Turn your words into exact modular arithmetic.
Original string
Sequential ID
Modulus
Remainder
ASCII · exact arithmeticEnd of calculation
The alphabet contains all 128 ASCII characters, ordered by their codes from 0 to 127. This includes control characters such as NUL, as well as printable characters. The single-line input is intended for printable ASCII text; it does not provide a way to type every control character.
Strings are numbered starting at 0: first the empty string, then every one-character string, then every two-character string, and so on. Within each length, strings are ordered lexicographically by ASCII code (comparing from left to right).
Start with ID = 0. Read the input from left to right and, for each character, update ID = 128 × ID + ASCII code + 1. The added 1 accounts for the positions occupied by shorter strings. For length L, this is the ordinary base-128 value of the ASCII codes plus 1 + 128 + … + 128^(L−1); for the empty string, both terms are 0.
The empty string has ID 0. Single-character IDs run from 1 (NUL, code 0) to 128 (DEL, code 127). Two-character IDs run from 129 to 16,512. Thus the numbering is consecutive and gives each distinct ASCII string a unique ID. Character order, letter case and spaces all matter.
Example: A has ASCII code 65, so its ID is 128 × 0 + 65 + 1 = 66. Appending B (code 66) gives AB → 128 × 66 + 66 + 1 = 8,515. With the default modulus: 8,515 mod 713 = 672.
The result is the remainder after dividing the ID by the positive integer n, so 0 ≤ result < n. Different strings can have the same remainder, even though their IDs differ. This app accepts up to 256 ASCII characters and a positive modulus entered using at most 100 decimal digits; the default is 713. PHP performs exact decimal arithmetic without additional extensions.
METHOD1 / GENERALIZED
Start with a difference. Follow the construction. Collect verified primes.
This agrees with the documented method1 for prime differences two, three, five, seven and eleven. Above that range, primality testing and the upward search are the extension; the original rounding theorem alone does not establish primality.
“Prime basis” means the distinct verified outputs of this run. It does not assert that every prime occurs. The finite set generates, by multiplication, the positive integers whose prime factors are all in that set.
Limits: inputs up to 1,000,000,000, and a difference ceiling up to 100,000 for a set. The lower input plus the ceiling must stay within the input limit. This finder requires 64-bit PHP and no additional extensions.
Prompt engineering. Systems integration. Technical prototyping.
I use prompt engineering to turn product ideas into explicit requirements, configurable software, reusable components and integrated prototypes. My portfolio spans interactive 3D tools, developer workbenches, animation, web applications and software for electronics workflows. My strongest demonstrated capabilities are defining what a system should do, giving AI relevant source context, decomposing complex work, extending existing architectures and producing deliverables with traceable verification evidence.
My contribution Specification, product direction, architectural direction and AI-assisted prototype delivery. The evidence shows how I define, connect and verify systems.
01 / CAPABILITIES
Open a group to explore the work.
Evidence labels lead to its project gallery.
Translate an idea into named deliverables, behaviours, technology choices, file formats and interaction requirements. The JSON Ball prompts specify world dimensions, configurable controls, visual appearance, placeable programming cubes and authentication requirements.
Identify the exact source applications and modules to reuse, while stating which design principles should carry forward. The engine, GIF and PHP requests reframe an existing widget editor; JSON Ball explicitly names all six engine dependencies.
Break a broad technical ambition into interoperable subsystems with distinct responsibilities. The six-stage engine roadmap separates input, camera, animation, physics, scene graph and rendering, providing a practical structure for incremental implementation.
Extend a product while retaining its existing abstractions. JSON Ball progresses from a playable world to an editor, natural-language operations and PowerShell terminals; the PHP application prompts refine migration, navigation and release behaviour.
Direct development of an interface that converts natural-language requests into bounded, typed operations. JSON Ball supplies selected-object context, recent history and a response schema, then validates the returned operation batch before applying changes. Its live report records a prompt creating a cube, writing a file and opening the editor.
Use implementation contracts to translate a broad request into APIs, ownership boundaries, compatibility requirements and acceptance checks. The SIMPLE and firmware contracts record separate runtime, bridge, interface and QA responsibilities. This supports modular delivery planning; it does not establish management of a human engineering team.
Specify systems that can gain new capabilities through registered plugins. The projects contain versioned manifests, namespaced registrations, dependency handling, failed-registration rollback and cleanup lifecycles. JSON Ball uses this approach for ordinary, Codex and PowerShell cube types.
Express application state and behaviour through JSON documents, schemas and validation rules. Examples include control bindings, scene objects, materials, animation tracks, circuit requirements and code-generation sessions. This enables editable configurations and reusable templates.
Define how people select objects, change modes, edit files, issue commands and recover from errors. Supporting implementations include remappable controls, focus handling, controller dead zones, persistent editor drafts, chat overlays and terminal interfaces.
Direct tools that represent spatial relationships through camera projections, transforms, scene hierarchies and object queries. The portfolio includes perspective and orthographic views, parent-child transforms, physics bindings and tested reparenting behaviour.
Direct development of a configurable rendering pipeline with materials, lights, draw queues, depth handling and transparency. Saved GPU checks record repeatable output and distinct results when visual settings change. This demonstrates a working prototype pipeline with measurable behaviour.
Specify motion over time using tracks, interpolation, easing and playback rules, and support exportable results. Evidence spans quaternion animation and repeat/ping-pong playback in the engine, plus GIF and H.264 export implementations with timing and output-validation logic.
Direct implementation and integration of fixed-step movement, forces, collisions and constraints. JSON Ball links physical displacement to rolling orientation; the physics subsystem includes tests for contacts, sensors and distance joints. The evidence supports bounded simulation prototyping.
Specify workbenches with command registries, buffers, project files, sessions and shared GUI/headless behaviour. The C++-named directory is a Python/Tk IDE workbench; JSON Ball embeds a file editor and configurable program execution inside a 3D environment.
Connect an application to external runtimes while exposing output, status, cancellation and timeouts. JSON Ball has persistent PowerShell sessions and recorded natural-language-to-shell execution; the PHP REPL project includes native-service dispatch and browser-side execution workflows.
Direct implementation of validation before mutation, conflict detection, atomic writes and rollback where applicable. Examples preserve changed files, unsaved drafts and previous application state when an operation fails. External program side effects have separate limits and are not generally reversible.
Specify software that records requirement IDs, acceptance criteria, verification methods, connector pinouts, electrical limits and mechanical constraints. The design project also generates bounded KiCad/DXF draft outputs from its model. This demonstrates engineering-information modelling and tool specification.
Define operating-point, transient, AC and DC analyses, parameter sweeps, tolerance cases and numerical acceptance checks. The simulation project includes raw-result parsing and stored native-tool evidence covering 12 analysis cases, with nine PASS checks and three operating points without acceptance checks.
Model bills of materials, part numbers, do-not-populate flags, placement conventions, stack-up constraints and assembly acceptance steps. The fabrication project implements controlled external-tool invocation and DRC/Gerber workflows. This evidences manufacturing-support software, rather than completed physical manufacture.
Specify workflows that connect firmware identity, requirements, test definitions, supplied measurements and release evidence. The implementation checks units, timestamps, calibration validity and limits; a saved report records successful host compilation and assertion execution. Device verification and compliance remain explicitly unestablished.
Provide programmable access to existing application capabilities through persistent sessions, command layers and inspectable APIs. SIMPLE uses Python as its runtime and bridges six widget backends; the PHP project extends this pattern to browser/native dispatch.
Define reusable generation of PHP, JavaScript, CSS, JSON and supporting files, then extend the generated application through follow-up requirements. Evidence includes deterministic export logic, dashboard-to-Worksheet-Hub integration and stored browser verification.
Specify migration behaviour and retain evidence that content and structure survive conversion. The saved SQL-to-JSON audit records matching data across 66 tables, 429 columns, 109,787 rows and 772,535 values, with source and output hashes.
Define version selection, publishing, maintenance behaviour and controlled access. A saved PHP application report records private release activation and checks for anonymous access, maintenance behaviour and configuration protection. It documents a historical release exercise, not current service availability.
Work with acceptance checks that address observable outcomes and failures: movement, visual changes, persistence, invalid input, cancellation, timeouts and rollback. The portfolio combines unit tests, integration tests, GPU checks, browser reports and live CLI verification. JSON Ball's saved prompt4 report records 145 passed tests and one skipped test.
Preserve the relationship between source inputs, generated outputs and verification results using manifests, hashes and reload/export checks. JSON Ball records copied engine sources; the PHP REPL report records exact-byte regeneration of 52 files and verification of 30 dispatch pairings.
Produce deliverables with usage instructions, configuration examples, API contracts, launch commands and explicit scope limits. The READMEs and contracts make the prototypes inspectable and operable by another person, connecting product intent to implementation and verification.
02 / PROJECT EVIDENCE
Select any screenshot to inspect it.
Every image opens at full size.
51 new print-screens show excerpts from the cited source files, prompts, contracts and saved reports, alongside 6 archived application images. A source excerpt shows implementation or test definitions; a saved result documents its historical run. These captures do not establish current live availability or a fresh test pass.
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Implementation, saved test and live-verification records; engine provenance was checked in the source review.
Configurable 3D prototype integrating six engine subsystems, an editor, validated natural-language operations and persistent PowerShell sessions.
Existing saved project image, shown unchanged alongside the newly captured source evidence. This is an archived output, not a fresh execution.
prompt4-world.png
Existing saved project image, shown unchanged alongside the newly captured source evidence. This is an archived output, not a fresh execution.
prompt4-editor.png
Browser print-screen of prompts2026.txt, lines 1–29. Original world specification followed by the editor extension; complete prompts 1 and 2.
prompts2026.txt · lines 1–29
Browser print-screen of runtime.py, lines 114–150.
runtime.py · lines 114–150
Browser print-screen of codex_controller.py, lines 187–220.
codex_controller.py · lines 187–220
Browser print-screen of prompt3-live-verification.json, lines 1–34.
prompt3-live-verification.json · lines 1–34
Browser print-screen of prompt4-verification.json, lines 1–22.
prompt4-verification.json · lines 1–22
Browser print-screen of prompt4-live-verification.json, lines 1–36. Local/private identifiers are visibly redacted; other source text is unchanged.
prompt4-live-verification.json · lines 1–36
Browser print-screen of provenance.json, lines 1–35.
provenance.json · lines 1–35Scope Prototype scope. Historical results do not establish a currently passing suite or physical Xbox input verification.
Implementation and saved animation-frame checks.
Interpolation, quaternion animation, repeat and ping-pong playback.
Existing saved project image, shown unchanged alongside the newly captured source evidence. This is an archived output, not a fresh execution.
animation-canvas-t1.png
Browser print-screen of animation_runtime.py, lines 287–319.
animation_runtime.py · lines 287–319
Browser print-screen of animation-frame-smoke-result.json, lines 1–35.
animation-frame-smoke-result.json · lines 1–35Scope Bounded prototype behaviour.
Implementation and saved projection check.
Perspective and orthographic camera projection tools.
Browser print-screen of camera_runtime.py, lines 125–160.
camera_runtime.py · lines 125–160
Browser print-screen of projection-smoke-result.json, lines 1–33.
projection-smoke-result.json · lines 1–33Scope Physical input was explicitly untested.
Implementation, behaviour-test definitions and a saved GL smoke result.
Configurable input bindings, focus handling and state management.
Browser print-screen of input_runtime.py, lines 238–268.
input_runtime.py · lines 238–268
Browser print-screen of test_input_runtime.py, lines 105–138.
test_input_runtime.py · lines 105–138
Browser print-screen of gl-smoke-result.json, lines 1–35.
gl-smoke-result.json · lines 1–35Scope Test definitions do not establish a currently passing suite or physical controller verification.
Implementation and saved physics-frame checks.
Fixed-step movement, forces, collisions and constraints.
Existing saved project image, shown unchanged alongside the newly captured source evidence. This is an archived output, not a fresh execution.
physics-canvas-t1.png
Browser print-screen of physics_runtime.py, lines 466–500.
physics_runtime.py · lines 466–500
Browser print-screen of physics-frame-smoke-result.json, lines 1–35.
physics-frame-smoke-result.json · lines 1–35Scope Bounded simulation prototype.
Implementation and saved GPU checks.
Versioned renderer contract and configurable materials, lighting and draw queues.
Existing saved project image, shown unchanged alongside the newly captured source evidence. This is an archived output, not a fresh execution.
renderer-frame.png
Browser print-screen of RENDERER_CONTRACT.md, lines 1–35.
RENDERER_CONTRACT.md · lines 1–35
Browser print-screen of renderer_runtime.py, lines 434–463.
renderer_runtime.py · lines 434–463
Browser print-screen of renderer-gpu-checks.json, lines 1–34.
renderer-gpu-checks.json · lines 1–34Scope Prototype pipeline, not evidence of a complete production game engine.
Implementation and saved scene checks.
Transforms, hierarchies, object queries and physics bindings.
Existing saved project image, shown unchanged alongside the newly captured source evidence. This is an archived output, not a fresh execution.
scene-canvas-t1.png
Browser print-screen of scene_runtime.py, lines 93–127.
scene_runtime.py · lines 93–127
Browser print-screen of scene-frame-smoke-result.json, lines 1–26.
scene-frame-smoke-result.json · lines 1–26Scope Results apply to the recorded configurations.
Implementation and export-failure test definitions.
Engineering requirements, interface models and bounded KiCad/DXF draft generation.
Browser print-screen of README.md, lines 43–59. Widget-model table and inclusion rule; short range avoids oversized paragraphs unrelated to the cited model.
README.md · lines 43–59
Browser print-screen of stage1_cad.py, lines 320–354.
stage1_cad.py · lines 320–354
Browser print-screen of test_stage1.py, lines 458–494.
test_stage1.py · lines 458–494Scope Limited connector-board draft tooling; no manufactured board established.
Implementation.
BOM, placement and assembly definitions with native-command and DRC integration.
Browser print-screen of README.md, lines 49–77.
README.md · lines 49–77
Browser print-screen of fabrication_native.py, lines 213–247.
fabrication_native.py · lines 213–247Scope Starter has no source PCB and disables native exports; completed physical manufacture is not established.
Implementation and saved host build/test report.
Firmware identity, measurement validation and requirements-to-release traceability.
Browser print-screen of contract.md, lines 1–14. Contract opening establishes ownership boundaries, core interface, and host-only build requirements.
contract.md · lines 1–14
Browser print-screen of run_release.py, lines 224–258.
run_release.py · lines 224–258
Browser print-screen of build-report.json, lines 119–156. Both host compile and assertion commands, return codes, and the explicit statement that no device was tested. Local/private identifiers are visibly redacted; other source text is unchanged.
build-report.json · lines 119–156Scope Measurement fixtures are synthetic; no device testing or regulatory compliance is established.
Implementation contract, transactional bridge and failure/session test definitions.
Python runtime and transactional session interface bridging six widget backends.
Browser print-screen of contract.md, lines 1–14. Contract opening records the prompt, AI-agent responsibilities, Python runtime and bridge architecture.
contract.md · lines 1–14
Browser print-screen of matrix_bridge.py, lines 256–285.
matrix_bridge.py · lines 256–285
Browser print-screen of test_simple.py, lines 233–265.
test_simple.py · lines 233–265Scope Embeds Python; does not establish a new language implementation, human-team management or a current passing suite.
Implementation and saved native-tool verification.
Operating-point, transient, AC and DC analyses with sweeps and result parsing.
Browser print-screen of README.md, lines 70–97.
README.md · lines 70–97
Browser print-screen of run_simulation.py, lines 27–61.
run_simulation.py · lines 27–61
Browser print-screen of native-verification.json, lines 1–31.
native-verification.json · lines 1–31Scope The saved record covers 12 simulation cases: nine PASS checks and three operating points without acceptance checks. These are simulated results, not physical measurements.
Implementation and test definitions.
Commands, buffers, project files, sessions and transactional plugin loading.
Browser print-screen of ide_000_readme.md, lines 1–33.
ide_000_readme.md · lines 1–33
Browser print-screen of ide_300_plugins.py, lines 68–102.
ide_300_plugins.py · lines 68–102
Browser print-screen of ide_900_tests.py, lines 229–263.
ide_900_tests.py · lines 229–263Scope The C++-named directory contains Python/Tk tooling. No saved test-run report was identified in the source review.
Implementation, test definitions and example GIF/MP4 outputs.
Animation tracks and interpolation with GIF and H.264 export workflows.
Browser print-screen of gif_engine.py, lines 151–176.
gif_engine.py · lines 151–176
Browser print-screen of gif_engine.py, lines 498–532.
gif_engine.py · lines 498–532
Browser print-screen of mp4_export.py, lines 184–218.
mp4_export.py · lines 184–218
Browser print-screen of test_mp4_export.py, lines 107–141.
test_mp4_export.py · lines 107–141Scope No saved test-run report was identified in the source review.
Implementation and multiple saved audit, browser, REPL and private-release verification records.
Reusable web-application generation, migration, browser/native dispatch and release workflows.
Browser print-screen of prompt2026.txt, lines 1–3. The entire three-line prompt is the concrete evidence; no longer excerpt is possible.
prompt2026.txt · lines 1–3
Browser print-screen of propmt2026.txt, lines 1–11. Two complete migration and browser-navigation prompts.
propmt2026.txt · lines 1–11
Browser print-screen of prompt2-database-value-audit.json, lines 1–22.
prompt2-database-value-audit.json · lines 1–22
Browser print-screen of prompt2-browser-verification.json, lines 1–15.
prompt2-browser-verification.json · lines 1–15
Browser print-screen of lrc_5_verification.json, lines 1–31.
lrc_5_verification.json · lines 1–31
Browser print-screen of published-site-verification.json, lines 1–28. Release identity and maintenance activation history. Local/private identifiers are visibly redacted; other source text is unchanged.
published-site-verification.json · lines 1–28Scope Historical release checks do not establish current availability, adoption or a general security guarantee.
03 / DIRECT PROMPTS
Original prompt records show
product intent and direction.
These records connect my requests to the resulting systems. They directly support the prompt engineering and specification work described above.
Browser print-screen of prompts2026.txt, lines 1–29. Direct P1 prompt-source citation; complete world/editor prompts 1 and 2.
prompts2026.txt · lines 1–29
Browser print-screen of prompts2026-2.txt, lines 1–34. GIF source-grounding prompt and the six-stage engine roadmap.
prompts2026-2.txt · lines 1–34
Browser print-screen of prompt2026.txt, lines 1–3. Direct P3 source citation; entire three-line generator prompt.
prompt2026.txt · lines 1–3READING THE EVIDENCE
AI-assisted delivery is the supported authorship claim These files support specification, architectural direction and technical prototyping. They do not establish sole manual authorship or expert fluency in every language and algorithm represented.
Hardware and certification remain separate Physical Xbox interaction, fabricated/assembled circuits, device firmware validation and regulatory compliance are not established by this evidence. Firmware measurement fixtures are synthetic, and the host test explicitly excludes device testing.
Names and aspirations are not qualifications The C++-named workbench is implemented in Python; SIMPLE embeds Python rather than proving a new language implementation. The engine has documented prototype limits and does not establish a complete production game engine.
Historical verification has a defined scope Reports support the recorded runs and configurations. They do not establish current live availability, current full-suite success, commercial adoption or a general security guarantee.