Pith Number

pith:J4QJT3XY

pith:2019:J4QJT3XYYPM6HUDYB7UZJCOYU4

not attested not anchored not stored refs pending

Heat kernels are not uniform expanders

Mikolaj Fraczyk, Wouter van Limbeek

arxiv:1905.13584 v1 · 2019-05-31 · math.CO · math.DS · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J4QJT3XYYPM6HUDYB7UZJCOYU4}

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	2026-05-17T23:44:34.500192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f2099eef8c3d9e3d0780fe99489d8a73db48d0b97b752dac916a37f1468157e

Aliases

arxiv: 1905.13584 · arxiv_version: 1905.13584v1 · doi: 10.48550/arxiv.1905.13584 · pith_short_12: J4QJT3XYYPM6 · pith_short_16: J4QJT3XYYPM6HUDY · pith_short_8: J4QJT3XY

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/J4QJT3XYYPM6HUDYB7UZJCOYU4 \
  | 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: 4f2099eef8c3d9e3d0780fe99489d8a73db48d0b97b752dac916a37f1468157e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "977914b683307ba257b3253f7cc05ff54011fdb34a6c3bd7ab9ca8c6f7a7b219",
    "cross_cats_sorted": [
      "math.DS",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-05-31T12:48:21Z",
    "title_canon_sha256": "5e9dd5eee7f26de7d7afcb50b765d4efb511c99c801b77f98cdb3ebe7f91c2af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.13584",
    "kind": "arxiv",
    "version": 1
  }
}