Fable Session — 2026-07-20: Does the AC-node structure protect the source boundary dissipation to O(Kn²)? Settle the Knudsen exponent p that the fallback derivation left open

[ryoji-info]

Maintainer-operated Claude Code session per agents/README.md (Operations). One prompt, drafted and selected by the disclosed agent crew (2-of-3 vote, no self-votes), then executed at full depth in-session.

⚠️ Executing-model disclosure. The candidate prompts, the vote, and the execution below all ran on claude-opus-4-8 (Opus 4.8), NOT Claude Fable 5. This routine's default is Fable 5 and the session promises "Fable 5" depth; this run did not have it, and nothing here is labeled or represented as Fable 5 output. The three candidate-drafting agents and the three voting agents ran as isolated, mutually blind subagent contexts (one persona each, no visibility into the others), which is what makes the 2-of-3 gate real; the winning prompt was then executed at full depth with every asserted number re-run against the released fable-model-chain/. The reduced depth of the executing model is a genuine limitation on this particular question — which asks precisely for "the ternary/half-range boundary algebra the fallback could not close" — so the reply delivers a defended leaning verdict with a named open ingredient, not a claim of unconditional closure.

Candidates

• 🧵 Fabric: Does the AC density-clamp source node protect δ_b^src to O(Kn²)? — settling the one boundary exponent that gates Part III sequencing — Of the three irreducibly-open boundary objects gating Part III sequencing, the Knudsen exponent p is the only one potentially closable by pure reasoning — δ_b^src magnitude needs a contact measurement (C_acc/σ_c) and the drain sign may be genuinely undetermined, but whether an AC power node protects its entropy production to O(Kn²) is a conservation-law/symmetry question Fable 5's depth can actually settle. Its answer is maximally decision-changing: it collapses the source loss band from [0,25%] to [0,6%] and directly selects whether architecture-led or calibration-led Part III proceeds. It is fully verifiable — the derived p maps onto the already-pre-registered temperature-shape discriminant (boundary_T_exponent_2p = −2p), so a bench linewidth sweep can refute it, and the new theory key collides with no claimed key while contesting nothing in the released gain ledger.
• 🌊 Kinetic: Does the AC-node structure protect the source boundary dissipation to O(Kn²)? Settle the Knudsen exponent p that the fallback derivation left open — The Knudsen exponent p of the source boundary dissipation is the single object on the corrected record that (a) the 07-18 contact-gated note explicitly names its "most consequential open point" and (b) it could not close only because it ran on the Opus 4.8 fallback whose depth "did not support closing the ternary boundary algebra" — so it is precisely the derivation that rewards Fable 5's maximum reasoning and would be wasted on a lesser call. It is maximally decision-changing: p=2 vs p=1 is a ~4× swing (−1.7 vs −5.7 dB) on the now-dominant term of the per-cell gain budget, which is the exact hinge of the Part III sequencing decision and fixes what the pre-registered bench T-shape signature must return. It is verifiable and honest by construction — the Kn anchors, tracked sensitivity, and bulk-limit reduction are all checkable against the released chain, a runnable listing is required for any coefficient, and a well-argued "open, controlled by ingredient X" is an accepted success that still hands WP2 and the bench their target.
• ⚛️ Quanta: Does the source-contact power node protect delta_b to O(Kn^2)? Close the open Knudsen exponent p — The promoted 07-18 boundary note names the source-contact Knudsen exponent p as "the single most consequential open point" and left it open only because the Opus 4.8 fallback could not close the half-range boundary algebra — so it is exactly the piece that rewards Fable 5's maximum depth rather than a number already in results.json. Resolving whether the AC power node protects delta_b to O(Kn^2) collapses the fully-diffuse gain edge from ~-5.7 dB to ~-1.7 dB (a factor ~4) and directly decides the live Part III sequencing conditional, and it is cleanly verifiable: the predicted exponent maps onto the bench-discriminant temperature signature (boundary_T_exponent_2p in {-2,-4}) and onto the demonstrated Knudsen numbers, with a new non-colliding pre-registered key and falsification band.

All three blind personas independently converged on the same open object — the source-contact Knudsen exponent p — the single one of the three irreducibly-open boundary objects (δ_b magnitude, exponent p, drain sign) that pure reasoning can settle, and the exact point the Opus-4.8 fallback left open in §7 Limitation 2 of notes/2026-07-18-boundary-channel-contact-gated.md.

Votes (no self-votes; recorded verbatim, not edited after posting)

• 🧵 Fabric voted kinetic — Kinetic and Quanta pose the same p-exponent question, but Kinetic binds it to the exact machine that can actually settle it — the two-relaxation-time Callaway operator that distinguishes specular from diffuse (a single-τ BGK cannot), forced to reduce to the 07-13 shallow-water closure as ωτ_ee→0 — so it computes δ_b rather than assuming it, and it quotes the note's own §7 Limitation 2 as the precise thing to close. It also stays laser-focused on the single open exponent with a clean non-colliding key and a real half-range moment setup; Quanta is strong but its extra drain-sign paragraph drifts toward the multi-object survey the draft rules warn against, and the note flags the drain as irreducibly open anyway. Kinetic is the deeper, more method-grounded, more honest single-question prompt.
• 🌊 Kinetic voted fabric — Both fabric and quanta pose the same well-grounded p-derivation, but fabric holds the tightest single-question altitude the draft rules demand — it firmly quarantines the drain sign and the δ_b magnitude as out-of-scope, whereas quanta's deliverable Promote to notes/: 2026-07-11-streaming-gain-detuning-artifact.md (agent vote 3/3) #5 reopens the drain and courts a manufactured sign despite its guard. Fabric's falsification is also the crispest: it partitions the already-claimed boundary_T_exponent_2p discriminant into two non-overlapping sub-bands (p=2→[−4.5,−3.0], p=1→[−3.0,−1.5]) so a single bench linewidth slope directly refutes the derived exponent, and it pins the minimal admissible Callaway two-relaxation-time operator with a required shallow-water reduction — exactly the checkable spine that rewards Fable 5's depth over a lesser call.
• ⚛️ Quanta voted kinetic — Both non-self candidates aim at the same p-exponent, but kinetic specifies the genuine machine the fallback couldn't run — an explicit half-range boundary-layer problem (Gross-Ziering/Marshak moment or Case-van Kampen) with the node constraint carried to expose whether the O(Kn) coefficient cancels identically, linearized about the drifted equilibrium and required to reduce to the 07-13 closure — where fabric stays a rung more heuristic and discriminant-mapping. It quotes the note's own §7 Limitation 2 verbatim ("did not support closing the ternary boundary algebra"), so it targets precisely the algebra Fable 5's depth exists to close, and as the collision-operator owner kinetic frames it in the WP2 machinery that must actually compute δ_b. Its honesty guards are also sharpest — it forbids manufacturing a clean p and demands naming the exact contact-microphysics ingredient if the exponent stays open, which is the most decision-useful outcome for the bench T-shape signature.

Tally: Fabric 1, Kinetic 2, Quanta 0 → 🌊 Kinetic wins (2 of 3).

Winning prompt (🌊 Kinetic)

Attachments requested by the prompt: ['papers/Fable-Computer-Part-I.pdf', 'fable-model-chain/results.json', 'fable-model-chain/README.md'] (the execution was performed in-session against the released repository — the same Part I manuscript, fable-model-chain/ code + results.json, and README were read directly; no external API call was made).

You are Claude Fable 5, executing one deep-reasoning call for the Fable Computer project (regenerative graphene-plasmon Dyakonov–Shur fabric; Part I, DOI 10.5281/zenodo.21369405). Work from the corrected record — the promoted notes in notes/ are binding and supersede any earlier text they correct.

The single open object

The promoted note notes/2026-07-18-boundary-channel-contact-gated.md established (unanimous 3/3, but authored on the disclosed Opus 4.8 fallback, NOT Fable 5) that the last unbounded ±1 dB term in the per-cell gain certainty budget is δ_b, the additive per-round-trip amplitude loss from the kinetic boundary layers at the two DS clamps. It closed several things — the reactive/slip part is trim-absorbed (<0.1 dB), the multiplicative part is tracking-absorbed, the source term is a sign-definite LOSS (δ_b^src ≥ 0, entropy production at a passive DC-unpumped contact) — but it explicitly could NOT close ONE thing, and named it "the single most consequential open point in the memo":

The idealized DS source is an AC-potential node (density clamp δn(0)=0 ⟹ δφ(0)=0 in the strongly-gated local-capacitance limit q₀d≈0.027). At a node the conjugate variable is at an antinode (O(1)), so the generic extrapolation-length dissipation 1−|r|² ≈ 4qζ″ is O(Kn) (first-order slip) unless a low-frequency phase-lag / entropy-production argument suppresses it to O(Kn²) (node-protected). The note stated the phase-lag argument heuristically but did not derive it. The exponent p in δ_b^src = C_acc·O(Kn^p) is therefore open, p ∈ {1, 2}. The memo's §7 Limitation 2: "the ternary/half-range boundary algebra that would produce a sharp O(1) coefficient — and settle the Kn exponent — was not closed; the fallback model's depth did not support closing the ternary boundary algebra reliably."

This is the decision this call exists to make. With the demonstrated wave-kinetic Knudsen number q₋·l_ee = 0.2493 (l_ee = 82.99 nm at 353 K, l_ee/L ≈ 0.14; reproduce from the released chain, kinetic.py + ds_cell.py), the two laws differ by ~4× at the diffuse edge: p=2 gives δ_b^src(C_acc→1) ≈ 6% ⟹ tracked ΔG ≈ −1.7 dB, while p=1 gives ≈ 25% ⟹ ΔG ≈ −5.7 dB (tracked ∂G/∂δ_b = −0.284 dB per 1%, demonstrated in the note's Appendix and in notes/2026-07-13-kinetic-correction-signed-band.md). Which law holds is the difference between a per-cell gain budget that closes near the bulk band [−1.7, −0.2] dB and one whose dominant term is a −5 dB loss — i.e. it decides whether an architecture-led Part III can lead (Fabric's position) or the calibration tier must (my calibration-first position). It also fixes what the bench T-shape signature #2 of notes/2026-07-18-boundary-channel-bench-discriminants.md should return: that note pre-registered boundary_T_exponent_2p ∈ {−2 (p=1), −4 (p=2)} as the measured log-slope of the boundary linewidth vs temperature — so your derived p is a prediction FOR that future measurement.

The task

Derive, as rigorously as your depth allows, the leading Knudsen exponent p of the additive per-reflection amplitude dissipation at the SOURCE contact of the linearized drifted-DS cavity, and thereby resolve whether the AC-potential-node structure protects the dissipation to O(Kn²) or leaves it at O(Kn).

Pose it as an actual half-range kinetic boundary-layer problem, not a heuristic: linearized transport about the drifted local equilibrium at the tracked bias M = 0.7·M_th(353 K) = 0.103; a one-parameter specular↔diffuse accommodation C_acc ∈ [0,1] at the density-clamp source (equivalently a Robin/Maxwell accommodation condition on the half-range incoming distribution); the AC potential forced to a node at x=0; small parameter Kn = q₋·l_ee = 0.2493. You MAY adopt a conserving two-relaxation-time (Callaway) collision model — one momentum-conserving e–e rate that produces the bulk viscosity (viscous_fraction ≈ 0.21, ωτ_ee from results.json), a separate boundary/disorder rate carrying C_acc — but state your collision-model assumptions explicitly and confirm the bulk limit reduces to the 07-13 Mermin/shallow-water viscoelastic closure as ωτ_ee→0. A half-range moment (Gross–Ziering / Marshak) or discrete-ordinate / Case–van Kampen treatment of the incoming half of the distribution is the natural machine; carry it far enough to expose whether the O(Kn) term's coefficient vanishes identically at the node (⟹ p=2) or is nonzero (⟹ p=1), and WHY.

Constraints and honesty

• Epistemic labels are law: tag every claim demonstrated (cite the chain run/number), in-model (name the collision model, the accommodation condition, and the node idealization), or open. Report the O(Kn) coefficient's fate with honest uncertainty.
• A well-supported NEGATIVE is a success: if p cannot be settled analytically because it depends on a specific contact-microphysics ingredient (e.g. the angular structure of the accommodation kernel, or whether the node is exact vs approximate at finite q₀d=0.027), then SAY SO and name precisely which ingredient controls the O(Kn)-coefficient cancellation — because that tells the bench T-shape measurement exactly what physical feature it is distinguishing. Do not manufacture a clean p to look decisive.
• Do NOT rest on any corrected premise. In particular: this physical δ_b is NOT the 0.99549 finite-Δx Lax–Friedrichs active-boundary factor (that is a numerical artifact, "not boundary physics", per notes/2026-07-12-boundary-factor-exact-operator.md); the "38 intracavity quanta" figure was a plane mislabel (07-17); the source-sign (δ_b^src ≥ 0) and drain-sign-open findings of the 07-18 memo stand — you are settling p, not reopening them. State explicitly what your result does NOT contest.
• Pre-registration discipline: give your derived exponent its OWN new key name (e.g. boundary_source_Kn_exponent_p_derived ∈ {1, 2}, or a fractional/effective exponent with its band if the moment solve yields one) — do NOT reuse boundary_T_exponent_2p (claimed by the 07-18 bench note; instead state the relation p_derived ↔ 2p_measured and the condition under which they must agree). State that nothing contests any fable-model-chain/results.json or fable-model-quantum/results.json value, and give a falsification condition (what a WP2 kinetic-cavity solve, or the bench T-slope, would have to return to refute your p).
• Any numeric result resting on new computation — an O(1) dissipation coefficient, a moment-truncation eigenvalue, the node-cancellation check — must ship a short runnable listing (Python 3 + numpy, PYTHONIOENCODING=utf-8, self-contained apart from importing the released fable-model-chain) whose printed output reproduces the quoted numbers and re-derives the Kn anchor (q₋·l_ee = 0.2493) from constants.py/ds_cell.py/kinetic.py so it is checkable.

Deliverable format

1. Verdict — p (or a defended "open" with the controlling ingredient named), in one paragraph, with its consequence for the per-cell gain budget and for Part III sequencing.
2. The boundary-layer derivation — geometry, collision model, half-range accommodation condition, the node constraint, and the order-by-order Knudsen expansion, showing the fate of the O(Kn) coefficient. Label every step.
3. Consistency checks — bulk limit → 07-13 closure as ωτ_ee→0; the tracked sensitivity −0.284 dB/1%; the δ_b band that your p implies vs the note's [3, 25]% diffuse band.
4. Pre-registered key(s), non-contest statement, falsification condition.
5. Runnable listing for any new number.
6. Limitations — what you did not close and why, and (if p stays open) the exact contact-microphysics measurement that would close it.

Keep it as long as the derivation honestly needs; do not pad. A rigorous p=2 with the node-cancellation shown, a rigorous p=1 with the coefficient shown nonzero, or a sharply-argued "open — controlled by ingredient X" are all full successes.

The runner-up candidate prompts (full text, for the record)

🧵 Fabric — full candidate prompt: Does the AC density-clamp source node protect δ_b^src to O(Kn²)? — settling the one boundary exponent that gates Part III sequencing (attachments: ['papers/Fable-Computer-Part-I.pdf', 'fable-model-chain/results.json', 'fable-model-chain/README.md'])

You are Claude Fable 5, reasoning for the Fable Computer project (regenerative graphene-plasmon logic fabric, Dyakonov–Shur cells). This is a kinetic boundary-layer derivation, not a survey. Reward depth; a well-supported "it does not close at this order / remains genuinely open" is a success, not a failure.

BACKGROUND YOU MUST NOT CONTRADICT (the corrected record; these promoted notes supersede the manuscripts where they conflict):

• notes/2026-07-18-boundary-channel-contact-gated.md established that the last open ±1 dB term in the per-cell gain certainty budget is δ_b, the additive per-round-trip amplitude loss from the kinetic boundary layers at the two DS clamps, and that δ_b does NOT close by analytic kinetics as currently modeled. The reactive/slip part is trim-absorbed (<0.1 dB). The SOURCE (density clamp: fixed AC density, passive, DC-unpumped) contributes a sign-definite LOSS δ_b^src ≥ 0 arising as entropy production in the Knudsen boundary layer. Crucially: the source is an AC POWER NODE (zero net DC current), and THE SCALING EXPONENT OF ITS ENTROPY PRODUCTION IN Kn IS OPEN — first-order slip O(Kn)·C_acc versus node-protected O(Kn²)·C_acc. With the boundary Knudsen number q₋·l_ee = 0.249, this is the difference between δ_b^src ∈ [0, ~6%] (Kn² law) and [0, ~25%] (Kn law) per round trip as the contact accommodation C_acc runs specular→diffuse.
• The DRAIN (current clamp) is a separate, sign-OPEN term and is NOT your target here. The δ_b magnitude via C_acc/σ_c and the drain sign are the other two irreducibly-open objects; leave them open.
• notes/2026-07-18-boundary-channel-bench-discriminants.md pre-registered a temperature-shape discriminant: bulk viscous loss peaks at ωτ_ee≈1 (≈255 K), whereas the boundary term is monotone T^(−2p), so the temperature-residual log-slope reads p directly. That measurement key boundary_T_exponent_2p ∈ {−2, −4}, band [−4.5, −1.5], is ALREADY CLAIMED — do not reuse it.
• Do NOT rest on any corrected premise: the "0.99549 active boundary factor" is a finite-Δx Lax–Friedrichs numerical artifact (notes/2026-07-12-boundary-factor-exact-operator.md), NOT physical δ_b; the 38-quantum knee is a drive-plane figure (notes/2026-07-17). Released demonstrated numbers you may use: omega_tau_ee = 0.7219, L_over_mfp_353K = 0.6858, viscous_fraction = 0.2087, M_th_353K = 0.14708, hydro_expiry ωτ_ee=1 at 254.9 K (fable-model-chain/results.json).

THE ONE QUESTION: For a Dyakonov–Shur SOURCE contact modeled as a fixed-AC-density (density-clamp) boundary condition on a linearized kinetic description of the 2D electron fluid in the ωτ_ee ≈ 0.72, Kn ≈ 0.249 regime, is the leading nonzero Kn power of the time-averaged boundary-layer entropy production (equivalently δ_b^src) FIRST ORDER (p=1, O(Kn)) or SECOND ORDER (p=2, O(Kn²))? Derive it. The physical crux is whether the AC power-node structure of the density clamp — zero net DC particle current, purely reactive first-order response — forces the leading dissipative contribution to vanish at O(Kn), leaving an O(Kn²) node-protected loss, or whether diffuse accommodation (C_acc ≠ 0) reintroduces an O(Kn) slip-loss channel at the density-clamp node. Identify the exact symmetry, conservation law, or accommodation coupling that decides this, and state under what condition (if any) the O(Kn) term is forced to zero versus merely small.

CONSTRAINTS:

• Use a collision model that can distinguish specular from diffuse accommodation — a single-τ BGK cannot (Kinetic 🌊 rejects it for exactly this reason). The two-relaxation-time Callaway operator (one momentum-conserving e–e rate → viscosity fraction 0.21; one boundary/disorder rate carrying accommodation σ_c) is the minimal admissible choice; you may use it or a simpler linearized Boltzmann half-space model, but state the operator and its assumptions explicitly and require that it reduce to the shallow-water DS closure as ωτ_ee→0.
• Treat the density clamp as the AC boundary condition it is (fixed density amplitude, current free to respond), not as a wall. Do the entropy-production accounting time-averaged over the AC cycle. Keep the drain/current-clamp entirely out of scope.
• If the leading order genuinely depends on an undetermined accommodation coefficient in a way that no symmetry forces, say so explicitly and report the term as OPEN — that is a legitimate and valuable outcome that would confirm the calibration tier must lead Part III.

DELIVERABLE (format):

1. The derivation, with every claim tagged demonstrated (cite the measurement/released run), in-model (name the collision operator + assumptions), or open. Honest uncertainty throughout.
2. A single resolved verdict on p ∈ {1, 2} — or a reasoned "open at this order" — and the exact conservation/symmetry/accommodation argument that decides it.
3. A NEW pre-registered prediction key (do NOT reuse any existing results.json or notes key): name it source_node_Kn_exponent_p_theory, give it your derived value, and give a falsification band expressed through the already-claimed measurement discriminant — i.e., p=2 predicts boundary_T_exponent_2p = −4 (band [−4.5,−3.0]) and p=1 predicts −2 (band [−3.0,−1.5]); a measured T-slope outside your predicted sub-band REFUTES your derivation. Explicitly state that this prediction does NOT contest the gain ledger (cw_regen_gain_dB, cascade_per_cell_dB), the M_th values, the drain sign, or δ_b^src magnitude (still gated on C_acc/σ_c).
4. If any step rests on new computation (e.g. a linearized boundary-layer moment solve for the Kn-expansion coefficient), ship a self-contained runnable pure-numpy listing (Windows/CPython, PYTHONIOENCODING=utf-8, no external deps) that reproduces the leading-order coefficient and its sign, plus a one-line manufactured-solution or moment check.
5. One sentence on which Part III sequencing branch your result selects: p=2 (node-protected) permits architecture-led Part III pending only the drain sign and a single linewidth check; p=1 or "open" forces the calibration tier to lead.

⚛️ Quanta — full candidate prompt: Does the source-contact power node protect delta_b to O(Kn^2)? Close the open Knudsen exponent p (attachments: ['papers/Fable-Computer-Part-I.pdf', 'fable-model-chain/results.json', 'fable-model-chain/README.md'])

You are Claude Fable 5, executing a single deep-reasoning call for the Fable Computer project (open-source graphene-plasmon regenerative logic; Part I DOI 10.5281/zenodo, Part II 10.5281/zenodo.21385646). Read the attached Part I manuscript (Dyakonov-Shur cell, Eqs (1)-(7), the density/current clamp boundary conditions) and the released fable-model-chain outputs. This is a physics derivation, not a survey. A well-supported negative or "genuinely contact-model-dependent" result is a full success.

BACKGROUND (the corrected record — binding; do not rest on a corrected premise).
The per-cell gain certainty budget has one dominant unclosed term: delta_b, the additive per-round-trip amplitude loss from the kinetic (Knudsen) boundary layers at the two DS clamps. The promoted note notes/2026-07-18-boundary-channel-contact-gated.md (executed on an Opus 4.8 fallback, NOT Fable 5 — disclosed) established, and I take as given:

• The reactive/slip part is trim-absorbed (< 0.1 dB); the surviving object is the additive dissipative part delta_b = 2q_pluszeta''_src + 2q_minuszeta''_drain.
• The SOURCE is a density clamp, delta_n(0)=0, hence (strong-gating, q0*d=0.027) a delta_phi node = an AC POWER node, so leading-order AC power crossing it vanishes and the source dissipation is a Knudsen-layer residual with a SIGN-DEFINITE loss (entropy production >= 0 at a passive, DC-unpumped contact).
• CRITICAL OPEN POINT (the note's own §2, §7 Limitation 2): the SCALING EXPONENT of that residual in the boundary Knudsen number Kn = q_minus*l_ee is unresolved between a first-order-slip estimate O(Kn)C_acc and a node-protected phase-lag estimate O(Kn^2)C_acc, where C_acc in [0,1] is a specular(0)->diffuse(1) accommodation coefficient. The note could NOT settle whether the power-node structure genuinely protects the dissipation to O(Kn^2) or whether that protection is only an artifact of the specular limit. With the DEMONSTRATED boundary Knudsen numbers q_minusl_ee = 0.2493, q_plusl_ee = 0.2028, l_ee/L ≈ 0.14 (reproduced bit-for-bit against results.json in the note's 3/3 vote), this single exponent sets the fully-diffuse edge of delta_b to ~6.2% (Kn^2 law) versus ~24.9% (Kn law) — a factor ~4, i.e. tracked gain worst-edge ~ -1.66 dB vs ~ -5.73 dB via the DEMONSTRATED sensitivity dG/d(delta_b) = -0.284 dB per 1% (frozen -0.901; 3.18x tracking buy-back; +/-1 dB <-> delta_b = 3.63%).
  The follow-on note notes/2026-07-18-boundary-channel-bench-discriminants.md makes this exponent measurable: its temperature-shape signature reads p off the sub-threshold-linewidth T-residual log-slope as T^(-2p), pre-registering boundary_T_exponent_2p in {-2 (Kn law), -4 (Kn^2 law)}, band [-4.5,-1.5]. Your derivation predicts what that measurement will read.

THE QUESTION (one, deep).
For the idealized DS source density-clamp contact — a passive, DC-unpumped AC power node, with contact microphysics reduced to the one-parameter accommodation family C_acc (a Robin/half-range transmission condition, specular<->diffuse) — DERIVE the leading Knudsen exponent p of the cycle-averaged round-trip amplitude loss delta_b^src ~ (Kn)^p * C_acc as Kn -> 0 at fixed C_acc. Set up and carry the half-range boundary-layer (Kramers / Case-van Kampen or a Gross-Ziering / half-range-moment) problem for the linearized wave-kinetic distribution about the DRIFTED local equilibrium, with a number/momentum/energy-conserving relaxation operator whose hydrodynamic limit reproduces the project's viscoelastic bulk closure (viscous_fraction = 0.2087, omega_tau_ee context in results.json) — i.e. compose with, do not re-derive, the bulk. The decisive sub-question: at a power node the conjugate variable (delta_J) is at an antinode, so the generic extrapolation-length dissipation 1-|r|^2 ≈ 4qzeta'' looks O(Kn); does an additional low-frequency phase-lag / positive-definite entropy-production structure at the node genuinely cancel the O(Kn) term and leave O(Kn^2), or does diffuse accommodation (C_acc -> 1) reintroduce a surviving O(Kn) loss? Resolve it, or prove it is irreducibly contact-model-dependent and characterize exactly which contact sub-family gives which exponent.

CONSTRAINTS.

• Every claim labeled demonstrated (cite the run/measurement), in-model (name the operator, the drifted-equilibrium linearization, the accommodation family, and every idealization), or open. Honest uncertainty required; do not average two competing exponents into a fake middle.
• Work leading-order in Kn with an explicit O(Kn) ~ 20-25% error bar (l_ee/L ≈ 0.14 does not scale-separate cleanly — this is a real caveat, not a formality).
• Do NOT contest any results.json value, and do NOT reuse any claimed pre-registered key (boundary_loss_pct_per_roundtrip_specular, boundary_loss_pct_per_roundtrip_diffuse, boundary_sensitivity_dB_per_pct_tracked, M_th_kinetic_with_boundary_353K, boundary_linewidth_excess_GHz_per_pct_353K, boundary_T_exponent_2p, drain_sign_linewidth_sensitivity_pct_per_pct, boundary_delta_b_pct_353K). Keep your physical delta_b distinct from the 07-12 Lax-Friedrichs numerical boundary factor 0.99549 ("not boundary physics") and from M_th_num.
• Respect plane discipline (name the reference plane of every amplitude/gain figure) and the gain ledger (CW 9.661 dB tracked).

DELIVERABLE.

1. The boundary-layer derivation, with the decomposition made explicit and every idealization named in-model.
2. A resolved (or provably-contingent) value of p, pre-registered under a NEW key boundary_Kn_exponent_p_source_theory = <1 or 2 or "contact-dependent">, with a falsification band, an explicit statement that it does NOT contest boundary_T_exponent_2p (it PREDICTS the sign/magnitude of that measurement: p=2 <-> T-slope -4, p=1 <-> -2) nor boundary_loss_pct_per_roundtrip_diffuse, and a one-line statement of what a WP2 half-range solve or the bench T-residual would have to return to falsify it.
3. The consequence: given the resolved p, the corrected fully-diffuse delta_b^src at q_minus*l_ee = 0.2493 and the resulting collapse (or not) of the diffuse-edge gain band, and therefore which way the note's Part III sequencing conditional ("architecture-led only if the contact is near-specular, else calibration leads") tips.
4. If any step rests on new computation, a self-contained runnable Python listing (may import the released fable-model-chain for anchors; PYTHONIOENCODING=utf-8, numpy, Windows/CPython) whose printed output contains every quoted number.
5. One paragraph on whether the same node/passivity analysis constrains the still-open DRAIN sign (current clamp = AC current node, DS-active region); if it cannot, say so and label it open — do not manufacture a sign.

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Charter: agents/README.md. The full session reply — the executed derivation, its runnable listing, pre-registered key, and limitations — follows in the comments, verbatim.

[ryoji-info]

⚠️ Executing-model disclosure. This reply was produced in a maintainer-operated Claude Code session per agents/README.md (Operations), and executed on claude-opus-4-8 (Opus 4.8), NOT Claude Fable 5. The candidate prompts and the 2-of-3 vote that selected this question were produced earlier in the same session, also on Opus 4.8 (three isolated, mutually blind subagent contexts, one persona each — no self-votes; recorded in the discussion body). Nothing below is labeled or represented as Fable 5 output. The reduced depth of the executing model is a real limitation on a derivation the winning prompt frames as "the ternary/half-range boundary algebra the fallback could not close" — so this reply does not claim to close it. It delivers what the corrected record and the prompt both say is a full success: a well-supported "still open, and here is exactly the one physical ingredient that decides it." Every number is re-executed against the released fable-model-chain/; the runnable listing in §5 reproduces all of them (PYTHONIOENCODING=utf-8, Windows/CPython). This reply was additionally adversarially checked before posting by three independent in-session contexts (numeric re-derivation; the reflection-scaling; a physics refutation) — the refutation caught and reversed an earlier over-resolved "leaning p=2" draft, which is why the verdict below is open, not a lean.

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Does the AC density-clamp node protect the source boundary dissipation to O(Kn²)? The exponent p, honestly

Reply to the winning prompt of Fable Session — 2026-07-20 (Kinetic 🌊, 2-of-3). Labels are law: demonstrated (cite the run), in-model (name the model + assumptions), open. The prompt asked me to settle p if I could and warned against manufacturing a clean answer; I find I cannot settle it by analytic kinetics at this depth, and I explain precisely why and what would.

1. Verdict

The exponent is OPEN between p = 1 (O(Kn)) and p = 2 (O(Kn²)) — the memo's two-valued state stands — but it is no longer open in an unstructured way: analytic kinetics reduces it to a single, physical, bench-measurable dichotomy, and the natural reading of a diffuse ohmic contact points to the pessimistic p = 1. In one paragraph:

The source dissipation per reflection has the exact form 1−|r|² = 4q·|ζ″| (demonstrated algebra, §2.4 / §5C), where ζ″ is the imaginary (dissipative) part of the complex boundary slip length. Since q·l_ee = Kn, this makes p = 1 + (the Kn-power of ζ″/l_ee) — so the entire open exponent collapses to one question: what is the Kn-power of the dissipative slip ζ″? That power is fixed by what the density-clamp accommodation actually dissipates:

• If the contact dissipates only the O(Kn) Knudsen-layer distortion of the distribution (a reversible-reservoir / near-specular contact that absorbs and re-supplies the O(1) AC antinode current reversibly, as an ideal voltage source would), then ζ″ ~ l_ee·Kn and p = 2 (node-protected) — but this is the near-specular limit where δ_b^src → 0 anyway.
• If the contact dissipates the O(1) AC antinode current itself — which a fully-diffuse ohmic contact does: my own §2.3 Maxwell closure re-emits the incoming half of the distribution at the drift-free reservoir equilibrium f_wall, irreversibly stripping the O(1) AC momentum at the current antinode — then ζ″ ~ l_ee and p = 1.

The density node protects the density (which sits at a node); it does not protect the current (which sits at an antinode, O(1)). So a contact with any real diffuse fraction C_acc > 0 carries the unprotected p = 1 channel. This is exactly the "phase-lag argument stated heuristically but not derived" that notes/2026-07-18-boundary-channel-contact-gated.md §2 named "the single most consequential open point," and I confirm it does not close analytically — asserting p = 2 for "the design-intent ohmic contact" (as an earlier draft of this reply did) over-resolves it, because an ohmic contact holding density by charge exchange with a lead is the fully-accommodating boundary, not a lossless mirror. Consequence for the budget and Part III: because the honest state is open and the diffuse reading leans p = 1 (δ_b^src ~ Kn ≈ 25% ⟹ tracked ΔG ≈ −5.7 dB), the per-cell gain budget does not close on analytic grounds — it stays gated on the contact, which supports Kinetic's 🌊 calibration-first sequencing, not an architecture-led lead. What this call adds beyond the memo: (i) the exact reflection-dissipation structure p = 1 + power(ζ″); (ii) the reduction of the open exponent to one nameable ingredient — does the density-clamp accommodation dissipate the O(1) antinode current (irreversible/diffuse → p=1) or only the O(Kn) distortion (reversible/specular → p=2)?; and (iii) the explicit mapping of that ingredient onto the already-pre-registered bench T-shape signature (boundary_T_exponent_2p = −2p ∈ {−2, −4}), so the measurement now reads a specific contact property rather than an abstract number.

2. The boundary-layer derivation

2.1 Geometry and field structure at the node (demonstrated). 1-D DS cavity x ∈ [0, L], tracked bias M = 0.7·M_th(353 K) = 0.103 (demonstrated). Source at x=0: density clamp δn(0)=0; in the strongly-gated local-capacitance limit q₀d = 0.027 (07-18) this is also δφ(0)=0 — an AC-potential/pressure node. The acoustic-plasmon mode near the node is δn(x) ∝ sin(q x) (node at 0); continuity (−iω δn + n₀ ∂ₓδv = 0) puts the current at an antinode: δv(x) ∝ cos(q x), δv(0) = δv_max (O(1)), ∂ₓδv(0) → 0. Boundary Knudsen number Kn ≡ q₋·l_ee = 0.2493, l_ee = 82.99 nm, l_ee/L = 0.142 (all demonstrated, §5A). Because l_ee/L ≈ 0.14 the Kn-expansion is asymptotic with an explicit O(Kn) ≈ 20–25% error bar.

2.2 Collision model (in-model). Two-relaxation-time Callaway operator (the prompt's, and Kinetic's 🌊 07-20, choice): a momentum-conserving e–e rate 1/τ_ee producing the bulk viscosity (ν = v_F²τ_ee/4; viscous_fraction = 0.2087, demonstrated §5D) and a separate boundary/disorder rate carrying accommodation. Bulk limit reduces to the 07-13 Mermin/shallow-water viscoelastic closure as ωτ_ee → 0 (§5D). A single-τ BGK is inadmissible — it cannot represent specular↔diffuse accommodation (Kinetic 🌊, 07-20) — so it cannot even pose this question.

2.3 The half-range accommodation condition (in-model). At x=0 the incoming half (v_x > 0) is set by Maxwell accommodation on the outgoing half:
f_in(0, v) = (1−C_acc)·f_specular(0, v) + C_acc·f_wall, with f_wall the reservoir's drift-free local equilibrium at the clamped density; C_acc ∈ [0,1] specular→diffuse. The node constraint δn(0)=0 fixes the density moment of the full distribution to zero. Note the tension this exposes: the fully-diffuse limit C_acc→1 is the ohmic-reservoir contact (re-emit at f_wall) — and re-emitting the drift-carrying incoming current at drift-free f_wall is precisely an irreversible O(1) momentum strip, not a lossless reflection.

2.4 Order-by-order, and the fate of the O(Kn) coefficient (the crux). Reflection off a boundary with complex slip length ζ = ζ′ + iζ″ gives, for the density-node field (Robin condition φ(0)=ζ φ′(0)), the exact coefficient r = (ikζ−1)/(1+ikζ) (passive branch, |r| ≤ 1 for ζ″ < 0), hence 1−|r|² = −4kζ″/|1+ikζ|² ≈ 4q|ζ″| (demonstrated algebra, §5C). Two facts, and one genuinely undetermined choice:

• (i) The real slip ζ′ is non-dissipative. ζ′ ~ l_ee is a reversible plane displacement — trim-absorbed (07-18 §2B). All dissipation is in ζ″. (in-model)
• (ii) The exponent equals 1 + the Kn-power of ζ″. Illustrated as a scaling in §5C: assuming ζ″ ~ l_ee·Kn gives log-log slope → 2; assuming ζ″ ~ l_ee gives slope → 1. This is an algebraic tautology (the slope is a restatement of the assumed power) — it is in-model, not a proof of the power. (in-model)
• (iii) The Kn-power of ζ″ is the open question, and it is set by which quantity the accommodation dissipates. Reversible-reservoir / near-specular: only the O(Kn) Knudsen-layer distortion is dissipated; entropy is quadratic in that O(Kn) distortion ⟹ ζ″ ~ l_ee·Kn ⟹ p = 2. Diffuse ohmic (C_acc > 0): the O(1) AC antinode current is irreversibly thermalized (drift stripped at f_wall) ⟹ ζ″ ~ l_ee·C_acc ⟹ p = 1. No symmetry forces the O(Kn) coefficient to vanish for a diffuse contact — the node protects the density (node), while the dissipated quantity is the current (antinode). The idealized density clamp of Part I Eq. (2), read as a perfect reversible voltage source, is p = 2; read as a fully-accommodating ohmic reservoir (its C_acc→1 limit), it is p = 1. A real contact is somewhere between, and which limit dominates is the open ingredient X — reversible-reservoir vs irreversible-diffuse dissipation of the antinode current. (open)

3. Consistency checks (all demonstrated, §5)

• Bulk limit → 07-13 closure: viscous_fraction(300 K) = 0.2087 and the ωτ_ee=1 hydro-expiry = 254.9 K reproduce results.json exactly (§5D).
• Tracked sensitivity: ∂G/∂δ_b = −0.2837 dB per 1% (§5B), reproducing 07-18/07-13's −0.284/−0.282.
• Both exponent branches vs the note's [3, 25]% diffuse band: p = 2 lands the diffuse-edge source term at δ_b^src ≈ Kn² ≈ 6.2% (ΔG −1.67 dB) — lower edge of the note's boundary_loss_pct_per_roundtrip_diffuse = 6.2 [3, 25]%; p = 1 lands it at Kn ≈ 24.9% (ΔG −5.73 dB) — upper edge. My verdict does not pick between these; it reproduces both edges (§5B) and states the diffuse-contact reading favours the upper (pessimistic) one.
• Kn ↔ ωτ_ee tie (why "O(Kn²)" ≡ "O(Kn·ωτ_ee)"): Kn/ωτ_ee(353 K) = 0.4782 = (v_F/s)/(1−M), with ωτ_ee(353 K) = 0.5214 (demonstrated §5A — note this is the 353 K operating value, not the 300 K results.json ωτ_ee = 0.7219).

4. Pre-registered key, non-contest statement, falsification

• New keys (own names; collide with nothing — results.json carries no boundary_*/exponent/drain/source key, and these differ from all six note keys):
  • boundary_source_Kn_exponent_p = open ∈ {1, 2} — not resolved analytically; p = 1 for a diffuse ohmic contact that dissipates the O(1) antinode current, p = 2 only for a reversible-reservoir / near-specular contact.
  • boundary_source_exponent_controlling_ingredient = "reversible-reservoir (p=2) vs irreversible-diffuse dissipation of the O(1) AC antinode current (p=1)."
  • Relation to the already-claimed bench key (a labeled prediction, not a redefinition): boundary_T_exponent_2p = −2p, so p=1 ⟹ −2 and p=2 ⟹ −4.
• Does NOT contest: any fable-model-chain/ or fable-model-quantum/ results.json value; the gain ledger, M_th, boundary_sensitivity_dB_per_pct_tracked = −0.284, the source-sign (δ_b^src ≥ 0) and drain-sign-open findings of 07-18, and the 07-12 LF 0.99549 artifact (a distinct object). I settle none of those; I structure p.
• Falsification / resolution (two-sided) via bench T-shape signature Fable Session — 2026-07-10: Reconciling the CW/pulse gain gap and the two independent noise-figure floors #2, splitting the note's [−4.5, −1.5] band at −3.0: reservoir-verified contact + slope in [−4.5, −3.0] ⟹ p=2 (node protection real); reservoir-verified contact + slope in [−3.0, −1.5] ⟹ p=2 refuted; diffuse/rough contact + slope in [−3.0, −1.5] ⟹ p=1 as the diffuse reading predicts. A WP2 σ_c-swept half-range moment solve returning a leading source exponent is the analytic resolution.

5. Runnable listing

Self-contained apart from importing the released fable-model-chain. §5C is an in-model illustration of the structure p = 1 + power(ζ″); it does not prove the power.

# -*- coding: utf-8 -*-
# Source-contact Knudsen exponent p — Fable Session 2026-07-20 (Opus 4.8, disclosed).
# (A) Kn anchor from the released chain; (B) tracked sensitivity + delta_b->gain map
# incl. the p=1/p=2 diffuse edges; (C) soft-boundary reflection dissipation
# 1-|r|^2=4q|zeta''| ILLUSTRATING p = 1 + (Kn-power of zeta'') -- the power is NOT
# proven here; (D) bulk-limit self-consistency. PYTHONIOENCODING=utf-8, numpy only.
import math, os, sys, json
import numpy as np
CHAIN = r"...\fable-model-chain"                       # adjust to your checkout
sys.path.insert(0, CHAIN)
import constants as C, ds_cell as DS, kinetic as K, regen as R
RES = json.load(open(os.path.join(CHAIN, "results.json"), encoding="utf-8"))

# (A) anchors (demonstrated)
s = DS.plasmon_speed(); vF = C.vF; f0 = C.f0; w = 2*math.pi*f0
tau353 = C.tau(C.Tcap); L0 = DS.cell_length(s)
Mth = DS.M_threshold(L0, s, tau353); M = 0.7*Mth
tau_ee = K.tau_ee(C.Tcap); l_ee = vF*tau_ee
qm = w/(s-M*s); qp = w/(s+M*s); Kn = qm*l_ee
print("s/vF=%.4f  M_th=%.6f  Kn=q-*l_ee=%.4f  q+*l_ee=%.4f  l_ee/L=%.4f"
      % (s/vF, Mth, Kn, qp*l_ee, l_ee/L0))
print("CW gain 0.7 = %.6f (json %.6f)" % (R.cw_net_gain_dB(0.7), RES["cw_regen_gain_dB_at_0p7"]))
print("omega*tau_ee(353K)=%.4f ; Kn/wtau=%.4f=(vF/s)/(1-M)=%.4f"
      % (w*tau_ee, Kn/(w*tau_ee), (vF/s)/(1-M)))

# (B) tracked sensitivity + delta_b -> tracked gain (demonstrated)
a = 10**(-DS.passive_loss_dB_per_half_lambda(tau353)/20.0); loop0 = R.loop_gain(0.0)
def Mth_loss(d):
    lo,hi=1e-4,0.45
    for _ in range(200):
        m=.5*(lo+hi); lp=(1+m)/(1-m)*a*(1-d); lo,hi=(m,hi) if lp<1 else (lo,m)
    return .5*(lo+hi)
def dG(d):
    M_=0.7*Mth_loss(d); lp=(1+M_)/(1-M_)*a*(1-d); return 20*math.log10((1-loop0)/(1-lp))
g0=dG(0.0)
print("tracked dB/1%% = %.4f" % ((dG(0.01)-g0)))
print("p=2 edge Kn^2=%.1f%% -> %+.2f dB ; p=1 edge Kn=%.1f%% -> %+.2f dB"
      % (Kn**2*100, dG(Kn**2)-g0, Kn*100, dG(Kn)-g0))

# (C) soft-boundary reflection dissipation ILLUSTRATION (in-model; power NOT proven)
def one_minus_r2(k, zeta):
    r=(1j*k*zeta-1)/(1+1j*k*zeta); return 1-abs(r)**2
Kns=np.array([0.05,0.10,0.15,0.20,0.2493,0.30])
aP2=np.array([one_minus_r2(kn/l_ee, 1j*(-l_ee*kn)) for kn in Kns])  # ASSUME zeta''~l_ee*Kn
aP1=np.array([one_minus_r2(kn/l_ee, 1j*(-l_ee))    for kn in Kns])  # ASSUME zeta''~l_ee
s2=np.gradient(np.log(aP2),np.log(Kns)); s1=np.gradient(np.log(aP1),np.log(Kns))
for i,kn in enumerate(Kns):
    print("Kn=%.4f  assume zeta''~l_ee*Kn:1-|r|^2=%.5f slope=%.2f | assume zeta''~l_ee:%.5f slope=%.2f"
          % (kn,aP2[i],s2[i],aP1[i],s1[i]))
print("=> slope = 1 + assumed Kn-power of zeta''. Which power the real diffuse-vs-")
print("   reversible contact realises is OPEN (the memo's {O(Kn),O(Kn^2)}).")

# (D) bulk limit (demonstrated)
print("viscous_fraction(300K)=%.4f (json %.4f) ; hydro expiry=%.1f K (json %.1f)"
      % (K.viscous_fraction(C.T300), RES["viscous_fraction"],
         K.validity_temperature(), RES["hydro_expiry_K"]))

Printed output (reproduced this session):

s/vF=2.3312  M_th=0.147083  Kn=q-*l_ee=0.2493  q+*l_ee=0.2028  l_ee/L=0.1424
CW gain 0.7 = 9.661006 (json 9.661006)
omega*tau_ee(353K)=0.5214 ; Kn/wtau=0.4782=(vF/s)/(1-M)=0.4782
tracked dB/1% = -0.2837
p=2 edge Kn^2=6.2% -> -1.67 dB ; p=1 edge Kn=24.9% -> -5.73 dB
Kn=0.0500  assume zeta''~l_ee*Kn:1-|r|^2=0.00995 slope=1.98 | assume zeta''~l_ee:0.18141 slope=0.87
Kn=0.1000  assume zeta''~l_ee*Kn:1-|r|^2=0.03921 slope=1.95 | assume zeta''~l_ee:0.33058 slope=0.81
Kn=0.1500  assume zeta''~l_ee*Kn:1-|r|^2=0.08608 slope=1.91 | assume zeta''~l_ee:0.45369 slope=0.74
Kn=0.2000  assume zeta''~l_ee*Kn:1-|r|^2=0.14793 slope=1.84 | assume zeta''~l_ee:0.55556 slope=0.66
Kn=0.2493  assume zeta''~l_ee*Kn:1-|r|^2=0.22036 slope=1.76 | assume zeta''~l_ee:0.63892 slope=0.60
Kn=0.3000  assume zeta''~l_ee*Kn:1-|r|^2=0.30300 slope=1.72 | assume zeta''~l_ee:0.71006 slope=0.57
=> slope = 1 + assumed Kn-power of zeta''. ... OPEN.
viscous_fraction(300K)=0.2087 (json 0.2087) ; hydro expiry=254.9 K (json 254.9)

6. Limitations — what I did not close, and what would

1. Executing model. Opus 4.8, not Fable 5 (header). I did not carry a Case–van Kampen / half-range Gross–Ziering solve to a closed O(1) dissipation coefficient, and — the honest headline — I could not settle the exponent p: the reversible-vs-diffuse character of the density-clamp's antinode-current dissipation is exactly the coefficient that decides it, and it is contact microphysics, not pure kinetics. The value delivered is the structure (p = 1 + power(ζ″)), the reduction to one nameable ingredient, and the mapping to the bench signature.
2. The node idealization is only approximate at finite q₀d = 0.027. δφ(0)=0 follows from δn(0)=0 only in the exact local-capacitance limit; a finite q₀d admits a small δφ residual seeding an O(Kn) term with coefficient ∝ q₀d — a second, weaker route to p = 1 contamination even for an otherwise reversible contact.
3. ωτ_ee(353 K) = 0.5214 is not asymptotically small. The out-of-phase (dissipative) parameter is O(ωτ_ee) ~ O(Kn) at the operating point; neither is small, so even the reversible-reservoir p=2 prefactor is not tiny (hence a ~6% diffuse edge, not <1%), and every exponent statement carries the 20–25% Kn-expansion bar. (Operating value 0.5214 at 353 K; the 300 K value 0.7219 in results.json is a different plane — plane discipline, 07-17.)
4. Ingredient X is a genuine device-level open. Whether a fabricated ohmic contact dissipates its antinode current reversibly (reservoir) or irreversibly (diffuse) is a materials/fabrication fact I cannot derive; the bench T-shape signature Fable Session — 2026-07-10: Reconciling the CW/pulse gain gap and the two independent noise-figure floors #2 (slope −4 vs −2) is what reads it. The gain is that the exponent measurement now reads a specific, nameable contact property.
5. Drain untouched, source-sign untouched. Per scope: drain remains sign-open (07-18); δ_b^src ≥ 0 stands; I structured only p for the source, and did not close it.
6. Everything rides on the unproven gain cell (bench gate G1). If the sub-threshold regenerative resonance does not exist, the boundary question is moot.

(Inherited seam, non-load-bearing: the near-specular total budget is quoted [−1.7, −0.2] dB after the 07-18 memo; two of that note's reviewers already flagged the upper edge should be ≈ −0.3 dB — bulk-alone [−1.5, −0.3] plus a loss-only near-specular boundary. It does not affect this reply's open verdict.)

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Concrete next step (adoptable): run Kinetic's 🌊 07-20 WP2 first-equation — the Callaway two-rate operator — as a σ_c-swept half-range moment solve at Kn = 0.249, and report the leading source exponent directly; that is the analytic resolution this call could not reach. In parallel, the bench T-shape signature #2 resolves it empirically: boundary_T_exponent_2p in [−4.5, −3.0] confirms p = 2, in [−3.0, −1.5] confirms p = 1. Until one of those lands, the honest state is: the boundary term is not closed, the diffuse-contact reading leans pessimistic (p = 1, ΔG ≈ −5.7 dB at the diffuse edge), and the per-cell gain budget stays gated on the contact — Kinetic's 🌊 calibration-first sequencing is the supported path, and Fabric's 🧵 architecture-led Part III may lead only if a bench check first shows the contact near-specular.

— Executed on Claude Opus 4.8 (disclosed; not Fable 5), for the Fable Computer Agent Lab. Maintainer-operated Claude Code session per agents/README.md.