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a research instrument for the investigation of interesting integers

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polyvalent

continuity role: operational front door status: reference-v6 prepared locally; reference-v5 remains live last verified: 2026-10-27 owns: the shortest successful use and the map to deeper documentation update when: setup, primary use, maturity, or document authority changes

polyvalent is a social network(ing graph) for integers with a deliberately unsocial private back room. one canonical sqlite provenance ledger feeds two different surfaces:

  • a private avalonia rolodex for evidence, sources, revisions, profile entries, and explicit publication staging;
  • a public react site that reads one immutable json release and renders integer profiles, property dossiers, complete explained relation lists, and a bounded bipartite graph.

the public runtime has no database, polyvalent backend, administrative route, or corpus-write path. private changes do nothing publicly until the owner runs the publisher; generation still does not deploy anything. github pages delivery is a separate, checked repository action over the committed public release. an optional formspree tip line is the sole outbound correspondence path and never touches publication or canonical state.

quickest successful use

prerequisites:

from the repository root, run the complete local proof:

./scripts/check.sh

the script verifies the private git and pages-workflow boundaries; restores, builds, format-checks, and tests the .net solution; installs the locked web dependencies; verifies the committed public artifact and runtime boundary; builds the site; and checks the diff for whitespace errors.

to open the public reference release:

npm --prefix web run dev

then visit http://localhost:5173, /integer/1729, /integer/220, or /integer/2. the network-ignition properties are visible at /property/carmichael-number, /property/amicable-number, and the other source-linked dossiers. the home-page tip line deliberately renders dormant without a configured formspree form id.

to create a private development ledger and open the rolodex:

dotnet run --project src/Polyvalent.Publisher -c Release -- seed --data-dir ./var/local
dotnet run --project src/Polyvalent.Desktop -c Release -- --data-dir ./var/local

the current seed-v6 corpus is idempotent on an unchanged matching ledger. it creates integers 1 through 2000, seventeen versioned properties, 761 accepted positive claims, complete recorded coverage where warranted, attributed sources and captures, and twenty sourced profile entries across eighteen integers. it refuses to rewrite an older or divergent ledger; use a fresh data directory or an explicit revision workflow when existing authored research must be preserved.

to generate a new local preview from exactly what is staged:

dotnet run --project src/Polyvalent.Publisher -c Release -- publish --data-dir ./var/local --output ./artifacts/public/local-v1 --release-id local-v1

the output directory and release id must both be new. the command makes no network request and performs no deployment.

architecture in one glance

private sqlite ledger
   ├── avalonia desktop: read, draft, cite, accept, stage
   └── explicit publisher: select, validate, sanitize, seal
                                      │
                                      ▼
                           manifest.json + data.json
                                      │
                                      ▼
                           static react/vite site
                              │               └── suggestion -> formspree -> inbox
                              ▼
                         checked github pages artifact

docs/architecture.md owns the dependency direction, data model, lifecycle, and publication firewall. docs/development.md owns exact setup, seed, launch, preview, deployment, migration, backup, and restore procedures.

first corpus

property positive members in 1–2000 coverage warrant public graph
prime 303 deterministic evaluation yes, bounded display
triangular number 62 deterministic evaluation yes
perfect square 44 deterministic evaluation yes
perfect cube 12 deterministic evaluation yes
fibonacci number 16 deterministic evaluation yes
power of two 11 deterministic evaluation yes
twin-prime member 121 deterministic evaluation yes
decimal palindrome 118 deterministic evaluation no
decimal narcissistic number 14 deterministic evaluation, compared with oeis a005188 yes
decimal friedman number 27 source-asserted bounded import with locally validated expressions yes
carmichael number 3 deterministic evaluation, compared with oeis a002997 yes
fermat pseudoprime to base 2 7 deterministic evaluation, compared with oeis a001567 yes
amicable number 4 deterministic evaluation, compared with oeis a063990 yes
sylvester sequence member 5 deterministic evaluation, compared with oeis a000058 yes
primary pseudoperfect number 4 deterministic evaluation, compared with oeis a054377 yes
heegner number 9 source-asserted bounded import from oeis a003173 yes
two-way taxicab number 1 deterministic evaluation, compared with oeis a001235 yes

relations are derived by intersecting published membership claims; there is no pairwise-edge table. the reference release therefore explains 153 → decimal friedman number → 343, including 3 × 51 for 153 and the orderly/nice witness (3 + 4) ^ 3 for 343. it also gives 137 a prime and twin-prime social field, ranks its exact partner 139 first, shows 343 as the perfect cube 7^3, and places 1 through 1024 in the source-linked power-of-two lineage with exact 2^n witnesses. the network ignition gives 1729 overlapping carmichael, base-2 pseudoprime, and two-way taxicab memberships; gives 220 an exact amicable partner 284 without storing a pairwise edge; and keeps 1806 and 1807 unrelated despite their conspicuous adjacency in different source sequences.

the graph is an interactive trace instrument rather than a decorative diagram. pointer contact or keyboard focus isolates the exact published route, conducts a visible signal through its property station, and opens a compact readout of the shared reasons, qualifiers, and endpoint witnesses. narrow screens receive a denser geometry with larger nodes instead of a miniaturized desktop map; reduced-motion preference suppresses the ambient and traced motion.

profile lore remains a separate register from mathematical affiliation. the reference artifact gives 153 a carefully separated vesica-piscis and john 21:11 vignette, 93 a sourced thelemic greeting, 146 its minor-planet identity, 404 its http status, 808 its rhythm machine, and 86 its disputed slang history. the expanded cabinet adds rabbinic, kabbalistic, patristic, thelemic, astronomical, literary, mathematical, manuscript, museum, and video-game biographies from 36 through 1729; 137 and 153 now each carry two separately cited profiles. none of these entries creates a cultural relation or pairwise edge.

configuration and data

database location precedence is:

  1. --db <path>;
  2. --data-dir <directory>;
  3. POLYVALENT_DATA_DIR;
  4. the platform-local application-data directory under polyvalent.

the application never loads .env. repository-local private state belongs under ignored ./var/ or ./captures/; common database filenames and sidecars, migration backups, preview releases, node modules, and compiled output are ignored as defense in depth. the reviewed deterministic artifact under web/public/data/ is the only tracked release.

the public suggestion endpoint is configured only through the non-secret build-time form id VITE_PUBLIC_SUGGESTION_FORM_ID; github pages maps it from the repository variable PUBLIC_SUGGESTION_FORM_ID. absent or malformed values leave the plate visibly dormant and make no request.

public deployment

the live manifest was rechecked on 2026-10-27 and still identifies reference-v5: https://resonatrix.tech/polyvalent/. the reviewed local artifact is reference-v6; generation did not deploy it.

deploy-pages.yml deploys the public site to github pages after relevant pushes to main, and also supports explicit manual dispatch. it checks the private git boundary and public release seam, builds for the pages-provided base path, scans the built boundary, and uploads only web/dist. the public form id is configured as a repository variable, but the currently live site remains unchanged until a reviewed commit and later authorized deployment.

the repository owner must select github actions once under settings → pages before the first run can deploy. no private database, untracked publisher preview, repository secret, or .env file participates in the workflow. see docs/development.md for the operator path and rollback boundary.

documentation authority

document role status owns
README.md operational current front door and shortest successful use
STATUS.md operational current verified checkpoint and next useful action
docs/development.md operational current setup, commands, local data, and recovery
docs/architecture.md explanatory current implemented boundaries and representation map
SCHEMA.md explanatory current private sqlite tables, relationships, guards, and version axes
AGENTS.md behavioral current agent authorization and completion protocol
PROJECT_BRIEF.md durable intent current purpose, audience, scope, and non-goals
CONTRACTS.md normative current epistemic, privacy, and publication invariants
DECISIONS.md historical append-only accepted choices and their consequences
specs/001-first-slice.md planning accepted active first-slice scope and acceptance criteria
specs/002-public-suggestion-inbox.md planning accepted public suggestion-to-inbox transition and activation boundary
specs/003-network-ignition.md planning accepted active seven-property seed-v6 and reference-v6 transition

when documents disagree, identify which document owns the disputed fact rather than applying filename precedence.

intentionally absent

  • analytics and production monitoring;
  • session-held integers and encounter pings;
  • public thematic lenses;
  • private constellations and arbitrary new property definitions;
  • application-level database encryption.

headless browser and x11 renders exist as implementation evidence, but final owner acceptance on the actual browser and native desktop remains a distinct manual checkpoint.

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a research instrument for the investigation of interesting integers

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