Formula Pipeline
Makes formulas from textbooks structurally comparable across disciplines. Its own parser.
Formulas are pulled from PDF textbooks through the text layer, not through image recognition, and translated into structural signatures by a parser built for the purpose. The same shape becomes findable across different fields.
As of 2 September 2026: 274,244 formulas in the graph. The last full signing run, on 26 July 2026, covered 225,607 of them at 30 microseconds per formula; what came in since is signed on ingest.
What goes in
Snapshot 3 September 2026PDF textbooks, read through the text layer rather than image recognition. A LaTeX-set PDF says where its mathematics is through its fonts: one family for variables, one for blackboard letters, one for script; the converter reads the font names and lifts the formulas out as LaTeX. Then a parser built for the purpose turns each formula into a structural signature: the shape of the expression, independent of which letters were chosen for it. The signatures are the part that works. Turning them into reliable bridges between fields is not solved here, and the numbers below say so rather than implying otherwise.
In the graph
| formulas in the graph | 274,244 |
| variables | 169,861 |
| canonical variables the same quantity under different letters, merged | 12,558 |
Parser benchmark
Share of formulas parsed completely. A partial parse counts as failure; the parser refuses to sign a fragment.
- own parser57.9 %
- latex2sympy21.4 %
- hard cases: 4,000 real parse failures from the old parser
- own parser88.1 %
- latex2sympy24.8 %
- ordinary material
30 microseconds per formula; the whole stock in eight seconds. Measured 26 July 2026 on PDF-converted material; handwritten arXiv LaTeX not yet tested.
What comes out
Why signatures, not values
The parser does not evaluate anything. Unknown notation becomes an opaque node instead of an error, so two formulas can be compared by shape alone, whatever letters they use. What a signature is good for is finding the same expression again when it appears in another book under different letters.
What was learned the hard way
The first parser returned partial trees without saying so; measured, 51.5 % of its "successes" were fragments. The second one has three states, complete, partial, failed, and only complete gets a signature. The whole stock was re-signed on 26 July 2026.
What is actually in there
Not a sample chosen to look good: two formulas from each of the best represented subject areas, filtered only for being complete expressions rather than single symbols. Shown as they are stored, in LaTeX.
mathematics
x_i^{(1)} = \sum_{a_{ji} \neq 0} y_j^{(0)}y_i^{(1)} = \sum_{a_{ij} \neq 0} x_j^{(1)}
financial regimes
\Phi_{t+s}(z) = \Phi_{X_{t+s}}(z) = \Phi_{X_s}(z)\Phi_{X_{t+s}-X_s}(z)\Phi_{X_s}(z)\Phi_{X_t}(z) = \Phi_s\Phi_t
category theory
(f \circ g) \circ h = f \circ (g \circ h)G(f) \circ \alpha_{C'} = \alpha_C \circ F(f)
nonlinear science
q = 2\kappa^2 \operatorname{sech}^2 \kappa (x - 4\kappa^2 t - x_0)iq_t + q_{xx} + \sigma |q|^2 q = 0, \tag{3}
information theory
E(\mathbf{x}; J, H) = -\left[\frac{1}{2} \sum_{m,n} J_{mn} x_m x_n + \sum_n H x_n\right],P(\mathbf{x}|\beta, J, H) = \frac{1}{Z(\beta, J, H)} \exp[-\beta E(\mathbf{x}; J, H)], \qquad (31.2)
active inference
\sum_{x} P(x,y) = \sum_{x} P(y)P(x|y) = \underbrace{P(y)\sum_{x} P(x|y) = P(y)}_{\text{Sum rule}}\underbrace{P(x)P(y|x) = P(x,y)}_{\text{Product rule}} \underbrace{P(x)P(x|y)}_{\text{Product rule}}
physics
\mathbf{a} \bullet \mathbf{b} = a_1b_1 + a_2b_2 + a_3b_3\pi - (\alpha + \beta + \gamma) = C\Delta
probability theory
X_t = X_0 \exp\left(\left(a - \frac{1}{2}b^2\right)t + bW_t\right) ,f_X(x) = \int_{-\infty}^{\infty} f_{X,Y}(x,y) \mathrm{d}y
Filtered for complete expressions: entries that are a single symbol rather than a formula are left out of this list.