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research: Mathematica Notebooks deep dive; SHARD-WP-0004 T2

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Original computational notebook (.nb = a Wolfram expression); confirms
UC-84 notebook page shape is a genus. Refinements: nestable cell groups
(outline tree), structured re-evaluable outputs (new opacity point).
Manipulate/Dynamic = snapshot-only. Enrichment-only (UC-84/54/55).
Marks T2 done.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Bernd Worsch
2026-06-14 23:45:45 +02:00
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| Research | yawex prior art; c2 origins; federation concepts; wikiengines overview (`research/260608-*/`); XWiki/TWiki/Foswiki deep dives (`research/260613-*/`); Xanadu + ZigZag + Roam + Obsidian + Notion + Joplin + Logseq + local-first workspaces (Anytype/AFFiNE/AppFlowy) + Trilium + Wiki.js + Federated Wiki + Wikibase + git-forge wikis + TiddlyWiki + ikiwiki + Quip + MojoMojo + Oddmuse + UseModWiki deep dives & shard-spectrum synthesis (`research/260614-*/`) |
| Demand | NetKingdom integration asks captured, not yet negotiated |
| Spec | Architecture blueprint drafted; UseCaseCatalog 84 UCs from research; PRD/TSD scaffolds |
| Work | `SHARD-WP-0001` active (6 tasks); `SHARD-WP-0002` active (16 tasks: T1–T10 federation + T11–T16 adapter contract); `SHARD-WP-0003` **done** (9 engine dives complete); `SHARD-WP-0004` active (8 computational-knowledge dives: T1 literate programming, T3 Jupyter, T7 Glamorous Toolkit done) |
| Work | `SHARD-WP-0001` active (6 tasks); `SHARD-WP-0002` active (16 tasks: T1–T10 federation + T11–T16 adapter contract); `SHARD-WP-0003` **done** (9 engine dives complete); `SHARD-WP-0004` active (8 computational-knowledge dives: T1 literate programming, T2 Mathematica, T3 Jupyter, T7 Glamorous Toolkit done) |
## In Scope (today)

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# 260614 — Mathematica Notebooks deep dive
Date: 2026-06-14 · Source: **SHARD-WP-0004 T2**
## What this is
A deep dive into **Wolfram Mathematica Notebooks** — the **original computational notebook**
(1988), the ancestor Jupyter descends from. The `.nb` document **is itself a Wolfram Language
expression** (`Notebook[{Cell[…], …}]`) with **nested cell groups**, kernel evaluation
(`In`/`Out`), **structured (symbolic/graphics) results**, live `Manipulate`/`Dynamic`
widgets, and CDF as a reduced-runtime distribution projection.
## Why it matters
- Confirms the **notebook page shape (UC-84) is a genus**, not a Jupyter quirk: cells +
cached outputs + fragile counter provenance + kernel-gated re-execution predate `.ipynb`.
- Two refinements: notebooks have **nestable cell groups (an outline tree)**, not just an
ordered list; outputs can be **structured re-evaluable values**, not only MIME blobs →
adds a "structured re-evaluable value" point to the content-opacity spectrum.
- `Manipulate`/`Dynamic` join the **static-projection-impossible** end (snapshot-only) —
foreshadows Strudel (T5).
## Yield
- **No new UC** (lineage/reinforcement). Reinforces **UC-84**; enriches **UC-54, UC-55**;
links UC-34, UC-83.
## Contents
| Path | Role |
|------|------|
| `findings.md` | `.nb` expression/cell model, evaluation & provenance, CDF, capability delta vs Jupyter, INTENT mapping, UC disposition (enrichment-only), architecture notes |

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# Mathematica Notebooks — deep dive (findings)
**Date:** 2026-06-14 · **Source:** SHARD-WP-0004 T2 · **Subject:** Wolfram Mathematica
Notebooks — the `.nb` format, the cell/expression model, symbolic evaluation.
## Why this dive
Mathematica (1988) is the **original computational notebook** — the ancestor Jupyter (T3)
descends from. This dive checks whether the notebook page-model conclusions from UC-84 hold
at the genus level or need extension. It is **medium priority / lineage**: a candidate
*content type* like Jupyter, but closed/proprietary, so the expected yield is **reinforcement
of UC-84** plus a couple of distinct wrinkles (the document *is itself* a Wolfram-language
expression; symbolic, not just textual, results).
## 1. The `.nb` document model
A Mathematica notebook is itself a **Wolfram Language expression** — `Notebook[{Cell[...],
Cell[...], ...}, opts]`. So the document format and the language are the *same* substrate:
- **Cells** are typed: `Input`, `Output`, `Text`, `Title`/`Section` (structure), `Code`,
with **cell groups** nesting into an **outline tree** (the document has real hierarchy, not
just a flat list like `.ipynb`).
- An **`Input` cell** holds an expression; evaluating it produces a linked **`Output` cell`**
containing the **result expression** (symbolic, graphical via `Graphics[...]`, or
typeset). The result is a **first-class expression**, not a MIME blob — it can be
re-evaluated, edited, transcluded.
- The whole `.nb` is **plain-text-serializable** (it's an expression) but verbose and
proprietary in conventions; output cells are **cached results** stored in the file.
So like Jupyter: **source + cached computed output fused in one document**, with **out-of-
band reproducibility** (kernel + package/version state). Unlike Jupyter: **nested cell
groups (a tree)** and **results that are structured Wolfram expressions** rather than MIME
bundles.
## 2. Evaluation, provenance, reproducibility
- A **kernel** evaluates input cells; `In[n]`/`Out[n]` counters mirror Jupyter's
`execution_count` and carry the **same fragility** (out-of-order evaluation, hidden
symbol/global state, kernel-version dependence). No environment capture in the file.
- **Dynamic/interactive output** (`Manipulate`, `Dynamic`) embeds **live interactive
widgets** whose state is computed on view — these have **no faithful static form** beyond a
snapshot frame (echoes Strudel T5's "live, time/interaction-based content" limit).
- **CDF (Computable Document Format)** is Wolfram's *projection-for-distribution*: a notebook
rendered with a free runtime so readers can interact without a full license — a
derivation-projection (T1) with a reduced-capability viewer.
## 3. Capability profile (delta vs Jupyter UC-84)
| Dimension | Mathematica `.nb` (delta from Jupyter) |
|-----------|----------------------------------------|
| Structure | **nested cell groups → outline tree** (richer than `.ipynb`'s flat cell list) |
| Output type | **structured Wolfram expressions** (symbolic/graphics), not MIME blobs |
| Document = language | the `.nb` **is** a Wolfram expression (format ≡ language) |
| Liveness | `Manipulate`/`Dynamic` = **interactive widgets**, snapshot-only when static |
| Opacity | proprietary serialization; results re-evaluable only with a Wolfram kernel |
| Projection-for-distribution | **CDF** = reduced-runtime interactive projection |
| Otherwise | same as UC-84: cells, cached outputs, fragile `In/Out` provenance, kernel-gated |
## 4. INTENT mapping
### Reinforcements (mostly confirms UC-84)
- **Notebook page shape (UC-84) is a genus, not a Jupyter quirk.** Mathematica predates and
matches it: cells + cached computed outputs + fragile counter provenance + kernel-gated
re-execution. Confirms the page model should carry a **notebook shape** generically (T12),
not a `.ipynb`-specific one.
- **Outputs as derivation-projection snapshots (UC-83/84).** Cached `Output` cells are
snapshots; honest treatment marks them "evaluated run N, kernel/env unguaranteed."
- **Derivation-projection for distribution (T1).** CDF is a clean "reduced-capability
interactive projection of a source" — a real-world instance of degrade-by-capability.
### Distinct wrinkles (extend the notes, not new UCs)
- **Nested cell-group outline** — the notebook page model should allow **hierarchical cell
grouping**, not just an ordered list (generalize UC-84's "ordered cells" to "ordered/
*nestable* cells"). Feeds T12.
- **Structured (non-MIME) results** — outputs can be **typed structured values** (symbolic
expressions), not only MIME blobs; reinforces UC-55's "typed asset" reading over "opaque
blob," and links the typed-record page model (UC-34) — the content-opacity spectrum needs a
"structured re-evaluable value" point, not just text↔blob.
- **Format ≡ language** — a curiosity, not actionable for us beyond noting that some shards'
document format is *the same artifact* as their computation (don't assume doc/code split).
- **Live interactive widgets** — `Manipulate`/`Dynamic` join Strudel (T5) at the
**static-projection-impossible** end: capture a snapshot frame, never imply interactivity.
### Boundaries
- Proprietary + kernel-gated → default **read/projection/snapshot**; attach the `.nb`
(or an exported form), present cached outputs as snapshots, offer a static/CDF projection;
**no kernel host** (same rule as Jupyter UC-84, GT T7).
## 5. UC disposition (enrichment-only — no new UC)
| Mechanism (findings §) | Catalog UC |
|------------------------|------------|
| Cells + cached computed outputs + fragile In/Out provenance; kernel-gated (§1, §2) | UC-84 (reinforced) |
| Nested cell groups → outline tree (richer than flat `.ipynb`) (§1) | UC-84 (enriched: nestable cells); links UC-34 |
| Output = structured re-evaluable Wolfram expression, not MIME blob (§1) | UC-55 (enriched: structured value point on opacity spectrum) |
| Input cell = computation-defined content (§1) | UC-54 (enriched) |
| `Manipulate`/`Dynamic` interactive output = snapshot-only (§2) | links UC-55, foreshadows T5 |
| CDF = reduced-runtime interactive distribution projection (§2) | links UC-83 (derivation-projection) |
Mathematica is a **lineage/reinforcement** dive — it **adds no new UC**, confirming UC-84's
notebook page shape as a genus and contributing two refinements (nestable cells; a
**structured re-evaluable value** point on the content-opacity spectrum).
## 6. Architecture notes for SHARD-WP-0002
- **T12 (page model):** generalize the notebook shape from "ordered cells" (UC-84) to
**ordered/nestable cell groups (an outline tree)**; allow code-cell outputs to be **typed
structured values**, not only MIME blobs.
- **T11/T15 (content opacity / fidelity):** add a **"structured re-evaluable value"** point
to the content-opacity spectrum between transparent-text and opaque-blob (Wolfram
expression, symbolic result) — relevant to how outputs are stored/surfaced.
- **T16 (projection):** CDF is a **reduced-capability interactive projection**; with
`Manipulate`/`Dynamic`, static projection is a **snapshot frame only** (join the
live-content limit recorded for Strudel T5).
## 7. Open questions
1. Is a **structured re-evaluable result** (Wolfram expression) modeled as a typed value in
the page model, or stored opaquely with provenance like other computed outputs? (Ties
UC-55 open-Q #10 and UC-84 Q3.)
2. Do interactive outputs (`Manipulate`, `Dynamic`, and Jupyter widgets) deserve a shared
**"interactive, snapshot-only" content marker** in the contract? (Recurs at T4/T5.)
## 8. Sources
- Wolfram documentation: notebook format (`Notebook`/`Cell` expressions), cell types &
groups, evaluation (`In`/`Out`), `Manipulate`/`Dynamic`, CDF.
- prior: `research/260614-jupyter-deep-dive/` (UC-84 notebook shape; the descendant);
`research/260614-literate-programming-deep-dive/` (derivation-projection, UC-83).
## 9. Traceability
**No new UC** (lineage/reinforcement). Reinforced: UC-84; enriched: UC-54, UC-55; links
UC-34, UC-83. Architecture cross-refs: SHARD-WP-0002 T12 (nestable cell-group outline; typed
structured outputs), T11/T15 (structured-re-evaluable-value point on the opacity spectrum),
T16 (CDF reduced-capability projection; interactive = snapshot-only).

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| 2026-06-14 | `260614-literate-programming-deep-dive/` | Literate programming (Knuth's WEB / weave / tangle) — one source → N co-equal derived projections (docs + code); named-chunk transclusion; splits replication- vs derivation-projection; SHARD-WP-0004 T1; UC-83 |
| 2026-06-14 | `260614-jupyter-deep-dive/` | Jupyter Notebooks — `.ipynb` JSON cells + embedded computed outputs with fragile execution provenance; derived output stored *inside* the source; non-Markdown/lossy; kernel = capability; SHARD-WP-0004 T3; UC-84 |
| 2026-06-14 | `260614-glamorous-toolkit-deep-dive/` | Glamorous Toolkit (moldable development on Pharo) — `gtView` open set of co-equal type-keyed computed views (none canonical) = moldable view registry; Lepiter live notebook over git files; SHARD-WP-0004 T7; enrichment-only (UC-47/48/54) |
| 2026-06-14 | `260614-mathematica-deep-dive/` | Mathematica Notebooks — the original computational notebook (`.nb` = a Wolfram expression); nestable cell groups, structured re-evaluable outputs, `Manipulate` live widgets, CDF; confirms UC-84 notebook shape is a genus; SHARD-WP-0004 T2; enrichment-only (reinforces UC-84; UC-54/55) |

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derivation-/dimensional-/query-projection; content types declaring their views; attach
Lepiter files, not the Pharo image.
### mathematica mapping
(Lineage dive — **no new UC**; reinforces UC-84. Source: the **Mathematica deep dive**,
`research/260614-mathematica-deep-dive/findings.md`.)
| Mathematica mechanism (findings §) | Catalog UC |
|------------------------------------|------------|
| Cells + cached computed outputs + fragile In/Out provenance; kernel-gated (§1, §2) | UC-84 (reinforced) |
| Nested cell groups → outline tree (richer than flat `.ipynb`) (§1) | UC-84 (enriched: nestable cells); links UC-34 |
| Output = structured re-evaluable Wolfram expression, not MIME blob (§1) | UC-55 (enriched: structured-value opacity point) |
| Input cell = computation-defined content (§1) | UC-54 (enriched) |
| `Manipulate`/`Dynamic` interactive output = snapshot-only (§2) | links UC-55 (→ T5 Strudel) |
| CDF = reduced-runtime interactive distribution projection (§2) | links UC-83 |
Note: Mathematica is the **original computational notebook** (1988) and confirms the
**notebook page shape (UC-84) is a genus**, not a Jupyter quirk — cells + cached outputs +
fragile `In`/`Out` provenance + kernel-gated re-execution all predate `.ipynb`. Two
refinements: notebooks have **nestable cell groups (an outline tree)**, not just an ordered
list (generalize UC-84's "ordered cells" to "ordered/nestable"); and outputs can be
**structured re-evaluable values** (Wolfram expressions, symbolic/graphics), adding a
**"structured re-evaluable value"** point to the content-opacity spectrum between
transparent-text and opaque-blob. `Manipulate`/`Dynamic` interactive output is **snapshot-
only** (joins the live-content limit at T5). **Boundary recorded:** proprietary + kernel-
gated → default read/projection/snapshot, **no kernel host** (same rule as Jupyter UC-84, GT
T7); attach the `.nb`/export, present cached outputs as snapshots, offer a static/CDF
projection. Architecture logged for `SHARD-WP-0002` (T12/T11/T15/T16): nestable cell-group
outline + typed structured outputs, structured-re-evaluable-value opacity point, CDF
reduced-capability projection.
---
## Open questions

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```task
id: SHARD-WP-0004-T2
status: todo
status: done
priority: medium
state_hub_task_id: "6e46ec45-3c4a-4eb0-815d-d401d72394d5"
```