Pith Number

pith:BGPNZ7DV

pith:2026:BGPNZ7DVYDOJUJ4IOMBNNLU6DT

not attested not anchored not stored refs pending

Equivalences of promise compactness principles

Bertalan Bodor

When a pair of finite structures lacks an Olšák polymorphism, its promise compactness principle is equivalent to the ultrafilter principle over ZF.

arxiv:2604.08365 v2 · 2026-04-09 · math.CO

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\usepackage{pith}
\pithnumber{BGPNZ7DVYDOJUJ4IOMBNNLU6DT}

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Record completeness

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4 Citations open

5 Replications 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

if (𝔄,𝔅) has no Olšák polymorphism, then K_(𝔄,𝔅) is equivalent to the ultrafilter principle over ZF. This includes the statements K_(K3,K5) and K_(H2,Hc) for all c≥2.

C2weakest assumption

The pair (𝔄,𝔅) has no Olšák polymorphism (and 𝔄 homomorphically maps to 𝔅); the equivalence holds specifically under this algebraic condition on the finite structures.

C3one line summary

For structure pairs (A,B) without Olšák polymorphisms, the promise compactness K_(A,B) is equivalent to the ultrafilter principle over ZF, including K_(K3,K5) and K_(H2,Hc).

Receipt and verification

First computed	2026-05-28T01:04:39.743267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

099edcfc75c0dc9a27887302d6ae9e1cd7087170904ac7499f1957769d7389ea

Aliases

arxiv: 2604.08365 · arxiv_version: 2604.08365v2 · doi: 10.48550/arxiv.2604.08365 · pith_short_12: BGPNZ7DVYDOJ · pith_short_16: BGPNZ7DVYDOJUJ4I · pith_short_8: BGPNZ7DV

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BGPNZ7DVYDOJUJ4IOMBNNLU6DT \
  | 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: 099edcfc75c0dc9a27887302d6ae9e1cd7087170904ac7499f1957769d7389ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c145f6f84be906bcb1dd9365c612ea6dc1ac6f2c1f8fb29fdd4e4b94e79ae854",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-09T15:31:02Z",
    "title_canon_sha256": "311398897b27a35480699ecfb3293aaf7b2a4e0ae849da3c7589c77d4bd1a294"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.08365",
    "kind": "arxiv",
    "version": 2
  }
}