World Alignment: unpaired cross-modal correspondence by relational identifiability

Method: scene states are sets of part states; relation fields are built
within each modality and are invariant to how each side labels its own
features; the cross-modal bridge is a coupling searched under an energy
that is a closed-form functional of one matrix; solving is spectral
initialisation followed by exact local refinement.

Evidence: in a procedurally generated closed world, blind recovery of a
hidden image-caption correspondence reaches 95.3% at 256 scenes against
0.39% chance, and the recovered pairs transfer to 200 held-out scenes at
93.0% exact retrieval with random-pair and shuffled-image controls at or
near chance. Cross-modal value correspondence is derived from disjoint
corpora rather than declared. On Visual Genome the field correlation
reaches 0.656 against the 0.9 that polynomial recovery needs, with the
deficit attributed away from segmentation and discretisation.

Protocol: no image-text pair enters any objective, optimiser,
initialisation, or model selection; hidden pairs score orderings only.

Co-Authored-By: Claude <noreply@anthropic.com>

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+# WorldAlign research log
+
+This file records research decisions, failed hypotheses, and the current
+experimental gate. Exact metrics live in the result reports and machine-readable
+artifacts. The collaborator-facing statement of the project is maintained in
+`PROJECT_CONCEPT.md`.
+
+## Research target
+
+The target is a real multimodal large-model system, not a geometry result or a
+toy correspondence benchmark.
+
+The working hypothesis is that independently trained, sufficiently informative
+unimodal representations may recover the same world structure up to a change
+of coordinates. Multimodal alignment could then be obtained by descending a
+high-level shared-world energy, without paired contrastive supervision.
+
+Important constraints:
+
+- Do not treat the word "graph" as a commitment to explicit semantic nodes.
+  It is only an analogy for richly constrained relations in learned states.
+- Node-wise or sample-wise sufficiency is not enough. The observations must be
+  overcomplete enough to constrain relations among world states.
+- Generic encyclopedia text is not a closed counterpart of the visible world:
+  it contains many latent factors that images cannot identify.
+- The target method is not an image-to-language MLP bridge. The bridge baseline
+  is useful only as an interface/control.
+- Paired examples may be used for held-out diagnosis, never by the unpaired
+  energy, optimizer, initialization, model selection, or stopping rule.
+
+## 2026-07-28: learned-bridge baseline
+
+Flickr30k, frozen DINOv2 and frozen Qwen were aligned with static
+GW/SWD/isometry objectives.
+
+- Cross-modal relational similarity is measurably non-random.
+- Static GW produces sharp but mostly incorrect correspondences.
+- A paired bridge verifies that the frozen-language-model interface works.
+- The unpaired learned bridge does not produce usable multimodal ability.
+
+See `RESULTS.md`.
+
+## 2026-07-29: overcomplete observations
+
+Five independent captions of the same scene were treated as an observation
+orbit. On 512 held-out examples, the correct-vs-shuffled relation-energy gap
+increased from 0.316 with one caption to 0.582 with five captions.
+
+This supports the narrower claim that relational overcompleteness makes the
+correct configuration easier to distinguish. It does not establish that the
+current energy identifies the correct absolute configuration.
+
+## 2026-07-29: energy descent without a cross-modal map
+
+Free Qwen-side latent particles were initialized from real text states and
+optimized using:
+
+- standardized relation-field matching;
+- multiscale conditional-neighborhood matching;
+- sliced text-population matching;
+- proximity to text-only prototypes.
+
+Weak manifold regularization briefly improved held-out R@10 from 2.34% to
+12.11%, but left the decodable language manifold. Strong regularization
+improved it only to 6.25% at the best intermediate step.
+
+Language-prior-only and shuffled-vision controls showed that caption-generation
+improvements were not reliably image-conditioned.
+
+## 2026-07-29: convergence audit and falsification
+
+The original logged total was not a fixed objective because relation and
+conditional weights were annealed. Therefore that curve could not establish
+convergence.
+
+Starting from the strong-manifold (`m30`) endpoint, the final weights were
+frozen and optimization was continued at one tenth of the learning rate:
+
+- fixed energy decreased from 2.767 to approximately 1.54;
+- R@10 decreased from 5.86% to approximately 3--4%;
+- median rank worsened from 103 to approximately 120--123;
+- random R@10 for 256 candidates is 3.91%;
+- gradients remained nonzero and Adam continued to oscillate.
+
+Most decisively, the true paired language configuration has fixed energy about
+4.49, while an incorrect synthetic configuration reaches about 1.54.
+
+Therefore the present energy is falsified as an alignment objective:
+
+\[
+E(\text{correct paired state}) >
+E(\text{incorrect synthetic state}).
+\]
+
+The early retrieval gain was a trajectory transient, not evidence that further
+energy descent would recover the correct gauge. More steps or optimizer tuning
+cannot repair this ordering.
+
+## 2026-07-29: on-manifold assignment gate
+
+Decision, confirmed with the project owner: restrict the configuration space
+to permutations of real frozen text states. On this space the language-only
+terms of the falsified energy are permutation-invariant constants, and the
+continuous counterfeit route is closed by construction. Per the standing
+gate, only ranking and local-ordering diagnostics were run; no new descent.
+
+Result: the falsification survives the restriction.
+
+- Global ordering always passes: the true assignment ranks below all 1,000
+  random permutations in every condition (z 2.7--18.7).
+- Local ordering always fails: 6.8--33% of transpositions of the true
+  assignment lower the energy (exact closed-form enumeration); at N=5,000
+  the count is 2.70M of 12.50M. Scale does not repair it.
+- Exact steepest 2-swap descent from the truth keeps 2.7--13.9% of nodes;
+  random-start quenches reach energies 0.9--1.9 below the true
+  configuration at 0.0--0.4% accuracy. On-manifold counterfeits exist in
+  every condition.
+
+Mechanism, from three audits: pooled states are extremely anisotropic
+(99.5% of Flickr caption pairs above cosine 0.8); the cross-modal share of
+standardized relational structure is Spearman 0.19--0.31; that share is
+spectrally concentrated (top-16 population directions: 0.367; full space:
+0.306; whitening collapses it to 0.03). Five-caption orbits and visible
+relations denoise within this coarse subspace; distribution-valued edge
+channels (std/q10/q90 of view-pair cosines) carry no shared signal and
+dilute the energy; model scale was already known to be inert. A roughly
+sixteen-dimensional topical code cannot separate 512 instances, so no
+energy over these node states can identify the assignment.
+
+See `MANIFOLD_RESULTS.md`.
+
+## 2026-07-29: view-level shared structure inside VG nodes
+
+The per-node view permutation hidden at preparation time is exactly
+replayable from the seed and the private image IDs; the replay reconstructs
+all 5,000 released phrase bundles verbatim and is used only for evaluation.
+
+- Within-node relation fields align across modalities: matched Spearman
+  0.128 against -0.002 shuffled, z = 46.6 over 5,000 nodes.
+- With the true node-level alignment as a coarse frame, population-context
+  profiles match the 16 views at 14.5% accuracy against 6.25% chance
+  (top-3 29.5%); a larger frame helps (200 nodes: 12.9%). This is an upper
+  bound: a blind system must substitute its own recovered coarse frame.
+- Within-node relations alone stay near chance (7.0%), so the population
+  context carries the signal.
+
+The fine-grained shared structure missing at node level exists one level
+down, in the compositional structure that pooling discards.
+
+## 2026-07-29: Ricci-flow control and static view-level gate
+
+Two same-day continuations, both requested before the structural redesign.
+
+Ollivier-Ricci flow on each modality's kNN geometry (independent,
+identical hyperparameters, diffusion-only baseline for attribution) more
+than doubles the global ranking z (Flickr 21.4 to 47.8; VG 6.9 to 22.5)
+and changes no verdict: 9--14% improving transpositions, descent retention
+1--5%, counterfeits at about half the true energy in all four conditions.
+Geometric smoothing is a frame ingredient, not a resolver; it cannot be
+part of the alignment transform itself (information loss), matching the
+whitening result.
+
+The static view-level gate fails at scale: with the true coarse frame,
+none of 5,000 nodes has the true view assignment as a strict local
+minimum (32.0% improving for the within-node relational energy, 28.3% for
+the profile energy, 25.5% joint). Frame-free internal-field matching is
+null at 512 nodes over three seeds (R@10 at chance, zero margin-decile
+precision, true-pair z 0.1--1.8 after a capacity null; the negative z
+seen at 96-node smoke scale did not replicate). Consequence: the view
+level needs model-internal relations or true re-encoding interventions --
+the R3/R8 battery in `STRUCTURE_DESIGN.md` is the critical path.
+
+## 2026-07-29: representation batteries and the first passed basin audit
+
+The R6 and R3 batteries of `STRUCTURE_DESIGN.md` were run the same day.
+
+R6, within-scene noise whitening: directions maximizing between-scene
+over within-scene variance, fitted per modality on unpaired orbits
+(train-only for Flickr, holdout-only for VG). Cross-modal relational
+Spearman rises 0.298 to 0.358 (Flickr orbit), 0.189 to 0.326 (single
+caption, now above the raw orbit mean), 0.213 to 0.614 (VG both sides,
+k=8); improving-swap fractions collapse 7.8% to 0.5% and 23.5% to 0.25%.
+Population whitening had destroyed the same signal; the only difference
+is whitening the within-scene rather than the total covariance.
+
+R3, model-layer readout: joint-context encoding on all 5,000 VG nodes.
+Attention weights are modality-specialized (best attention-attention
+matched rho 0.076); in-context states carry rho 0.216 against the 0.128
+isolated baseline (z 69.6 vs 46.6). Relations do live in the model layer,
+and the shared readout is the mixed states, not the mixing weights.
+
+Full gate on the new states: nine of nine VG conditions pass the basin
+audit -- ten random-restart quenches per run all end 5--19% above the
+true energy, replicated over subset seeds 0--2, for both isolated
+projected states and the in-context composite (which roughly doubles the
+margin at matched k). First energies in the project whose descent finds
+nothing below the truth. Flickr still fails by under 1%: one visual view
+means no visual orbit to whiten, so two-sided multi-view observation is a
+data-protocol requirement. The true assignment is still not a strict
+local minimum (0.17--0.28% improving swaps; descent keeps 52--59%), so
+what is licensed is soft-coupling recovery, not hard matching.
+
+See `BATTERY_RESULTS.md`.
+
+## 2026-07-29: blind recovery enters the hard phase
+
+First Phase-2 experiment on the gate-passing states, hidden-shuffle
+protocol, three search arms. Parallel tempering (eight replicas, exact
+closed-form deltas, 60k rounds) equilibrates into the quench band of the
+gate report -- ending 9--20% above the true energy at 1--3% accuracy --
+and never enters the true funnel; entropic Sinkhorn and spectral-band
+homotopy stall at +62--100% with zero verified seed mass. Discrete
+annealing beats continuous relaxation everywhere and still loses to the
+landscape.
+
+Diagnosis: the classic hard phase of planted assignment -- the gate shows
+the configuration is information-theoretically identifiable while local
+dynamics equilibrate into an exponential shelf of wrong states. The gap
+between the statistical and algorithmic thresholds is now the central
+quantity.
+
+The N-scaling probe closes the cheapest hypothesis: at matched per-node
+move budget (N=2,048, 320k rounds), the reachable shelf returns to the
+same +9--10% band as N=512 and the small accuracy signal vanishes.
+Density alone does not approach an algorithmic threshold in the tested
+range.
+
+The first C5 anchor wave closes the second-cheapest. Pixel- and
+lexicon-derived unary anchors carry population signal (combined z = 17.2)
+with no per-pair reliability (top-margin precision 2%, mutual-NN 0.17%),
+and dense injection into the tempering energy degrades recovery
+monotonically in the weight (accuracy 3.1% to 1.0--2.0%, relational
+energy +9% to +30--115%). Scene-level anchors are coarse-redundant with
+the shared subspace; usable side information must be per-pair reliable or
+independent of the relational field. Fine-grained anchors (numerals,
+spatial predicates, box geometry) live at view level with sixteen
+candidates, so the second wave merges into the view recursion. Remaining
+search-side lever: cavity/message-passing dynamics.
+
+The second wave (2026-07-30) delivers the first seeds. Per-view color,
+light, size, and position anchors against crop pixels and box geometry:
+frame-free view matching 11.5% vs 6.25% chance, 35.6% precision on
+top-1%-margin views (354 seeds; every prior high-confidence channel was
+0--4%). Aggregated per-pair Hungarian values give the best frame-free
+node affinity to date (R@10 4.4--4.9x chance over three seeds), with
+node-level seed precision still at 2--6%. Pixel and lexicon statistics
+are exhausted; the next package is a factor graph over node and view
+assignments -- anchor unaries, relational pairwise, message passing --
+plus the untested numeral-to-repetition anchor.
+
+See `RECOVERY_RESULTS.md`.
+
+## 2026-07-30: synthetic closed world v0 -- the objective becomes the bottleneck
+
+A procedural world with exact closure (43-word vocabulary, unique
+referents, ring-placement multiplicity, relation-constrained rendering,
+ground-truth interventions) and from-scratch unimodal towers on disjoint
+splits. First measurement inverts the natural-data pattern: linear CKA
+matches (0.278 vs 0.262) while relational Spearman collapses six-fold
+(0.030 vs 0.184, z 2.4 vs 12.3). The gate fails accordingly; content
+projection restores ranking (z = 117) but not the basin (counterfeit at
+-13%).
+
+Attribution is clean because data sufficiency is total by construction:
+InfoNCE's uniformity pressure turned the vision tower into a
+near-orthogonal instance codebook, erasing between-scene geometry.
+Sufficiency of the data does not transfer to sufficiency of the
+representation; the unimodal objective decides which world geometry
+survives, and R1 is a property of the data-objective pair. The SSL
+objective is now a phase-diagram axis. Next: reconstruction-family
+towers (doubling as the masked predictors of the prediction-transfer
+energy), then the structure identification battery.
+
+See `SYNTH_RESULTS.md` and the 2026-07-30 additions to
+`STRUCTURE_DESIGN.md` (unified element-relation object; the three-rung
+energy ladder ending in lifted unimodal world models).
+
+## 2026-07-30/31: objective battery, set machinery, and the first phase coordinates
+
+The synthetic world's second day closes three questions and opens one.
+
+Objective battery, complete: five standard self-supervised recipes
+(orbit-InfoNCE, SimMIM, their hybrid, data2vec-lite, slot attention at
+two resolutions) all fail to produce factor-complete global states, each
+by a distinct mechanism -- shortcut selection, local-only knowledge,
+non-merging losses, softened shortcut, and spatial tiling instead of
+object binding. Slot attention carries the most relational sharing
+(0.128 against 0.030 for InfoNCE) and the set-versus-pool doctrine is
+confirmed quantitatively: pooling slot sets without correspondence drops
+color decodability from 0.99 to 0.55.
+
+Set-kernel machinery, taken to a hand-crafted ceiling
+(connected-component descriptors against phrase bag-of-words): seven
+measured iterations moved the gate from z = -0.1 and 45% improving swaps
+to z = 51, 0.15% improving swaps, and 77% descent retention. Priced en
+route: mass-weighting inside matching destroys grading; multi-view field
+averaging cancels segmentation noise; a factor present on one side only
+(shape) is a counterfeit lever; so is size-dependent matching bias.
+
+End to end, honestly: blind tempering on the best fields still finds
+assignments 4--9% below the truth at chance accuracy, and size
+residualization removes shared signal along with the nuisance. With VG's
+passing configuration at field validity 0.61 and this ceiling near 0.45,
+the basin-pass boundary at N = 512 is bracketed between them: the first
+coordinates of the identifiability phase diagram.
+
+See `SYNTH_RESULTS.md`.
+
+## 2026-07-31: the Fock lift and the (validity, N) boundary
+
+The out-of-the-box program's first invention went to flight the same
+morning. A symmetric-tensor moment kernel on object sets (the truncated
+second-quantized lift: composition as algebra, multiplicity as an
+observable, no matching step and hence none of the measured matching
+biases) with factor-mirrored one-hot descriptors gives the synthetic
+world its first full basin pass at N = 64 -- no counterfeit, 92%
+retention. At N = 512 counterfeits return 18--22% below the truth and
+recovery stays at chance; residual segmentation error (30% wrong counts)
+and shape-cluster impurity suffice at eight times the configuration
+space. Identifiability is now measured as a joint boundary in field
+validity and population size: pass at (0.45, 64), fail at (0.45, 512),
+pass at (0.61, 512). Queued inventions, in order: orbit-derived
+per-entry precision weighting (channel-matched energy), third-order
+triangle invariants (holonomy against pairwise counterfeits), moment
+ideals as gauge-free content coordinates; mixed-curvature products noted
+as a symmetry-breaking device and deprioritized.
+
+See `SYNTH_RESULTS.md` and the tool inventory in `STRUCTURE_DESIGN.md`.
+
+## 2026-07-31: the gate statistic was measuring the searcher
+
+A methodological correction that supersedes part of the same day's
+optimism. Third-order (triangle) invariants were added and, in a harness
+whose descent proposes 64 sampled pairs per step, the truth became
+essentially immovable at N=512 (retention 99.6%, no counterfeit, z=50),
+replicated over three hidden shuffles. Two controls dismantled the
+reading: the pairwise-only energy passes identically in that harness
+(retention 100%), and long tempering on the triangle energy at N=128
+reaches 10% below the truth at zero accuracy.
+
+Conclusion: descent retention measures the strength of the search
+operator, not the identifiability of the energy. Exact all-pairs
+enumeration (yesterday's harness) is a strictly stronger searcher than
+sampled proposals, and long tempering is stronger still. The gate
+statistic is therefore redefined:
+
+\[
+E(\text{truth}) \le E(\text{deepest state a strong searcher reaches}),
+\]
+
+measured with long parallel tempering from random starts plus a
+truth-initialized arm, uniformly across candidate energies. Retention and
+improving-swap fractions remain as diagnostics, never as verdicts. All
+candidate energies are being re-measured on this basis
+(`synth_deep_gate.py`); readings from the weaker harness are marked
+superseded in `SYNTH_RESULTS.md`.
+
+## 2026-07-31: closed form, spectral solvers, and a clean Tier 0
+
+Three results and one protocol decision, all same day.
+
+Closed form: the triangle energy equals a constant minus 2 trace(M^3)/6
+with M the elementwise product of permuted text and visual fields, so
+one batched matrix product scores hundreds of permutations over all
+C(N,3) triples. Validated to 3e-7 against brute force; opens trace(M^k)
+for any k. Iteration time per configuration falls from hours to minutes.
+
+Spectral solvers (Umeyama, GRAMPA) were added because they are
+polynomial and dimension-free -- relation fields are N x N whatever the
+embedding widths -- and therefore bypass the glassy landscape. They
+return 3--13x chance. Correlated-graph-matching theory explains it: at
+N=256 the information-theoretic threshold sits near rho = 0.29 and the
+polynomial threshold near rho = 0.9, and our fields are at 0.51--0.57.
+The project is squarely in the computationally hard phase, which now has
+a quantitative account rather than an empirical one.
+
+Identifiability is not correlation. The colour-only field reaches rho =
+0.863 yet caps at 49% because only 126 of 256 scenes have distinct
+colour multisets; its eigenvalue degeneracy is that collision structure.
+Full descriptors are 100% distinct. Channel mixing inside one moment
+kernel dilutes 0.86 to 0.51.
+
+Protocol, decided with the user: anchors that declare "red means this
+hue" are not labels but are hand-supplied cross-modal prior, so results
+must be reported by tier. Tier 0 forbids any declared correspondence.
+Achieved the same day on world v1 (Zipf-skewed factor marginals, since
+uniform v0 makes the correspondence information-theoretically
+unrecoverable): text factor families discovered by mutual exclusivity,
+vision colour classes by k-means on raw RGB, the two paired by marginal
+frequency rank -- 10/10 entries semantically correct, fields at rho =
+0.570 with a 97.3% identifiability ceiling.
+
+See `SYNTH_RESULTS.md`.
+
+## 2026-07-31: first recovery, and it was segmentation all along
+
+The rho decomposition settled the target: oracle segmentation gives field
+correlation exactly 1.0 and the Tier 0 derived dictionary is free (oracle
+and derived fields are identical), while connected-component segmentation
+gives 0.5696. Three unimodal fixes closed most of it -- Gestalt
+appearance grouping (exact group count 71.9 to 90.2%),
+distance-transform watershed for touching ring members (exact object
+count 74.2 to 100%), and one-dimensional k-means on radial extent for
+size classes (52.7 to 87.9%, because area confounds size with shape and
+the classes are gap-separated rather than equally populated).
+
+Field correlation went 0.570 to 0.671 to 0.928, and GRAMPA recovery
+followed it 5.1% to 9.4% to **53.9%** at N=256 (0.39% chance), replicated
+at 53.9/53.9/54.7% over three hidden shuffles, and 26.3% at N=600 (0.17%
+chance). First end-to-end world matching in the project: no pairs, no
+declared dictionary, no learned cross-modal map -- factor families from
+mutual exclusivity, colour correspondence from marginal frequency rank,
+object states from pixels, assignment from a polynomial spectral solver
+on two independently built relation fields.
+
+Composing the two solvers closes most of the remaining gap: GRAMPA
+initialisation 53.5%, plus pairwise-energy steepest descent 86.7%, plus
+pairwise-and-triangle refinement **95.3%**. Spectral never gets trapped
+but rounds badly; the energy rounds well but cannot find the basin; the
+composition does both. The final state sits 0.04% below the truth in
+energy at 95.3% accuracy -- residual field noise, not a counterfeit.
+
+The theoretical account held throughout: nothing worked below rho = 0.9
+and recovery appeared as soon as the fields crossed it. Reporting-bias
+worlds show the derivation degrades gracefully -- text-versus-pixel rank
+correlation 1.00/0.98/0.84/0.77 gives dictionaries of 8/8/6/6 out of ten
+-- with errors concentrated in the close-frequency tail, so
+margin-calibrated entries are the natural seed set.
+
+The recovered assignment then transfers: used as pseudo-pairs for a ridge
+map and applied to 200 held-out scenes that took no part in matching,
+retrieval is 93.0% exact against 0.5% chance, colour set F1 0.989, count
+multiset 97.5%. The random-pair control sits exactly at chance and the
+shuffled-image control drops colour F1 to 0.295, so the output is
+image-conditioned and extrapolates. Rungs four and five of the evidence
+ladder are closed inside the synthetic world; matching is a bootstrap for
+the map, not the deployment mechanism.
+
+Unchanged by this: object states are hand-built upper-bound descriptors
+that no tested self-supervised recipe reproduces, and the world is
+procedurally generated.
+
+See `SYNTH_RESULTS.md`.
+
+## 2026-08-01: reporting bias, and three solver-versus-information calls
+
+Worlds v3 and v4 test whether the derived dictionary survives reporting
+bias. v3 couples colour to shape cyclically and biases mentions toward
+rare colours, so captions name half the groups and the pixel and text
+colour rankings diverge in the tail; v4 replaces the cyclic coupling with
+a distinct Dirichlet shape profile per colour.
+
+v3 results: marginal rank 4/10, joint structure 6/10, joint plus marginal
+under exact enumeration of the 720 shape permutations 7/10, oracle shape
+columns with measured clusters 8/10, oracle labels 10/10. Vision-side
+extraction is not the limit (colour cluster purity 1.000, shape 0.998).
+The 6/10 initially looked like an information bound -- ten colours over
+six shapes leaves exactly four twin profiles, and exactly four appeared
+-- but the twins separate by frequency, and the combined evidence has
+minimum pairwise distance 0.2322 against 0.0008 for shape alone. The
+bound is 10/10; what is left is one entry of solver gap and two of
+estimation noise from the thinned joint table.
+
+v4 results: exact enumeration recovers 10/10 under the same bias and
+mention rate, across frequency weights including zero. Non-degenerate
+joint structure suffices on its own, which is the regime real corpora
+occupy.
+
+Three times now a limit has looked intrinsic and proved to be the
+solver's: descent retention, the triangle-energy pass, and this ceiling.
+The rule stands -- compute the bound, do not infer it.
+
+See `SYNTH_RESULTS.md`.
+
+## 2026-08-01: factor families on real language
+
+First step of the port to natural data, text side only, on 80,000 Visual
+Genome region descriptions with no lexicon and no labels.
+
+The synthetic pipeline found families by mutual exclusivity: template
+phrases carry exactly one colour word, so colour terms never co-occur.
+That does not transfer. In real descriptions colour words are
+statistically independent or better -- observed over expected
+co-occurrence is 1.29 for black with white, 0.93 for red with blue --
+while head nouns are the genuinely exclusive family (0.14 for car with
+truck). Run as written, the method recovers clean noun classes and no
+attribute families at all. Mutual exclusivity is a template artifact.
+
+Standard distributional word-class induction, of which exclusivity is a
+degenerate case, does transfer. Positive PMI context vectors, truncated
+SVD, k-means over the 300 most frequent words yields a colour family at
+0.67 purity (red, brown, gray, dark, grey, pink, tan, purple) plus
+coherent object categories: vehicles, animals, clothing, people, water
+scenes. Colour terms split into three clusters rather than one, and the
+split is structural rather than noisy -- white and blue cluster with sky
+and clouds, because what a colour word modifies shapes its distribution.
+That dependence is the signal cross-modal value alignment feeds on.
+
+Next: the vision side under unsupervised segmentation, then the field
+correlation as the go/no-go before any recovery run.
+
+## 2026-08-01: first natural-data coordinate, and a correction
+
+The Tier 0 recipe was ported to Visual Genome: DINOv2 patch features,
+spectral segmentation of the affinity graph, segment feature classes on
+one side; distributional word classes on the other. Field correlation at
+the hidden pairing is **0.166**, far under the 0.9 that recovery needs,
+so by our own go/no-go no recovery run is warranted yet.
+
+A correction came with it. Aligning vision classes to text classes by
+frequency rank and by an oracle give bit-identical fields -- 0.1662 both
+ways -- while agreeing on 0 of 23 classes. Moment fields are built from
+within-modality inner products, and permuting feature coordinates
+consistently leaves every inner product unchanged, so relation fields are
+gauge-invariant in the class labels and the dictionary never enters them.
+The same was true unnoticed in the synthetic world, where oracle and
+derived dictionaries produced identical fields. The dictionary is
+required for encoding a new image into text coordinates, not for
+matching; matching has always run on the fields alone.
+
+The 0.166 therefore reads as representation quality, and localises the
+deficit at vision-side granularity: six segments per image, background
+included, against sixteen phrases about specific objects. A sixteen-
+segment run is measuring whether granularity is the binding constraint.
+
+## 2026-08-01: natural data reaches 0.656, and segmentation was not the wall
+
+Full port to Visual Genome, measured by the go/no-go statistic. Three
+results overturned expectations, each checked rather than inferred.
+
+Discretisation was the dominant loss: hard class codes give 0.166,
+continuous states 0.489. Relation fields need scene similarity only, so
+quantising states first is pure attrition; the synthetic world hid this
+because its states are discrete by construction.
+
+Segmentation is not the bottleneck on photographs. Oracle region boxes
+buy 0.061 over unsupervised spectral segmentation of DINOv2 patches
+(0.550 against 0.489), the inverse of the synthetic world where
+segmentation was the whole gap. Flat untextured scenes are adversarial
+for object discovery in a way photographs are not.
+
+Content projection is again the largest lever: 0.489 to **0.656**,
+matching its earlier role at node level (0.21 to 0.61). Protocol-legal
+and oracle-box configurations land within 0.007, so the residual is not
+about object localisation.
+
+Control: frozen general-purpose encoders underperform corpus-fitted
+statistics (0.19 for DINOv2 crop CLS against Qwen phrase states), so
+in-context features and corpus-specific distributional vectors are the
+better substrate.
+
+Verdict: 0.656 against the 0.9 recovery needs; no recovery run. The
+untried lever is observation orbits, which VG lacks by construction --
+one photograph per scene. Multi-view natural data is the next protocol
+requirement.
+
+See `NATURAL_RESULTS.md`.
+
+## Current experimental gate
+
+The node-level ordering-and-basin gate is passed on VG by content-projected
+states (isolated and in-context composite). The standing rules extend
+rather than retire:
+
+1. Blind recovery next: unpaired soft-coupling optimization (Sinkhorn over
+   real states, preserving the decodable path) must place calibrated
+   coupling mass on the hidden truth from scratch. Its score is coupling
+   mass at truth and verified seed precision, never retrieval means alone.
+2. The view-level gate stands unchanged for the coarse-to-fine recursion:
+   static view fields failed it; in-context view states plus projection
+   are the next candidate, with replayed view truth evaluation-only.
+3. Any new energy or state family still passes ordering before descent,
+   including single-transposition local ordering.
+4. Flickr-style single-view data cannot host the current pass; two-sided
+   multi-view observation is a protocol requirement for now.