Pith Number

pith:Y2DPYVC5

pith:2019:Y2DPYVC5HBSDEGDXJ77OAQD6W4

not attested not anchored not stored refs pending

Quasi-local Algebras and Asymptotic Expanders

J\'an \v{S}pakula, Jiawen Zhang, Kang Li, Piotr Nowak

arxiv:1908.07814 v3 · 2019-08-21 · math.OA · math.CO · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y2DPYVC5HBSDEGDXJ77OAQD6W4}

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	2026-07-05T00:52:06.230292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c686fc545d38643218774ffee0407eb70333c9da003a936264f43351a9f9b23f

Aliases

arxiv: 1908.07814 · arxiv_version: 1908.07814v3 · doi: 10.48550/arxiv.1908.07814 · pith_short_12: Y2DPYVC5HBSD · pith_short_16: Y2DPYVC5HBSDEGDX · pith_short_8: Y2DPYVC5

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/Y2DPYVC5HBSDEGDXJ77OAQD6W4 \
  | 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: c686fc545d38643218774ffee0407eb70333c9da003a936264f43351a9f9b23f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27db491454fb228bf6320432344ed68d0becfa5c3e1b83cf2b0bf4e512cf99a5",
    "cross_cats_sorted": [
      "math.CO",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2019-08-21T12:36:49Z",
    "title_canon_sha256": "2e341b21ee3bb61f3a531758476f84a1999b28ee64415c81a3d2564cddfbe826"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07814",
    "kind": "arxiv",
    "version": 3
  }
}