Purpose
Public Survey projections are paused. Statement pages, homepage previews, generated Markdown, and print views omit them. The model and this contract remain in the repository while the product shape is reconsidered.
The Survey gives a mathematician a readable account of the reviewed work attached to one problem. It reads as an English-language survey article. Mathematical notation uses LaTeX delimiters and renders with the same conventions as the problem statement.
The Survey is a derived projection of the research packet. Its prose remains traceable to current reviewed records, while a parallel structured manifest exposes the same passages to machines.
Source boundary
Every mathematical sentence in a Survey comes from one or more current reviewed packet records. The passage links those records at the point of use. Its qualification preserves the recorded status, evidence classification, scope, and reference indices.
Packet relations may select an order and place related work in the same section. A relation supplies no mathematical conclusion beyond the records at its endpoints.
The Survey excludes superseded records and the selected Status or Resolution record. Status and Resolution remain the sole projections of the packet’s current outcome. A comparison, inference, theorem, bound, or conjecture first enters the packet as its own reviewed object before the Survey may state it.
Article structure
Every nonempty Survey has this structure:
- An Abstract explains the mathematical subject and how the account is organized.
- Each available body section opens with one or more sentences that explain the role of the records that follow.
- Each passage names and links its source record, states the record’s reviewed summary in complete prose, and gives its evidence and scope qualification.
- A short handoff links to the complete Research packet.
The projections render a passage by medium. In HTML, a passage is one run-in labeled paragraph in the manner of a theorem environment: the record’s stable article label opens in bold, colored by its evidence tone; a parenthetical qualifier follows with the linked record title, the evidence tier in small caps, the stored status when it differs, and the scope label; the reviewed summary continues the paragraph in complete prose with its reference indices, and a small trailing cross-reference points into the complete packet. The label and tier wear the same tone vocabulary as the confidence stamps, so evidence strength is scannable without boxes around the prose. In generated Markdown and print, the same passage renders as sentences: a lead names and links the record, the summary follows, and the qualification sentence states evidence, status, and scope.
The standard section order is:
- Recorded results
- Approaches and obstructions
- Open questions and directions, or Further directions for a resolved problem
- Formalization
- Artifacts and reproducibility
Empty sections disappear. This order keeps mathematical conclusions ahead of methods, unfinished work, formal encodings, and replay material.
Writing standard
Survey prose uses complete English sentences and the register of a concise mathematical paper. It explains why a section exists before presenting its records. Record titles sit inside complete sentences.
The Abstract names the subject and the provenance boundary. Record counts, storage terms, filter instructions, evidence tokens, and interface instructions stay out of the Abstract.
Each body passage should answer these questions:
- What result, method, direction, formalization, or artifact is being discussed?
- What does its reviewed summary say?
- Which record supplies the statement?
- What scope and evidence qualification limits the statement?
- Which bibliography rows support it?
Use the notation of the displayed problem. Preserve quantifiers, parameter ranges,
normalizations, hypotheses, and uncertainty words. Render inline mathematics with \( \)
and display mathematics with \[ \]. Raw proof-assistant syntax belongs in the linked
formalization record unless the syntax itself is the subject of the sentence.
Concise transitions may explain the section order. They carry no new mathematical claim. Repeated metadata stays out of the summary prose: the HTML passage carries it in the run-in qualifier, and the text projections carry it in the qualification sentence, so the main prose stays readable in both.
Citations and links
The title of every discussed record links to its permanent record page. A separate Research entry link may point to the record inside the complete packet.
Every external claim keeps the record’s reference indices. HTML links each index to the corresponding row in References. Generated Markdown uses the same indices and destinations. The reference and source-use standard governs the bibliography rows and the rights basis of any reused text.
A Survey uses independently written connective prose. Record summaries remain the reviewed source text for mathematical passages. Source prose does not enter the Survey unless its recorded use and rights basis permit that reuse.
Machine projection
Every rendered Survey includes one application/json manifest with
version: "theoremdb-survey-v1". The manifest contains:
problem_ref;- the Abstract paragraphs;
- displayed, eligible, and total record counts;
- ordered sections with stable IDs, titles, introductions, and omission counts;
- ordered passages with stable IDs, the lead text used by the text projections, reviewed summary text, and qualification text;
- the permanent record slug, URL, object type, stored status, evidence grade, evidence tier, structured scope, human-readable scope label, and reference indices for every passage.
The visible article and manifest come from the same in-memory survey model. A release fails when their passage order, record bindings, or summary wording disagree. The manifest’s lead and qualification sentences are the text projections’ rendering of facts the HTML entry shows structurally; both derive from the same record fields.
The manifest complements the complete research-packet index. It describes the human survey projection and never replaces the packet’s immutable records or typed relation graph.
Empty and partial surveys
A packet with no eligible reviewed records receives a short English empty state and a link to Research. The renderer may explain the mathematical subject in the Abstract when neutral problem context is available.
Each section displays a bounded set of representative records. The prioritization favors records related to the selected outcome, followed by the recommended route or reusable failure when those selectors apply. Omitted records remain available through the Research packet. The visible handoff states the number omitted.
Review
Review the HTML, print, and generated Markdown projections together. Confirm that:
- the Abstract explains the subject without turning into a record-count report;
- body sections read as connected mathematical prose, and each passage’s label, tier, and scope qualifier agree with the record they cite;
- every mathematical passage links to its source record;
- summaries, qualifications, and reference indices match the reviewed packet;
- the Survey adds no unsupported synthesis;
- superseded and selected outcome records remain outside the body;
- the structured manifest matches the visible article;
- LaTeX notation renders and survives in Markdown;
- the homepage and statement page use the same survey model.
Run the survey model tests, the problem-content separation tests, the built-runtime checks, the full web test suite, and the production build after changing this projection.