Pith Number

pith:Z2TIW2O4

pith:2020:Z2TIW2O4CIJTB5IGVBKUH2SBPB

not attested not anchored not stored refs pending

Persistent Laplacians: properties, algorithms and implications

Facundo M\'emoli, Yusu Wang, Zhengchao Wan

arxiv:2012.02808 v3 · 2020-12-04 · math.CO · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z2TIW2O4CIJTB5IGVBKUH2SBPB}

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	2026-07-05T04:40:22.805538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cea68b69dc121330f506a85543ea417847a955a78692da17b9307f54273242ce

Aliases

arxiv: 2012.02808 · arxiv_version: 2012.02808v3 · doi: 10.48550/arxiv.2012.02808 · pith_short_12: Z2TIW2O4CIJT · pith_short_16: Z2TIW2O4CIJTB5IG · pith_short_8: Z2TIW2O4

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/Z2TIW2O4CIJTB5IGVBKUH2SBPB \
  | 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: cea68b69dc121330f506a85543ea417847a955a78692da17b9307f54273242ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "751cb762f34c8e0c2f4d5ec6dd103861a0eed01c2d0835cda525e131942f139c",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-12-04T19:21:52Z",
    "title_canon_sha256": "6843df0ee1cae03c641a57134c774722515e57e3d141b45320419c9824251884"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.02808",
    "kind": "arxiv",
    "version": 3
  }
}