ERDŐS/DAILY
DAY 4 // EVERY ATTEMPT ON RECORD

THE FULL LEDGER.

The Log shows what shipped. This page shows everything: every attempt we've made on a numbered Erdős problem, every reasoning seat we ran, every round, every dead end. The 35 internal attempts that went nowhere are here on purpose — "we tried and it didn't work" is data too.

60
ATTEMPTS
25
IN THE LOG
6
PROOF CLAIMED
1
CLOSED BY US
35
INTERNAL ONLY

Shipped to the Log

Every published entry, in problem-number order — each carries its full rounds, receipts, and retractions on its own page. This section maintains itself.

#44LOG
JUL 25, 2026
#122LOG
JUL 25, 2026
#142LOG
JUL 26, 2026
#156LOG
JUL 26, 2026
#324LOG
JUL 24, 2026
#349LOG
JUL 26, 2026
#357LOG
JUL 24, 2026
#388LOG
JUL 26, 2026
#389LOG
JUL 24, 2026
#409LOG
JUL 25, 2026
#452LOG
JUL 26, 2026
#458LOG
JUL 25, 2026
#477LOG
JUL 23, 2026
#489LOG
JUL 25, 2026
#593LOG
JUL 25, 2026
#614LOG
JUL 26, 2026
#677LOG
JUL 24, 2026
#700LOG
JUL 24, 2026
#768LOG
JUL 25, 2026
#796LOG
JUL 25, 2026
#931LOG
JUL 24, 2026
#1063LOG
JUL 25, 2026
#1108LOG
JUL 24, 2026
#1109LOG
JUL 24, 2026
#1151LOG
JUL 25, 2026

Internal Attempts — Never Shipped

Reasoner briefs and Codex waves that produced nothing publishable. PARTIAL = a real sub-result, not a close · NO RESULT = tried hard, got nothing · STILL OPEN = probed, learned, own nothing. Sorted by problem number.

#23INTERNAL

Triangle-free bipartite edge-bipartization

No counterexample found — search exhausted its budget. Problem open.

NO RESULTCODEX
JUL 25, 2026
#28INTERNAL

Representation functions of asymptotic bases

Early batch run — no verdict recovered (run JSON only).

NO RESULTCODEX
MAY 26, 2026
#39INTERNAL

Density of infinite Sidon sets

Early batch run — no verdict recovered (run JSON only).

NO RESULTCODEX
MAY 26, 2026
#41INTERNAL

Density of distinct-triple-sum sets

May run had no verdict; a fresh density-bound brief is dispatched. Open ($500).

STILL OPENPROCODEX
MAY 26, 2026
#51INTERNAL

Least inverse-totient ratios

No counterexample — ratio behavior verified computationally. Open.

STILL OPENCODEX
JUL 25, 2026
#52INTERNAL

Erdős–Szemerédi sum-product

Early batch run — no verdict recovered (run JSON only).

NO RESULTCODEX
MAY 26, 2026
#64INTERNAL

Erdős–Gyárfás powers-of-two graph problem

Verifier built and checked; no verdict write-up was ever produced.

NO RESULTCODEX
MAY 26, 2026
#74INTERNAL

Infinite-chromatic bipartite graphs

A reduction plus a conditional construction — no resolution. Open.

STILL OPENCODEX
JUL 25, 2026
#97INTERNAL

Convex-position point sets

The one that beat every model at every budget in our cross-model bench. Best outcome: an honest decline.

NO RESULTPROGROKCODEX×3 ROUNDS
MAY 26, 2026
#126INTERNAL

Prime factors of pairwise sums

Two rounds, decorrelated second opinions included — both unsolved.

NO RESULTPROGROKCODEX×2 ROUNDS
JUL 25, 2026
#159INTERNAL

Ramsey numbers R(C₄, Kₜ)

No polynomial improvement in either direction. Open ($100).

NO RESULTCODEX
JUL 25, 2026
#201INTERNAL

Worst-case progression-free subsets

The requested limiting ratio was never proved. Open.

STILL OPENCODEX
JUL 26, 2026
#256INTERNAL

Littlewood-type sup-norm bounds

Computational upper bounds for f(4), f(5) verified. General problem open.

PARTIALCODEX
MAY 26, 2026
#313INTERNAL

Unit-fraction sums and reciprocal primes

New computational contribution landed; infinitude still open unconditionally.

PARTIALCODEX
JUL 26, 2026
#345INTERNAL

Completeness thresholds for distinct powers

Subset-sum checker built; the asymptotic threshold is unresolved.

STILL OPENCODEX
JUL 26, 2026
#421INTERNAL

Sneiderman's conjecture (AND-graphs)

Remote-witness obstruction unresolved; a blind reattempt corroborated the architecture, no summable bound.

NO RESULTPROCODEX×2 ROUNDS
JUL 25, 2026
#445INTERNAL

Modular inverses in short intervals

Search produced no proof claim. Open.

STILL OPENCODEX
JUL 25, 2026
#475INTERNAL

Valid orderings in F_p

Decidable up to the computed range, no counterexample — general case open.

PARTIALCODEX
JUL 25, 2026
#486INTERNAL

Primitive sets and activated congruence sieves

Sieve machinery explored; the full problem appears untouched. Open.

STILL OPENCODEX
JUL 26, 2026
#488INTERNAL

Divisor-closed set densities

Round 2: proofs for 3 and 4 primitive generators. General case open.

PARTIALCODEX×2 ROUNDS
JUL 25, 2026
#530INTERNAL

Unavoidable Sidon subsets

The order is already Θ(√N) — the refinement is the question. Open.

STILL OPENCODEX
JUL 26, 2026
#611INTERNAL

Clique transversals

Open — a related variant was solved by others (Joret–Micek–Reed–Smid) while we worked it.

STILL OPENCODEX
JUL 26, 2026
#617INTERNAL

Rigidity in Ramsey r ≥ 5 constructions

Two computational obstructions independently confirmed (affine K₂₅→K₂₆ nonexistent; non-rigidity).

PARTIALCODEX
MAY 26, 2026
#686INTERNAL

A Diophantine non-representability claim

Complete N=4, k=4 certificate — no integers m, n exist. Full problem stays open.

PARTIALPROCODEX
#701INTERNAL

Chvátal's conjecture (intersecting down-set ideals)

No counterexample, no general proof. Open.

NO RESULTCODEX
JUL 25, 2026
#708INTERNAL

Erdős–Surányi product covering

Round 2 pins g(4) = 5. The asymptotic remains open.

PARTIALPROGROKCODEX×2 ROUNDS
JUL 25, 2026
#740INTERNAL

Infinite chromatic number with short odd cycles

Literature map plus several open cases — no resolution.

STILL OPENCODEX
JUL 26, 2026
#766INTERNAL

Minimum Turán numbers, small (k, ℓ)

Counterexamples to eventual strictness found and checked. Unresolved.

PARTIALCODEX
JUL 26, 2026
#773INTERNAL

Sidon subsets of the squares

No proof of the N^(1−o(1)) bound. Open.

STILL OPENCODEX
JUL 25, 2026
#805INTERNAL

Cliques and independent sets in induced subgraphs

Two rounds — still open.

NO RESULTCODEX×2 ROUNDS
JUL 25, 2026
#885INTERNAL

Factor-difference sets, k = 5

No k=5 witness found — does not settle the question either way.

NO RESULTPROGROKCODEX
JUL 25, 2026
#972INTERNAL

Primes at prime indices in Beatty sequences

Strong partial — the universal statement remains open.

PARTIALCODEX
JUL 25, 2026
#993INTERNAL

Non-unimodal independence-polynomial trees

Found non-log-concave trees, but still unimodal — the target was never met across 11 search runs.

NO RESULTCODEX×4 ROUNDS
MAY 26, 2026
#1061INTERNAL

Additive identities for the divisor sum

Open — a recent Eric Li preprint claims more; we treat it as an external candidate, not ours.

STILL OPENCODEX
JUL 25, 2026
#1139INTERNAL

Large gaps between integers with Ω(n) ≤ 2

Strong partial, verified — not closed by us (Price's claimed proof is unauditable).

PARTIALPRO×2 ROUNDS

The Seats

PRO

ChatGPT Pro (GPT‑5.6 Sol). The heavy reasoner — Patrick relays briefs by hand, one at a time.

CODEX

Codex at max reasoning. A separate usage bucket, so it runs as parallel waves while Pro works.

GROK

Grok Heavy. The decorrelated second opinion — bake-offs and blind re-attempts.

CLAUDE

Scouting, verification, shipping. Trusts nothing downstream of any seat's enthusiasm.

Nothing reaches the Log until a second, independent seat re-verifies the load-bearing claims — and claims die more often than they survive. That's the point of doing it in public.