# Research Execution Plan — 2026-06-10

**Status:** EXECUTION_PLAN_ACTIVE
**Rule:** every goal below has a receipt-shaped success criterion. A goal
without its receipt is not done, regardless of how much work happened near it.
**Companion docs:** `erdos329-synthesis-program-2026-06-10.md` (Track C
rationale), `NUTBREAKER_*.md` ×4 in this directory (Track B payloads),
`sidon-lifting-relaxation-program.md` (guardrails, inherited everywhere).

---

## Track A — Substrate repair (unblocks everything; do first)

### A1. cupfox back on the Tailscale mesh
- **Goal:** `tailscale status` on this machine lists cupfox (100.72.130.76)
  and `kubectl get nodes -o wide` returns all agents Ready.
- **How:** console/physical access to cupfox → check `systemctl status
  tailscaled` and `tailscale up`; if the box is down, boot it. Then from the
  laptop: `kubectl get nodes`.
- **Blocks:** C1 (Ray jobs), C3, any fabric-tier work.

### A2. Fix neon IP drift
- **Goal:** no file in `distributed-compute-fabric` references the stale
  Tailscale IP 100.100.75.113; `verify-internal.sh` exits 0.
- **Status:** ✅ DONE — 3 files updated (infrastructure-status.md, research plan,
  SSH config). Live IP 100.92.88.64. MagicDNS name `neon-64gb` is the durable
  reference moving forward.

### A3. ENE database access from this machine
- **Goal:** `psql "$DATABASE_URL" -c "select count(*) from <equations table>"`
  returns ~33,890 from the neon-hosted Postgres.
- **Status:** ✅ DONE — Postgres 16 running on neon (arxiv-pg container, port 5432).
  Shared user `services`, databases created for `appflowy`, `obsidian_sync`, `ene`.
  DATABASE_URL exported in `~/.bashrc` and `~/.config/ene/ene.env`.
  Redis (port 6379) and CouchDB (port 5984) also running on neon for service support.

### A4. Relocate singer-theorem-lean out of /tmp
- **Goal:** repo lives at a permanent path, builds there
  (`lake build` exit 0), ContextStream mapping updated.
- **How:** `mv /tmp/singer-theorem-lean ~/Projects/singer-theorem-lean` (create
  dir), rebuild, update the pattern in `~/.contextstream/mappings.json` (and
  legacy `~/.contextstream-mappings.json`).
- **Risk if skipped:** /tmp is wiped on reboot; the public Erdos30 export
  vanishes.

### A5. Session restart to load the MCP stack
- **Goal:** in a fresh Claude Code session, `/mcp` shows contextstream,
  lean-lsp, nixos, k8s, arxiv all connected and their tools callable.
- **How:** restart Claude Code. Nothing else needed; all five are registered
  at user scope and health-check ✔.

---

## Track B — Formal debt (sorry + axiom elimination)

Fire order is chosen so each success de-risks the next. All prompts are in
`6-Documentation/docs/`. Verification commands are inside each prompt.

### B1. Singer port — fire `NUTBREAKER` (Singer prompt, already existed)
- **Goal:** `SidonSets.lean:738` sorry closed; `lake build` 0 errors;
  `grep -n sorry Semantics/SidonSets.lean` empty.
- **Why first:** clearest success criteria, upstream reference exists
  (Erdos30/SingerTheorem.lean), and C2 consumes the result.

### B2. SSMS — fire `NUTBREAKER_SSMS_PROMPT.md`
- **Goal:** `ssms_step_nonexpansive` + `ssms_contraction_theorem` proven;
  no sorry in SSMS.lean; Compiler + full build at baseline.

### B3. AdjugateMatrix — fire `NUTBREAKER_ADJUGATE_MATRIX_PROMPT.md`
- **Goal:** `cofactor_identity` closed OR formally classified (exactness
  hypotheses added, epistemic branch documented). Both outcomes are receipts.

### B4. BraidSpherionBridge — fire `NUTBREAKER_BRAID_SPHERION_BRIDGE_PROMPT.md`
- **Goal:** all 9 drift-repair sorries closed, zero new axioms.

### B5. Burgers bridge — fire `NUTBREAKER_BURGERS_BRIDGE_PROMPT.md`
- **Goal:** `burgersToBraidDef` constructive def + shim-replay witness +
  energy/mass correspondence lemmas on a stated domain; bare-axiom uses
  contained. Step-correspondence level (exact / bounded-error / witnessed
  conjecture) explicitly reported.

### B6. Axiom census receipt (cheap, high leverage — can run today)
- **Goal:** AGENTS.md gains a standing "Axiom Census" table: per-module axiom
  count + one-line justification status; regenerating it is part of the
  post-interaction workflow.
- **How:** `grep -rn '^axiom\|^\s*axiom ' Semantics/Semantics/*.lean
  Semantics/Semantics/**/*.lean | sort` → table. Add the regeneration command
  to the workflow section.
- **Why:** converts the "746 verified modules" claim from vulnerable to
  audit-proof; the ledger starts pricing axioms the way RRC prices everything.

Failed nutbreaker runs route down-pipeline per the existing tier map:
DeepSeek-Prover MCP for lemma-sized fragments, fix-* subagents for
context-heavy residue, epistemic blocks to manual decision.

---

## Track C — Erdős #329 attack ladder (from the synthesis doc)

### C1. Obstruction mining run on neon  *(needs A1 or direct neon access + A3)*
- **Goal:** RRC-tagged receipt rows in the ENE DB for Singer(q) and
  Bose–Chowla(p,h) witnesses across ≥100 prime powers: collision_count (must
  be 0), |Forbidden ∩ [1,cN]| for c ∈ {1,2,4,8}, Ω_N, Γ, M_Sidon. Mirror to
  Garage S3.
- **How:** integer-only Python batch (pattern: `rrc_ray_tagger.py`), Ray over
  the fabric or run directly on neon. The Γ growth curves decide which family
  carries the program.

### C2. Statement-level interop  *(needs B1)*
- **Goal:** `LimsupDensityOne` in SidonSets.lean matches
  `formal-conjectures/ErdosProblems/329.lean`'s formulation;
  `finiteWitness_requiresCollisionZero` and
  `additiveEmbedding_preservesCollisions` proven (both short).
- **How:** Tier 2 (DeepSeek-Prover) or in-session with lean-lsp MCP; the
  second lemma is the parent doc's "additive inclusion creates no slack"
  warning made permanent.

### C3. Evolutionary digit-rule search  *(needs A1, C1)*
- **Goal:** first generation of p-adic digit-choice rules evaluated with
  M_Sidon fitness and collision-zero hard gate; best-of-generation receipts
  archived; survivor rules converted to `native_decide` finite certificates.
- **How:** AlphaEvolve-shaped loop on the fabric — Hermes/Gemma for mutation
  volume, Fable for escape moves, neon for audits. Outputs are
  `R_finite + U_asymptotic` by construction.

### C4. K/M → Forbidden-set formal bridge — promote or refute
- **Goal:** a Lean statement transporting the `totalKS`/`kmReflectanceBound`
  residual functional to Forbidden-set counting for one explicit lift family,
  either proven (subquadratic obstruction bound — major) or refuted (the
  analogy is formula-shape only — also a receipt, closes S1 as P_analogy).

### C5. Nesting theorem attempt on the best C1/C3 family
- **Goal:** the actual #329 swing: a compatible-lift-chain theorem for the
  empirically best family. No deadline; this rung is earned by the others.

---

## Track D — Metamathematical grounding (from the Chaitin discussion)

### D1. Mass Numbers ⇄ resource-bounded Kolmogorov complexity
- **Goal:** the mass-number doctrine gains a formal-grounding section mapping
  MassNumber(S,D,C,R) onto resource-bounded K / Levin's Kt, with the
  decoder-sup trap door named as forbidden; one Lean lemma tying a concrete
  MassNumber receipt to a decidable resource-bounded bound.
- **How:** doc edit in `mass_numbers_deanthropocentric_revision.md` +
  small module or extension near MassNumberAdapter.lean.

### D2. Weld the trap doors into RRC
- **Goal:** RRC_OPERATING_CONTRACT.md gains three explicit QUARANTINE
  triggers: (1) any claim taking the supremum over all decoders, (2) any
  claim made from the limit of the certification ladder rather than a stage,
  (3) any signed incompressibility certificate. W-axis cross-ref to the
  Turing–Feferman ordinal-logic literature added to the Omega extension doc.
- **Why:** the framework currently survives Chaitin by good habits; this makes
  survival structural.

---

## Track E — External interface

### E1. Community-legible Sidon/Singer artifact  *(needs A4, B1)*
- **Goal:** singer-theorem-lean (at its permanent home) builds against its
  pinned mathlib with zero OTOM vocabulary, README maps every theorem to
  community-standard names, definitions align with 329.lean.
- **Why:** first externally verifiable OTOM output; mathlib's difference-set
  coverage is thin; this is the lineage of Pilatte's frontier method.

### E2. Upstream contribution (after E1 stabilizes)
- **Goal:** statement-level PR to google-deepmind/formal-conjectures (or
  lemma-level to mathlib) accepted, or constructive review feedback received.
- **How:** start with the 329-adjacent finite lemmas from C2; smallest
  publishable unit first.

---

## Dependency graph and firing order

```text
Today, no blockers:   B1 → B2/B3/B4 (parallel) → B5, and B6 any time
Needs user input:     A3 (DATABASE_URL), A1 (cupfox physical access)
After A1+A3:          C1 → C3        After B1: C2 → E1 → E2
Independent:          A2, A4, A5, D1, D2
Earned, not scheduled: C4 → C5
```

## Standing rules for every track

1. Narrow build target before broad; broad before claiming.
2. A refutation receipt counts as success (C4 explicitly).
3. No new axioms anywhere except via the documented epistemic branch (B3).
4. Receipts to ENE DB + Garage when fabric is up; to `shared-data/` when not.
5. Post-interaction workflow (root AGENTS.md) applies to every session.