Pith Number

pith:WBR7AHJX

pith:2015:WBR7AHJXEU6QTABLHG5P6CP3MS

not attested not anchored not stored refs pending

$\mu$-Abstract Elementary Classes and other generalizations

Jiri Rosicky, Michael Lieberman, Rami Grossberg, Sebastien Vasey, Will Boney

arxiv:1509.07377 v2 · 2015-09-24 · math.LO · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WBR7AHJXEU6QTABLHG5P6CP3MS}

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	2026-05-18T01:16:17.850307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b063f01d37253d09802b39baff09fb6488108251eee7cef8293e75d192e04bae

Aliases

arxiv: 1509.07377 · arxiv_version: 1509.07377v2 · doi: 10.48550/arxiv.1509.07377 · pith_short_12: WBR7AHJXEU6Q · pith_short_16: WBR7AHJXEU6QTABL · pith_short_8: WBR7AHJX

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/WBR7AHJXEU6QTABLHG5P6CP3MS \
  | 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: b063f01d37253d09802b39baff09fb6488108251eee7cef8293e75d192e04bae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e79d22baf9b6a7f0c87fde4fe374f1c3c62b7c8a8068efa2162290b4c4ca8aa2",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2015-09-24T14:00:19Z",
    "title_canon_sha256": "e21e44152d54fc45c070b5b634b717606bd67a431797ffa990932e79f4056314"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07377",
    "kind": "arxiv",
    "version": 2
  }
}