Pith Number

pith:32Q3OKEE

pith:2011:32Q3OKEEY3HGRYMAPHZQDU6DDC

not attested not anchored not stored refs pending

Consecutive singular cardinals and the continuum function

Arthur W. Apter, Brent Cody

arxiv:1112.1890 v2 · 2011-12-08 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{32Q3OKEEY3HGRYMAPHZQDU6DDC}

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.

Receipt and verification

First computed	2026-05-18T01:21:05.830766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dea1b72884c6ce68e18079f301d3c318a7b63f381bdfcb9d8b86a50bd7398bb1

Aliases

arxiv: 1112.1890 · arxiv_version: 1112.1890v2 · doi: 10.48550/arxiv.1112.1890 · pith_short_12: 32Q3OKEEY3HG · pith_short_16: 32Q3OKEEY3HGRYMA · pith_short_8: 32Q3OKEE

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/32Q3OKEEY3HGRYMAPHZQDU6DDC \
  | 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: dea1b72884c6ce68e18079f301d3c318a7b63f381bdfcb9d8b86a50bd7398bb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86e527823b50aad76d3b0c122cfe3c18e7fd72048dbd41b253d192a488318d7d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2011-12-08T17:29:32Z",
    "title_canon_sha256": "b14fc6c79105f19335f12ccf055f06c6b8b07af5db19013217800ecf89fd4c55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1890",
    "kind": "arxiv",
    "version": 2
  }
}