Pith Number

pith:5WLKTJCO

pith:2013:5WLKTJCOY5RJUYGODQ4BYYOKF4

not attested not anchored not stored refs pending

The Ax-Kochen Theorem: an application of model theory to algebra

Alex Kruckman

arxiv:1308.3897 v1 · 2013-08-18 · 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{5WLKTJCOY5RJUYGODQ4BYYOKF4}

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	2026-05-18T03:15:42.241595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed96a9a44ec7629a60ce1c381c61ca2f187e9b5d920b94da3f03f7f983d7f411

Aliases

arxiv: 1308.3897 · arxiv_version: 1308.3897v1 · doi: 10.48550/arxiv.1308.3897 · pith_short_12: 5WLKTJCOY5RJ · pith_short_16: 5WLKTJCOY5RJUYGO · pith_short_8: 5WLKTJCO

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/5WLKTJCOY5RJUYGODQ4BYYOKF4 \
  | 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: ed96a9a44ec7629a60ce1c381c61ca2f187e9b5d920b94da3f03f7f983d7f411

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f658f4edf78a9e0969c1bea97286663f7bc9518133bfdcb2b8ecf674d4e1fe26",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2013-08-18T21:42:39Z",
    "title_canon_sha256": "2f6d8e7d1ae24c11c77ab4beca9a46fa3daf45ea58e29193a750e9e6e3be6459"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3897",
    "kind": "arxiv",
    "version": 1
  }
}