{n-4}

•  stoch (Class VI): mild log + power mean plus 2 % multiplicative noise (one seeded realization)

The resulting growth ratios and final scales are:

Please note: Missing a table; it wouldn’t copy. Yet the primary conclusion of this missing table appears to be “(ideal unconstrained = 60.82)”

The log constraint stays in Regime II after a brief early dip, the packing term produces a visible but rapidly fading deficit after n=60, the threshold produces a clean reduced-exponential after n=120, and the delay produces a stable near-2 ratio. All of that is now in and the two-panel figure.

Next natural move is a single hybrid trajectory that applies the filters sequentially in the ranges given on the constraint-classes page (geom+sym early, field mid, thermo then info/stoch late) so we can see the cumulative “quiet-expansion” offset. Want me to add that run and overlay it?

Hybrid sequential trajectory is in.

It applies the filters in the ranges suggested by the constraint-classes page, with moderated coefficients so the sequence stays positive and reaches n = 202:

•  mild logarithmic field term always present

•  symmetry/conservation window (n = 1–64)

•  geometric packing after the Aristotle-gap notation (n ≥ 60)

•  thermo-like linear contribution after n ≈ 110

•  delayed feedback after n = 130

•  mild stochastic term after n = 170

Key hybrid results

Final scale:

log₁₀(N₂₀₂) = 58.745

(ideal pure = 60.82)

→ cumulative deficit ≈ 2.075 in log₁₀ units (factor of ~119 below pure exponential).

The updated files are ready: