Pith Number

pith:FTAFGPOA

pith:2026:FTAFGPOAFGVYM3XQSI2JFFKFK3

not attested not anchored not stored refs pending

A Ceiling Continued Fraction Approach to the Erd\H{o}s-Straus Conjecture: Heuristic finiteness of counterexamples

Andres Ventas

A ceiling continued fraction approach provides heuristic evidence that the Erdős-Straus conjecture has only finitely many counterexamples.

arxiv:2605.04551 v2 · 2026-05-06 · math.NT

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\pithnumber{FTAFGPOAFGVYM3XQSI2JFFKFK3}

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Record completeness

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We derive a super-polynomial upper bound on the failure probability; its convergence, together with the Borel-Cantelli lemma, provides heuristic evidence that counterexamples, if any exist, form a finite set.

C2weakest assumption

That the super-polynomial upper bound on failure probability derived from the FCT framework is tight enough and that the failure events across primes satisfy the conditions needed for the Borel-Cantelli lemma to conclude finiteness.

C3one line summary

A new ceiling continued fraction method finds no counterexamples in searches over 10^9 primes near 10^17 and 10^52 plus 10^7 near 10^131, and derives a super-polynomial failure probability bound whose convergence with the Borel-Cantelli lemma heuristically implies only finitely many counterexamples,

Receipt and verification

First computed	2026-05-27T01:04:58.697326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cc0533dc029ab866ef0923492954556ff12b3e4648488b42bf299f3f66bb2d9

Aliases

arxiv: 2605.04551 · arxiv_version: 2605.04551v2 · doi: 10.48550/arxiv.2605.04551 · pith_short_12: FTAFGPOAFGVY · pith_short_16: FTAFGPOAFGVYM3XQ · pith_short_8: FTAFGPOA

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FTAFGPOAFGVYM3XQSI2JFFKFK3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2cc0533dc029ab866ef0923492954556ff12b3e4648488b42bf299f3f66bb2d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "613b401d1c043d339ecc91baf93841c2e59d74edf2c3c2c653e4157701d829ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-06T06:56:14Z",
    "title_canon_sha256": "0ede7462f44f08c80062d56db5c40afdc2a6b23eca67c3b513797e31202601ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04551",
    "kind": "arxiv",
    "version": 2
  }
}