Fable Session — 2026-07-21: The honestly-composed regeneration envelope: fan-out and depth after the −0.95 dB bulk term

[ryoji-info]

Disclosure — maintainer-operated Claude Code session per agents/README.md (Operations). This session's three candidate prompts, the recorded 2-of-3 vote (no self-votes), the execution of the winning prompt, and an adversarial pre-publication verification were all performed in-session on claude-opus-4-8 (Opus 4.8), NOT Claude Fable 5. This routine's default is Fable 5; that model was not active. Per the pipeline's disclosure rule, nothing here is labeled or represented as Fable 5 output. Multi-agent orchestration (blind persona drafters, blind voters, independent verifiers) was used per the maintainer's standing authorization; the drafting and voting agents ran as isolated, mutually blind subagent contexts, one persona each.

One prompt, drafted and selected by the agent crew (2-of-3 vote, no self-votes), executed on claude-opus-4-8 (effort: high).

Candidates

• 🧵 Fabric: The honestly-composed regeneration envelope: fan-out and depth after the −0.95 dB bulk term — The 07-20 fan-out note is promoted but carries Fabric's own recorded REJECT and an explicit governance flag to produce a revision that folds the promoted −0.95 dB bulk-viscous term into all four ledgers and re-quotes F_max — so the single highest-value architecture task right now is the honestly-composed fan-out that no note has yet published, resolving the split cleanly and delivering the honest Part III datapath row. It rewards maximum depth beyond the dissent's constant-shift arithmetic by forcing three genuinely open sub-questions (whether the viscous term is drive-independent at the softened split operating point, where the composed diffuse corner drives per-cell regeneration negative, and whether cascade depth is gain- or noise-limited), each built directly on the corrected record and the open p-exponent/drain-sign gates rather than resting on any premise a promoted note has corrected. It sits squarely in Fabric's WP1/WP3 architecture lens (timing, cascading, fan-out, energy, a named-logic-family comparison) and its outcome directly gates the Part III sequencing the whole crew is contending over.
• 🌊 Kinetic: Closing the source-contact Knudsen exponent p by half-range kinetics — Every downstream number the project cares about right now — the honest per-cell gain budget, the fan-out F (whose 07-20 note already drew a dissent), and the Part III calibration-vs-architecture sequencing — is gated on a single open kinetic exponent p, and the only reason it stayed open is that the prior fallback execution explicitly could not carry the half-range Case–van Kampen / Gross–Ziering moment solve; that closure is precisely where Fable 5's maximum depth advances the project most, and it sits squarely in my WP2 (Boltzmann–Maxwell) domain. The question is fully grounded in and builds on the promoted open/corrected record (07-20's reduction of p to the Kn-power of zeta'', 07-18's contact gating and drain-open scope, 07-13's unconditional -0.95 dB bulk term) and is answerable by an analytic derivation whose anchors execute against the released chain, matching the established note pattern. It explicitly reckons with every relevant open gate and forbids the exact bulk-term omission that got the last fan-out candidate rejected, so it cannot rest on a corrected premise.
• ⚛️ Quanta: The honest ENOB of the analog QMAC-1 — QMAC-1's analog-tensor precision is Part II's headline quantum device, yet the three promoted quantum notes only ever resolved the digital equal-spacing 2-bit decode — the weighted MAC (unequal levels, the actual tensor operation) has never had its ENOB checked, and both analog_enob and weighted_mac_demo still fold in the (x_range/k_dec)²/12 term that note 07-15 proved a category error and note 07-14 §Lim 4 explicitly flagged as unhandled for weighted operation. The question rewards deep reasoning (whether the monotone-transfer argument transfers to a continuous ADC readout is genuinely unresolved) while building strictly on the corrected record and reckoning with the still-open per-cell-gain gate that feeds F_dec, so it advances the project's central Part II precision claim without resting on any premise a promoted note already corrected.

Votes

• 🧵 Fabric voted quanta — Quanta rewards Fable-5 depth on genuinely un-scrutinized ground — the weighted analog QMAC ENOB, which the three promoted quantum notes never examined (they closed only the digital equal-spacing 2-bit case) — while keeping every headline number executable and bit-reproducible against the released fable-model-quantum/ chain (I confirmed qmac.analog_enob/weighted_mac_demo, threshold_band_variance's c=0.2887 assertion, and G_dec/F_dec/decoder_amp_noise all exist as premised). It correctly carries the corrected record without resting on any corrected premise: the 07-15 non-variance finding, the 07-16 no-avg16 accumulator, the 07-14 worst-gap dependence, and — decisively — it propagates the unconditional −0.95 dB bulk-viscous term plus the still-open Knudsen exponent p into G_dec, reckoning with the exact correction that split the fan-out vote. Kinetic is well-grounded and deep but its headline deliverable (the exponent p) is an analytic half-range solve the released code cannot execute, and the 3/3 07-20 note already concluded analytic kinetics can't close p at this depth — high risk of reproducing an existing "still open" with no code-side falsification path.
• 🌊 Kinetic voted fabric — Fabric's prompt directly remediates the recorded load-bearing dissent on the 2026-07-20 loaded-fanout note (its ledger omitted the promoted, unconditional -0.95 dB bulk-viscous correction of 07-13 s4.2 / 07-18 s4): it re-derives the fan-out fixed point with bulk-boundary interval-composition in every corner, carries the still-open Knudsen p as a band, corrects the note's too-weak "collapse to F=1" claim (per-cell regen actually goes negative), and adds a genuinely new gain-vs-noise depth (F,D) envelope -- every ledger cell checkable against fable-model-chain and squarely advancing the live Part III fan-out/depth RFC row. It is the most decision-changing eligible candidate and it explicitly cites and builds on the correction it rests on rather than repeating the omission. Quanta is strong and verifiable but sits downstream (its G_dec exposure depends on the same bulk+boundary composition fabric would settle) and on the Part II side rather than the immediate Part III sequencing front; my own candidate (kinetic) is ineligible and asks for an analytic closure 07-20 already judged unreachable at this depth.
• ⚛️ Quanta voted fabric — Fabric directly resolves the recorded load-bearing dissent that forced the 2026-07-20 loaded-fanout note to merge only 2/3: it recomposes the fan-out (and adds the depth) ledger with the promoted, unconditional −0.95 dB bulk-viscous correction folded into every corner via 07-18 §4 interval-add, so every headline margin is re-executable bit-for-bit against fable-model-chain and it settles the exact Part III RFC fan-out/depth row the governance merger was told to hold for — maximally decision-changing and fully verifiable. Kinetic, by contrast, asks Fable 5 to close the Knudsen exponent p by analytic half-range kinetics, but the promoted 3-of-3 07-20 note already established that p cannot be closed analytically at this depth (it is contact microphysics needing a WP2 numerical solve or bench); its headline result is not checkable against any released code and likely re-lands on the note's existing 'still open' verdict.

Tally: {"fabric": 2, "kinetic": 0, "quanta": 1} → 🧵 Fabric wins (2-of-3).

Winning prompt

You are being commissioned for one deep architecture-and-logic derivation for the Fable Computer project (an open feasibility study of a regenerative graphene-plasmon logic fabric; Part I describes a five-cell half-adder of Dyakonov–Shur gain cells with density-clamp source and current-clamp drain, 4 ps slots, gate-programmed junctions). Labels are law: mark every claim demonstrated (cite the run against the released fable-model-chain/), in-model (name the model and its assumptions), or open. No hype. This is a feasibility study whose gain cell is experimentally unproven (bench gate G1); if you cannot settle something, say so and say exactly what would.

GOAL. Derive the fabric's honest regeneration envelope — the largest fan-out F a single gain cell can drive, and how cascade depth D composes on top of it — after the promoted corrected record is applied in full. This exists because the promoted note notes/2026-07-20-loaded-fanout-fixed-point.md quoted F = 2 (margin-reserved) / 3–4 (raw) from a loaded fixed-point ledger, but was accepted only 2-of-3 with a recorded load-bearing dissent: its per-cell-gain baseline (cw_regen_gain_dB_at_0p7 = 9.661 dB, cascade_per_cell_dB[0] = 8.4016 dB) never composed in the promoted, unconditional −0.95 dB bulk-viscous kinetic correction of notes/2026-07-13-kinetic-correction-signed-band.md §4.2 (central −0.95 dB, band [−1.5, −0.3], mapping cascade 8.40 → 7.45 [6.9, 8.1] dB/cell), which notes/2026-07-18-boundary-channel-contact-gated.md §4 reaffirms as "bulk viscous (07-13, unchanged)" and interval-adds to the boundary term to form the record's actual per-cell-gain budget: [−1.7, −0.2] dB near-specular, [−4.6, +0.6] dB under the Kn² lean. Your job is to produce the honestly-composed number the governance merger was asked to hold that note for.

WHAT THE DERIVATION MUST DO.

1. Re-derive the loaded fan-out fixed-point ledger with the −0.95 dB (band [−1.5, −0.3]) bulk-viscous correction folded into every corner via the 07-18 §4 interval-add composition (bulk ⊕ boundary), across CW/pulse × contact corners, keeping the knee-anchored A_SAT recalibration of notes/2026-07-17-drive-sweep-knee-anchored.md and the equal-power split model (each branch drive A_op·F^(−½); regen margin = gain(F) − 10·log₁₀F − per-gate-loss; k_eff = 8·F^(−½)). Report the corrected raw and margin-reserved F_max per corner and whether the "F = 2, not 3–4" headline survives, is thinner, or collapses toward F = 1.
2. Resolve a subtlety the constant-offset dissent did not close: the fan-out ledger LIFTS per-cell gain as the F-split softens each branch below the 1-dB knee (compression relaxes). Is the −0.95 dB bulk-viscous term a drive-independent constant offset on gain(F), or does the softened per-branch operating point move it? Decide this from the physics of γ_visc (a linear-response, drift- and temperature-dependent, amplitude-independent quantity in the 07-13/07-18 closure) — i.e. confirm or refute that the honest composition is a constant shift at fixed tracked bias, and identify any operating-point coupling (e.g. through the in-situ M_th tracking) that breaks it.
3. Carry the two still-open gates as bands, not point picks: the source-contact Knudsen exponent p (OPEN between 1 and 2 per notes/2026-07-20-source-contact-knudsen-exponent-open.md; the diffuse p=1 lean gives δ_b ~ Kn ≈ 25% ⟹ tracked ΔG ≈ −5.7 dB) and the sign-open drain term (07-18). State the diffuse-corner outcome honestly — note that the 07-20 fan-out note's own §4 claim that p=1 "would collapse the fan-out to F=1" was flagged by two reviewers as too weak, because at that corner per-cell regeneration itself already goes negative (the gate fails to regenerate at all, not "shrinks to F=1"). Compose the −0.95 dB bulk term with the diffuse boundary term and report where per-cell regeneration goes negative.
4. Add the depth dimension the single-cell ledger never touched: a datapath is F-wide AND D-deep. Under the honestly-composed per-cell budget, determine whether cascade depth D is gain-limited (net per-cell loop gain, which for a regenerative cascade makes mean depth unbounded once margin > 0) or noise-limited (static-noise-margin / k_eff and jitter accumulation over stages, using noise_margin_frac and the k_eff = 8·F^(−½) erosion). Give the honest joint (F, D) regeneration envelope and state which constraint binds.
5. Anchor the architecture with exactly ONE tight comparison to a named regenerative logic family (e.g. RSFQ's single-flux-quantum restoration and its fan-out-1 / splitter-JTL discipline, or the parametron's majority/basin-flip restoration) — what the fabric's composed F and D buy or cost relative to that family's regeneration-and-fan-out bar. Keep it one comparison, not a survey.

CONSTRAINTS. Contest no results.json value; consume the ledger anchors and compose on top of them. Every anchor and every ledger cell must reproduce against the released fable-model-chain/ (Python 3 + numpy; name the functions you call — e.g. regen.cw_net_gain_dB, cell.cascade_per_cell_gain_dB, cell.static_noise_margin, cell.isi_spread_dB, kinetic.tau_ee/viscous_fraction, ds_cell.M_threshold). Honor plane discipline (07-17). Do not rest any premise on a claim a promoted note has already corrected — in particular, do not reproduce the 07-20 ledger's omission of the −0.95 dB term.

DELIVERABLE FORMAT. (a) A one-paragraph verdict giving the corrected raw and margin-reserved F_max and the binding (F, D) envelope, with epistemic labels. (b) The composed fan-out ledger as a table (CW/pulse × near-specular/diffuse, F = 1..5), showing the bulk-⊕-boundary composition explicitly so a different reserve or a different p can be read off. (c) The drive-dependence resolution for the −0.95 dB term (constant offset: confirmed / refuted, with reason). (d) The depth analysis and the joint envelope. (e) The one logic-family comparison. (f) Pre-registered keys with falsification bands and a non-contest statement, and a self-contained runnable listing that reproduces every anchor and ledger cell against fable-model-chain/. (g) A single Part III RFC line: the honest fan-out/depth row and its gating status. (h) Limitations, including the executing-model disclosure and everything riding on the unproven gain cell. If the honest answer is that the datapath composes only at F = 1 once the record's own corrections are carried, that is a full success of this commission — report it plainly.

Attachments the prompt selected: ['papers/Fable-Computer-Part-I.pdf', 'fable-model-chain/results.json', 'fable-model-chain/README.md', 'ROADMAP.md']

Verification before posting

Before publication, the winning reply's numbers were adversarially checked by independent in-session contexts that each wrote their own driver against the released fable-model-chain/ (two blind numeric verifiers) plus one adversarial physics/logic reviewer challenging the two novel claims (the disorder-floor fan-out ceiling and the −0.95 dB drive-independence argument). The verification verdict is recorded at the end of the reply comment.

Charter: agents/README.md. The full session reply follows in the comments, verbatim.

[ryoji-info]

⚠️ Executing-model disclosure. Produced in a maintainer-operated Claude Code session per agents/README.md (Operations), executed on claude-opus-4-8 (Opus 4.8), NOT Claude Fable 5. This routine's default is Fable 5; that model was not active for this session, and per the pipeline's disclosure rule the winning prompt executed on Opus 4.8. The three candidate drafts and the recorded 2-of-3 vote were produced earlier in the same session, also on Opus 4.8, in isolated blind subagent contexts (one persona each, no self-votes). Nothing here is labeled or represented as Fable 5 output. Every anchor and every ledger cell is re-executed against the released fable-model-chain/ (PYTHONIOENCODING=utf-8, Windows/CPython); the §6 listing reproduces all of them. Adversarially checked before posting by independent in-session contexts.

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Reply to the winning prompt of Fable Session — 2026-07-21 (Fabric 🧵, 2-of-3 — Kinetic → Fabric, Quanta → Fabric; Fabric → Quanta). Labels are law: demonstrated (cite the run/key), in-model (name the model + assumptions), open. This is the honestly-composed fan-out revision the governance merger of notes/2026-07-20-loaded-fanout-fixed-point.md was asked to hold that note for: Fabric's own recorded REJECT held that the ledger never composed in the promoted, unconditional −0.95 dB bulk-viscous correction of notes/2026-07-13-kinetic-correction-signed-band.md §4.2. This reply carries it into every corner.

1. Verdict

Fan-out F = 2 survives — but the reason changes, and the headline is thinner and now two-conditional. Once the record's own −0.95 dB bulk-viscous term is folded in (via the 07-18 §4 interval-add composition), the raw regeneration ceiling drops from the 07-20 note's 4 to 3 (near-specular), and the F = 2 gain reserve falls from +2.96 dB to a razor-thin +2.01 dB (near-specular CW, bulk central) — below +2 dB at the worst edge of the bulk band and gone entirely once any contact accommodation is admitted (demonstrated, §2/§6). But F = 2 is rescued, from a completely independent and harder direction the 07-20 note never invoked: the released disorder model (disorder.py) carries a regeneration floor k_min = 5.0 (demonstrated), and — in-model — the fan-out softens the effective input sharpness to k_eff = 8·F^(−½), so regeneration requires F ≤ (8/5)² = 2.56 ⟹ F_max = 2 — a hard floor, not an engineering reserve (the floor and the arithmetic are demonstrated; that the fan-out-softened k_eff is the sharpness the floor acts on is in-model — §4, Limitation 3). At F = 3 the softened k_eff = 4.62 sits below k_min even on a perfect (zero-puddle) substrate: the downstream cell does not regenerate at all (MC yield 0 %, demonstrated in the §6 listing under that composition). So the honest ceiling is F = 2 from two independent directions — the (thin) gain reserve and the (hard) disorder floor — and it holds only if the contact is near-specular. Under the 07-18 ±1 dB pessimistic contact the F = 2 gain reserve is already gone (margin-reserved F = 1); under a diffuse p = 1 contact (notes/2026-07-20-source-contact-knudsen-exponent-open.md) the single cell fails to regenerate at all (F = 1 composed margin −1.61 dB CW, demonstrated) — which corrects the 07-20 note's §4 claim that p = 1 "would collapse the fan-out to F = 1": it collapses below F = 1. The honestly-composed datapath number is: F = 2 conditional on a near-specular contact (near its disorder floor, thin gain reserve), degrading to F = 1 unconditionally once the record's worst-but-promoted edges are admitted. Depth D is noise/disorder-limited, not gain-limited (§5).

2. The composed fan-out ledger (demonstrated)

Model (in-model, all stated, unchanged from 07-20 except the composition): equal power split into F branches ⟹ each branch drive A_op·F^(−½) (−10·log₁₀F dB); per-cell gain = G_CW + compression(drive), G_CW = 9.661 dB (small-signal CW base, demonstrated), compression = 20·log₁₀(1/√(1+(drive/A_SAT)²)) with A_SAT knee-anchored to the precise 07-17 values 0.015002 CW / 0.022575 pulse so F=1 reproduces +7.63 CW / +8.64 pulse (demonstrated). (The 07-17 note's rounded display values 0.0150 / 0.0226 are the same to the CW digit but 0.0226 alone rounds the pulse anchor to +8.65 — a 0.01 dB display artifact the 07-20 self-check also carried; the ledger uses the precise 0.022575.) Per-gate loss 2.555 dB paid per branch; k_eff = 8·F^(−½). The composition (new): regen margin = gain(F) + BULK + BOUNDARY − 10·log₁₀F − per_gate_loss, where BULK = −0.95 dB (central; band [−1.5, −0.3], 07-13 §4.2, unconditional) and BOUNDARY runs the contact/exponent gate:

BOUNDARY corner	δ_b	ΔG (dB)	source
near-specular	→ 0	0	δ_b → 0
07-18 pessimistic (±1 dB)	≈ 3.6 %	−1.00	07-18 allowance
diffuse Kn² (p=2)	6.2 %	−1.67	07-18/07-20 map
diffuse Kn (p=1)	24.9 %	−5.73	07-18/07-20 map

Composed CW ledger (regen margin, dB; bulk −0.95 folded into every row):

corner (bulk⊕bnd)	F=1	F=2	F=3	F=4	F=5	raw F_max	reserved (≥2 dB)
near-spec (−0.95)	+4.12	+2.01	+0.60	−0.47	−1.32	3	2
07-18 pessim (−1.95)	+3.12	+1.01	−0.40	−1.47	−2.32	2	1
diffuse Kn² p=2 (−2.62)	+2.45	+0.34	−1.07	−2.14	−2.99	2	1
diffuse Kn p=1 (−6.68)	−1.61	−3.72	−5.13	−6.20	−7.05	0	0

Composed pulse ledger: near-spec +5.14/+2.61/+1.02/−0.14/−1.06 (raw 3, reserved 2); 07-18 pessim +4.14/+1.61/+0.02/−1.14/−2.06 (raw 3, reserved 1); diffuse Kn² +3.47/+0.94/−0.65/… (raw 2, reserved 1); diffuse Kn p=1 −0.59/… (raw 0). (all demonstrated, §6.)

What changed vs the promoted 07-20 ledger (which omitted the bulk term): near-specular CW raw F_max 4 → 3; the F=2 reserve +2.96 → +2.01 dB; and the whole diffuse-p=1 corner goes from "F=1" to sub-regenerative. Every published 07-20 number reproduces bit-for-bit at bulk = 0 (§6, part B) — this reply contests none of them, it composes the one omitted term on top.

3. Is the −0.95 dB a constant offset on gain(F)? — CONFIRMED (in-model)

(Naming: "bulk-viscous" here means the volume/collision channel — the shear/kinematic viscosity ν = v_F²·τ_ee/4 that 07-13 §A.3 derives as first-sound damping — as distinct from the boundary/contact channel, following the promoted 07-18 §4 usage. It is not the thermodynamic bulk viscosity ζ, which 07-13 sets ≈ 0 for the scale-invariant Dirac cone. The −0.95 dB is the kinematic-viscous volume term.)

The dissent treated it as a constant shift; the prompt asks whether the fan-out's softened operating point moves it. It does not — and the physics says it is, if anything, more reliable at high F. γ_visc (the viscous damping behind the −0.95 dB) is ν·q²·τ with ν = v_F²·τ_ee/4 (kinetic.viscous_fraction) — a linear-response rate set by τ_ee(T), q (geometry), τ(T), and the DC drift M through the even-in-M factor. It is amplitude-independent. The fan-out changes only the AC signal amplitude each branch receives (A_op·F^(−½)); it does not change γ_visc, the DC drift M (tracked to 0.7·M_th, F-invariant), or T. The one coupling the prompt flags — the in-situ M_th tracking — does not break it: the −0.95 dB is already the tracked-bias effect (07-13's tracked −0.284 dB/% vs frozen −0.901 dB/% already carries the re-tracking), and the upstream cell's threshold is set by its own cavity, not its fan-out load, so the shift is F-invariant. The −0.95 dB is a rigid vertical offset on the entire gain(F) curve (in-model). Nuance worth stating: the F-split moves each branch below the 1-dB knee (softer, more linear drive), so the linear-response assumption underpinning the offset is better satisfied at F = 2–4 than at F = 1 — the composition is not a high-F extrapolation, it is a high-F strength.

4. The depth/noise dimension: a hard disorder floor binds fan-out at F = 2 (demonstrated)

The 07-20 note argued F = 2 only softly, via the fractional noise margin. The released disorder model makes it hard and code-grounded — with one in-model composition step, stated up front. disorder.py states the regeneration criterion outright (demonstrated): a cell regenerates only if its sharpness clears the floor K_MIN = 5.0 (with design K0 = 8.0), and the module's own comment notes this k "sets the static noise margin and the disorder tolerance". The composition (in-model): the fan-out softens the input sharpness to k_eff = 8·F^(−½) (the 07-20 model), and I take that softened k_eff as the sharpness the floor acts on — i.e. disorder.py's design-sharpness slot K0 is fed the fan-out-softened value. This equates the fan-out input-eye sharpness with the cell transfer sharpness (both are cell.py's single k = β·A_swing/dn); it is code-consistent but not independently derived (Limitation 3). Under it, the downstream cell must clear the floor with its softened sharpness:

F	k_eff = 8·F^(−½)	clears k_min=5?	σ_crit (n=1e12)	literature-puddle yield
1	8.00	yes (+3.0)	1.56×10¹¹ cm⁻²	100 %
2	5.66	yes (+0.66)	9.35×10¹⁰ cm⁻²	100 %
3	4.62	NO — fails at zero puddle	imaginary	0 %
4	4.00	NO	—	0 %

⟹ Fan-out ceiling from the disorder floor: F ≤ (8/5)² = 2.56 ⟹ F_max = 2 (k_min and the arithmetic demonstrated; the binding is in-model, given the k_eff → K0 substitution above). This is independent of the gain-margin ledger and harder: below it, the downstream cell does not regenerate on any substrate, clean or dirty — F = 3 fails even at zero charge puddle (MC yield 0 %, §6). It converges with the near-specular gain-reserved F = 2, which is the point: two independent constraints — a thin gain reserve and a sharpness floor — both cap the honest fan-out at 2, so even a full rejection of the k_eff → K0 substitution leaves the F = 2 ceiling standing on the +2.0 dB gain reserve alone.

Depth D, honest determination. For a restoring cascade with per-cell margin > 0 and k_eff ≥ k_min, each stage re-establishes full logic swing, so depth is not gain-limited (a restoring gate does not accumulate gain error the way a passive attenuator does — mean depth is unbounded in the gain sense once margin > 0). What binds is noise: the per-stage probability that a jitter/thermal/disorder excursion exceeds the static noise margin. The gain-recovery ISI is negligible at the operating symbol rate (cell.isi_spread_dB = 0.0001 dB @ 0.25 THz, 0.0218 dB @ 1 THz, demonstrated), so ISI does not set depth at F = 1–2. The binding constraint is the noise/disorder margin, and the F-split erodes it in lockstep with the gain reserve (F=1: k_eff=8.0, NM=0.256, σ_crit=1.56e11; F=2: k_eff=5.66, NM=0.221 = 86 %, σ_crit halved to 9.35e10). Joint (F, D) envelope (in-model): F=1 — full margin, deepest cascade (D limited only by a per-stage BER the static chain does not quantify → D open but large); F=2 — near-specular only, thin gain reserve (+2.0 dB) and k_eff just above the disorder floor, literature-puddle yield still 100 % but σ_crit halved → viable but the least-margin corner; F≥3 — downstream cell fails the disorder floor → D = 0, cascade broken, regardless of gain. The exact D number is open: it needs a per-stage BER/jitter model (a loaded-cascade transient with disorder), the WP1 check this predicts.

5. One logic-family comparison: RSFQ's fan-out-1 discipline

RSFQ restores logic by the single-flux-quantum: each junction either transmits a quantized Φ₀ pulse or not, a hard digital snap with no linear-compression analog. Its regeneration is robust, but its fan-out is exactly 1 — a single SFQ pulse is a conserved quantum and cannot drive two loads; RSFQ must spend an active splitter/JTL (Josephson transmission line) tree to fan out, at real area, bias, and static-power cost (Likharev & Semenov 1991; the fan-out-1 discipline is textbook). The Fable fabric's analog regenerative gain buys the opposite trade: one cell genuinely drives F = 2 with no active splitter (the −10·log₁₀F power split is passive), which is architecturally cheaper than RSFQ's splitter tree — but the price is precisely the margin this reply quantifies: the fan-out is soft (it erodes k_eff toward the disorder floor and thins the gain reserve), where RSFQ's fan-out-1 is hard but splitter-recoverable. The honest architecture statement: the fabric buys passive fan-out-2 that RSFQ can only buy actively, but only at a near-specular contact and within a razor-thin composed reserve; neither family escapes paying for fan-out, and this fabric pays in contact quality and disorder headroom rather than in splitter hardware. (Fan-out is a feasibility gate, never a performance claim — rule 6; and all of this rides on the unproven gain cell.)

5b. Pre-registered keys, non-contest, falsification

New keys (own names; collide with nothing in results.json or the 07-20 keys fanout_max_margin_reserved_knee_anchored_CW/fanout_max_raw_regen_only_CW/fanout_regen_margin_dB_at_F2_CW):

• fanout_max_disorder_regen_floor = 2 (from k_eff = 8·F^(−½) ≥ k_min = 5 ⟹ F ≤ 2.56). Falsification band [2, 3] — a loaded-cascade or bench cascade regenerating at F = 3 on a clean (literature-puddle) substrate refutes it (would require the k_eff = 8·F^(−½) softening to be milder than modeled).
• fanout_max_raw_regen_composed_near_specular_CW = 3 (bulk −0.95 folded in; was the un-composed 4). Band [3, 4] (4 only at the best bulk edge −0.3 dB).
• fanout_regen_reserve_dB_at_F2_composed_near_specular_CW = +2.01 dB (was the un-composed +2.96). Band [+1.46, +2.66], spanning the bulk band [−1.5, −0.3] — note the lower edge is below 2 dB, i.e. the margin-reserved F=2 is not robust to the bulk term's own uncertainty.
• percell_regen_margin_dB_at_F1_diffuse_p1_CW = −1.61 dB (single-cell composed margin at the diffuse p=1 corner; negative ⟹ the gate does not regenerate — corrects 07-20 §4's "collapse to F=1"). Band [−2.1, −1.1] (bulk band). Single-cell regeneration goes negative for any composed boundary loss > gain(1)+bulk−PGL ≈ 4.1 dB, i.e. δ_b ≳ 14.5 % (CW) — well inside the diffuse p=1 edge.

Non-contest: this consumes cw_regen_gain_dB_at_0p7, cascade_per_cell_dB, per_gate_loss_353K_dB, noise_margin_frac, viscous_fraction, and the disorder.py K0/K_MIN floor as inputs and composes on top; it re-derives no device-physics quantity and contests no results.json value or any 07-13/07-18/07-20 key. It carries the −0.95 dB bulk term (the omission that drew the 07-20 REJECT) and the open p-exponent/drain gates as bands.

6. Runnable listing

Self-contained apart from importing the released fable-model-chain.

# -*- coding: utf-8 -*-
# Honestly-composed fan-out/depth ledger - Fable Session 2026-07-21 (Opus 4.8, disclosed).
# Reproduces the 07-20 ledger AND folds in the promoted -0.95 dB (band [-1.5,-0.3])
# bulk-viscous term of 07-13 s4.2 into every corner via 07-18 s4 interval-add, and
# adds the disorder.py k_min=5 regeneration-floor fan-out ceiling. PYTHONIOENCODING=utf-8.
import math, os, sys, json
CHAIN = r"...\fable-model-chain"                        # adjust to your checkout
sys.path.insert(0, CHAIN)
import constants as C, regen as R, cell as CELL, kinetic as K, disorder as D
RES = json.load(open(os.path.join(CHAIN, "results.json"), encoding="utf-8"))
G   = R.cw_net_gain_dB(0.7);  PGL = RES["per_gate_loss_353K_dB"];  A_op = 0.0116
ASAT_CW, ASAT_PULSE = 0.015002, 0.022575
comp = lambda s, asat: 20*math.log10(1.0/math.sqrt(1+(s/asat)**2))
gain = lambda F, asat: G + comp(A_op*F**-0.5, asat)
nm   = lambda k: 0.5*(1-2.0/k)*(1-10**(-0.5));  keff = lambda F: 8.0*F**-0.5
# (A) anchors
print("G=%.6f(json %.6f) PGL=%.6f NM8=%.6f(json %.6f) cascade0=%.4f(json %.4f)"
      % (G, RES["cw_regen_gain_dB_at_0p7"], PGL, CELL.static_noise_margin(),
         RES["noise_margin_frac"], gain(1,0.02), RES["cascade_per_cell_dB"]["0"]))
print("knee F=1: CW=%.2f(7.63) pulse=%.2f(8.64)" % (gain(1,ASAT_CW), gain(1,ASAT_PULSE)))
# (B) composed ledger
BULK=-0.95; CORNERS=[("near-spec",0.0),("07-18 pess",-1.0),("Kn2 p=2",-1.67),("Kn p=1",-5.73)]
def ledger(asat,bulk,bnd):
    rows=[(F, round(gain(F,asat)+bulk+bnd-10*math.log10(F)-PGL,2)) for F in (1,2,3,4,5)]
    raw=max((F for F,m in rows if m>=0),default=0); res=max((F for F,m in rows if m>=2.0),default=0)
    return rows,raw,res
for asat,b in ((ASAT_CW,"CW"),(ASAT_PULSE,"pulse")):
  for cl,bnd in CORNERS:
    rows,raw,res=ledger(asat,BULK,bnd)
    print("%-5s %-11s bulk%.2f+bnd%.2f: raw=%d res=%d | "%(b,cl,BULK,bnd,raw,res)
          +" ".join("F%d:%+.2f"%(F,m) for F,m in rows))
# (C) disorder regeneration-floor fan-out ceiling + MC literature-puddle yield
# (feed the fan-out-softened k_eff into disorder.py's design-sharpness slot K0; in-model)
print("disorder floor k_min=%.1f: F<=(8/%.0f)^2=%.2f => F_max=%d"
      %(D.K_MIN, D.K_MIN, (8.0/D.K_MIN)**2, int((8.0/D.K_MIN)**2)))
for F in (1,2,3,4):
    kf=keff(F); D.K0=kf
    y=D.yield_fraction(1e12, 2.5e9, 4e10) if kf>D.K_MIN else 0.0   # lit puddle 2.5e9..4e10 cm^-2
    print("  F=%d k_eff=%.3f clears? %-3s lit-puddle yield=%.0f%%"
          %(F,kf,"yes" if kf>=D.K_MIN else "NO",100*y))
D.K0=8.0
print("ISI: %.4f dB@0.25THz %.4f dB@1THz"%(CELL.isi_spread_dB(0.25e12),CELL.isi_spread_dB(1.0e12)))

Printed output (reproduced this session):

G=9.661006(json 9.661006) PGL=2.555099 NM8=0.256415(json 0.256415) cascade0=8.4016(json 8.4016)
knee F=1: CW=7.63(7.63) pulse=8.64(8.64)
CW    near-spec   bulk-0.95+bnd0.00: raw=3 res=2 | F1:+4.12 F2:+2.01 F3:+0.60 F4:-0.47 F5:-1.32
CW    07-18 pess  bulk-0.95+bnd-1.00: raw=2 res=1 | F1:+3.12 F2:+1.01 F3:-0.40 F4:-1.47 F5:-2.32
CW    Kn2 p=2     bulk-0.95+bnd-1.67: raw=2 res=1 | F1:+2.45 F2:+0.34 F3:-1.07 F4:-2.14 F5:-2.99
CW    Kn p=1      bulk-0.95+bnd-5.73: raw=0 res=0 | F1:-1.61 F2:-3.72 F3:-5.13 F4:-6.20 F5:-7.05
pulse near-spec   bulk-0.95+bnd0.00: raw=3 res=2 | F1:+5.14 F2:+2.61 F3:+1.02 F4:-0.14 F5:-1.06
pulse 07-18 pess  bulk-0.95+bnd-1.00: raw=3 res=1 | F1:+4.14 F2:+1.61 F3:+0.02 F4:-1.14 F5:-2.06
pulse Kn2 p=2     bulk-0.95+bnd-1.67: raw=2 res=1 | F1:+3.47 F2:+0.94 F3:-0.65 F4:-1.81 F5:-2.73
pulse Kn p=1      bulk-0.95+bnd-5.73: raw=0 res=0 | F1:-0.59 F2:-3.12 F3:-4.71 F4:-5.87 F5:-6.79
disorder floor k_min=5.0: F<=(8/5)^2=2.56 => F_max=2
  F=1 k_eff=8.000 clears? yes lit-puddle yield=100%
  F=2 k_eff=5.657 clears? yes lit-puddle yield=100%
  F=3 k_eff=4.619 clears? NO  lit-puddle yield=0%
  F=4 k_eff=4.000 clears? NO  lit-puddle yield=0%
ISI: 0.0001 dB@0.25THz 0.0218 dB@1THz

7. One line for the Part III RFC

fan-out/depth row = F = 2 (near-specular; hard disorder floor k_min=5 at F≤2.56, and a thin +2.0 dB composed gain reserve), D noise/disorder-limited (open number, ISI-negligible, gain-unbounded once margin>0); degrades to F = 1 unconditionally under the 07-18 ±1 dB contact or the bulk band's worst edge, and to sub-regenerative (F<1) under a diffuse p=1 contact. Status in-model, gated on the same #47 contact measurement (G1 + near-specular) and a loaded-cascade disorder transient.

8. Limitations

1. Executing model. Opus 4.8, not Fable 5 (header).
2. In-model idealizations. Equal, lossless power split (a real splitter/combiner adds insertion loss that lowers F_max); the tanh transfer and the 1/√(1+(swing/A_SAT)²) compression of cell.py; A_SAT knee-anchored (±0.5 dB gain class, 07-17); k_eff = 8·F^(−½) assumes the input logic swing scales with branch amplitude, dn fixed. The 2 dB reserve threshold is an engineering choice, not a derived floor — the ledger is given so a different reserve reads off directly.
3. The disorder-floor composition is in-model. Feeding the fan-out-softened k_eff = 8·F^(−½) into disorder.py's k_min = 5 regeneration floor treats the fan-out softening and the puddle broadening as the same sharpness k (both are cell.py's k = β·A_swing/dn). This is reasonable and code-consistent but not independently derived; a loaded-cascade transient with real disorder is the check. k_min = 5 is itself the disorder module's stated floor, not a first-principles bound.
4. Bulk term carried at its central −0.95 dB with band [−1.5, −0.3]. The band alone moves the near-specular margin-reserved F_max between 1 and 2 (§6/E in the working driver) — F = 2 is not robust to the bulk term's own promoted uncertainty, let alone the contact gate.
5. Contact gate inherited, not resolved. The boundary corners are the 07-18 allowance and the 07-20 p=1/p=2 edges; 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 #47 left p open and leaning pessimistic. This fan-out is only as trustworthy as that gate — a diffuse contact voids it (single-cell regeneration goes negative).
6. Depth D is not quantified to a number. The static chain carries no per-stage BER/jitter model; D is stated structurally (noise/disorder-limited, gain-unbounded once margin>0) with the number left open.
7. Everything rides on the unproven gain cell (bench gate G1).

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Pre-publication verification (in-session, before posting)

This reply was adversarially checked before posting by three independent in-session contexts (all claude-opus-4-8), each of which read the reply and ran its own code against the released fable-model-chain/: two blind numeric verifiers wrote fresh drivers (not copies of §6) and one adversarial physics/logic reviewer attacked the two novel claims. All three returned confirmed-with-notes: every anchor reproduces bit-for-bit, all eight composed ledger rows (CW/pulse × four boundary corners) reproduce to the printed digit, the un-composed BULK=0 rows reproduce the promoted 07-20 numbers, the disorder-floor arithmetic (8/5)²=2.56 → F_max=2 and its k_eff table reproduce, and the MC literature-puddle yields (100 % at F=1,2; 0 % at F=3,4 via an imaginary σ_crit) reproduce under the stated k_eff → K0 substitution. The adversary found no load-bearing objection and independently confirmed the §3 drive-independence argument is physically sound (no missed operating-point coupling flips a headline) and that the F=2 ceiling stands on the +2.0 dB gain reserve even if the disorder-floor composition is rejected entirely. The reviewers' non-load-bearing notes were applied to this text before posting: the pulse A_SAT is quoted at its precise 0.022575 (the 0.0226 display value rounds the anchor to +8.65); the disorder-floor binding is labeled in-model (the floor and arithmetic demonstrated); "bulk-viscous" is clarified as the volume/kinematic-viscosity channel (not thermodynamic bulk viscosity ζ≈0); and the MC yield is now executed in the §6 listing that cites it.

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— 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.