Classify topologies, decompose workflows into fork/race/fold/vent primitives, optimize topology, mixture-of-agents routing, and cover space computation.
classify_topologyClassify a process graph by its topology class and compute its first Betti number (beta_1). Input is a list of steps with dependency edges. Returns: topology class (path, tree, DAG, diamond, complete)...
decompose_frfDecompose a workflow into fork/race/fold/vent primitives. Each step is classified as: FORK (one input, multiple outputs -- spawns parallel work), RACE (multiple concurrent paths, first-to-finish wins)...
optimize_topologyGiven a topology with deficit (Delta-beta > 0), suggest concrete transformations to reduce it. Strategies include: parallelize sequential bottlenecks, merge redundant forks, eliminate unnecessary vent...
moa_routingMixture-of-agents sparse routing analysis. Given N agents with capability vectors and a task, compute the optimal fork/race/fold routing DAG that minimizes redundant computation while maximizing cover...
cover_spaceCompute the cover space for a sequential topology: the multiplexed, out-of-order version that can be projected back to the sequential base space via a covering map. This is the paper's key insight for...
diversity_concurrencyCompute the diversity=concurrency identity. Effective concurrency equals diversity, not parallelism. 100 copies of SVD running in parallel produce the same RMSE as one copy -- zero information gain, b...
post_linearCompute the Post-Linear World diagnostic. The linear world (streams=1, monoculture) is the unique global pessimum -- no arrangement wastes more. The first fork (streams=2) is a strict Pareto improveme...
thm_covering_causalityIf β₁(computation) > 0 and β₁(transport) = 0 (TCP-style single ordered stream), there exists a reachable state where loss on path pⱼ stalls progress on independent path pᵢ. Constructive blocking witne...
thm_covering_matchIf β₁(transport) ≥ β₁(computation), no cross-path blocking state is reachable. Each path maps to its own transport stream (covering map is injective). [LEDGER: THM-COVERING-MATCH]
thm_deficit_latency_separationTopological deficit Δ = β₁(G) - β₁(transport) lower-bounds worst-case latency inflation. TCP deficit equals pathCount - 1. Deficit is monotonically decreasing in transport stream count. Positive defic...
thm_deficit_capacity_gapFor a system with `k` independent computation paths on `m < k` transport streams, the per-step information capacity gap is `≥ (k - m) · c_min` where `c_min` is the minimum per-stream capacity. Quantif...
thm_deficit_information_lossTopological deficit `Δβ > 0` forces positive information loss under any multiplexing strategy. The multiplexing function is non-injective (pigeonhole), so by the data processing inequality, informatio...
thm_deficit_erasure_chainFull chain from topology to thermodynamics: deficit → pigeonhole collision → information erasure → Landauer heat → observable waste. Composes deficit_information_loss with fold_erasure and fold_heat. ...
thm_zero_deficit_preserves_informationWhen `Δβ = 0` (streams ≥ paths), there exists a multiplexing strategy achieving lossless transport. Each path gets its own stream; the multiplexing function is injective. [LEDGER: THM-ZERO-DEFICIT-PRE...
thm_deficit_monotone_in_streamsInformation loss under optimal multiplexing is monotonically decreasing in transport stream count, reaching zero when `m ≥ k`. Adding transport streams can only reduce deficit. [LEDGER: THM-DEFICIT-MO...
thm_american_frontierPareto frontier of diversity vs waste: the frontier function is monotone, zero at the matched topology, positive below, and admits a pigeonhole witness for any topology with fewer streams than require...
thm_american_frontier_codec_racingCodec-racing instantiation of the Buley frontier: monotone wire size, zero deficit at matched codec, and subsumption of smaller codecs by larger ones [LEDGER: THM-AMERICAN-FRONTIER-CODEC-RACING]
thm_american_frontier_unifiedUnified topological + codec frontier composition: the combined frontier inherits monotonicity and zero-at-match from both the topological and codec layers [LEDGER: THM-AMERICAN-FRONTIER-UNIFIED]
thm_american_frontier_pareto_diagnosticPareto diagnostic: matched topology is optimal, monoculture is suboptimal, and there exists a monotone path from any suboptimal point toward the frontier [LEDGER: THM-AMERICAN-FRONTIER-PARETO-DIAGNOST...
thm_netflix_frontierTHM-AMERICAN-FRONTIER instantiated on published Netflix Prize data: monotone RMSE descent across algorithm-family and team-of-teams frontiers, positive waste for every monoculture ceiling, pigeonhole ...
thm_netflix_frontier_monotone_algoAlgorithm-family frontier RMSE is monotonically non-increasing across 6 published milestones [LEDGER: THM-NETFLIX-FRONTIER-MONOTONE-ALGO]
thm_netflix_frontier_monotone_teamTeam-of-teams frontier RMSE is monotonically non-increasing across 4 published milestones [LEDGER: THM-NETFLIX-FRONTIER-MONOTONE-TEAM]
thm_netflix_frontier_positive_belowEvery monoculture ceiling (Cinematch, timeSVD++, k-NN, RBM, NNMF) has strictly higher RMSE than the observed floor [LEDGER: THM-NETFLIX-FRONTIER-POSITIVE-BELOW]
thm_netflix_frontier_pigeonholeBest single model (timeSVD++, 0.8762) is strictly worse than first 3-family blend (BellKor 2007, 0.8712) [LEDGER: THM-NETFLIX-FRONTIER-PIGEONHOLE]
thm_netflix_frontier_recursiveTeam frontier floor (50/50 blend, 0.8555) is strictly below algorithm frontier floor (BellKor 2008, 0.8643) [LEDGER: THM-NETFLIX-FRONTIER-RECURSIVE]
thm_netflix_residual_gapGrand Prize winner (0.856704) has strictly higher RMSE than 50/50 finalist blend (0.8555): 0.0012 RMSE of optimization left on the table [LEDGER: THM-NETFLIX-RESIDUAL-GAP]
thm_netflix_independent_convergenceTwo independent mega-ensembles (BPC and The Ensemble) converged to the same RMSE to 4 decimal places (0.8567) [LEDGER: THM-NETFLIX-INDEPENDENT-CONVERGENCE]
thm_netflix_oracle_hierarchyOn synthetic 8-dimensional taste space: void-designed oracle monoculture (time-traveled optimal single strategy) loses to void-walking ensemble; god-mode (all-dims-visible, unrealizable) beats ensembl...
thm_dmn_void_walkerThe Default Mode Network as void walking engine: energy allocation (K-1)/K predicts Raichle's 95% within 0.45pp, mind-wandering duty cycle (K-1)/(2K-1) predicts Killingsworth & Gilbert's 46.9% within ...
thm_dmn_void_gain_indexThree predictive metrics -- VGI = (K_total-1)/(K_env-1) = 0.905, CVI = (K_conscious-1)/(K_total-1) = 0.40, CFP = 0.995 -- with pathological threshold at VGI > 1.0 (rumination = void-walking on phantom...
thm_dmn_prediction_matrix8×8 prediction matrix: 8 observable measures (DMN energy, mind-wandering rate, saccade rate, fixation duration, pupil dilation, EEG alpha, EEG theta, reaction time) × 8 populations (rest/task, creativ...
thm_diversity_is_concurrencyDiversity and concurrency are the same property. β₁ counts both. Effective concurrency = diversity. Redundant parallelism (K copies of one strategy) produces zero information gain. Serialization destr...
thm_bule_is_valueThe grand unification: the Bule is the unit of value. Six faces of one number: topological deficit = diversity lost = concurrency lost = information erased = waste generated = work required = heat qua...
thm_neurodivergent_vgiUnified VGI model of neurodivergence: 4 profiles (NT/AUT/ADHD/AuDHD) × 6 environments = 24-cell VGI matrix. Autism = wider aperture (K_perceived=8 vs NT 3), ADHD = gait oscillation (VGI swings 7.5× wi...
thm_dmn_shape_and_forcesThe framework describes the geometry of consciousness (the topology, the deficit, the frontier) but not the phenomenology (why the fold feels like something). The relationship to the hard problem is s...
thm_covering_causality_constructiveCovering space causality: mismatch causes blocking [LEDGER: THM-COVERING-CAUSALITY-CONSTRUCTIVE]
thm_covering_match_constructiveMatched paths prevent blocking [LEDGER: THM-COVERING-MATCH-CONSTRUCTIVE]
thm_tcp_deficitTCP deficit equals path count minus one [LEDGER: THM-TCP-DEFICIT]
thm_frame_header_covering_mapFrame header is a covering map [LEDGER: THM-FRAME-HEADER-COVERING-MAP]
thm_translation_retractionTranslation is a retraction [LEDGER: THM-TRANSLATION-RETRACTION]
thm_basin_stabilityEach language is a stable fixed point [LEDGER: THM-BASIN-STABILITY]
thm_scaffold_gap_is_voidScaffold gap is the void boundary [LEDGER: THM-SCAFFOLD-GAP-IS-VOID]
thm_forest_convergenceForest convergence [LEDGER: THM-FOREST-CONVERGENCE]
thm_diversity_unwoundMaster unwinding theorem [LEDGER: THM-DIVERSITY-UNWOUND]
thm_linear_is_pessimumLinear (beta-1 = 0) is the global pessimum [LEDGER: THM-LINEAR-IS-PESSIMUM]
thm_first_fork_paretoFirst fork is a Pareto improvement [LEDGER: THM-FIRST-FORK-PARETO]
thm_each_fork_saves_one_buleEach fork saves one Bule [LEDGER: THM-EACH-FORK-SAVES-ONE-BULE]
thm_frontier_zero_bulesFrontier has zero Bules [LEDGER: THM-FRONTIER-ZERO-BULES]
thm_reversion_dominatedReversion is dominated [LEDGER: THM-REVERSION-DOMINATED]
thm_post_linear_worldMaster post-linear theorem [LEDGER: THM-POST-LINEAR-WORLD]
From "Being Irreversible" by Taylor William Buley.
LEDGER sections: Gnosis Compiler Proofs, Heterogeneous MoA Fabric
Layer 2: Formal Language Theory
Read the paper at Wallington Lab