Phi9 / research & engineering
The world a model must keep
A current reading edition connecting representation, motion, learning and evidence.
Shubham Attri · consolidated research edition 1 · 2 October 2026
Fourteen chapters. One recurring question: which distinctions must a model keep to predict what happens next?
Read the 54-page working edition ↗
This is a newly consolidated reading edition, not fourteen previously published papers or new experiments. Its fifteen figures separate explanatory drawings from retained measurements. It is not peer reviewed.
The chapter map
- 01
The world behind the number
Two box arrangements share a total. One action preserves that summary; another reveals what it discarded.
- 02
Coordinates and operations
Vectors keep distinctions separate. Matrices describe operations, and their order can change the answer.
- 03
A contract for the future
A representation must preserve the requested readout and the consequences of admitted actions.
- 04
Learning a rule is not inventing information
A fit changes a rule. It cannot recreate a distinction absent from its inputs. Work through one gradient step.
- 05
The state, the motion and the readout
State, transition and decoder have different jobs. An oscillator exposes why position alone can miss the future.
- 06
Fourier is a coordinate choice, not a fundamental law
Complex rotation and Fourier coordinates simplify specified dynamics. Keeping only a few coefficients is a different, lossy operation.
- 07
Memory, context and belief
History can reveal hidden distinctions, but only when it contains a signal. Context and beliefs make the assumptions visible.
- 08
Programs, proofs and roundoff
Exact affine composition has a mathematical contract. Floating-point arithmetic can break the corresponding executable identity.
- 09
Learning interaction rules
Compact learned interaction rules work in some retained conditions and lose in others. Tuning and execution costs stay separate.
- 10
A map of the model’s own mistakes
An error monitor ranks predictions, not consciousness. Replay fidelity does not establish predictive validity.
- 11
The price of observing more
Earlier fitting improves recovery in some sparse conditions; dense signals expose the price of a narrow representation.
- 12
Refit the rule, or ask another question?
Refitting a stale mapping and buying another observation are different repairs. Residual error alone cannot always tell them apart.
- 13
Calibration and the price of choosing
Calibration reduces false acquisitions in a bounded pilot. Selection optimism and a stronger full-sensing baseline remain.
- 14
From representations to useful agents
Options need timing and cost as well as endpoints. Physical-agent applications remain proposed, not demonstrated by this book.