Pith Number

pith:O3HJCKNK

pith:2013:O3HJCKNKFIMKD5PI52T74VYGVK

not attested not anchored not stored refs pending

Regular Ultrapowers at Regular Cardinals

Jouko Vaananen, Juliette Kennedy, Saharon Shelah

arxiv:1307.6396 v1 · 2013-07-24 · 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{O3HJCKNKFIMKD5PI52T74VYGVK}

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	2026-05-18T01:21:05.595059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76ce9129aa2a18a1f5e8eea7fe5706aa9cdce9fadb3c4ceff3969f394cd44342

Aliases

arxiv: 1307.6396 · arxiv_version: 1307.6396v1 · doi: 10.48550/arxiv.1307.6396 · pith_short_12: O3HJCKNKFIMK · pith_short_16: O3HJCKNKFIMKD5PI · pith_short_8: O3HJCKNK

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/O3HJCKNKFIMKD5PI52T74VYGVK \
  | 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: 76ce9129aa2a18a1f5e8eea7fe5706aa9cdce9fadb3c4ceff3969f394cd44342

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba38b7632e8b94fe7b0d8321ed72d2c0b3960bb62eae06a5d0de8bf42d0610d9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2013-07-24T11:55:36Z",
    "title_canon_sha256": "cf56cf58cac4fc4fabc667956592c5931a875a066712df085bf6c6e16d3fee5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6396",
    "kind": "arxiv",
    "version": 1
  }
}