Program standing board

Decides whether killing is adhesion-limited or occupancy-limited, and now has an external argument behind it. Two accounts predict values 200× apart and they are mutually exclusive. The quantity was an apology two sessions ago; it is now the discriminating observable.

new this session

Item 02's prediction test says our N₂₀ is 2.6–7.2× too high to be carried by a real cell line that a published engager kills. N₂₀ inherits this fork directly — so somebody else's calibrated beads now bear on which end of it is right.

the fork

0.1 µm² → the inferred threshold is the adhesion requirement, no gap to explain. ~20 µm² → a large absolute receptor count is required, and both surviving readings need it.

evidence so far

The glycocalyx favors the small value on a mechanism: membranes reach 14 nm only where a 86–127 nm barrier has been parted, so the cleared area is set by displacement, not footprint.

cost

One imaging measurement, by methods the source papers already use.

Executed this session. One construct passes, one rules our own N₂₀ out. We claim a killing threshold is computable rather than being a property of the cell. The recipe turned out to be portable — our N₂₀ is Langmuir occupancy at a measured endpoint, σ × EC₂₀/(EC₂₀ + K_D), needing no gating arm and no on-rates — so it could be run against two published constructs directly.

result

cibisatamab: ours at 5.02 µm⁻² sits inside its capacity ceiling of 3.98–17.83 at both clocks. PASS, conditional on the avidity factor below. PF-07062119: it kills LS174T at 0.82 nM with 875 receptors/cell, so its threshold is ≤1.93 µm⁻². Ours is 2.6–7.2× that. FAIL, and binding rather than marginal.

a bound corrected on re-check

The cibisatamab ceiling was first published as 3.98–11.05, which quietly assumed every bivalent molecule uses both arms. A bivalent binder can also bind with one arm, and those molecules still occupy surface — so the true ceiling is an interval between σ/2 and σ: 3.98–17.83 µm⁻². It widens upward, so the pass only gets safer. The monovalent GUCY2C construct has no such loophole and its failure is untouched.

why the missing constant didn't block it

Occupancy is bounded by one, so the capacity ceiling is the best case for agreement and the unknown GUCY2C K_D can only push their threshold down. At a plausible 1 nM it falls to ~0.6 µm⁻². The verdict is unaffected; only its magnitude is open.

and three effects stack the same way

Occupancy < 1, the EC₂₀-from-EC₅₀ conversion, and the cell-diameter bracket all widen the gap rather than closing it. Reconciliation would need d ≤ 7.4 µm — lymphocyte scale, on a colorectal epithelial line.

what it did to the board

It stopped being blocked on fetching rate constants and started being blocked on items 01 and 06, which were already ranked first and sixth. Our N₂₀ inherits the contact-area fork and the assumed Hill coefficient, and a 2.6–7.2× overestimate sits inside that uncertainty. So those two measurements now carry an external argument, not only an internal one.

λ = 1000 — used once, refused once

The same number does two jobs and they must be kept apart. Used: it sets the CEA arm's effective affinity, which sets occupancy, which is what makes cibisatamab's threshold actually reach its ceiling. Citing a published parameter as an input is ordinary. Refused: pointing at λ = 1000 next to our retention ratio of 730–1,069× and calling it corroboration — a round power of ten stated as a model input cannot support a claim, and this program already killed a 201×/200× agreement of exactly that shape.

and the pass depends on it, quantified

At a ~1 nM dose: λ = 1 → occupancy 0.008, FAIL; λ = 10 → 0.071, FAIL; λ = 100 → 0.435, PASS; λ = 1000 → 0.885, PASS. So the one construct that agrees with our threshold needs λ ≥ ~100 to do so. That makes the provenance question a gate on a result, not a footnote — and raises it from curiosity to the top of the reading list.

All that is left of a former top item. The question was whether solution rate constants transfer to a live interface. For T-cell receptors the two-dimensional off-rate runs 4–12× faster and our criterion tolerates only 3.2× — but that is the wrong molecule class, and reading it across was an error.

what the reading task found

For an antibody-format paratope the modeled penalty falls on association — on-rate 100–1,000× slower from restricted rotational diffusion — while the rotational contribution to dissociation is about 2× lower. That is the safe direction: it lengthens relaxation and puts all six variants on the trapped side, including the two that were intermediate at no correction.

why the on-rate penalty does not hit us

It applies to membrane-anchored binders. Our engager is in solution when its first arm binds, so that encounter is genuinely three-dimensional. The tethered second arm already uses an effective local concentration with a diffusion factor rather than a solution on-rate.

what survives

Force. The rotational account says nothing about it, it is the proposed cause of the T-cell-receptor acceleration, and our bridged complex spans two cells being pulled apart. Nobody has measured it for a two-cell bridge.

The retention advantage belongs to the arm nobody mutated. The gating arm's off-rate cancels from the ratio of the two lifetimes, leaving 1 / [k_off,A · (1/k_r,B + 1/k_r,A)] — verified against the exact first-passage result to better than 0.5%.

the evidence

Gating-arm k_off spans 138-fold along the published ladder; the retention ratio moves 1.53-fold, and the residual is carried by the k_on drift we already record — not by affinity.

what it implies

Both published series laddered the gating arm, so neither changed the retention advantage. Their selectivity came from displacing the comparator, which is a different operation and does not survive a change of comparator.

the prediction

Retention goes as 1/k_off,A — a tenfold slower anchoring arm should give a tenfold larger advantage with the gating arm untouched. Table 34.

The only thing that separates a lifetime claim from a plain affinity dependence. Along both ladders k_off and K_D are collinear at r = 0.997 and 0.985, so a persistence threshold and a dependence on the equilibrium constant are the same regression. An assay clock is not collinear with anything.

design

Binding must be measured alongside killing at each timepoint — time-dependent killing alone does not establish time-dependent binding, since killing accumulates under equilibrium binding too.

prediction

Selectivity falls as exposure approaches the dual-positive relaxation time. The equilibrium account contains no clock at all.

and now a second use

It is also the in-house version of the clock invariant that passed on external data in item 02. Same plate, two tests.

Our own limitations call this the single most valuable missing number. No Hill coefficient has been measured for any system of this kind. Without it the asymmetric window runs anywhere from 0.01× to 35× — a range this literature assumes without measuring.

candidate mechanism

A multi-hit requirement: three events inside a ~50 min window against an hour-scale decay brackets an exponent between 1 and 3, and we assume 2. A bracket, not an agreement.

cost

EC₂₀ and EC₅₀ on every curve with binding measured at the same concentrations.

The floor is capacity, not transport, and its approach is a divergence rather than a decline. The diffusion-capture account of the floor was excluded this session — margins 681× to 61,609×. What survives is an inequality with no rate constants in it: each bridge consumes one antigen, so bound engager can never exceed accessible antigen, and below N₂₀ the cell is unkillable at any dose. Margin on our own lines: 3.6×.

the shape

Required dose rises as 1/(1 − N₂₀/σ). A 73% fall in accessible density is enough to take a killable cell to unkillable, and the last stretch is a divergence — so the failure should look like a cliff, not a slope. Shedding, trogocytosis and a thicker glycocalyx are all plausibly that large.

what would test it

A density ladder on one background sampled densely near the failure point rather than across decades. Published panels sample for dynamic range and would miss a cliff.

what the inequality already did

Run backwards it bounds other people's thresholds from their own calibrated panels, with no free parameters — see the closed log. That result is why this item is on the board and why item 01 now has an external argument behind it.

prior art

Searched under the standing rule. The published non-monotonicity for engagers is on the concentration axis — the bell-shaped curve from single-arm occupancy outcompeting bridging — not the density axis, and it is not ours. No density-axis conservation floor for a bridging construct was found.

Kills or keeps the environment-as-gate idea cheaply. Tumor extracellular pH of 6.5–7.0 is measured and pH-dependent antibody binding is established chemistry, but that a given arm's k_off moves 2–3× across 0.4–0.9 pH units is assumed by us.

if it fails

Takes the environment-gate direction entirely and leaves everything else. That is why it belongs early despite ranking low — an early clean kill is worth buying.

note

Distinct from the architecture gate, which prior art has already claimed — see the closed log.

Checks for a confound inside our own data. If the barrier differs between the dual-positive and single-positive lines our selectivity ratios compare, then part of a measured ratio is a difference in access rather than in binding — and every slope in the paper inherits it.

status

Unknown. Neither source reports it, and we have not looked for it in the lines they used.