Book 03 · The theory-extension challenge

Infinitesimal Creativity

Learning by Double Involution

448 pagesDraftAugust 27, 2026
Cover of Infinitesimal Creativity by Sridhar Mahadevan

Scope

A novel framework for modeling creativity as a dual involution over assimilation of experience into an existing theory, and an accommodation process that instead seeks to augment the theory.

Start here

Begin with Chapter 0 for a compact primer, then use the trail map. Readers primarily interested in applications can enter at the DIAL-X contract before choosing a testbed.

Chapter outline

Part I

Foundations of Infinitesimal Creativity

p. 23
  1. A Working Language for Creative Theory Changep. 25
  2. Initial Sketch Acquisitionp. 41
  3. Creativity as Theory Constructionp. 53
  4. The Differential Geometry of Creativityp. 65
  5. Skill Optimization for Creative Explorationp. 93
  6. Algebraic Theories as Creative Targetsp. 107
  7. Landscapes of Computational Creativityp. 123
  8. Combinational Creativityp. 147
  9. Exploratory Creativityp. 155
  10. Transformational Creativityp. 163
Part II

Algorithmic Realizations

p. 173
  1. DIAL as an Algorithmic Familyp. 175
  2. Causal Learning with Infinitesimal Creativityp. 197
  3. Skill Optimization with Infinitesimal Creativityp. 207
  4. Reinforcement Learning with Infinitesimal Creativityp. 219
  5. Composing Creative Workflowsp. 235
Part III

AGENTIC Testbeds and Open Domains

p. 249
  1. Mathematical Theory Constructionp. 251
  2. Simulator-Grounded Theory Extensionp. 285
  3. From Scientific Documents to Testable Theoriesp. 303
  4. Generative Visual Languagesp. 349
  5. Artistic Theory Extensionp. 385
  6. Creativity as Compositional Theory Changep. 407

How to read the claims

Component experiments are controlled demonstrations at different levels of maturity. AGENTIC and DILATE remain proposed architectures; ARTISTIC repair is not itself evidence of transformational creativity.

Selected supporting record

Papers, software, and evidence packets

This is a claim-scoped selection, not a complete bibliography. Local experiment packets are described but not publicly attached.

paper

Infinitesimal Causality

Develops the infinitesimal intervention and tangent-causal language inherited by the causal and simulator-grounded chapters.

Ch. 11 · Ch. 16

software

LINCS software companion

Inspectable implementations of the axiomatic core and the BRIDGE/SKFM, ALLORA, LASKO, GIRL, LINCS-RLHF, RADAR, and SID application packages.

Ch. 4 · Ch. 11 · Ch. 12 · Ch. 13

experiment packet

Scientific theory-extension evidence packet

Collects the SGTE, CTTE, GLP-1 pilot, and GLP1-GRANT registered records used to separate simulator-, corpus-, and external-admission claims.

Ch. 16 · Ch. 17

Open the curated evidence library

Experiment-to-code map

From chapter summaries to executable records

Each family records its chapter destination, code package, executable entry points, result artifacts, and evidentiary boundary.

Ch. 10

DIAL core ablation ladder

Exact, differentiated, mixed-witness, operator-estimation, static-causal, active, sequential, and nonstationary DIAL tests.

Local core code · frozen run records
Ch. 10

DIAL-ALLORA prototype ladder

Adapter-subspace estimation, generative composition, oracle-language, selective-learning, and active-acquisition tests.

Local core code · frozen run records
Ch. 11

CLIC / DIAL-SKFM

Exact closure repair, finite operator uncertainty, active counter-witness acquisition, and unsupported-alternative posterior studies.

Local core code · frozen run records
Ch. 12

OPTIC / DIAL-SkillOpt

Held-out calibration, sealed compound-skill failure, and factored-interface repair.

Local core code · frozen run records
Ch. 13

RELIC and DIAL-Schema-GIRL

Switching-world filters, schema acquisition, TextWorld/ALFWorld planning, active counter-witnesses, composition, and behavioral quotients.

Local core code · frozen run records
Ch. 14

AGENTIC workflow composition

Exact and estimated CLIC/OPTIC/RELIC composition with active and hierarchical acquisition.

Local core code · frozen run records
Ch. 15

AGENTIC-Lea theorem-construction ladder

Tool capability, scaffolded abstraction, fixed-vocabulary proof construction, structural repair, and early-stop tests.

Local core code · frozen run records
Ch. 15

Infinitesimal pattern-construction ladder

Symmetry, latent factors, entangled worlds, counter-witnesses, predictive-state sheaves, holonomy, power/coverage, and active intervention studies.

Local core code · frozen run records
Ch. 15

Categorical AI-Feynman ladder

Categorical symbolic regression, ambiguity, unnamed generators, sequential probes, open generator search, and proposal-aware acquisition.

Local core code · frozen run records
Ch. 16

Simulator-grounded theory extension

Singing-mouse mechanism recovery, observer construction, active probe selection, and latent-mediator extension.

Local core code · frozen run records
Ch. 17

Corpus-to-testable-theory construction

Generated corpora, alias registration, context covers, active acquisition, sketch extension, and domain transport.

Local core code · frozen run records
Ch. 17

GLP-1 theory and grant construction

Hidden-context pilots, semantic admission, typed IR, cross-field invariants, auditable realization, length bounds, and controlled paraphrase.

Local core code · frozen run records
Ch. 18

ARTISTIC Bongard problems

Rule reuse, composition, declaration extension, blind corpus tests, typed selection, and active oracle queries.

Local core code · frozen run records
Ch. 19

DILATE paintbrush geometry

Residual calibration, intent-conditioned paintbrushes, algebroid paths, fiber metrics, connections, and held-out transport.

Local core code · frozen run records
Open the complete experiment atlas

Code companions

Public repositories and release gaps

Public links open the inspectable GitHub package. A local-only package is shown explicitly so an unpublished research archive is never mistaken for a reproducible public release.

software package

LINCS LASKO package

Lie-algebroid skill optimization and validation-economics experiments.

Apache-2.0

software package

LINCS GIRL package

Infinitesimal reinforcement learning, policy transport, and structural-admission experiments.

Apache-2.0

registered research archive

Infinitesimal Creativity registered experiment archive

Registered, developmental, negative, and transport experiment directories underlying Chapters 10–19. Public packets require separate provenance, dependency, rights, and privacy review.

Local only · curation required

external dependency

Lea theorem prover

External Lean-based theorem-proving dependency used by the AGENTIC–Lea studies.

upstream license

external dependency

Hugging Face Diffusers

External diffusion and textual-inversion infrastructure used in the ARTISTIC experiments.

Apache-2.0

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