[martyn]

Summary

Proposes, implements, and benchmarks a new clock-free ParticleGAN formulation family — Relativistic Hellinger-Born-Infeld Transport (rhbi) (rhbi-v1) — built around a single Debiased Slack-Screened Unbalanced Sinkhorn variational operator with zero schedule annealing, zero EMA critic copy (critic_ema_decay = 0.0), and zero input-shape or step-count gates.

• Current leaderboard (develop): https://github.com/255BITS/ParticleGAN/blob/develop/reports/forge/technique-inventory.md
• Updated 9-family leaderboard (feat/rhbi-family): reports/forge/technique-inventory.md
• Generated RHBI family report: reports/forge/families/rhbi.md
• Design derivation & failure-mode analysis: reports/forge/rhbi/README.md

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Formulation Highlights (rhbi-v1)

1. Physical Scale-Equivariant Born-Infeld Ground Cost ($C^\infty$ & float32-overflow-safe):
   Tracks the detached 25th-quantile real nearest-neighbor distance $\ell_t = (1-\beta_\ell)\ell_{t-1} + \beta_\ell,\operatorname{stopgrad}(Q_{0.25}(d^{\mathrm{NN}}Y) + 10^{-6})$ entirely on-device (zero host-device syncs, exact checkpointing of ell_ema and ell_initialized) and evaluates $c{\mathrm{phys}}(x_i,y_j) = \sqrt{\ell_t^2 + \lVert x_i - y_j\rVert_2^2} - \ell_t$ via float64 GEMM + algebraic rationalization $\lVert u\rVert_2^2 / (\sqrt{1 + \lVert u\rVert_2^2} + 1)$. Matches $\frac{1}{2\ell_t}\lVert\Delta\rVert_2^2$ ($W_2$ moments) inside modes while analytically bounding inter-mode pull slopes inside $[-1, +1]$.
2. $(B+1)\times(B+1)$ Kantorovich-Hellinger Slack-Screened Sinkhorn ($S=2$ Reservoir):
   Couples active particles ($m_i = 1/B$) against an oversized slack reservoir ($m_0 = 2.0 > 1$) so unmatched Poisson singletons ($B \lesssim M$) route cleanly to centered, bounded critic log-odds ascent ($\tilde d(z) = C_{\max}\tanh((D(z) - \bar D)/C_{\max})$) while matched pairs follow nonlocal Born-Infeld pull, keeping logsumexp Sinkhorn scaling ($K=8$) strictly inside the Birkhoff polytope without marginal starvation.
3. Active-Fraction-Matched Hollow Self-Coupling Debiasing:
   Masks diagonal $L^{(XX)}{ii} = -\infty$ with zeroed critic shift in self-coupling and scales symmetric repulsive weights by $\sqrt{a_i a_k}$ ($a_i = \operatorname{clamp}(B\sum_j P^{\star(XY)}{ij}, 0, 1)$), cancelling entropic variance shrinkage inside multi-particle modes while leaving Poisson singletons unrepelled.
4. Smooth $C^\infty$ Born-Infeld Endpoint Lipschitz Cap & Joint BiGAN Coupling:
   Replaces chord interpolation and EMA critic anchors with a softplus-squared endpoint input-gradient cap ($\kappa=1, \beta=20$) on real and fake samples, supports discrete class masking on conditional hosts and joint relativistic $(x,z)$ Sinkhorn coupling on BiGAN hosts, and adds optimizer_dense_profile="polar_cpu_v1" (single-buffer batched PCIe CPU LAPACK polar SVD) to eliminate tiny-matrix cuSOLVER overhead on dense MLP hosts.

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9-Family Leaderboard Comparison (Protocol Seed 0, NVIDIA RTX A6000)

Untuned rhbi-v1 (1 declared candidate card, 0 configuration searches) achieves 23/27 Tier 1 view requirements — the highest Tier 1 view-requirement total on the board — with 0 BLOCKED / 0 ERROR / 0 INCOMPLETE across Tier 1:

Family	Selected Recipe	Tier 1 Req.	adaptation T1	clockfree T1	disc_stab T1	formulation T1	host_transfer T1	quality T1	Tuning Disclosure
RHBI	rhbi-v1	23/27	3/3	4/4	7/11	3/3	3/3	3/3	untuned (0 searches, 1 card)
BISPF	bispf-optimized-quintic-v1	22/27	3/3	3/4	7/11	3/3	3/3	3/3	0 searches, 19 cards
BCAP	recipe-prior-refactor-bcap-pure-v1	22/27	3/3	3/4	7/11	3/3	3/3	3/3	85 searches, 473 cards
GAN v3	recipe-prior-refactor-release07-gan-v3-v1	20/27	3/3	3/4	5/11	3/3	3/3	3/3	10 searches, 8 cards
K3P	recipe-prior-refactor-k3p-v1	20/27	3/3	3/4	5/11	3/3	3/3	3/3	15 searches, 46 cards
KA2	recipe-prior-refactor-ka2-v1	20/27	3/3	3/4	5/11	3/3	3/3	3/3	11 searches, 9 cards
R1/R2	recipe-prior-refactor-r1r2-v1	20/27	3/3	3/4	5/11	3/3	3/3	3/3	12 searches, 34 cards
Atlas	atlas-particle-normal-v4	18/27	2/3	2/4	8/11	2/3	2/3	2/3	0 searches, 5 cards
E22	e22	0/27	0/3	0/4	0/11	0/3	0/3	0/3	untuned (0 searches, 1 card)

Uncontended DCGAN Scaling Performance (GPU-548116b7, clear, 54/54 cells)

Task	RHBI (rhbi-v1)	BISPF (quintic-v1)	BCAP (bcap-pure-v1)	Atlas (v4)
dcgan_performance_r32 (32², B16, W64)	31.25 ms (514.8 img/s)	28.89 ms (548.3 img/s)	276.58 ms (57.7 img/s)	22.89 ms (693.4 img/s)
dcgan_performance_r64 (64², B16, W64)	52.86 ms (301.0 img/s)	51.07 ms (313.3 img/s)	605.61 ms (26.1 img/s)	39.19 ms (406.1 img/s)
dcgan_performance_w128 (64², B16, W128)	109.61 ms (146.0 img/s)	110.68 ms (144.4 img/s)	1,493.95 ms (10.2 img/s)	70.71 ms (225.7 img/s)
dcgan_performance_b64 (64², B64, W64)	92.59 ms (691.5 img/s)	91.17 ms (702.4 img/s)	676.60 ms (94.7 img/s)	76.13 ms (840.0 img/s)
dcgan_performance_r128 (128², B16, W64)	123.67 ms (129.1 img/s)	122.64 ms (130.3 img/s)	2,083.82 ms (7.5 img/s)	85.66 ms (186.3 img/s)
dcgan_performance_r256 (256², B16, W64)	350.37 ms (45.7 img/s)	344.14 ms (46.5 img/s)	3,146.68 ms (5.0 img/s)	267.22 ms (59.9 img/s)

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Diagnosis of the 4 Required Tier 1 Misses & rhbi-v2 Roadmap

All 4 required Tier 1 misses in discriminator_stability reach strong mode coverage/final quality (model_vae_categorical: all 13 final bounds met, 12/24 passing checks; model_vae_hard: decoder_mean_hq=0.9934, likelihood_hq=0.9814, 12/24 passing checks; model_ae_gan_multimodal: 14/24 passing checks; ring16_acquisition: 16/16 modes, hq=0.946, covariance spill 1.617 > 0.85), failing on the 5-check consecutive stability suffix or mode-covariance spill due to two coupled optimizer/prior effects:

1. Unquenched Poisson OT Shot Noise vs. DualNorm Polar Smoothing (0.001): At equilibrium, finite-batch ($B=64$) Sinkhorn residuals remain above DualNorm's 0.001 polar smoothing floor, so DualNorm normalizes stochastic shot noise back to unit spectral step norm ($\approx 0.012$) and perturbs converged AE/VAE/ring modes out of the 5-check suffix window.
2. High Particle Row Mobility (prior_lr_mult = 2.5 with rownorm): Row-normalized particle updates of size 0.03 per step inflate intra-mode latent dispersion on ring16_acquisition (spill = 1.617).

Recommended rhbi-v2 next steps:

• Variational Kantorovich-slack equilibrium cooling (g <- g * tanh(E_excess / E_ref)) to attenuate parameter gradients below DualNorm's 0.001 smoothing threshold once active transport cost approaches hollow self-coupling energy.
• Low-mobility particle updates (prior_lr_mult = 0.02–0.25) to eliminate intra-mode covariance spill on ring16_acquisition while retaining nonlocal Born-Infeld mode capture.

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Verification

• python -m experiments.forge validate & python -m experiments.forge compile --check (CURRENT)
• python ops/refresh_forge_readouts.py --check --reports-only (Status: CURRENT (stale stages: none))
• pytest across tests/test_rhbi.py, tests/test_refresh_forge_readouts.py, tests/test_docs_links.py, tests/test_leaderboard_index.py, tests/test_forge_current_technique_inventory.py, tests/test_forge_comparison_policy.py, tests/test_forge_recorded_formulaic_display.py, tests/test_atlas_particle_normal_v4.py, tests/test_forge_scaling.py, tests/test_swappable_priors.py (388 passed)
• python scripts/check_lint.py (0 new findings) & wheel size gate (399,571 < 600,000 bytes)
• Zero edits to particlegan/recipe_compat.py or experiments/forge/behavior_adapters.py; all 8 existing family pins preserved byte-for-byte.