# Marcella library layout - receipts Generated 2026-09-09. Source: `bge_v1_records.json` (GIGI bundle `marcella_source_embeddings_bge`). Pipeline: `data/build_layout.py`. Run time 11.9s. ## Records - raw records: 19,949 - kept: 13,371 records (as 9,134 passages after the near-duplicate merge) - dropped, vector str null or empty: 6,034 - dropped, vector str not 384 finite floats: 544 - dropped, tier not in keep set: 0 - dropped, doc id missing or has space: 0 - kept + dropped = 19,949 (checks against raw) - keep rule: vector_str is a non-empty string of exactly 384 finite floats AND tier in {bee-canon, bee-books-nonfiction, bee-books-fiction, context-math, self-code, kahler-catalog} AND doc_id is a non-empty string with no spaces. Every kept vector was L2-normalized. - near-duplicate merge: records with cosine >= 0.995 (scanning 16 neighbours each) are one passage: 13,371 records -> 9,134 passages; 2,679 merged groups, largest group 21, 4,237 union steps. Each passage keeps its lowest-index member as representative (doc, head, family) and carries `mult` = number of records it stands for and `mult_docs` = distinct docs among them; 719 passages span more than one doc (versions of the same paper). - distinct docs: 67 - distinct vectors (rounded 1e-6): 9,134 of 9,134 passages (near-duplicates at cos >= 0.995 were merged above; nothing is kept twice) - per family (passages): canon=2,793, nonfiction=3,606, fiction=928, context=1,687, self=120 - per family (records): canon=5,204, nonfiction=3,836, fiction=928, context=3,256, self=147 ## Graph - kNN: k=8, cosine (dot product on unit vectors), blockwise numpy, self excluded by index, symmetrized (edge if either side lists the other), deduped, no self-loops - undirected edges from kNN: 55,323; after bridging: 55,323 - degree min/mean/max: 8/12.11/158 - components_before: 1 - bridges_added: 0 (rounds: 0); up to 3 bridges per non-giant component per round, each joining one of its members to that member's nearest point (max cosine) in the giant component ## Spectrum (normalized Laplacian L = I - D^-1/2 A D^-1/2) - solver: eigsh shift-invert (sigma=-0.01, which='LM'), k=5 smallest, 3.6s - eigenvalues (ascending, index 0 is the trivial one): 0.00000000, 0.00400335, 0.01396581, 0.01730289, 0.01897846 - lambdas 1..4 (meta.lambdas): 0.00400335, 0.01396581, 0.01730289, 0.01897846 - residuals ||L v - lambda v|| per eigenpair: 7.43e-16, 5.54e-16, 6.71e-16, 9.08e-16, 1.97e-13 (all < 1e-6: PASS) - layout mode `contract`: axes x,y,z = random-walk coordinates D^-1/2 phi_k for k = 1, 2, 3 (the contract's eigenvectors 1,2,3, trivial 0 skipped); each axis divided by its RMS (unit RMS), multiplied by 1.1, sign fixed (below), then jitter uniform in [-0.035, 0.035] from numpy default_rng(seed=9), shape (n,3), applied x,y,z per point ## Layout localization check Participation ratio PR = (sum c^2)^2 / sum c^4 of the random-walk coordinates = effective number of points an eigenvector lives on (out of n). An eigenvector with PR of a few dozen is localized on one small clique and puts that clique at a huge coordinate while the rest of the library collapses to zero on that axis. - component sizes before bridging: one component of 9,134; no non-giant components (the near-duplicate merge at cos >= 0.995 removed the duplicate cliques that previously split the graph) - PR of eigenvectors 1..4: k=1: 1100.9, k=2: 1773.0, k=3: 844.5, k=4: 1471.8 - PR of the axes actually used: k=1: 1100.9, k=2: 1773.0, k=3: 844.5 - axis x (before jitter): 10.6% of the energy sits in the top 1% of points; 3.2% of points have |coord| < 0.1; p95 = 3.41; max = 3.6 - axis y (before jitter): 9.6% of the energy sits in the top 1% of points; 8.7% of points have |coord| < 0.1; p95 = 2.74; max = 3.6 - axis z (before jitter): 22.7% of the energy sits in the top 1% of points; 19.5% of points have |coord| < 0.1; p95 = 1.73; max = 5.7 - family canon: mean = (+0.43, -0.04, -0.64), std = (0.08, 0.43, 0.69) - family nonfiction: mean = (+0.25, +0.82, +0.15), std = (0.25, 0.69, 1.30) - family fiction: mean = (-3.07, -0.21, +0.02), std = (0.93, 0.33, 0.14) - family context: mean = (+0.53, -1.47, +0.67), std = (0.13, 1.23, 0.96) - family self: mean = (+0.32, +0.62, -0.45), std = (0.06, 0.29, 0.16) - VERDICT: spread. Worst axis has 23% of its energy on 1% of the points; families separate. ## Sign rule Eigenvector signs are arbitrary, so each axis is flipped deterministically: x is flipped so the mean x of family `canon` is positive, y so the mean y of `nonfiction` is positive, z so the mean z of `fiction` is positive (means taken before jitter). - axis x: mean of canon before flip = -0.4315 -> multiplied by -1 - axis y: mean of nonfiction before flip = -0.8180 -> multiplied by -1 - axis z: mean of fiction before flip = -0.0174 -> multiplied by -1 ## Questions - model `BAAI/bge-small-en-v1.5` via fastembed 0.8.0 `TextEmbedding.embed()`, L2-normalized - identical to marcella_cli.Embedder.encode() (the live gate client) and fiber_lm/embedding.py embed(); neither adds a query prefix. - distance d = sqrt(max(0, 2 - 2 cos)); inside = d < 0.80; brightness = clamp((0.95 - d)/0.30, 0, 1)^2 - both prefix variants were computed and compared with the August engine receipts (tolerance 0.03): - `plain`: nearest = holonomy=0.6184, massgap=0.6990, restaurant=0.8833, training=0.8785, fiber-bundle=0.6762, parallel-transport=0.6658, spinning-top=0.7629, fiedler-value=0.6578, curvature-attention=0.6616, davis-manifold=0.6173, pizza=0.9429, weather=0.8500, resignation=0.7517, game=0.9318; max deviation from receipts = 0.0004; all within tol = True - `bge_query_instruction`: nearest = holonomy=0.7066, massgap=0.7078, restaurant=0.9080, training=0.9022, fiber-bundle=0.6636, parallel-transport=0.6643, spinning-top=0.8053, fiedler-value=0.7006, curvature-attention=0.6760, davis-manifold=0.6751, pizza=0.9726, weather=0.8951, resignation=0.7615, game=0.9513; max deviation from receipts = 0.0886; all within tol = False - chosen variant: `plain` - plain embed (what the gate client does) reproduces every engine receipt within 0.03 | question | route | nearest_distance | engine_receipt | delta | inside (<0.80) | nearest doc | |---|---|---|---|---|---|---| | holonomy | gate | 0.6184 | 0.618 | +0.0004 | True | field_equations_semantic_coherence | | massgap | gate | 0.6990 | 0.699 | +0.0000 | True | superfluid_geometry_of_velocity | | restaurant | gate | 0.8833 | 0.883 | +0.0003 | False | murder_me_lovely | | training | self | 0.8785 | null | | False | hidden_variable | | fiber-bundle | gate | 0.6762 | null | | True | geodesic_computation_v11 | | parallel-transport | gate | 0.6658 | null | | True | gigi_builds | | spinning-top | gate | 0.7629 | null | | True | gigi_builds | | fiedler-value | gate | 0.6578 | null | | True | spectral_retrieval | | curvature-attention | gate | 0.6616 | null | | True | geodesic_computation_v7 | | davis-manifold | gate | 0.6173 | null | | True | spectral_branch | | pizza | gate | 0.9429 | null | | False | cosmological_nondecoupling_v2 | | weather | gate | 0.8500 | null | | False | geodesic_computation_v7 | | resignation | gate | 0.7517 | null | | True | a_pale_jewel | | game | gate | 0.9318 | null | | False | pure_fiber_lm_v1 | ## Hero questions The hero instrument on marcella.html rotates through every question with `hero: true` (14 of 14). The engine's live gate has been down since 2026-09-09, so no new engine receipts could be taken: a question whose `engine_receipt` is null has its distance measured here, for the picture, by the same embed + distance the gate client uses. That label travels with the number wherever a receipt tag is shown. inside/outside is decided by the measured distance against the 0.80 border, never pre-decided. | # | slug | question | nearest_distance | inside (<0.80) | nearest doc | receipt | |---|---|---|---|---|---|---| | 0 | `holonomy` | Explain holonomy simply. | 0.6184 | True | field_equations_semantic_coherence | engine receipt 0.618 (August gate) | | 1 | `massgap` | What is the mass gap? | 0.6990 | True | superfluid_geometry_of_velocity | engine receipt 0.699 (August gate) | | 2 | `restaurant` | Recommend a good restaurant. | 0.8833 | False | murder_me_lovely | engine receipt 0.883 (August gate) | | 3 | `training` | How long did it take to train you? | 0.8785 | False | hidden_variable | measured here (self route: never gated) | | 4 | `fiber-bundle` | What is a fiber bundle? | 0.6762 | True | geodesic_computation_v11 | measured here (gate down 2026-09-09) | | 5 | `parallel-transport` | What is parallel transport? | 0.6658 | True | gigi_builds | measured here (gate down 2026-09-09) | | 6 | `spinning-top` | Why does a spinning top resist being tilted? | 0.7629 | True | gigi_builds | measured here (gate down 2026-09-09) | | 7 | `fiedler-value` | What is the Fiedler value of a graph? | 0.6578 | True | spectral_retrieval | measured here (gate down 2026-09-09) | | 8 | `curvature-attention` | How does curvature show up in attention? | 0.6616 | True | geodesic_computation_v7 | measured here (gate down 2026-09-09) | | 9 | `davis-manifold` | What is the Davis manifold? | 0.6173 | True | spectral_branch | measured here (gate down 2026-09-09) | | 10 | `pizza` | Where's a good pizza place? | 0.9429 | False | cosmological_nondecoupling_v2 | measured here (gate down 2026-09-09) | | 11 | `weather` | What's the weather tomorrow? | 0.8500 | False | geodesic_computation_v7 | measured here (gate down 2026-09-09) | | 12 | `resignation` | Write my resignation letter for me. | 0.7517 | True | a_pale_jewel | measured here (gate down 2026-09-09) | | 13 | `game` | Who won the game last night? | 0.9318 | False | pure_fiber_lm_v1 | measured here (gate down 2026-09-09) | - hero_order (meta.hero_order, question indices): 0, 2, 1, 3, 4, 10, 5, 11, 6, 13, 7, 8, 9, 12 - rotation as slugs: holonomy (in) -> restaurant (out) -> massgap (in) -> training (out) -> fiber-bundle (in) -> pizza (out) -> parallel-transport (in) -> weather (out) -> spinning-top (in) -> game (out) -> fiedler-value (in) -> curvature-attention (in) -> davis-manifold (in) -> resignation (in) - 9 inside, 5 outside; starts at holonomy (0) and alternates inside/outside for as long as both sides have questions left, then drains the remainder in questions[] order - questions with a reply and a voice line (the demo section's chips, indices 0..3): `holonomy`, `massgap`, `restaurant`, `training`; every other hero question has reply null and voice null ### holonomy: Explain holonomy simply. - #2791 d=0.6184 [field_equations_semantic_coherence] From (2) Compositional Holonomy - #2957 d=0.6418 [cognitive_geometry_correspondence] Correspondence I: Holonomy Accumulation % ══════════════════════════════════════════════════════════… - #7580 d=0.6703 [superfluid_geometry_of_velocity] Holonomy is one of those ideas that sounds exotic but is actually experienced daily. A cat dropped u… - #3511 d=0.7037 [field_equations_semantic_coherence] [Holonomy Decomposition] Any holonomy _ for a complex loop can be decomposed into elementary loops a… - #8306 d=0.7107 [geometry_of_flight_v2] The first is the statement of Ambrose--Singer. Not the proof. Not the technical hypotheses. The stat… - field: 51.9% of points have nonzero brightness (d < 0.95); 0.02% fully lit (d <= 0.65); mean brightness 0.0156 ### massgap: What is the mass gap? - #5239 d=0.6990 [superfluid_geometry_of_velocity] At its core, the mass gap explains why the strong force is short-ranged. Electromagnetism, mediated … - #2634 d=0.7100 [geometry_of_fuel] \noindent\textbf{\large The Mass Gap Is a Void} \vspace{1em} Here is what the void means. The vacu… - #7609 d=0.7284 [superfluid_geometry_of_velocity] \item \textbf{Glueball spectrum is discrete.} Particles made entirely of gluons (``glueballs'') come… - #5324 d=0.7331 [davis_yang_mills_mass_gap_v5_1] [Plain English: Why the Gap Exists] The Library Analogy, continued: We've now arrived at the punchli… - #5451 d=0.7332 [geometry_of_fuel] This rules out most systematic errors. The ratchet works in both directions. Flip the dial, flip the… - field: 33.4% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0088 ### restaurant: Recommend a good restaurant. - #7136 d=0.8833 [murder_me_lovely] The second dinner is Thai. A place in Queens that looks like nothing from the outside—peeling paint,… - #8280 d=0.9111 [main] grigoryan2009heat - #7826 d=0.9178 [a_pale_jewel] Carl’s Diner looked like a forgotten dream. Neon half-lit. Windows smudged. But inside? Inside was l… - #6493 d=0.9193 [hidden_variable] There is humor in this, and pepper. In Trinidad, we speak of “sweet hand”—when somebody cook, the fo… - #4016 d=0.9283 [cosmological_nondecoupling_v2] barbero1995 - field: 0.1% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0000 ### training: How long did it take to train you? - #3055 d=0.8785 [hidden_variable] I stripped the request to job-to-be-done nouns and verbs I could satisfy without touching unreleased… - #8070 d=0.9076 [geometry_of_fuel] \noindent\textbf{\large The Night I Ran the Validation} \vspace{1em} Let me tell you what it was li… - #3575 d=0.9096 [murder_me_lovely] Fast. Faster than anyone human should be able to move. She was across the space between us in a hear… - #7889 d=0.9134 [desbrun_dec_v1] By construction. - #6418 d=0.9177 [murder_me_lovely] I feinted left. She bought it—shifted her weight to intercept—and I went right instead, ducking unde… - field: 0.6% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0000 ### fiber-bundle: What is a fiber bundle? - #8713 d=0.6762 [geodesic_computation_v11] [Fiber bundle for sequence transport] The v11 fiber bundle is the triple (E, , B) where: itemize E =… - #2870 d=0.6762 [geometry_of_flight_v2] \noindent \textbf{Fiber bundle.} A \emph{fiber bundle} is a shape with something attached over every… - #8512 d=0.6880 [geodesic_computation_v11] Mathematical Foundations: Fiber Bundle Transport % ═════════════════════════════════════════════════… - #8956 d=0.6915 [gigi_builds] \item[Fiber bundle.] \emph{Math.} A total space $E$ with a continuous projection $\pi : E \to B$ to … - #6317 d=0.7224 [no_paralellel_lines] [Principal fiber bundle] A principal G-bundle is a smooth fiber bundle : P M together with a free, p… - field: 8.9% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0033 ### parallel-transport: What is parallel transport? - #5850 d=0.6658 [gigi_builds] Parallel transport, the mathematical object L1.5 names, is what happens to a vector --- a belief, a … - #1800 d=0.7080 [crane_ddg_v1] 8.3. CONNECTIONS AND PARALLEL TRANSPORT 152 - #2698 d=0.7369 [no_paralellel_lines] () A global section s: M P is parallel iff its horizontal lift is tangent to s(M) everywhere, i.e., … - #6857 d=0.7379 [geometry_of_fuel] On a flat surface, this is unambiguous. Parallel transport around any loop returns $\mathbf{v}$ to i… - #2086 d=0.7389 [no_paralellel_lines] [Connection and parallel transport] A connection on : P M is a smooth G-equivariant distribution H T… - field: 25.3% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0056 ### spinning-top: Why does a spinning top resist being tilted? - #7894 d=0.7629 [gigi_builds] The Panthéon pendulum was a closed loop in time as much as in space. It swung, and the floor rotated… - #2589 d=0.7710 [geometry_of_fuel] But the asymmetric loop shows a current of $\langle J \rangle = 0.0341 \pm 0.0023$, a detection at n… - #8326 d=0.7902 [gigi_builds] The engine-job voice can sharpen the picture by naming where the equivalent slot does not exist on m… - #5473 d=0.7914 [geometry_of_flight] It is also the architectural commitment that breaks when the maneuver is aggressive enough to demand… - #6240 d=0.7948 [a_pale_jewel] Q: Then let’s start simple. Describe your operational understanding of cross-thread displacement eff… - field: 40.4% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0085 ### fiedler-value: What is the Fiedler value of a graph? - #7573 d=0.6578 [spectral_retrieval] [Fiedler Vector and Partition] The Fiedler vector _1 ^t is the eigenvector corresponding to the smal… - #5636 d=0.6944 [spectral_retrieval] The Fiedler Partition as Constraint Localization %==================================================… - #8109 d=0.6968 [spectral_branch] The lower bound follows from the discrete co-area formula applied to the Fiedler eigenvector: _1 = _… - #3533 d=0.7195 [spectral_branch] Part~(a) follows from the discrete Cheeger inequality (Lemma~lem:graph_cheeger): h_G^2/(2d_) _1 2h_G… - #4422 d=0.7196 [davis_hilbert_polya] Bass's Determinant Formula For a d-regular graph on n vertices with cycle rank r = 1 + n(d-2)/2: [EQ… - field: 60.2% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0315 ### curvature-attention: How does curvature show up in attention? - #8235 d=0.6616 [geodesic_computation_v7] [Curvature from Attention] This gives a principled route from attention matrices to curvature: symme… - #2599 d=0.6660 [geodesic_computation_v7] Universal layer-wise geometry% Across all tasks and models examined, the curvature profile K^() as a… - #532 d=0.6846 [protocol_10_5_v3_spec] Protocol 10.5 measured curvature and coherence on **different manifolds**: - #8367 d=0.6982 [geodesic_computation_v11] *The Central Idea tocsectionThe Central Idea % ═════════════════════════════════════════════════════… - #8096 d=0.7162 [main] Relationship Between Spectral and Riemannian Curvature The spectral curvature estimates developed he… - field: 39.1% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0172 ### davis-manifold: What is the Davis manifold? - #3708 d=0.6173 [spectral_branch] Setup: The Davis Manifold as a Spectral Object %% ==================================================… - #2937 d=0.6218 [curvature_guided_wavefront] [On the Rigor of the Discrete Manifold] The Davis manifold is not a metaphorical application of geom… - #8560 d=0.6515 [curvature_guided_wavefront] Mathematical Foundation We work within the framework of the Davis manifold (M, g, ) as defined in~[@… - #3137 d=0.6786 [geometry_of_fuel] The book has four parts. Part I establishes the foundations: what is a Davis Manifold? It is a smoot… - #7399 d=0.6856 [geometry_of_medicine] What differentiates a Davis manifold from an ordinary latent space is not that it is more complicate… - field: 34.3% of points have nonzero brightness (d < 0.95); 0.02% fully lit (d <= 0.65); mean brightness 0.0158 ### pizza: Where's a good pizza place? - #4016 d=0.9429 [cosmological_nondecoupling_v2] barbero1995 - #6493 d=0.9934 [hidden_variable] There is humor in this, and pepper. In Trinidad, we speak of “sweet hand”—when somebody cook, the fo… - #4550 d=0.9946 [geometry_of_fuel] \textit{Solo pregunta si est\'as prestando atenci\'on.} \vspace{1em} The geometry does not ask who… - #6035 d=0.9963 [double_cover_v3] The Two Spaces %% ============================================================ - #7136 d=0.9995 [murder_me_lovely] The second dinner is Thai. A place in Queens that looks like nothing from the outside—peeling paint,… - field: 0.0% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0000 ### weather: What's the weather tomorrow? - #2044 d=0.8500 [geodesic_computation_v7] sun2009 - #1425 d=0.9227 [noether_davis_analysis] **Bee Rosa Davis** - #4987 d=0.9364 [gigi_builds] \paragraph{E10.3 --- Instrument FORECAST conservation.} \textbf{Build.} Hit \texttt{POST /v1/bundles… - #2127 d=0.9503 [pure_fiber_lm_v1] Discussion % ══════════════════════════════════════════════════════════════ - #2921 d=0.9529 [geodesic_computation_v7_1] The Geodesic Update % ══════════════════════════════════════════════════════════════ - field: 0.0% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0000 ### resignation: Write my resignation letter for me. - #6705 d=0.7517 [a_pale_jewel] \medskip \begin{quote} \textbf{\#2} \textit{Dear Reader,\\ This is the second letter, in case these … - #4617 d=0.8076 [a_pale_jewel] \noindent \textbf{\#16}\\ \textit{Dear Reader,\\ I have neglected you. It was hope. I was blinded by… - #8298 d=0.8170 [a_pale_jewel] \medskip \begin{quote} \textbf{\#3} \textit{Dear Reader,\\ I’ve found one way to help you: don’t be … - #7346 d=0.8192 [a_pale_jewel] Alex would usually say \emph{here}. She doesn’t. She swallows and says something necessary and worse… - #6597 d=0.8216 [a_pale_jewel] The car hums. My voice fades into it. Alex says nothing at first, and in that quiet I remember exact… - field: 8.7% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0018 ### game: Who won the game last night? - #2127 d=0.9318 [pure_fiber_lm_v1] Discussion % ══════════════════════════════════════════════════════════════ - #5437 d=0.9436 [dual_torus_sha256] Experimental Results - #6628 d=0.9546 [murder_me_lovely] ``We can't save them all.'' Nick's voice was brutal with honesty. ``We don't have time. The other te… - #5768 d=0.9571 [davis_hilbert_polya] Discussion and Assessment %% ==================================================================== - #7156 d=0.9607 [a_pale_jewel] I KNOW WHAT YOU DID LAST SUMMER The opening in the trees was a coin—bright, wrong, tossed into the w… - field: 0.0% of points have nonzero brightness (d < 0.95); 0.00% fully lit (d <= 0.65); mean brightness 0.0000 ## Output - `layout.json`: meta (incl. hero_order, 14 indices), docs (67), doc/fam/head (n=9,134), questions (14: 4 with reply+voice, 14 in the hero rotation) - `layout.bin`: 1,063,696 bytes little-endian; xyz Float32 at 0 (len 27,402), edges Uint32 at 109608 (len 110,646, pairs a