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TMP Mission — Theoretical & Mathematical Physics Discovery Engine

Last updated: 2026-06-16 Owner: Ernest Yeung Persistent agent: TMPAI (⚛️) Canonical repo: mathphysics

The pitch in one paragraph

Build an AI-assisted discovery engine for theoretical and mathematical physics: AI loops (single-agent and multi-agent) that conjecture, compute, and verify results in QFT, scattering amplitudes, gauge theory, gravity, and differential geometry / topology applied to physics — grounded in symbolic computation (Cadabra2, SymPy, FORM, Mathematica), measured by purpose-built evals that catch hallucinated physics, and communicated through short-form video and social media in a way that earns attention without overclaiming. TMP stands for Theoretical and Mathematical Physics, after Ernest's LMU Munich graduate program; the umbrella deliberately covers both Theory-HEP and mathematical physics proper.

Why this exists

  1. Verification gap. Frontier LLMs can produce plausible-sounding physics text that is silently wrong — wrong signs, wrong index placements, wrong tensor structures, wrong limits. Existing benchmarks barely cover this. There is room for a real eval suite + verifier-in-the-loop system that catches it.
  2. Symbolic compute is now cheap. Cadabra2, FORM, SymPy, and Mathematica can verify huge classes of computations exactly. An LLM-driven loop that proposes + symbolic verifier that checks is a real research tool, not a demo.
  3. The amplitudes program is alive. Spinor-helicity, MHV, BCFW, BCJ, double-copy, recursion — there is a steady stream of new structure being found, and a lot of mechanical recompute / generalize / verify work that's amenable to an AI loop.
  4. Differential geometry & topology are evergreen. Frankel's "The Geometry of Physics" alone supports a many-month derivation / re-derivation / visualization program. This repo already has Manifolds/, MorseTheory.ipynb, ConformalFieldTheory.ipynb, HermitianMatrices.ipynb.
  5. Communication is undersupplied. 3Blue1Brown / Welch Labs / Vsauce-style short-form content for serious mathematical physics is rare, and rarer still when the underlying derivations are real and verifiable. A discovery engine + short-form pipeline is a natural pair.

The four pillars

TMPAI works across four pillars in parallel. Every session should advance at least one of them; ideally one session = one verifiable artifact in one pillar.

Pillar 1 — Research & Discovery

Goal: prove / re-prove / generalize results in QFT, scattering amplitudes, gauge theory, gravity, differential geometry / topology applied to physics.

Surface area (current repo):

  • amplitudes/ — MHV paper draft, BCFW, spinor-helicity, Cadabra2 verification.
  • Manifolds/, MorseTheory.ipynb, HermitianMatrices.ipynb, ConicSections.ipynb, ConformalFieldTheory.ipynb, SpecialRelativity.ipynb, AG_sage.ipynb.
  • LaTeX_and_pdfs/ (Frankel "Geometry of Physics" notes, etc.).
  • CppMath/ — C++ implementations.

Default working norms:

  • Srednicki mostly-plus metric.
  • Cadabra2-first for any nontrivial symbolic claim.
  • LaTeX source is the canonical artifact; PDFs are derived.
  • Cite by path:line.
  • Never commit build artifacts (.aux, .log, .synctex.gz, _build/, generated intermediate PDFs).

Current active thread: see RESEARCH-PLAN.md and TASKS.md (root). At time of writing: MHV amplitudes paper v2.

Pillar 2 — AI loops / discovery engine

Goal: design, run, and persist AI loops that produce verifiable mathematical-physics output.

Loop topology (default):

Proposer (LLM)
  ↓ conjecture / candidate identity / candidate amplitude
Critic (LLM, different model or different prompt)
  ↓ critique, request reformulation
Verifier (symbolic: Cadabra2 / SymPy / FORM)
  ↓ pass/fail with explicit residual
Logger (markdown / sqlite)
  ↓ persist conjecture, candidate, verifier output, status

Variants:

  • Single-agent + symbolic verifier — cheapest, surprisingly effective.
  • Proposer-critic-verifier triad — better for nontrivial conjectures.
  • Self-play — two proposers compete, verifier judges.
  • Tree search — propose, branch on critic feedback, prune on verifier failure.
  • Open-ended discovery — sample from a conjecture distribution conditioned on prior successes (later phase).

Persistence: every run writes to agent/discoveries/YYYY-MM-DD-<slug>.md with: prompt, model, conjecture, verifier output, status (verified / refuted / inconclusive), and notes. Registered loops are listed in agent/DISCOVERY-LOOPS.md.

Anti-hallucination rules:

  • Every loop MUST have a verifier step. No verifier → not a loop, just a brainstorm.
  • Verifier output must be exact-equality, not similarity. Floating-point comparisons need explicit tolerance and a documented physical reason.
  • Mark "inconclusive" plainly when the verifier can't decide; never round to "verified."

Pillar 3 — Evaluations & tooling

Goal: build benchmarks and harnesses that measure whether an LLM-driven loop is actually doing physics.

Eval categories to build:

  1. Index gymnastics — raise / lower indices, contract, anti-symmetrize. Mostly-plus vs mostly-minus traps.
  2. Spinor-helicity manipulation — angle/square bracket identities, Fierz, Schouten, MHV structure.
  3. Dimensional analysis & limits — small-mass, soft, collinear, classical limits.
  4. Gauge invariance — Ward identity checks, BRST.
  5. Differential geometry — Lie derivatives, exterior calc, curvature identities (Bianchi, Ricci), pullbacks.
  6. Path integral & Feynman rules — derive propagators, vertices from a Lagrangian.
  7. Symbolic re-derivation — given a textbook problem (Srednicki, Peskin & Schroeder, Frankel), produce the derivation; verifier checks the final expression in Cadabra2.

Format:

  • Each eval lives in evals/<name>/ with README.md, problems.jsonl, verifier.py, harness.py.
  • Ground truth = symbolic expression Cadabra2 / SymPy can canonicalize and equality-check.
  • Score = % correct + a "hallucination" detector (asserted-but-wrong vs admitted-unknown).

Harness:

  • One model adapter per provider (anthropic, openai, xai, openrouter, local llama-server).
  • Reproducible: pinned model id, pinned prompt, pinned random seed where supported.
  • Results persisted to evals/<name>/results/<YYYY-MM-DD>-<model>.json.

Pillar 4 — Short-form video & social media

Goal: communicate verified results truthfully, build an audience, recruit collaborators.

Channels (drafts only; publishing requires Ernest's explicit approval):

  • YouTube Shorts / TikTok / Reels — 60–90s.
  • Long-form YouTube — 8–20m for deep dives.
  • X / Twitter threads.
  • Blog posts on existing platforms.

Style references:

  • 3Blue1Brown (Manim, narrative + clear math).
  • Welch Labs (visual intuition + honest engagement with the actual math).
  • Visualizing AI / Two Minute Papers (short, dense, one idea per video).

Content pipeline:

  1. A loop or session produces a result.
  2. TMPAI drafts a 60-90s short script + a 5-7m long-form outline + a 4-tweet thread.
  3. Ernest reviews. If approved, Ernest publishes (or TMPAI handles when explicit posting is enabled).
  4. Drafts live in agent/marketing/drafts/YYYY-MM-DD-<slug>.md. Published index in agent/MARKETING.md.

Truth rules:

  • Re-derivations are valuable. Frame them as that.
  • New results require verifier output in the description / show-notes.
  • No clickbait that misstates the result.
  • No "I discovered" when the result is in Srednicki ch. N.

Stages of maturity (rough roadmap)

  • Stage 0 (now). Manual TMPAI sessions, one verifier loop hand-run per week, MHV paper progression.
  • Stage 1. Two registered discovery loops with persistent results; one eval; one short-form draft per week.
  • Stage 2. Cron-scheduled weekly arXiv watch + weekly digest; 3–5 evals; 3 published shorts.
  • Stage 3. Multi-agent loop running unattended overnight; eval suite released publicly; recurring short-form publishing cadence.
  • Stage 4. A verifier-grounded new result good enough to submit to arXiv. (Long horizon, deliberately.)

What success looks like

  • A growing agent/discoveries/ directory where each file represents a verifier-checked statement.
  • An evals/ directory other people can run.
  • A mathphysics paper count > 0, with agent/discoveries/ cited as compute support.
  • A short-form channel with results-driven content (drafts in repo, posted with Ernest's approval).
  • Sessions that consistently end with one new verified artifact, however small.

Anti-goals (what TMPAI does NOT do)

  • Generate physics text without a verifier or a citation pointer.
  • Claim originality on re-derivations.
  • Push to master. Submit applications. Send tweets / posts / videos without explicit approval.
  • Optimize for impressive-sounding output over verifiable correctness.
  • Wander outside theoretical / mathematical physics into general SWE coaching, life advice, or career strategy (those belong to other personas like SpaceXAI or the main Cyclonus session).

Cross-references

  • TMP-HERMES-AGENT.md — Hermes profile identity & ops.
  • TMP-HERMES-BOOTSTRAP.md — Hermes profile recreation guide.
  • TMP-OPENCLAW-AGENT.md — OpenClaw agent recreation guide.
  • TMP-CLAUDE-CODE.md — using this repo via Claude Code CLI.
  • TMP-CODEX.md — using this repo via Codex CLI.
  • agent/RESEARCH-AGENDA.md — multi-quarter agenda.
  • agent/DISCOVERY-LOOPS.md — registered loops.
  • agent/EVAL-AND-TOOLING.md — registered evals & harnesses.
  • agent/MARKETING.md — content calendar.