Independent researcher running an AI-assisted science lab. One hard rule: the AI never gets to mark its own work as verified — every claim passes deterministic gates and independent adversarial review. Every paper ships with an "explain it to anyone" story.
Site with all works & media: andreiplk.github.io
Updated: Sep 3, 2026 — the theorem the whole programme was waiting on is proved, and a 1988 conjecture nobody had touched is proved over most of its range. Package ready, release in progress.
In plain words: Newton showed in 1707 that a certain staircase built from any list of numbers never has a dent in it — but he never said by how much. For the list that decides whether a deformed string amplitude is physically allowed, the answer is now known exactly: four fifths, never less, and it cannot be improved. The proof is five machine-checked pieces, each re-derived by an independent validator, and it is complete.
What checking caught, on release day: two adversarial reviews were run against the second result. Every number was right; one derivation leaned on an approximation that is off by 2.8× where it was used. The step was rewritten with no approximation in it, re-run, and both review reports ship with the package. We think that is what checking is for.
| Front | What it means | Status |
|---|---|---|
| Theorem A — the 4/5 floor | complete: ladder of 627 exact certificates + 3 analytic certificates, each independently validated | ✅ proved |
| Theorem B — Sibuya's 1988 conjecture | proved for j ≤ 1000 (every n), for θ ≤ 0.9, and at the top of the row with ≤ 802 indices missing | ✅ large parts · one corner open |
| The open corner | the two sides agree to leading order; exact shape of the obstruction recorded | 🔬 needs a new idea, not more computing |
| Literature | no quantitative gap bound exists; Sibuya's line was never cited as a conjecture in 38 years | 📚 verdict recorded |
| Release | GitHub v1.0.0 · Zenodo 10.5281/zenodo.22282840 | ✅ published |
| Physics application | the 4/5 floor read back onto the map of consistent amplitudes | ⏭️ next paper |
Next milestone: a journal submission — the human referee is the one check we cannot run ourselves.
Question: within explicitly stated assumptions, are consistent gravitational amplitudes forced to be string-like — and what are the minimal assumptions?
| # | Work | Result | Status |
|---|---|---|---|
| 1 | The Island Has Edges | exact edge laws for the open-string island | published · DOI |
| 2 | The Shore of Closed-String Gravity | the boundary in closed form; the string exactly on it at D=23 | published · DOI |
| 3 | A Master Positivity Formula | every trajectory constraint in one line; 3M-point battery | published · DOI |
| 4 | The Blades Never Touch the Shore | the lab's first fully proven theorem (1,047 exact certificates) | published · DOI |
| 5 | A floor under Newton's inequality | the 4/5 floor, proved in full; most of Sibuya's 1988 conjecture | published · DOI |
| 6 | The floor read back onto the amplitude map | the physics consequence of #5 | ⏭️ next |
Progress toward the grand theorem: ████████████░░░ ~80% — the inequality the programme
rested on is proved; what remains is to carry it back to the amplitudes.
Sep 3, 2026 — Four fifths, never less. The theorem the whole programme was waiting on is proved: for the list of numbers that decides whether a deformed string amplitude stays physical, Newton's 1707 inequality holds with a margin of exactly 4/5, sharp, for every case. Five machine-checked pieces, each re-derived independently. On the way we found a 1988 conjecture by Masaaki Sibuya that nobody had cited in thirty-eight years, and proved it over most of its range — with the open corner stated honestly. Release-day honesty: two adversarial reviews caught a derivation that leaned on an approximation off by 2.8×; it was rewritten without one, re-run, and both reports ship with the package. Read →
Aug 16, 2026 — Checking is not knowing: first theorem proved. What 3,053,832 exact checks suggested is now mathematics: no kill-window of the second knife ever cuts below the shore. The delicate part: at infinity the fleet of blades sails exactly tangent to the shore (discriminant identically zero at ρ = 1+1/√3) — and the proof survives because every window is confined strictly inside. Bonus honesty: the first prover version skipped 740 cases while claiming success; our adversarial reviewer caught it, we fixed it, and the story is in the paper. Read →
Aug 15, 2026 — Two papers in one day. The shore of closed-string gravity derived in closed form (the string stands exactly on it at 23 dimensions), then the master formula: the sign of every Regge-trajectory partial wave in one line, blind-verified on a trajectory its construction never used. Shore → · Master formula →
Aug 14, 2026 — The island has edges. The allowed island of string amplitudes, previously known only as a computer scan, gets closed-form boundaries — 11,994 exact verdicts, adversarially reviewed. Read →
Corrections policy: any published error gets fixed everywhere and logged in the public errata register. This dashboard is updated by the lab at every milestone. AI involvement is disclosed in full in every work; humans hold every publication gate.