Pith Number

pith:YG5VZUTB

pith:2014:YG5VZUTBRFZMNHOF2P6VUP3VSL

not attested not anchored not stored refs pending

Liv\v{s}ic Theorem for Banach Rings

Genady Ya. Grabarnik, Misha Guysinsky

arxiv:1408.5639 v1 · 2014-08-24 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YG5VZUTBRFZMNHOF2P6VUP3VSL}

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	2026-05-18T02:44:24.648837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1bb5cd2618972c69dc5d3fd5a3f7592d474bcb4ea85de62e51ec58f315d081d

Aliases

arxiv: 1408.5639 · arxiv_version: 1408.5639v1 · doi: 10.48550/arxiv.1408.5639 · pith_short_12: YG5VZUTBRFZM · pith_short_16: YG5VZUTBRFZMNHOF · pith_short_8: YG5VZUTB

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/YG5VZUTBRFZMNHOF2P6VUP3VSL \
  | 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: c1bb5cd2618972c69dc5d3fd5a3f7592d474bcb4ea85de62e51ec58f315d081d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c395634ccc209c00cedb55797d7e470895298b31df434138cb94bbf970d61ede",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-08-24T21:56:24Z",
    "title_canon_sha256": "db9418e99bee9a230386f4370f0a568a3f2faaa9c4ceabcabe368491a2ed7e88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.5639",
    "kind": "arxiv",
    "version": 1
  }
}