Pith Number

pith:NLCAFEYX

pith:2015:NLCAFEYXSWS2M6I65ST453WYRG

not attested not anchored not stored refs pending

The \Gamma-Ultraproduct and Averageable Classes

Will Boney

arxiv:1511.00982 v4 · 2015-11-03 · 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{NLCAFEYXSWS2M6I65ST453WYRG}

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	2026-05-18T00:37:54.970443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ac402931795a5a6791eeca7ceeed889a83e3043de4986c45e4fe1e403173571

Aliases

arxiv: 1511.00982 · arxiv_version: 1511.00982v4 · doi: 10.48550/arxiv.1511.00982 · pith_short_12: NLCAFEYXSWS2 · pith_short_16: NLCAFEYXSWS2M6I6 · pith_short_8: NLCAFEYX

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/NLCAFEYXSWS2M6I65ST453WYRG \
  | 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: 6ac402931795a5a6791eeca7ceeed889a83e3043de4986c45e4fe1e403173571

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c8bccdc798eb22a53e4d7ffa328f625122569024da540b2fcd6128eda565903",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2015-11-03T16:57:25Z",
    "title_canon_sha256": "6c3e90b3b8044f03d761622b6ce1ca415236c12c86e4d578b82b2a78e86c5f1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.00982",
    "kind": "arxiv",
    "version": 4
  }
}