Pith Number

pith:FVKVYWTU

pith:2026:FVKVYWTUWNJFO7X6GAGIQ7PMES

not attested not anchored not stored refs pending

Hindman and Owings-like theorems without the Axiom of Choice

David J. Fern\'andez Bret\'on, Eliseo Sarmiento Rosales, Jos\'e A. Guzm\'an-Vega

The uncountable analog of Hindman's theorem fails for the additive group of the reals under ZF and for Q-vector spaces of uncountable dimension under DC when the dimension is not well-orderable.

arxiv:2603.27163 v4 · 2026-03-28 · math.LO · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FVKVYWTUWNJFO7X6GAGIQ7PMES}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

the uncountable analog of Hindman's theorem fails for the additive group of R (under ZF), and for Q-vector spaces of uncountable dimension (under DC if such dimension is not well-orderable)

C2weakest assumption

That the uncountable dimension is not well-orderable when working under DC; if every set of reals is well-orderable then the negative result may not hold.

C3one line summary

Uncountable Hindman theorems fail in ZF and under DC for non-well-orderable dimensions, while Owings configurations hold under AD.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:04:00.956988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d555c5a74b352577efe300c887dec248e8250ac42c230453bf8d2a9cb44224a

Aliases

arxiv: 2603.27163 · arxiv_version: 2603.27163v4 · doi: 10.48550/arxiv.2603.27163 · pith_short_12: FVKVYWTUWNJF · pith_short_16: FVKVYWTUWNJFO7X6 · pith_short_8: FVKVYWTU

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/FVKVYWTUWNJFO7X6GAGIQ7PMES \
  | 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: 2d555c5a74b352577efe300c887dec248e8250ac42c230453bf8d2a9cb44224a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03f6e76b51c5c5f27166f07b710e808049bcf4c04ecdde3847e26a4f956ba4e9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-03-28T06:59:02Z",
    "title_canon_sha256": "68670f24c2eeb81c31e3ec7359fd037013a158ae4c8c6c8300bec6e2b55d5439"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.27163",
    "kind": "arxiv",
    "version": 4
  }
}